A t-test should not be used to measure differences among more than two groups, because the error structure for a t-test will underestimate the actual error when many groups are being compared.
If you want to compare the means of several groups at once, it’s best to use another statistical test such as ANOVA or a post-hoc test.
If you are unsure whether a word is an action verb, consider whether it is describing an action (e.g., “run”) or a state of being (e.g., “understand”). If the word describes an action, then it’s an action verb.
The function of an action verb is to describe what the subject of the sentence is doing. For example, in the sentence “You have been working since 7 o’clock this morning,” the action verb “work” shows us what the subject (“you”) has been doing.
A real-life example of the planning fallacy is the construction of the Sydney Opera House in Australia. When construction began in the late 1950s, it was initially estimated that it would be completed in four years at a cost of around $7 million.
Because the government wanted the construction to start before political opposition would stop it and while public opinion was still favorable, a number of design issues had not been carefully studied in advance. Due to this, several problems appeared immediately after the project commenced.
The construction process eventually stretched over 14 years, with the Opera House being completed in 1973 at a cost of over $100 million, significantly exceeding the initial estimates.
The planning fallacy and procrastination are not the same thing. Although they both relate to time and task management, they describe different challenges:
In other words, the planning fallacy refers to inaccurate predictions about the time we need to finish a task, while procrastination is a deliberate delay due to psychological factors.
Algorithms are valuable to us because they:
In computer science, an algorithm is a list of unambiguous instructions that specify successive steps to solve a problem or perform a task. Algorithms help computers execute tasks like playing games or sorting a list of numbers. In other words, computers use algorithms to understand what to do and give you the result you need.
Algorithms and artificial intelligence (AI) are not the same, however they are closely related.
Algorithms and computer programs are sometimes used interchangeably, but they refer to two distinct but interrelated concepts.
An example of appeal to pity fallacy is the following appeal by a student to their professor:
“Professor, please consider raising my grade. I had a terrible semester: my car broke down, my laptop got stolen, and my cat got sick.”
While these circumstances may be unfortunate, they are not directly related to the student’s academic performance.
Argumentum ad misericordiam (Latin for “argument from pity or misery”) is another name for appeal to pity fallacy. It occurs when someone evokes sympathy or guilt in an attempt to gain support for their claim, without providing any logical reasons to support the claim itself. Appeal to pity is a deceptive tactic of argumentation, playing on people’s emotions to sway their opinion.
While both the appeal to pity fallacy and red herring fallacy can serve as a distraction from the original discussion topic, they are distinct fallacies. More specifically:
Both fallacies can be used as a tool of deception. However, they operate differently and serve distinct purposes in arguments.
A rhetorical tautology is the repetition of an idea of concept using different words.
Rhetorical tautologies occur when additional words are used to convey a meaning that has already been expressed or implied. For example, the phrase “armed gunman” is a tautology because a “gunman” is by definition “armed.”
A logical tautology is a statement that is always true because it includes all logical possibilities.
Logical tautologies often take the form of “either/or” statements (e.g., “It will rain, or it will not rain”) or employ circular reasoning (e.g., “she is untrustworthy because she can’t be trusted”).
A key challenge that arises in reinforcement learning (RL) is the trade-off between exploration and exploitation. This challenge is unique to RL and doesn’t arise in supervised or unsupervised learning.
Exploration is any action that lets the agent discover new features about the environment, while exploitation is capitalizing on knowledge already gained. If the agent continues to exploit only past experiences, it is likely to get stuck in a suboptimal policy. On the other hand, if it continues to explore without exploiting, it might never find a good policy.
An agent must find the right balance between the two so that it can discover the optimal policy that yields the maximum rewards.
Deep reinforcement learning is the combination of deep learning and reinforcement learning.
Some real-life applications of reinforcement learning include:
We use the present continuous tense (also called the present progressive) to describe a temporary action that is currently occurring (e.g., “I am gardening right now”) or sometimes a planned future event (e.g., “We are traveling to Greece this summer”).
It’s used differently from the simple present, which instead indicates a habit (e.g., “I garden on Tuesdays”), a general truth (e.g., “Bears hibernate in the winter”), or a fixed situation or state (e.g., “She speaks French and German”).
Generative art is art that has been created (generated) by some sort of autonomous system rather than directly by a human artist. Nowadays, the term is commonly used to refer to images created by generative AI tools like Midjourney and DALL-E. These tools use neural networks to create art automatically based on a prompt from the user (e.g., “an elephant painted in the style of Goya”).
However, the term has been in use since before this technology existed, and it can also refer to any technique use by an artist (or writer, musician, etc.) to create art according to a process that proceeds autonomously—i.e., outside of the artist’s direct control. Examples of generative art that does not involve AI include serialism in music and the cut-up technique in literature.
In classification, the goal is to assign input data to specific, predefined categories. The output in classification is typically a label or a class from a set of predefined options.
In regression, the goal is to establish a relationship between input variables and the output. The output in regression is a real-valued number that can vary within a range.
In both supervised learning approaches the goal is to find patterns or relationships in the input data so we can accurately predict the desired outcomes. The difference is that classification predicts categorical classes (like spam), while regression predicts continuous numerical values (like age, income, or temperature).
Unsupervised learning should be used when your data is unlabeled and your goal is to discover the inherent structure or pattern in the data.
This approach is helpful for tasks like clustering, association, and dimensionality reduction.
Supervised learning should be used when your dataset consists of labeled data and your goal is to predict or classify new, unseen data based on the patterns learned from the labeled examples.
Tasks like image classification, sentiment analysis, and predictive modeling are common in supervised learning.
Generative AI technology typically uses large language models (LLMs), which are powered by neural networks—computer systems designed to mimic the structures of brains. These LLMs are trained on a huge quantity of data (e.g., text, images) to recognize patterns that they then follow in the content they produce.
For example, a chatbot like ChatGPT generally has a good idea of what word should come next in a sentence because it has been trained on billions of sentences and “learned” what words are likely to appear, in what order, in each context.
This makes generative AI applications vulnerable to the problem of hallucination—errors in their outputs such as unjustified factual claims or visual bugs in generated images. These tools essentially “guess” what a good response to the prompt would be, and they have a pretty good success rate because of the large amount of training data they have to draw on, but they can and do go wrong.
False cause fallacy examples include:
In each of these examples, we falsely assume that one event causes another without any proof.
To identify a false cause fallacy, you need to carefully analyze the argument:
By carefully analyzing the reasoning, considering alternative explanations, and examining the evidence provided, you can identify a false cause fallacy and discern whether a causal claim is valid or flawed.
ASAP is an abbreviation of the phrase “as soon as possible.”
It’s typically used to indicate a sense of urgency in highly informal contexts (e.g., “Let me know ASAP if you need me to drive you to the airport”).
“ASAP” should be avoided in more formal correspondence. Instead, use an alternative like at your earliest convenience.
“Earliest convenience” is part of the phrase at your earliest convenience, meaning “as soon as you can.”
It’s typically used to end an email in a formal context by asking the recipient to do something when it’s convenient for them to do so.
Just checking in is a standard phrase used to start an email (or other message) that’s intended to ask someone for a response or follow-up action in a friendly, informal way. However, it’s a cliché opening that can come across as passive-aggressive, so we recommend avoiding it in favor of a more direct opening like “We previously discussed …”
In a more personal context, you might encounter “just checking in” as part of a longer phrase such as “I’m just checking in to see how you’re doing.” In this case, it’s not asking the other person to do anything but rather asking about their well-being (emotional or physical) in a friendly way.
ChatGPT and other AI writing tools can have unethical uses. These include:
However, when used correctly, AI writing tools can be helpful resources for improving your academic writing and research skills. Some ways to use ChatGPT ethically include:
A real-life application of machine learning is an email spam filter. To create such a filter, we would collect data consisting of various email messages and features (subject line, sender information, etc.) which we would label as spam or not spam. We would then train the model to recognize which features are associated with spam emails. In this way, the ML model would be able to classify any incoming emails as either unwanted or legitimate.
Traditional programming and machine learning are essentially different approaches to problem-solving.
In traditional programming, a programmer manually provides specific instructions to the computer based on their understanding and analysis of the problem. If the data or the problem changes, the programmer needs to manually update the code.
In contrast, in machine learning the process is automated: we feed data to a computer and it comes up with a solution (i.e. a model) without being explicitly instructed on how to do this. Because the ML model learns by itself, it can handle new data or new scenarios.
Overall, traditional programming is a more fixed approach where the programmer designs the solution explicitly, while ML is a more flexible and adaptive approach where the ML model learns from data to generate a solution.
Although the terms artificial intelligence and machine learning are often used interchangeably, they are distinct (but related) concepts:
In other words, machine learning is a specific approach or technique used to achieve the overarching goal of AI to build intelligent systems.
No, having ChatGPT write your college essay can negatively impact your application in numerous ways. ChatGPT outputs are unoriginal and lack personal insight.
Furthermore, Passing off AI-generated text as your own work is considered academically dishonest. AI detectors may be used to detect this offense, and it’s highly unlikely that any university will accept you if you are caught submitting an AI-generated admission essay.
However, you can use ChatGPT to help write your college essay during the preparation and revision stages (e.g., for brainstorming ideas and generating feedback).
Yes, you use ChatGPT to help write your college essay by having it generate feedback on certain aspects of your work (consistency of tone, clarity of structure, etc.).
However, ChatGPT is not able to adequately judge qualities like vulnerability and authenticity. For this reason, it’s important to also ask for feedback from people who have experience with college essays and who know you well.
Alternatively, you can get advice using Scribbr’s essay editing service.
Yes, you can use ChatGPT to paraphrase text to help you express your ideas more clearly, explore different ways of phrasing your arguments, and avoid repetition.
However, it’s not specifically designed for this purpose. We recommend using a specialized tool like Scribbr’s free paraphrasing tool, which will provide a smoother user experience.
Yes, you can use ChatGPT to summarize text. This can help you understand complex information more easily, summarize the central argument of your own paper, or clarify your research question.
You can also use Scribbr’s free text summarizer, which is designed specifically for this purpose.
Knowledge representation and reasoning (KRR) is the study of how to represent information about the world in a form that can be used by a computer system to solve and reason about complex problems. It is an important field of artificial intelligence (AI) research.
An example of a KRR application is a semantic network, a way of grouping words or concepts by how closely related they are and formally defining the relationships between them so that a machine can “understand” language in something like the way people do.
A related concept is information extraction, concerned with how to get structured information from unstructured sources.
Information extraction refers to the process of starting from unstructured sources (e.g., text documents written in ordinary English) and automatically extracting structured information (i.e., data in a clearly defined format that’s easily understood by computers). It’s an important concept in natural language processing (NLP).
For example, you might think of using news articles full of celebrity gossip to automatically create a database of the relationships between the celebrities mentioned (e.g., married, dating, divorced, feuding). You would end up with data in a structured format, something like MarriageBetween(celebrity1,celebrity2,date).
The challenge involves developing systems that can “understand” the text well enough to extract this kind of data from it.
ChatGPT can sometimes reproduce biases from its training data, since it draws on the text it has “seen” to create plausible responses to your prompts.
For example, users have shown that it sometimes makes sexist assumptions such as that a doctor mentioned in a prompt must be a man rather than a woman. Some have also pointed out political bias in terms of which political figures the tool is willing to write positively or negatively about and which requests it refuses.
The tool is unlikely to be consistently biased toward a particular perspective or against a particular group. Rather, its responses are based on its training data and on the way you phrase your ChatGPT prompts. It’s sensitive to phrasing, so asking it the same question in different ways will result in quite different answers.
The ad populum fallacy plays on our innate desire to fit in (known as “bandwagon effect”). If many people believe something, our common sense tells us that it must be true and we tend to accept it. However, in logic, the popularity of a proposition cannot serve as evidence of its truthfulness.
The ad populum fallacy is common in politics. One example is the following viewpoint: “The majority of our countrymen think we should have military operations overseas; therefore, it’s the right thing to do.”
This line of reasoning is fallacious, because popular acceptance of a belief or position does not amount to a justification of that belief. In other words, following the prevailing opinion without examining the underlying reasons is irrational.
According to OpenAI’s terms of use, users have the right to reproduce text generated by ChatGPT during conversations.
However, publishing ChatGPT outputs may have legal implications, such as copyright infringement.
Users should be aware of such issues and use ChatGPT outputs as a source of inspiration instead.
According to OpenAI’s terms of use, users have the right to use outputs from their own ChatGPT conversations for any purpose (including commercial publication).
However, users should be aware of the potential legal implications of publishing ChatGPT outputs. ChatGPT responses are not always unique: different users may receive the same response.
Furthermore, ChatGPT outputs may contain copyrighted material. Users may be liable if they reproduce such material.
You can access ChatGPT by signing up for a free account:
A ChatGPT app is also available for iOS, and an Android app is planned for the future. The app works similarly to the website, and you log in with the same account for both.
ChatGPT was publicly released on November 30, 2022. At the time of its release, it was described as a “research preview,” but it is still available now, and no plans have been announced so far to take it offline or charge for access.
ChatGPT continues to receive updates adding more features and fixing bugs. The most recent update at the time of writing was on May 24, 2023.
ChatGPT is currently free to use. You just have to sign up for a free account (using your email address or your Google account), and you can start using the tool immediately. It’s possible that the tool will require a subscription to use in the future, but no plans for this have been announced so far.
A premium subscription for the tool is available, however. It’s called ChatGPT Plus and costs $20 a month. It gets you access to features like GPT-4 (a more advanced version of the model) and faster responses. But it’s entirely optional: you only need to subscribe if you want these advanced features.
It’s not clear whether ChatGPT will stop being available for free in the future—and if so, when. The tool was originally released in November 2022 as a “research preview.” It was released for free so that the model could be tested on a very large user base.
The framing of the tool as a “preview” suggests that it may not be available for free in the long run, but so far, no plans have been announced to end free access to the tool.
A premium version, ChatGPT Plus, is available for $20 a month and provides access to features like GPT-4, a more advanced version of the model. It may be that this is the only way OpenAI (the publisher of ChatGPT) plans to monetize it and that the basic version will remain free. Or it may be that the high costs of running the tool’s servers lead them to end the free version in the future. We don’t know yet.
Yes, ChatGPT is currently available for free. You have to sign up for a free account to use the tool, and you should be aware that your data may be collected to train future versions of the model.
To sign up and use the tool for free, go to this page and click “Sign up.” You can do so with your email or with a Google account.
A premium version of the tool called ChatGPT Plus is available as a monthly subscription. It currently costs $20 and gets you access to features like GPT-4 (a more advanced version of the language model). But it’s optional: you can use the tool completely free if you’re not interested in the extra features.
A good ChatGPT prompt (i.e., one that will get you the kinds of responses you want):
ChatGPT prompts are the textual inputs (e.g., questions, instructions) that you enter into ChatGPT to get responses.
ChatGPT predicts an appropriate response to the prompt you entered. In general, a more specific and carefully worded prompt will get you better responses.
Dissertation word counts vary widely across different fields, institutions, and levels of education:
However, none of these are strict guidelines – your word count may be lower or higher than the numbers stated here. Always check the guidelines provided by your university to determine how long your own dissertation should be.
Deep learning requires a large dataset (e.g., images or text) to learn from. The more diverse and representative the data, the better the model will learn to recognize objects or make predictions. Only when the training data is sufficiently varied can the model make accurate predictions or recognize objects from new data.
Deep learning models can be biased in their predictions if the training data consist of biased information. For example, if a deep learning model used for screening job applicants has been trained with a dataset consisting primarily of white male applicants, it will consistently favor this specific population over others.
Our research into the best summary generators (aka summarizers or summarizing tools) found that the best summarizer available in 2023 is the one offered by QuillBot.
While many summarizers just pick out some sentences from the text, QuillBot generates original summaries that are creative, clear, accurate, and concise. It can summarize texts of up to 1,200 words for free, or up to 6,000 with a premium subscription.
“No true Scotsman” arguments aren’t always fallacious. When there is a generally accepted definition of who or what constitutes a group, it’s reasonable to use statements in the form of “no true Scotsman.”
For example, the statement that “no true pacifist would volunteer for military service” is not fallacious, since a pacifist is, by definition, someone who opposes war or violence as a means of settling disputes.
No true Scotsman arguments are fallacious because instead of logically refuting the counterexample, they simply assert that it doesn’t count. In other words, the counterexample is rejected for psychological, but not logical, reasons.
The appeal to purity or no true Scotsman fallacy is an attempt to defend a generalization about a group from a counterexample by shifting the definition of the group in the middle of the argument. In this way, one can exclude the counterexample as not being “true,” “genuine,” or “pure” enough to be considered as part of the group in question.
Tools called AI detectors are designed to label text as AI-generated or human. AI detectors work by looking for specific characteristics in the text, such as a low level of randomness in word choice and sentence length. These characteristics are typical of AI writing, allowing the detector to make a good guess at when text is AI-generated.
But these tools can’t guarantee 100% accuracy. Check out our comparison of the best AI detectors to learn more.
You can also manually watch for clues that a text is AI-generated—for example, a very different style from the writer’s usual voice or a generic, overly polite tone.
AI detectors aim to identify the presence of AI-generated text (e.g., from ChatGPT) in a piece of writing, but they can’t do so with complete accuracy. In our comparison of the best AI detectors, we found that the 10 tools we tested had an average accuracy of 60%. The best free tool had 68% accuracy, the best premium tool 84%.
Because of how AI detectors work, they can never guarantee 100% accuracy, and there is always at least a small risk of false positives (human text being marked as AI-generated). Therefore, these tools should not be relied upon to provide absolute proof that a text is or isn’t AI-generated. Rather, they can provide a good indication in combination with other evidence.
Yes, using ChatGPT as a conversation partner is a great way to practice a language in an interactive way.
Try using a prompt like this one:
“Please be my Spanish conversation partner. Only speak to me in Spanish. Keep your answers short (maximum 50 words). Ask me questions. Let’s start the conversation with the following topic: [conversation topic].”
Begging the question fallacy is an argument in which you assume what you are trying to prove. In other words, your position and the justification of that position are the same, only slightly rephrased.
For example: “All freshmen should attend college orientation, because all college students should go to such an orientation.”
The complex question fallacy and begging the question fallacy are similar in that they are both based on assumptions. However, there is a difference between them:
In other words, begging the question is about drawing a conclusion based on an assumption, while a complex question involves asking a question that presupposes the answer to a prior question.
The false dilemma fallacy works in two ways:
In both cases, by using the false dilemma fallacy, one conceals alternative choices and doesn’t allow others to consider the full range of options. This is usually achieved through an“either-or” construction and polarized, divisive language (“you are either a friend or an enemy”).
The best way to avoid a false dilemma fallacy is to pause and reflect on two points:
False dilemma fallacy is also known as false dichotomy, false binary, and “either-or” fallacy. It is the fallacy of presenting only two choices, outcomes, or sides to an argument as the only possibilities, when more are available.
Pathetic fallacy is not a logical fallacy. It is a literary device or figure of speech that often occurs in literature when a writer attributes human emotions to things that aren’t human, such as objects, the weather, or animals.
Pathetic fallacy is used to reflect a character’s emotions. For example, if a character has lost a loved one, they may hear “mournful” birdsong.
A pathetic fallacy can be a short phrase or a whole sentence and is often used in novels and poetry. Pathetic fallacies serve multiple purposes, such as:
Pathetic fallacy and appeal to pathos sound similar but they refer to entirely different things.
In other words, pathetic fallacy and appeal to pathos both relate to pathos or emotion but to a different end.
The official ChatGPT app is currently only available on iOS devices. If you don’t have an iOS device, only use the official OpenAI website to access the tool. This helps to eliminate the potential risk of downloading fraudulent or malicious software.
OpenAI may store ChatGPT conversations for the purposes of future training. Additionally, these conversations may be monitored by human AI trainers.
Users can choose not to have their chat history saved. Unsaved chats are not used to train future models and are permanently deleted from ChatGPT’s system after 30 days.
ChatGPT conversations are generally used to train future models and to resolve issues/bugs. These chats may be monitored by human AI trainers.
However, users can opt out of having their conversations used for training. In these instances, chats are monitored only for potential abuse.
Fallacies are arguments that contain some type of reasoning error. Regardless of whether they are used intentionally or by error, they weaken an argument by using erroneous beliefs, illogical arguments, or deception.
As a result, they shift the focus of a discussion to unrelated topics or side issues and can thus be misleading. For example, the genetic fallacy shifts the attention to the source or origin of an argument instead of presenting evidence to refute the argument itself.
The ad hominem fallacy and the genetic fallacy are closely related in that they are both fallacies of relevance. In other words, they both involve arguments that use evidence or examples that are not logically related to the argument at hand. However, there is a difference between the two:
Fallacies of relevance are a group of fallacies that occur in arguments when the premises are logically irrelevant to the conclusion. Although at first there seems to be a connection between the premise and the conclusion, in reality fallacies of relevance use unrelated forms of appeal.
For example, the genetic fallacy makes an appeal to the source or origin of the claim in an attempt to assert or refute something.
In advertising, the equivocation fallacy is often used to create a pun. For example, a billboard company might advertise their billboards using a line like: “Looking for a sign? This is it!” The word sign has a literal meaning as billboard and a figurative one as a sign from God, the universe, etc.
Equivocation is a fallacy because it is a form of argumentation that is both misleading and logically unsound. When the meaning of a word or phrase shifts in the course of an argument, it causes confusion and also implies that the conclusion (which may be true) does not follow from the premise.
The equivocation fallacy is an informal logical fallacy, meaning that the error lies in the content of the argument instead of the structure.
Base rate fallacy can be avoided by following these steps:
Suppose there is a population consisting of 90% psychologists and 10% engineers. Given that you know someone enjoyed physics at school, you may conclude that they are an engineer rather than a psychologist, even though you know that this person comes from a population consisting of far more psychologists than engineers.
When we ignore the rate of occurrence of some trait in a population (the base-rate information) we commit base rate fallacy.
Cost-benefit fallacy is a common error that occurs when allocating sources in project management. It is the fallacy of assuming that cost-benefit estimates are more or less accurate, when in fact they are highly inaccurate and biased. This means that cost-benefit analyses can be useful, but only after the cost-benefit fallacy has been acknowledged and corrected for. Cost-benefit fallacy is a type of base rate fallacy.
Using AI writing tools (like ChatGPT) to write your essay is usually considered plagiarism and may result in penalization, unless it is allowed by your university. Text generated by AI tools is based on existing texts and therefore cannot provide unique insights. Furthermore, these outputs sometimes contain factual inaccuracies or grammar mistakes.
However, AI writing tools can be used effectively as a source of feedback and inspiration for your writing (e.g., to generate research questions). Other AI tools, like grammar checkers, can help identify and eliminate grammar and punctuation mistakes to enhance your writing.
AI writing tools can be used to perform a variety of tasks.
Generative AI writing tools (like ChatGPT) generate text based on human inputs and can be used for interactive learning, to provide feedback, or to generate research questions or outlines.
These tools can also be used to paraphrase or summarize text or to identify grammar and punctuation mistakes. You can also use Scribbr’s free paraphrasing tool, summarizing tool, and grammar checker, which are designed specifically for these purposes.
The fallacy of composition is similar to and can be confused with the hasty generalization fallacy. However, there is a difference between the two:
In other words, the fallacy of composition is using an unwarranted assumption that we can infer something about a whole based on the characteristics of its parts, while the hasty generalization fallacy is using insufficient evidence to draw a conclusion.
The opposite of the fallacy of composition is the fallacy of division. In the fallacy of division, the assumption is that a characteristic which applies to a whole or a group must necessarily apply to the parts or individual members. For example, “Australians travel a lot. Gary is Australian, so he must travel a lot.”
When someone uses an argument that claims there is a causal connection between two events, you can take the following steps to determine whether this is a post hoc fallacy:
An example of post hoc fallacy is the following line of reasoning:
“Yesterday I had ice cream, and today I have a terrible stomachache. I’m sure the ice cream caused this.”
Although it is possible that the ice cream had something to do with the stomachache, there is no proof to justify the conclusion other than the order of events. Therefore, this line of reasoning is fallacious.
Post hoc fallacy and hasty generalization fallacy are similar in that they both involve jumping to conclusions. However, there is a difference between the two:
In other words, post hoc fallacy involves a leap to a causal claim; hasty generalization fallacy involves a leap to a general proposition.
The difference between the post hoc fallacy and the non sequitur fallacy is that post hoc fallacy infers a causal connection between two events where none exists, whereas the non sequitur fallacy infers a conclusion that lacks a logical connection to the premise.
In other words, a post hoc fallacy occurs when there is a lack of a cause-and-effect relationship, while a non sequitur fallacy occurs when there is a lack of logical connection.
An example of a non sequitur is the following statement:
“Giving up nuclear weapons weakened the United States’ military. Giving up nuclear weapons also weakened China. For this reason, it is wrong to try to outlaw firearms in the United States today.”
Clearly there is a step missing in this line of reasoning and the conclusion does not follow from the premise, resulting in a non sequitur fallacy.
Although many sources use circular reasoning fallacy and begging the question interchangeably, others point out that there is a subtle difference between the two:
In other words, we could say begging the question is a form of circular reasoning.
Circular reasoning fallacy uses circular reasoning to support an argument. More specifically, the evidence used to support a claim is just a repetition of the claim itself. For example: “The President of the United States is a good leader (claim), because they are the leader of this country (supporting evidence)”.
GPT stands for “generative pre-trained transformer,” which is a type of large language model: a neural network trained on a very large amount of text to produce convincing, human-like language outputs. The Chat part of the name just means “chat”: ChatGPT is a chatbot that you interact with by typing in text.
The technology behind ChatGPT is GPT-3.5 (in the free version) or GPT-4 (in the premium version). These are the names for the specific versions of the GPT model. GPT-4 is currently the most advanced model that OpenAI has created. It’s also the model used in Bing’s chatbot feature.
ChatGPT was created by OpenAI, an AI research company. It started as a nonprofit company in 2015 but became for-profit in 2019. Its CEO is Sam Altman, who also co-founded the company. OpenAI released ChatGPT as a free “research preview” in November 2022. Currently, it’s still available for free, although a more advanced premium version is available if you pay for it.
OpenAI is also known for developing DALL-E, an AI image generator that runs on similar technology to ChatGPT.
ChatGPT is owned by OpenAI, the company that developed and released it. OpenAI is a company dedicated to AI research. It started as a nonprofit company in 2015 but transitioned to for-profit in 2019. Its current CEO is Sam Altman, who also co-founded the company.
In terms of who owns the content generated by ChatGPT, OpenAI states that it will not claim copyright on this content, and the terms of use state that “you can use Content for any purpose, including commercial purposes such as sale or publication.” This means that you effectively own any content you generate with ChatGPT and can use it for your own purposes.
Be cautious about how you use ChatGPT content in an academic context. University policies on AI writing are still developing, so even if you “own” the content, you’re often not allowed to submit it as your own work according to your university or to publish it in a journal. AI detectors may be used to detect ChatGPT content.
ChatGPT is a chatbot based on a large language model (LLM). These models are trained on huge datasets consisting of hundreds of billions of words of text, based on which the model learns to effectively predict natural responses to the prompts you enter.
ChatGPT was also refined through a process called reinforcement learning from human feedback (RLHF), which involves “rewarding” the model for providing useful answers and discouraging inappropriate answers—encouraging it to make fewer mistakes.
Essentially, ChatGPT’s answers are based on predicting the most likely responses to your inputs based on its training data, with a reward system on top of this to incentivize it to give you the most helpful answers possible. It’s a bit like an incredibly advanced version of predictive text. This is also one of ChatGPT’s limitations: because its answers are based on probabilities, they’re not always trustworthy.
To avoid a hasty generalization fallacy we need to ensure that the conclusions drawn are well-supported by the appropriate evidence. More specifically:
The opposite of the hasty generalization fallacy is called slothful induction fallacy or appeal to coincidence.
It is the tendency to deny a conclusion even though there is sufficient evidence that supports it. Slothful induction occurs due to our natural tendency to dismiss events or facts that do not align with our personal biases and expectations. For example, a researcher may try to explain away unexpected results by claiming it is just a coincidence.
The hasty generalization fallacy and the anecdotal evidence fallacy are similar in that they both result in conclusions drawn from insufficient evidence. However, there is a difference between the two:
Argumentum ad hominem means “argument to the person” in Latin and it is commonly referred to as ad hominem argument or personal attack. Ad hominem arguments are used in debates to refute an argument by attacking the character of the person making it, instead of the logic or premise of the argument itself.
Ad hominem tu quoque (‘you too”) is an attempt to rebut a claim by attacking its proponent on the grounds that they uphold a double standard or that they don’t practice what they preach. For example, someone is telling you that you should drive slowly otherwise you’ll get a speeding ticket one of these days, and you reply “but you used to get them all the time!”
Ad hominem is a persuasive technique where someone tries to undermine the opponent’s argument by personally attacking them.
In this way, one can redirect the discussion away from the main topic and to the opponent’s personality without engaging with their viewpoint. When the opponent’s personality is irrelevant to the discussion, we call it an ad hominem fallacy.
People sometimes confuse cognitive bias and logical fallacies because they both relate to flawed thinking. However, they are not the same:
In other words, cognitive bias refers to an ongoing predisposition, while logical fallacy refers to mistakes of reasoning that occur in the moment.
An appeal to ignorance (ignorance here meaning lack of evidence) is a type of informal logical fallacy.
It asserts that something must be true because it hasn’t been proven false—or that something must be false because it has not yet been proven true.
For example, “unicorns exist because there is no evidence that they don’t.” The appeal to ignorance is also called the burden of proof fallacy.
An ad hominem (Latin for “to the person”) is a type of informal logical fallacy. Instead of arguing against a person’s position, an ad hominem argument attacks the person’s character or actions in an effort to discredit them.
This rhetorical strategy is fallacious because a person’s character, motive, education, or other personal trait is logically irrelevant to whether their argument is true or false.
Name-calling is common in ad hominem fallacy (e.g., “environmental activists are ineffective because they’re all lazy tree-huggers”).
The plural of “crisis” is “crises.” It’s a loanword from Latin and retains its original Latin plural noun form (similar to “analyses” and “bases”). It’s wrong to write “crisises.”
For example, you might write “Several crises destabilized the regime.”
Normally, the plural of “fish” is the same as the singular: “fish.” It’s one of a group of irregular plural nouns in English that are identical to the corresponding singular nouns (e.g., “moose,” “sheep”). For example, you might write “The fish scatter as the shark approaches.”
If you’re referring to several species of fish, though, the regular plural “fishes” is often used instead. For example, “The aquarium contains many different fishes, including trout and carp.”
The correct plural of “octopus” is “octopuses.”
People often write “octopi” instead because they assume that the plural noun is formed in the same way as Latin loanwords such as “fungus/fungi.” But “octopus” actually comes from Greek, where its original plural is “octopodes.” In English, it instead has the regular plural form “octopuses.”
For example, you might write “There are four octopuses in the aquarium.”
The plural of “moose” is the same as the singular: “moose.” It’s one of a group of plural nouns in English that are identical to the corresponding singular nouns. So it’s wrong to write “mooses.”
For example, you might write “There are several moose in the forest.”
There are a number of ways you can deal with slippery slope arguments especially when you suspect these are fallacious:
A slippery slope argument is not always a fallacy.
Yes, it’s quite common to start a sentence with a preposition, and there’s no reason not to do so.
For example, the sentence “To many, she was a hero” is perfectly grammatical. It could also be rephrased as “She was a hero to many,” but there’s no particular reason to do so. Both versions are fine.
Some people argue that you shouldn’t end a sentence with a preposition, but that “rule” can also be ignored, since it’s not supported by serious language authorities.
Yes, it’s fine to end a sentence with a preposition. The “rule” against doing so is overwhelmingly rejected by modern style guides and language authorities and is based on the rules of Latin grammar, not English.
Trying to avoid ending a sentence with a preposition often results in very unnatural phrasings. For example, turning “He knows what he’s talking about” into “He knows about what he’s talking” or “He knows that about which he’s talking” is definitely not an improvement.
When forming the possessive of a plural noun that already ends in “s,” you should add an apostrophe after “s” and not add an extra “s.” For example, the plural noun houses becomes the possessive noun houses’.
This is different from forming the possessive of a singular noun (e.g., “house”) or an irregular plural noun that doesn’t end in “s” (e.g. “men”). In those cases, you add an apostrophe followed by an “s”: house’s; men’s.
The past simple form of “beat” is beat. It’s used to describe a past action or event (e.g., “You beat me”).
The past participle form of “beat” is beaten. It’s used to form perfect tenses (e.g., “I have beaten the record”) and to form the passive voice (e.g., “The champion has been beaten”).
It’s wrong to use the past simple form “beat” instead in these contexts. For example, “The champion has been beat” is incorrect.
When you are faced with a straw man fallacy, the best way to respond is to draw attention to the fallacy and ask your discussion partner to show how your original statement and their distorted version are the same. Since these are different, your partner will either have to admit that their argument is invalid or try to justify it by using more flawed reasoning, which you can then attack.
The straw man fallacy is a problem because it occurs when we fail to take an opposing point of view seriously. Instead, we intentionally misrepresent our opponent’s ideas and avoid genuinely engaging with them. Due to this, resorting to straw man fallacy lowers the standard of constructive debate.
A straw man argument is a distorted (and weaker) version of another person’s argument that can easily be refuted (e.g., when a teacher proposes that the class spend more time on math exercises, a parent complains that the teacher doesn’t care about reading and writing).
This is a straw man argument because it misrepresents the teacher’s position, which didn’t mention anything about cutting down on reading and writing. The straw man argument is also known as the straw man fallacy.
The past simple form of “ride” is rode. It’s used to describe a past action or event (e.g., “We rode our bikes”).
The past participle form of “ride” is ridden. It’s used to form perfect tenses (e.g., “I have ridden on an elephant before”) and to form the passive voice (e.g., “The bike hasn’t been ridden in a long time”).
It’s wrong to use the past simple form “rode” instead in these contexts. For example, “The bike hasn’t been rode” is incorrect.
The sunk cost fallacy and escalation of commitment (or commitment bias) are two closely related terms. However, there is a slight difference between them:
In other words, escalating commitment is a manifestation of the sunk cost fallacy: an irrational escalation of commitment frequently occurs when people refuse to accept that the resources they’ve already invested cannot be recovered. Instead, they insist on more spending to justify the initial investment (and the incurred losses).
The red herring fallacy is a problem because it is flawed reasoning. It is a distraction device that causes people to become sidetracked from the main issue and draw wrong conclusions.
Although a red herring may have some kernel of truth, it is used as a distraction to keep our eyes on a different matter. As a result, it can cause us to accept and spread misleading information.
Although both red herring fallacy and straw man fallacy are logical fallacies or reasoning errors, they denote different attempts to “win” an argument. More specifically:
Both the present perfect and past simple refer to past action. However, they have different functions:
The present perfect tense and the present perfect continuous can both be used to refer to the present consequences of a past action or situation:
Yes, the conjunction because is a compound word, but one with a long history. It originates in Middle English from the preposition “bi” (“by”) and the noun “cause.” Over time, the open compound “bi cause” became the closed compound “because,” which we use today.
Though it’s spelled this way now, the verb “be” is not one of the words that makes up “because.”
Yes, today is a compound word, but a very old one. It wasn’t originally formed from the preposition “to” and the noun “day”; rather, it originates from their Old English equivalents, “tō” and “dæġe.”
In the past, it was sometimes written as a hyphenated compound: “to-day.” But the hyphen is no longer included; it’s always “today” now (“to day” is also wrong).
Attribution is a term describing the inferences people make when trying to explain the causes of certain events, the behavior of others, or their own behavior. Because these inferences are based not only on objective facts but also on our mental state, emotions, and past experiences, attributions can be distorted and lead to bias.
An example of such bias is hostile attribution bias, or the tendency to attribute negative intentions to others, especially when their intentions are unclear.
To measure hostile attribution bias, studies typically present participants with a hypothetical situation in which an individual is provoked by a peer whose behavior is purposely ambiguous. Participants are then asked to indicate the intent of the peer. This can be done through videos, pictures, audio, vignettes, or staged interactions (with actors).
Two important considerations when choosing the format are ecological validity (i.e., the extent to which the results are generalizable to a real-life setting) and social desirability bias (i.e., participants may not have wanted to report hostile attributions).
Some synonyms and near synonyms of the verb compose (meaning “to make up”) are:
People increasingly use “comprise” as a synonym of “compose.” However, this is normally still seen as a mistake, and we recommend avoiding it in your academic writing. “Comprise” traditionally means “to be made up of,” not “to make up.”
Some synonyms and near synonyms of the verb comprise are:
People increasingly use “comprise” interchangeably with “compose,” meaning that they consider words like “compose,” “constitute,” and “form” to be synonymous with “comprise.” However, this is still normally regarded as an error, and we advise against using these words interchangeably in academic writing.
The vividness effect in communication is the persuasive impact that vivid information is thought to have on opinions and behaviors. In other words, information that is vivid, concrete, dramatic, etc., is more likely to capture our attention and sway us into believing or doing one thing rather than another. On the contrary, information that is dull or abstract is not so effective. The vividness effect relates to the vividness bias.
A real-life example of vividness bias can often be observed in the outcome of business negotiations. Price is usually the most vivid information, while other aspects, such the complexity of implementation, or the time needed to complete the project, might be ignored.
Vividness bias is important because it can affect our decisions and negotiations. It causes us to assign more weight to vivid information, like a perception of prestige, rather than other factors that, upon greater reflection, are more important to us. As a result, we get distracted and lose sight of our goals and priorities.
Some synonyms and near synonyms for “whenever” include:
There are numerous synonyms and near synonyms for the two meanings of anytime:
| Whenever | You’re welcome |
|---|---|
| At any time | My pleasure |
| On any occasion | No problem |
Anyway (no “s”) is often used at the start of a sentence to transition between two different topics (e.g., “Anyway, let’s discuss the report”).
“Anyways” (with an “s”) is sometimes used in informal contexts to mean the same thing as “anyway.” However, it’s considered incorrect by most dictionaries and should be avoided in formal contexts.
Some synonyms and near synonyms of anyway include:
Normality bias (or normalcy bias) is the tendency to underestimate the likelihood or impact of a potential hazard, based on the belief that things will continue as they have in the past. For example, you hear a sudden noise and think it must be fireworks. However, in reality it’s a gunshot. Instead of finding a safe spot, you go about your business because your brain “normalizes” the noise.
Normalcy bias and optimism bias are closely related as they both influence our risk perception. However, they are two separate phenomena.
Although normalcy bias and optimism bias are distinct types of bias, they may reinforce each other. For instance, an individual who receives a hurricane alert may underestimate how serious it is (normalcy bias) and may also think that even if the hurricane affects their area, nothing bad will happen to them personally (optimism bias).
The opposite of normalcy bias is overreaction or worst-case scenario bias. This happens when people exaggerate the likelihood of negative outcomes or consequences when faced with a threat warning. In other words, people jump to the worst possible conclusion, no matter how improbable it is. For instance panic-buying of toilet paper, face masks, and food in the early days of the COVID-19 outbreak are examples of overreaction.
To make quantitative observations, you need to use instruments that are capable of measuring the quantity you want to observe. For example, you might use a ruler to measure the length of an object or a thermometer to measure its temperature.
A real-life example of correspondence bias is how we think about people who cut in line. For example, you are waiting in line at the airport and someone cuts in front of you at the security checkpoint. Because of correspondence bias, your immediate reaction is to feel annoyed and think that the person must be entitled and rude. In reality, this person may never cut into lines and they are doing this only because they are about to miss their plane, which they are taking to visit a sick family member.
Correspondence bias is a problem because it can cause us to make incorrect judgments about other people’s behaviors. This can lead to misunderstandings that can negatively affect our relationship with them. When we overlook the situation and jump to conclusions about an individual’s character, it is also easier to justify reacting to them aggressively.
In a wider social context, if we ignore the situational factors that might have pushed someone to behave a certain way, we may also ignore systemic factors, like discrimination. For example, some people attribute poverty and unemployment to individuals rather than to social conditions.
Correspondence bias and fundamental attribution error were often seen as interchangeable in the past. However, researchers have recently proposed that there is a subtle difference between the two.
In the simple present tense, the stative verb “be” is used to describe temporary present situations (e.g., “I am tired”) and unchanging situations (e.g., “Laura is a doctor”). The form of the verb varies depending on the subject:
Some synonyms and near synonyms of continuously include:
Some synonyms and near synonyms of continually include:
Some synonyms and near synonyms for council include:
There are numerous synonyms and near synonyms for the two meanings of counsel:
| Advise (verb) | Advice (noun) |
|---|---|
| Direct | Direction |
| Guide | Guidance |
| Instruct | Instruction |
The comma before “and” (or comma before “or”) at the end of a list is optional. It’s referred to as an Oxford comma or serial comma. Most academic style guides recommend adding it (“salt, pepper, and paprika”). But it’s also not a grammatical error to write a list without it (“salt, pepper and paprika”). Some authorities, such as the AP Stylebook, do recommend leaving out the comma.
The Oxford comma tends to improve the clarity of lists, especially complex lists, by showing clearly where one list item ends and another begins. In academic writing, it’s recommended to use it.
Rest assured is an expression meaning “you can be certain” (e.g., “Rest assured, I will find your cat”). “Assured” is the adjectival form of the verb assure, meaning “convince” or “persuade.”
Some synonyms and near synonyms of assure include:
Some synonyms and near synonyms of ensure include:
Find more words that mean the same thing as “ensure” with the help of the paraphrasing tool.
“Tune in” is a phrasal verb meaning “watch a TV show” or “listen to a radio show.” The preposition “to” often comes immediately after this phrase; “in” and “to” should be written as separate words when this happens (e.g., “Tune in to the final episode next week”).
“Tune into” is sometimes used instead of “tune in to,” but this is generally considered incorrect.
“Log in” is a phrasal verb meaning “connect to an electronic device, system, or app.” The preposition “to” is often used directly after the verb; “in” and “to” should be written as two separate words (e.g., “log in to the app to update privacy settings”).
“Log into” is sometimes used instead of “log in to,” but this is generally considered incorrect (as is “login to”).
There’s no difference between the serial comma and the Oxford comma. They’re two different names for the same thing: a comma before the conjunction (“and” or “or”) in a list of three or more items (e.g., “ham, cheese, and tomato”).
The Oxford comma or serial comma is optional but recommended by most academic style guides. It’s sometimes also called the Harvard comma.
The serial comma is a comma that comes before the final item in a list of three or more items. It comes before the conjunction (“and” or “or”): “John, Mandy, and Lupita.” Without the serial comma, the same phrase would be “John, Mandy and Lupita.”
The serial comma is optional; different style guides have different recommendations. But most academic style guides do recommend using it consistently.
The serial comma is also called the Oxford comma or the Harvard comma.
The Oxford comma (a comma placed before the final item in a list of three or more items) is optional. It is not an error to leave it out. “Salt, pepper, and vinegar” and “salt, pepper and vinegar” are both grammatically correct.
Different style guides have different recommendations about using it. Most academic style guides (e.g., APA, MLA, Chicago) recommend using the Oxford comma consistently, so this is typically the best approach in academic writing.
Note that the earlier commas in a list are not optional: “salt pepper and vinegar” is not grammatically correct.
A real-life example of perception bias is the false consensus effect. Because we spend most of our time with friends, family, and colleagues who share the same opinions or values we do, we are often misled to believe that the majority of people think or act in ways similar to us. This explains, for instance, why some people take office supplies home: they may genuinely feel that this behavior is more common than it really is.
Perception bias is a problem because it prevents us from seeing situations or people objectively. Rather, our expectations, beliefs, or emotions interfere with how we interpret reality. This, in turn, can cause us to misjudge ourselves or others. For example, our prejudices can interfere with whether we perceive people’s faces as friendly or unfriendly.
Selective perception is the unconscious process by which people screen, select, and notice objects in their environment. During this process, information tends to be selectively perceived in ways that align with existing attitudes, beliefs, and goals.
Although this allows us to concentrate only on the information that is relevant for us at present, it can also lead to perception bias. For example, while driving, if you become hyper-focused on reaching your exit on a highway, your brain may filter visual stimuli so that you can only focus on things you need to notice in order to exit the highway. However, this can also cause you to miss other things happening around you on the road.
Despite is a preposition used to mean “regardless of,” “notwithstanding,” or “even though.”
It’s used in a subordinate clause to contrast with information given in the main clause of a sentence (e.g., “Despite the stress, Joe loves his job”).
In spite of is a preposition used to mean “regardless of,” “notwithstanding,” or “even though.”
It’s always used in a subordinate clause to contrast with the information given in the main clause of a sentence (e.g., “Amy continued to watch TV, in spite of the time”).
Some synonyms and near synonyms of between include:
Using the paraphrasing tool, look for other words that mean the same thing as “between.”
Some synonyms and near synonyms of among include:
Immediately find new synonyms for “among’ with the paraphrasing tool.
Myside bias is a type of cognitive bias where individuals process information in a way that favors their prior beliefs and attitudes. It occurs when people search for, interpret, and recall information that confirms their opinions, and refute opinions different from their own—such as selecting news sources that agree with one’s political affiliation, while ignoring any opposing arguments from other sources.
Myside bias is closely related to confirmation bias. Although some researchers use the terms interchangeably, others use myside bias to refer to the tendency of processing information that supports one’s own position.
Some synonyms and near synonyms of every time include:
“Everytime” is sometimes used to mean “each time” or “whenever.” However, this is incorrect and should be avoided. The correct phrase is every time (two words).
No, it is not possible to cite your sources with ChatGPT. You can ask it to create citations, but it isn’t designed for this task and tends to make up sources that don’t exist or present information in the wrong format. ChatGPT also cannot add citations to direct quotes in your text.
Instead, use a tool designed for this purpose, like the Scribbr Citation Generator.
But you can use ChatGPT for assignments in other ways, to provide inspiration, feedback, and general writing advice.
No, it’s not a good idea to do so in general—first, because it’s normally considered plagiarism or academic dishonesty to represent someone else’s work as your own (even if that “someone” is an AI language model). Even if you cite ChatGPT, you’ll still be penalized unless this is specifically allowed by your university. Institutions may use AI detectors to enforce these rules.
Second, ChatGPT can recombine existing texts, but it cannot really generate new knowledge. And it lacks specialist knowledge of academic topics. Therefore, it is not possible to obtain original research results, and the text produced may contain factual errors.
However, you can usually still use ChatGPT for assignments in other ways, as a source of inspiration and feedback.
You can use ChatGPT to assist in the writing process for your research paper, thesis, or dissertation in the following ways:
You normally form a possessive noun from a singular noun by adding an apostrophe and an “s,” but there’s disagreement about how to form the possessive of a name like “James.”
Most style guides recommend adding the apostrophe and “s” like normal: James’s. But some argue that it should depend on which version feels most natural to pronounce, so that you could instead write James’, without the additional “s.”
We recommend the first approach, adding the “s” consistently, as it’s recommended by most authorities. Whatever you choose, be consistent about how you form the possessive of a particular name. Don’t write James’ at some points and James’s at others.
Possessive is an adjective meaning “jealous” or “having the desire to own or dominate.” In a grammatical sense, it’s used as a noun or adjective referring to the ways in which possession (ownership) is shown in language.
Some grammatical concepts involving the word are possessive pronouns (e.g., “my”), possessive nouns (e.g., “Steven’s”), possessive apostrophes (apostrophes like the one in “Steven’s”), and possessive case (how words show possession in general).
A possessive noun is a noun like “farmer’s” that is used to indicate ownership (possession). It normally comes before another noun that indicates the thing possessed (e.g., “the farmer’s pitchfork”).
Possessive nouns are formed from regular nouns by adding an apostrophe followed by an “s,” or, in the case of plural nouns that already end in “s,” by just adding an apostrophe.
Nobody and no one are both indefinite pronouns meaning “no person.” They can be used interchangeably (e.g., “nobody is home” means the same as “no one is home”).
No one (two words) is an indefinite pronoun meaning “nobody.” People sometimes mistakenly write “noone,” but this is incorrect and should be avoided. “No-one” is also wrong.
The correct spelling of the phrase meaning “also” or “too” is as well, with a space. “Aswell,” combining the two words into one, is considered a mistake by all major dictionaries.
In other phrases involving these words, too, they are always written as separate words: “as well as,” “might as well,” “just as well,” etc.
As well is a phrase used to mean “also” or “too.” It’s used to indicate something additional (e.g., “I’m going to the bank as well”).
It’s also used in different senses in various common phrases, such as “as well as,” “might as well,” “you as well,” and “just as well.”
You as well is a short phrase used in conversation to reflect whatever sentiment someone has just expressed to you back at them. It’s commonly used to respond to well wishes:
The phrase is made up of the second-person pronoun you and the phrase as well, which means “also” or “too.”
This phrase is synonymous with another phrase, you too. Both are only used conversationally, not in formal writing, because they’re not complete sentences and don’t make sense outside of a conversational context.
“Mine as well” is a common misspelling of the expression might as well.
This expression is used alone or as part of a sentence to indicate something that makes little difference either way or that there’s no reason not to do (e.g., “We might as well ask her”). You should write might as well, not “mine as well,” to express this meaning.
On some occasions, mine as well can be the right choice. “Mine” is the first-person possessive pronoun, indicating something belonging to the speaker. So you might use this phrase in an exchange like the following:
Some synonyms and near synonyms of as well as are:
The planning fallacy refers to people’s tendency to underestimate the resources needed to complete a future task, despite knowing that previous tasks have also taken longer than planned.
For example, people generally tend to underestimate the cost and time needed for construction projects. The planning fallacy occurs due to people’s tendency to overestimate the chances that positive events, such as a shortened timeline, will happen to them. This phenomenon is called optimism bias.
A positive illusion is a form of self-deception under which people have inflated, favorable attitudes about themselves or others close to them.
The most common positive illusions involve:
The opposite of optimism bias is pessimism bias. Optimism bias occurs when we overestimate our chances of experiencing positive events in our lives, while pessimism bias occurs when we overestimate our chance of experiencing negative events.
For example, pessimism bias could cause someone to think they are going to fail an exam, even though they are well prepared and usually get good grades.
The opposite of implicit bias is explicit bias, or conscious bias. This refers to preferences, opinions, and attitudes of which people are generally consciously aware. In other words, explicit bias is expressed openly and deliberately.
A cycle of inquiry is another name for action research. It is usually visualized in a spiral shape following a series of steps, such as “planning → acting → observing → reflecting.”
Action research is particularly popular with educators as a form of systematic inquiry because it prioritizes reflection and bridges the gap between theory and practice. Educators are able to simultaneously investigate an issue as they solve it, and the method is very iterative and flexible.
Action research is focused on solving a problem or informing individual and community-based knowledge in a way that impacts teaching, learning, and other related processes. It is less focused on contributing theoretical input, instead producing actionable input.
Action research is conducted in order to solve a particular issue immediately, while case studies are often conducted over a longer period of time and focus more on observing and analyzing a particular ongoing phenomenon.
A fallacy is a mistaken belief, particularly one based on unsound arguments or one that lacks the evidence to support it. Common types of fallacy that may compromise the quality of your research are:
A research project is an academic, scientific, or professional undertaking to answer a research question. Research projects can take many forms, such as qualitative or quantitative, descriptive, longitudinal, experimental, or correlational. What kind of research approach you choose will depend on your topic.
The best way to remember the difference between a research plan and a research proposal is that they have fundamentally different audiences. A research plan helps you, the researcher, organize your thoughts. On the other hand, a dissertation proposal or research proposal aims to convince others (e.g., a supervisor, a funding body, or a dissertation committee) that your research topic is relevant and worthy of being conducted.
Fishbone diagrams (also called herringbone diagrams, cause-and-effect diagrams, and Ishikawa diagrams) are most popular in fields of quality management. They are also commonly used in nursing and healthcare, or as a brainstorming technique for students.
Fishbone diagrams have a few different names that are used interchangeably, including herringbone diagram, cause-and-effect diagram, and Ishikawa diagram.
These are all ways to refer to the same thing– a problem-solving approach that uses a fish-shaped diagram to model possible root causes of problems and troubleshoot solutions.
Although a few doesn’t refer to any specific number, it’s typically used to refer to a relatively small number that’s more than two (e.g., “I’m going home in a few hours”).
Some synonyms and near synonyms for few include:
The present participle of the verb “lie” is “lying.” The present participles of verbs ending in “ie” are usually formed by replacing “ie” with “y” and adding the suffix “-ing.”
The present participle of the verb “be” is “being” (e.g., “you are being callous”). The past participle of “be” is “been.”
The “-ing” form of a verb is called the present participle. Present participles can be used as adjectives (e.g., “a thrilling story”) and to form the continuous verb tenses (e.g., the present continuous: “We are partying”).
Gerunds also use the “-ing” form of a verb, but they function only as nouns (e.g., “I don’t enjoy studying”).
People sometimes mistakenly write “looking forward to hear from you,” but this is incorrect. The correct phrase is looking forward to hearing from you.
The phrasal verb “look forward to” is always followed by a direct object, the thing you’re looking forward to. As the direct object has to be a noun phrase, it should be the gerund “hearing,” not the verb “hear.”
“Looking forward in hearing from you” is an incorrect version of the phrase looking forward to hearing from you. The phrasal verb “looking forward to” always needs the preposition “to,” not “in.”
Some synonyms and near synonyms for the expression looking forward to hearing from you include:
Want automatically generated syonyms while you write? Check out the free paraphrasing tool.
Because of the framing effect, the way information is presented to us influences how attractive a proposition is.
Suppose you are considering joining a gym. A membership at $500 per year sounds like a considerable investment and might prevent you from signing up immediately. However, if they tell you it costs just $1.37 per day and emphasize that this is less than the cost of a cup of coffee, you might think it’s a great offer, even though in reality both offers cost you the same.
The framing effect is often used in advertising to positively influence consumer choice.
One common type of frame is “gain framing.” This shows consumers how they are going to benefit from a product or service. For example, dental care product advertisements use gain framing to display the benefits of using their product: white teeth, healthy gums, fresh breath, etc.
Apart from the obvious benefits, ads using the framing effect often imply other benefits, such as how a better-looking smile makes one more attractive to potential dating partners.
In survey research, such as political polling, the way questions are worded or the order in which answers are presented can influence how respondents answer the questions. This is called the framing effect.
For example, if voters are asked to select which of two candidates they plan to vote for, the order in which the candidates are listed affects the percentage of respondents selecting each candidate. Recognizing the potential for research bias, researchers typically rotate which major candidate is listed first and which is listed second.
Although both are common types of cognitive bias, they refer to different ways of processing information.
In other words, the availability heuristic gives preference to information that is easy to recall, while confirmation bias gives preference to information that aligns with our existing beliefs. Even though they are different, they both cause us to focus on only a subset of information.
Heuristics are mental shortcuts or rules of thumb that help people reduce the time and effort required to make a decision. An example of a heuristic in psychology is the availability heuristic (or availability bias). It involves relying on information that comes to mind quickly, (i.e., information that is available to us).
The availability heuristic can influence our perception of risk in everyday life. One common example occurs when we are considering buying insurance. The sharp increase in purchases of flood insurance in the aftermath of flood events illustrates this phenomenon.
Witnessing such events, knowing someone who was personally affected, or extensive media coverage can make us more aware of floods (or make floods more “available” to us). This can change our risk perception, even though statistically there may not be a change in the probabilities of future flooding.
Belief bias and confirmation bias are both types of cognitive bias that impact our judgment and decision-making.
Confirmation bias relates to how we perceive and judge evidence. We tend to seek out and prefer information that supports our preexisting beliefs, ignoring any information that contradicts those beliefs.
Belief bias describes the tendency to judge an argument based on how plausible the conclusion seems to us, rather than how much evidence is provided to support it during the course of the argument.
Yours truly is a phrase used at the end of a formal letter or email. It can also be used (typically in a humorous way) as a pronoun to refer to oneself (e.g., “The dinner was cooked by yours truly”). The latter usage should be avoided in formal writing.
It’s formed by combining the second-person possessive pronoun “yours” with the adverb “truly.”
There are numerous synonyms for the various meanings of truly:
| In a truthful way | Absolutely | Properly |
| Candidly | Completely | Accurately |
| Honestly | Really | Correctly |
| Openly | Totally | Exactly |
| Truthfully | Undoubtedly | Precisely |
The bandwagon effect is a type of cognitive bias. It describes the tendency of people to adopt behaviors or opinions simply because others are doing so, regardless of their own beliefs.
Formulating a main research question can be a difficult task. Overall, your question should contribute to solving the problem that you have defined in your problem statement.
However, it should also fulfill criteria in three main areas:
Use to and used to are commonly confused words. In the case of “used to have”, the latter (with “d”) is correct, since you’re describing an action or state in the past.
Cognitive bias is an umbrella term used to describe the different ways in which our beliefs and experiences impact our judgment and decision making. These preconceptions are “mental shortcuts” that help us speed up how we process and make sense of new information.
However, this tendency may lead us to misunderstand events, facts, or other people. Cognitive bias can be a source of research bias.
Some common types of cognitive bias are:
Research questions anchor your whole project, so it’s important to spend some time refining them.
In general, they should be:
All research questions should be:
A funnel plot shows the relation between a study’s effect size and its precision. It is a scatter plot of the treatment effects estimated from individual studies (horizontal axis) against sample size (vertical axis).
Asymmetry in the funnel plot, measured using regression analysis, is an indication of publication bias. In the absence of bias, results from small studies will scatter widely at the bottom of the graph, with the spread narrowing among larger studies.
The idea here is that small studies are more likely to remain unpublished if their results are nonsignificant or unfavorable, whereas larger studies get published regardless. This leads to asymmetry in the funnel plot.
A visual aid is an instructional device (e.g., a photo, a chart) that appeals to vision to help you understand written or spoken information. Aid is often placed after an attributive noun or adjective (like “visual”) that describes the type of help provided.
“Visual aide” is incorrect.
A job aid is an instructional tool (e.g., a checklist, a cheat sheet) that helps you work efficiently. Aid is a noun meaning “assistance.” It’s often placed after an adjective or attributive noun (like “job”) that describes the specific type of help provided.
“Job aide” is incorrect.
A dissertation prospectus or proposal describes what or who you plan to research for your dissertation. It delves into why, when, where, and how you will do your research, as well as helps you choose a type of research to pursue. You should also determine whether you plan to pursue qualitative or quantitative methods and what your research design will look like.
It should outline all of the decisions you have taken about your project, from your dissertation topic to your hypotheses and research objectives, ready to be approved by your supervisor or committee.
Note that some departments require a defense component, where you present your prospectus to your committee orally.
Confirmation bias is the tendency to search, interpret, and recall information in a way that aligns with our pre-existing values, opinions, or beliefs. It refers to the ability to recollect information best when it amplifies what we already believe. Relatedly, we tend to forget information that contradicts our opinions.
Although selective recall is a component of confirmation bias, it should not be confused with recall bias.
On the other hand, recall bias refers to the differences in the ability between study participants to recall past events when self-reporting is used. This difference in accuracy or completeness of recollection is not related to beliefs or opinions. Rather, recall bias relates to other factors, such as the length of the recall period, age, and the characteristics of the disease under investigation.
Placebos are used in medical research for new medication or therapies, called clinical trials. In these trials some people are given a placebo, while others are given the new medication being tested.
The purpose is to determine how effective the new medication is: if it benefits people beyond a predefined threshold as compared to the placebo, it’s considered effective and not the result of a placebo effect.
Although there is no definite answer to what causes the placebo effect, researchers propose a number of explanations such as the power of suggestion, doctor-patient interaction, classical conditioning, etc.
Our research indicates that the best free grammar checker available online is the Scribbr grammar checker.
We tested 10 of the most popular checkers with the same sample text (containing 20 grammatical errors) and found that Scribbr easily outperformed the competition, scoring 18 out of 20, a drastic improvement over the second-place score of 13 out of 20.
It even appeared to outperform the premium versions of other grammar checkers, despite being entirely free.
Common types of selection bias are:
Use to and used to are commonly confused words. In the case of “used to do”, the latter (with “d”) is correct, since you’re describing an action or state in the past.
Use to and used to are commonly confused words. In the case of “used to be”, the latter (with “d”) is correct, since you’re describing an action or state in the past.
Then and than are two commonly confused words. In the context of “better than”, you use “than” with an “a”.
Then and than are two commonly confused words with different meanings and grammatical roles.
| Examples: Then in a sentence | Examples: Than in a sentence |
|---|---|
| Mix the dry ingredients first, and then add the wet ingredients. | Max is a better saxophonist than you. |
| I was working as a teacher then. | I usually like coaching a team more than I like playing soccer myself. |
Its and it’s are often confused, but its (without apostrophe) is the possessive form of “it” (e.g., its tail, its argument, its wing). You use “its” instead of “his” and “her” for neuter, inanimate nouns.
Though they’re pronounced the same, there’s a big difference in meaning between its and it’s.
The indefinite articles a and an are used to refer to a general or unspecified version of a noun (e.g., a house). Which indefinite article you use depends on the pronunciation of the word that follows it.
Indefinite articles can only be used with singular countable nouns. Like definite articles, they are a type of determiner.
There are many ways to categorize determiners into various types. Some of the main types of determiners are:
A thesis is typically written by students finishing up a bachelor’s or Master’s degree. Some educational institutions, particularly in the liberal arts, have mandatory theses, but they are often not mandatory to graduate from bachelor’s degrees. It is more common for a thesis to be a graduation requirement from a Master’s degree.
Even if not mandatory, you may want to consider writing a thesis if you:
Yes, you should normally include an access date in an AMA website citation (or when citing any source with a URL). This is because webpages can change their content over time, so it’s useful for the reader to know when you accessed the page.
When a publication or update date is provided on the page, you should include it in addition to the access date. The access date appears second in this case, e.g., “Published June 19, 2021. Accessed August 29, 2022.”
Don’t include an access date when citing a source with a DOI (such as in an AMA journal article citation).
Yes, besides is a preposition meaning “apart from” (e.g., “Laura doesn’t like hot drinks besides cocoa”). It can also be used to mean “as well as” (e.g., “Besides traveling, Angie enjoys cooking”).
Beside and besides are related words, but they don’t have the same meaning.
There are different synonyms for the various meanings of besides.
| Except | In addition to | As well | Furthermore |
|---|---|---|---|
| Apart from | As well as | Also | Additionally |
| But | Along with | Too | Further |
| Other than | Together with | Moreover |
Let’s touch base is an expression used to suggest to someone that you touch base or briefly reconnect. It’s rarely used in formal or academic writing.
“Touch bases” is sometimes mistakenly used instead of the expression touch base, meaning “reconnect briefly.” In the expression, the word “base” can’t be pluralized—the idea is more that you’re both touching the same “base.”
“Touch basis” is a misspelling of “touch bases” and is also incorrect.
Some synonyms for touch base include:
The names of up to six authors should be listed for each source on your AMA reference page, separated by commas. For a source with seven or more authors, you should list the first three followed by “et al”: “Isidore, Gilbert, Gunvor, et al.”
In the text, mentioning author names is optional (as they aren’t an official part of AMA in-text citations). If you do mention them, though, you should use the first author’s name followed by “et al” when there are three or more: “Isidore et al argue that …”
Note that according to AMA’s rather minimalistic punctuation guidelines, there’s no period after “et al” unless it appears at the end of a sentence. This is different from most other styles, where there is normally a period.
Convergent validity shows how much a measure of one construct aligns with other measures of the same or related constructs.
On the other hand, concurrent validity is about how a measure matches up to some known criterion or gold standard, which can be another measure.
Although both types of validity are established by calculating the association or correlation between a test score and another variable, they represent distinct validation methods.
Validity tells you how accurately a method measures what it was designed to measure. There are four main types of validity:
Criterion validity evaluates how well a test measures the outcome it was designed to measure. An outcome can be, for example, the onset of a disease.
Criterion validity consists of two subtypes depending on the time at which the two measures (the criterion and your test) are obtained:
Some well-known examples of terms that are or have been viewed as misnomers, but are still widely used, include:
In AMA citation format, if you cite the same source more than once in your paper, it still only has one entry on your AMA reference page, numbered based on the first time you cite it.
This means you’ll always use the same number for the AMA in-text citation for that source, not a different number each time. You can add different page numbers to the citations to talk about specific parts of the source in each case, e.g. 1(pp13–15)
Attrition refers to participants leaving a study. It always happens to some extent—for example, in randomized controlled trials for medical research.
Differential attrition occurs when attrition or dropout rates differ systematically between the intervention and the control group. As a result, the characteristics of the participants who drop out differ from the characteristics of those who stay in the study. Because of this, study results may be biased.
“Bare with me” is a common misspelling of the phrase bear with me. While “bare” can be used as a verb meaning “uncover,” it doesn’t make sense in this phrase. The verb you need is “bear,” meaning “carry” or “endure.”
Some synonyms for bear with me include:
Please bear with me is a more polite version of the expression bear with me, meaning “have patience with me.”
It’s typically used along with a conjunction (e.g., “while”), to explain why you’re asking for patience (e.g., “please bear with me while I try to find the correct file”).
The standard spelling is copacetic. The variant spellings copasetic and copesetic are also listed as acceptable by the Merriam-Webster dictionary, but they’re less common.
The origin of the word is unclear (it’s thought to have originated as slang in the 20th century), which is why various spellings are deemed acceptable.
Copacetic has four syllables. It’s pronounced with emphasis on the third syllable: [koh-pah-set-ik].
Some synonyms for copacetic include:
The conclusion of your thesis or dissertation should include the following:
The conclusion of your thesis or dissertation shouldn’t take up more than 5–7% of your overall word count.
For a stronger dissertation conclusion, avoid including:
Your conclusion should leave the reader with a strong, decisive impression of your work.
While it may be tempting to present new arguments or evidence in your thesis or disseration conclusion, especially if you have a particularly striking argument you’d like to finish your analysis with, you shouldn’t. Theses and dissertations follow a more formal structure than this.
All your findings and arguments should be presented in the body of the text (more specifically in the discussion section and results section.) The conclusion is meant to summarize and reflect on the evidence and arguments you have already presented, not introduce new ones.
Some antonyms (opposites) for “callous” include:
Some synonyms for “callous” include:
Some antonyms (opposites) for “presumptuous” include:
Some synonyms for “presumptuous” include:
Verbiage has three syllables. It’s pronounced with emphasis on the first syllable: [ver-bee-ij].
There are numerous synonyms for the two meanings of verbiage.
| Excessive use of language | Manner/style of language |
|---|---|
| Circumlocution | Diction |
| Diffuseness | Language |
| Long-windedness | Phrasing |
| Redundancy | Style |
| Verboseness | Syntax |
| Verbosity | Turn of phrase |
| Windiness | Wording |
| Wordage | |
| Wordiness |
An AMA reference usually includes the author’s last name and initials, the title of the source, information about the publisher or the publication it’s contained in, and the publication date. The specific details included, and the formatting, depend on the source type.
References in AMA style are presented in numerical order (numbered by the order in which they were first cited in the text) on your reference page. A source that’s cited repeatedly in the text still only appears once on the reference page.
An AMA in-text citation consists of the number of the relevant reference on your AMA reference page, written in superscript1 at the point in the text where the source is used.
It may also include the page number or range of the relevant material in the source (e.g., the part you quoted2(p46)). Multiple sources can be cited at one point, presented as a range or list (with no spaces3,5–9).
AMA citation format is a citation style designed by the American Medical Association. It’s frequently used in the field of medicine.
You may be told to use AMA style for your student papers. You will also have to follow this style if you’re submitting a paper to a journal published by the AMA.
Some synonyms for “loquacious” include:
Automatically find more synonyms for “loquacious” with the paraphrasing tool.
Mea culpa has four syllables. It’s pronounced with emphasis on the first and third syllables: [May-uh-kuul-puh].
Mea maxima culpa is a term of Latin origin meaning “through my most grievous fault.” It is used to acknowledge a mistake or wrongdoing. Mea maxima culpa is a stronger version of mea culpa, which means “through my fault.”
Mea maxima culpa is traditionally used in a prayer of confession in the Catholic Church as the third and most emphatic expression of guilt (“mea culpa, mea culpa, mea maxima culpa”). Unlike mea culpa, mea maxima culpa is rarely used outside of a religious context.
Criterion validity and construct validity are both types of measurement validity. In other words, they both show you how accurately a method measures something.
While construct validity is the degree to which a test or other measurement method measures what it claims to measure, criterion validity is the degree to which a test can predictively (in the future) or concurrently (in the present) measure something.
Construct validity is often considered the overarching type of measurement validity. You need to have face validity, content validity, and criterion validity in order to achieve construct validity.
Convergent validity and discriminant validity are both subtypes of construct validity. Together, they help you evaluate whether a test measures the concept it was designed to measure.
You need to assess both in order to demonstrate construct validity. Neither one alone is sufficient for establishing construct validity.
Some words with a similar or identical meaning to albeit (depending on context) include:
Albeit has three syllables. It’s pronounced with emphasis on the second syllable: [awl-bee-it].
Because some people pronounce “I’ll” in a similar way to the first syllable, they sometimes mistakenly write “I’ll be it” in place of “albeit.” This is incorrect and should be avoided.
Vice versa is the only correct spelling (not “vice a versa” or “vice-versa”), but the phrase can be pronounced both ways: [vice–vur-suh] or [vice-uh-vur-suh].
There are two ways to pronounce vice versa:
Both pronunciations are considered acceptable, but “vice versa” is the only correct spelling.
Some synonyms of vice versa include:
Some synonyms for “indubitably” include:
You can find more synonyms for “indubitably” while using the paraphrasing tool. All you need to do is write the word into the tool and it will automatically suggest synonyms for you to use.
“Indubitably” has five syllables. It is pronounced with an emphasis on the second syllable: [in-doo-bit-uh-blee].
“Eponymous” has four syllables. It’s pronounced with an emphasis on the second syllable: [i-pon-uh-muss].
Some words that are synonyms or near synonyms of “eponymous” include:
Another easy way of finding synonyms for “eponymous” is using the paraphrasing tool. Copy or write the word in the tool and it will automatically suggest a variety of synonyms for you to use.
Convergent validity and discriminant validity are both subtypes of construct validity. Together, they help you evaluate whether a test measures the concept it was designed to measure.
You need to assess both in order to demonstrate construct validity. Neither one alone is sufficient for establishing construct validity.
Facetious has three syllables. It’s pronounced with an emphasis on the second syllable: [fuh-see-shuss].
Some antonyms (opposites) for facetious include:
Some synonyms for facetious include:
Regular verbs are verbs whose simple past and past participle are formed by adding the suffix “-ed” (e.g., “walked”).
Irregular verbs are verbs that form their simple past and past participles in some way other than by adding the suffix “-ed” (e.g., “sat”).
There are many ways to categorize verbs into various types. A verb can fall into one or more of these categories depending on how it is used.
Some of the main types of verbs are:
A collective noun is any noun that is used to name a group of something (people, animals, things, etc.). “Group” is one very common collective noun. Collective nouns can be common nouns (like “group”) or proper nouns (like “Google” and other company names).
Collective nouns are most commonly treated as singular (e.g., “the herd is grazing”), but usage differs between US and UK English:
The correct spelling of the term meaning “to a sickening degree” is ad nauseam, with an “a.” The common misspelling “ad nauseum,” with a “u,” is never correct.
Ad nauseam is usually used to refer to something going on for too long. Some rough synonyms of ad nauseam are:
In fiction, the opposite of a protagonist is an antagonist, meaning someone who opposes the protagonist.
More generally, some antonyms for “protagonist” include:
There are numerous synonyms for the various meanings of protagonist.
| Main character in a story | Main participant in an event | Leader or supporter of a cause |
| Central figure | Actor | Advocate |
| Hero(ine) | Key figure | Champion |
| Lead(ing) character | Main figure | Exponent |
| Main character | Principal player | Promoter |
| Proponent | ||
| Supporter | ||
| Upholder |
Content validity shows you how accurately a test or other measurement method taps into the various aspects of the specific construct you are researching.
In other words, it helps you answer the question: “does the test measure all aspects of the construct I want to measure?” If it does, then the test has high content validity.
The higher the content validity, the more accurate the measurement of the construct.
If the test fails to include parts of the construct, or irrelevant parts are included, the validity of the instrument is threatened, which brings your results into question.
Face validity and content validity are similar in that they both evaluate how suitable the content of a test is. The difference is that face validity is subjective, and assesses content at surface level.
When a test has strong face validity, anyone would agree that the test’s questions appear to measure what they are intended to measure.
For example, looking at a 4th grade math test consisting of problems in which students have to add and multiply, most people would agree that it has strong face validity (i.e., it looks like a math test).
On the other hand, content validity evaluates how well a test represents all the aspects of a topic. Assessing content validity is more systematic and relies on expert evaluation. of each question, analyzing whether each one covers the aspects that the test was designed to cover.
A 4th grade math test would have high content validity if it covered all the skills taught in that grade. Experts(in this case, math teachers), would have to evaluate the content validity by comparing the test to the learning objectives.
Cardinal numbers (e.g., one, two, three) can be placed before a noun to indicate quantity (e.g., one apple). While these are sometimes referred to as “numeral adjectives,” they are more accurately categorized as determiners or quantifiers.
There are many ways to categorize adjectives into various types. An adjective can fall into one or more of these categories depending on how it is used.
Some of the main types of adjectives are:
No, as a general rule, academic concepts, disciplines, theories, models, etc. are treated as common nouns, not proper nouns, and therefore not capitalized. For example, “five-factor model of personality” or “analytic philosophy.”
However, proper nouns that appear within the name of an academic concept (such as the name of the inventor) are capitalized as usual. For example, “Darwin’s theory of evolution” or “Student’s t table.”
The names of seasons (e.g., “spring”) are treated as common nouns in English and therefore not capitalized. People often assume they are proper nouns, but this is an error.
The names of days and months, however, are capitalized since they’re treated as proper nouns in English (e.g., “Wednesday,” “January”).
A proper adjective is an adjective that was derived from a proper noun and is therefore capitalized.
Proper adjectives include words for nationalities, languages, and ethnicities (e.g., “Japanese,” “Inuit,” “French”) and words derived from people’s names (e.g., “Bayesian,” “Orwellian”).
Common nouns are words for types of things, people, and places, such as “dog,” “professor,” and “city.” They are not capitalized and are typically used in combination with articles and other determiners.
Proper nouns are words for specific things, people, and places, such as “Max,” “Dr. Prakash,” and “London.” They are always capitalized and usually aren’t combined with articles and other determiners.
Snowball sampling is a non-probability sampling method. Unlike probability sampling (which involves some form of random selection), the initial individuals selected to be studied are the ones who recruit new participants.
Because not every member of the target population has an equal chance of being recruited into the sample, selection in snowball sampling is non-random.
Snowball sampling is a non-probability sampling method, where there is not an equal chance for every member of the population to be included in the sample.
This means that you cannot use inferential statistics and make generalizations—often the goal of quantitative research. As such, a snowball sample is not representative of the target population and is usually a better fit for qualitative research.
Snowball sampling relies on the use of referrals. Here, the researcher recruits one or more initial participants, who then recruit the next ones.
Participants share similar characteristics and/or know each other. Because of this, not every member of the population has an equal chance of being included in the sample, giving rise to sampling bias.
Snowball sampling is best used in the following cases:
The reproducibility and replicability of a study can be ensured by writing a transparent, detailed method section and using clear, unambiguous language.
Reproducibility and replicability are related terms.
Reproducibility and replicability are related terms.
Pronouns are words like “I,” “she,” and “they” that are used in a similar way to nouns. They stand in for a noun that has already been mentioned or refer to yourself and other people.
Pronouns can function just like nouns as the head of a noun phrase and as the subject or object of a verb. However, pronouns change their forms (e.g., from “I” to “me”) depending on the grammatical context they’re used in, whereas nouns usually don’t.
There are many ways to categorize nouns into various types, and the same noun can fall into multiple categories or even change types depending on context.
Some of the main types of nouns are:
A noun is a word that represents a person, thing, concept, or place (e.g., “John,” “house,” “affinity,” “river”). Most sentences contain at least one noun or pronoun.
Nouns are often, but not always, preceded by an article (“the,” “a,” or “an”) and/or another determiner such as an adjective.
Response bias is a general term used to describe a number of different conditions or factors that cue respondents to provide inaccurate or false answers during surveys or interviews. These factors range from the interviewer’s perceived social position or appearance to the the phrasing of questions in surveys.
Nonresponse bias occurs when the people who complete a survey are different from those who did not, in ways that are relevant to the research topic. Nonresponse can happen because people are either not willing or not able to participate.
Observer bias occurs when the researcher’s assumptions, views, or preconceptions influence what they see and record in a study, while actor–observer bias refers to situations where respondents attribute internal factors (e.g., bad character) to justify other’s behavior and external factors (difficult circumstances) to justify the same behavior in themselves.
Research bias affects the validity and reliability of your research findings, leading to false conclusions and a misinterpretation of the truth. This can have serious implications in areas like medical research where, for example, a new form of treatment may be evaluated.
Stratified sampling and quota sampling both involve dividing the population into subgroups and selecting units from each subgroup. The purpose in both cases is to select a representative sample and/or to allow comparisons between subgroups.
The main difference is that in stratified sampling, you draw a random sample from each subgroup (probability sampling). In quota sampling you select a predetermined number or proportion of units, in a non-random manner (non-probability sampling).
On the IEEE reference page, you should abbreviate the names of publishers (in IEEE book citations), journals (in IEEE journal article citations), universities, companies, conferences, and months. Authors’ first and middle names should also be presented as initials.
A list of the standard abbreviations for many common words can be found here. Note that these words are not abbreviated when they appear in the title of the source (e.g., the book or article title).
Purposive and convenience sampling are both sampling methods that are typically used in qualitative data collection.
A convenience sample is drawn from a source that is conveniently accessible to the researcher. Convenience sampling does not distinguish characteristics among the participants. On the other hand, purposive sampling focuses on selecting participants possessing characteristics associated with the research study.
The findings of studies based on either convenience or purposive sampling can only be generalized to the (sub)population from which the sample is drawn, and not to the entire population.
Random sampling or probability sampling is based on random selection. This means that each unit has an equal chance (i.e., equal probability) of being included in the sample.
On the other hand, convenience sampling involves stopping people at random, which means that not everyone has an equal chance of being selected depending on the place, time, or day you are collecting your data.
Convenience sampling and quota sampling are both non-probability sampling methods. They both use non-random criteria like availability, geographical proximity, or expert knowledge to recruit study participants.
However, in convenience sampling, you continue to sample units or cases until you reach the required sample size.
In quota sampling, you first need to divide your population of interest into subgroups (strata) and estimate their proportions (quota) in the population. Then you can start your data collection, using convenience sampling to recruit participants, until the proportions in each subgroup coincide with the estimated proportions in the population.
You can cite specific pages from a source in your IEEE in-text citations by including them within the brackets along with the number of the reference. A single page is preceded by “p.”, multiple pages by “pp.”: [11, p. 36].
To cite different pages from the same source, use the same reference number followed by different page numbers. Don’t include multiple references for the same source on your IEEE reference page, and don’t include the page numbers there.
When a whole book is written by the same author (or group of authors), you should list information about the whole book in your IEEE book citation. This applies even if you only refer to one chapter of the book.
When different chapters of a book are written by different authors, you should include a reference for the chapter you cite, with the chapter author at the start and the editor of the whole book mentioned late in the reference. If you cite multiple chapters, include a separate reference for each.
In an IEEE book citation, you should mention the edition of the book (e.g., second edition, revised edition) when this information is provided on the cover or title page of the book. Otherwise, you can assume it’s the first or only edition and omit this part.
Editions are written in abbreviated form (e.g., “11th ed.”).
If you cite the same source more than once in your writing, use the same number for all of the IEEE in-text citations for that source, and only include it on the IEEE reference page once. The source is numbered based on the first time you cite it.
For example, the fourth source you cite in your paper is numbered [4]. If you cite it again later, you still cite it as [4]. You can cite different parts of the source each time by adding page numbers [4, p. 15]. Don’t use “ibid.”
You should include an IEEE in-text citation whenever you integrate a source into your text by quoting, paraphrasing, or summarizing it. The citation appears in the sentence where the source is integrated, often after the author name or after any quoted text:
Narayana [15, p. 22] describes the encounter as “copacetic.”
In IEEE citation format, you should list the names of up to six authors in a reference on your IEEE reference page. If the source has seven or more authors, just list the first author’s name followed by “et al.” (in italics): “F. Gupta et al., …”
In the main text, if you mention a source with three or more authors, you should use “et al.”: “Fowler et al. [11] argue that …”
Note that you’re not required to mention author names at all in the text though—just the IEEE in-text citation number is enough, in which case “et al.” isn’t needed: “[11] argues that …”
A research aim is a broad statement indicating the general purpose of your research project. It should appear in your introduction at the end of your problem statement, before your research objectives.
Research objectives are more specific than your research aim. They indicate the specific ways you’ll address the overarching aim.
Once you’ve decided on your research objectives, you need to explain them in your paper, at the end of your problem statement.
Keep your research objectives clear and concise, and use appropriate verbs to accurately convey the work that you will carry out for each one.
I will compare …
I will calculate …
Your research objectives indicate how you’ll try to address your research problem and should be specific:
Research objectives describe what you intend your research project to accomplish.
They summarize the approach and purpose of the project and help to focus your research.
Your objectives should appear in the introduction of your research paper, at the end of your problem statement.
The IEEE reference page consists of a list of references numbered in the order they were cited in the text. The title “References” appears in bold at the top, either left-aligned or centered.
The numbers appear in square brackets on the left-hand side of the page. The reference entries are indented consistently to separate them from the numbers. Entries are single-spaced, with a normal paragraph break between them.
An IEEE in-text citation consists of a number in brackets at the relevant point in the text, which points the reader to the right entry in the numbered IEEE reference page at the end of the research paper. For example, “Smith [1] states that a new protocol will indubitably pay off.”
A location marker such as a page number is also included within the brackets when needed: “Smith [1, p. 13] argues that the poet made facetious comments.”
IEEE citation format is defined by the Institute of Electrical and Electronics Engineers and used in their publications.
It’s also a widely used citation style for students in technical fields like electrical and electronic engineering, computer science, telecommunications, and computer engineering.
As the degrees of freedom increase, Student’s t distribution becomes less leptokurtic, meaning that the probability of extreme values decreases. The distribution becomes more and more similar to a standard normal distribution.
A sampling frame is a list of every member in the entire population. It is important that the sampling frame is as complete as possible, so that your sample accurately reflects your population.
Stratified and cluster sampling may look similar, but bear in mind that groups created in cluster sampling are heterogeneous, so the individual characteristics in the cluster vary. In contrast, groups created in stratified sampling are homogeneous, as units share characteristics.
Relatedly, in cluster sampling you randomly select entire groups and include all units of each group in your sample. However, in stratified sampling, you select some units of all groups and include them in your sample. In this way, both methods can ensure that your sample is representative of the target population.
When your population is large in size, geographically dispersed, or difficult to contact, it’s necessary to use a sampling method.
This allows you to gather information from a smaller part of the population (i.e., the sample) and make accurate statements by using statistical analysis. A few sampling methods include simple random sampling, convenience sampling, and snowball sampling.
Synthesizing sources means comparing and contrasting the work of other scholars to provide new insights.
It involves analyzing and interpreting the points of agreement and disagreement among sources.
You might synthesize sources in your literature review to give an overview of the field of research or throughout your paper when you want to contribute something new to existing research.
A theoretical framework can sometimes be integrated into a literature review chapter, but it can also be included as its own chapter or section in your dissertation. As a rule of thumb, if your research involves dealing with a lot of complex theories, it’s a good idea to include a separate theoretical framework chapter.
A literature review and a theoretical framework are not the same thing and cannot be used interchangeably. While a theoretical framework describes the theoretical underpinnings of your work, a literature review critically evaluates existing research relating to your topic. You’ll likely need both in your dissertation.
While a theoretical framework describes the theoretical underpinnings of your work based on existing research, a conceptual framework allows you to draw your own conclusions, mapping out the variables you may use in your study and the interplay between them.
The three categories of kurtosis are:
A scientific citation style is a system of source citation that is used in scientific disciplines. Some commonly used scientific citation styles are:
There are many different citation styles used across different academic disciplines, but they fall into three basic approaches to citation:
A systematic review is secondary research because it uses existing research. You don’t collect new data yourself.
A source annotation in an annotated bibliography fulfills a similar purpose to an abstract: they’re both intended to summarize the approach and key points of a source.
However, an annotation may also evaluate the source, discussing the validity and effectiveness of its arguments. Even if your annotation is purely descriptive, you may have a different perspective on the source from the author and highlight different key points.
You should never just copy text from the abstract for your annotation, as doing so constitutes plagiarism.
You can find sources online using databases and search engines like Google Scholar. Use Boolean operators or advanced search functions to narrow or expand your search.
For print sources, you can use your institution’s library database. This will allow you to explore the library’s catalog and to search relevant keywords.
Most academics agree that you shouldn’t cite Wikipedia as a source in your academic writing, and universities often have rules against doing so.
This is partly because of concerns about its reliability, and partly because it’s a tertiary source. Tertiary sources are things like encyclopedias and databases that collect information from other sources rather than presenting their own evidence or analysis. Usually, only primary and secondary sources are cited in academic papers.
A Wikipedia citation usually includes the title of the article, “Wikipedia” and/or “Wikimedia Foundation,” the date the article was last updated, and the URL.
In APA Style, you’ll give the URL of the current revision of the article so that you’re sure the reader accesses the same version as you.
There’s some disagreement about whether Wikipedia can be considered a reliable source. Because it can be edited by anyone, many people argue that it’s easy for misleading information to be added to an article without the reader knowing.
Others argue that because Wikipedia articles cite their sources, and because they are worked on by so many editors, misinformation is generally removed quickly.
However, most universities state that you shouldn’t cite Wikipedia in your writing.
Probability distributions belong to two broad categories: discrete probability distributions and continuous probability distributions. Within each category, there are many types of probability distributions.
Probability is the relative frequency over an infinite number of trials.
For example, the probability of a coin landing on heads is .5, meaning that if you flip the coin an infinite number of times, it will land on heads half the time.
Since doing something an infinite number of times is impossible, relative frequency is often used as an estimate of probability. If you flip a coin 1000 times and get 507 heads, the relative frequency, .507, is a good estimate of the probability.
Categorical variables can be described by a frequency distribution. Quantitative variables can also be described by a frequency distribution, but first they need to be grouped into interval classes.
A histogram is an effective way to tell if a frequency distribution appears to have a normal distribution.
Plot a histogram and look at the shape of the bars. If the bars roughly follow a symmetrical bell or hill shape, like the example below, then the distribution is approximately normally distributed.
A thesis or dissertation outline is one of the most critical first steps in your writing process. It helps you to lay out and organize your ideas and can provide you with a roadmap for deciding what kind of research you’d like to undertake.
Generally, an outline contains information on the different sections included in your thesis or dissertation, such as:
When you mention different chapters within your text, it’s considered best to use Roman numerals for most citation styles. However, the most important thing here is to remain consistent whenever using numbers in your dissertation.
APA footnotes use superscript numbers and should appear in numerical order. You can place footnotes at the bottom of the relevant pages, or on a separate footnotes page at the end:
For both approaches, place a space between the superscript number and the footnote text.
APA Style requires you to use APA in-text citations, not footnotes, to cite sources.
However, you can use APA footnotes sparingly for two purposes:
Hanging indents are used in reference lists in various citation styles to allow the reader to easily distinguish between entries.
You should apply a hanging indent to your reference entries in APA, MLA, and Chicago style.
A hanging indent is used to indent all lines of a paragraph except the first.
When you create a hanging indent, the first line of the paragraph starts at the border. Each subsequent line is indented 0.5 inches (1.27 cm).
APA and MLA style both use parenthetical in-text citations to cite sources and include a full list of references at the end, but they differ in other ways:
Lateral reading is the act of evaluating the credibility of a source by comparing it with other sources. This allows you to:
As you cannot possibly read every source related to your topic, it’s important to evaluate sources to assess their relevance. Use preliminary evaluation to determine whether a source is worth examining in more depth.
This involves:
In most styles, the title page is used purely to provide information and doesn’t include any images. Ask your supervisor if you are allowed to include an image on the title page before doing so. If you do decide to include one, make sure to check whether you need permission from the creator of the image.
Include a note directly beneath the image acknowledging where it comes from, beginning with the word “Note.” (italicized and followed by a period). Include a citation and copyright attribution. Don’t title, number, or label the image as a figure, since it doesn’t appear in your main text.
You can use the CHISQ.INV.RT() function to find a chi-square critical value in Excel.
For example, to calculate the chi-square critical value for a test with df = 22 and α = .05, click any blank cell and type:
=CHISQ.INV.RT(0.05,22)
You can use the qchisq() function to find a chi-square critical value in R.
For example, to calculate the chi-square critical value for a test with df = 22 and α = .05:
qchisq(p = .05, df = 22, lower.tail = FALSE)
An abstract concisely explains all the key points of an academic text such as a thesis, dissertation or journal article. It should summarize the whole text, not just introduce it.
An abstract is a type of summary, but summaries are also written elsewhere in academic writing. For example, you might summarize a source in a paper, in a literature review, or as a standalone assignment.
All can be done within seconds with our free text summarizer.
You might have to write a summary of a source:
You can assess information and arguments critically by asking certain questions about the source. You can use the CRAAP test, focusing on the currency, relevance, authority, accuracy, and purpose of a source of information.
Ask questions such as:
Critical thinking skills include the ability to:
Critical thinking refers to the ability to evaluate information and to be aware of biases or assumptions, including your own.
Like information literacy, it involves evaluating arguments, identifying and solving problems in an objective and systematic way, and clearly communicating your ideas.
You can use the chisq.test() function to perform a chi-square test of independence in R. Give the contingency table as a matrix for the “x” argument. For example:
m = matrix(data = c(89, 84, 86, 9, 8, 24), nrow = 3, ncol = 2)
chisq.test(x = m)
You can use the CHISQ.TEST() function to perform a chi-square test of independence in Excel. It takes two arguments, CHISQ.TEST(observed_range, expected_range), and returns the p value.
Definitional terms often fall into the category of common knowledge, meaning that they don’t necessarily have to be cited. This guidance can apply to your thesis or dissertation glossary as well.
However, if you’d prefer to cite your sources, you can follow guidance for citing dictionary entries in MLA or APA style for your glossary.
A glossary is a collection of words pertaining to a specific topic. In your thesis or dissertation, it’s a list of all terms you used that may not immediately be obvious to your reader. In contrast, an index is a list of the contents of your work organized by page number.
The title page of your thesis or dissertation goes first, before all other content or lists that you may choose to include.
The title page of your thesis or dissertation should include your name, department, institution, degree program, and submission date.
Glossaries are not mandatory, but if you use a lot of technical or field-specific terms, it may improve readability to add one to your thesis or dissertation. Your educational institution may also require them, so be sure to check their specific guidelines.
A glossary or “glossary of terms” is a collection of words pertaining to a specific topic. In your thesis or dissertation, it’s a list of all terms you used that may not immediately be obvious to your reader. Your glossary only needs to include terms that your reader may not be familiar with, and is intended to enhance their understanding of your work.
A glossary is a collection of words pertaining to a specific topic. In your thesis or dissertation, it’s a list of all terms you used that may not immediately be obvious to your reader. In contrast, dictionaries are more general collections of words.
Chi-square goodness of fit tests are often used in genetics. One common application is to check if two genes are linked (i.e., if the assortment is independent). When genes are linked, the allele inherited for one gene affects the allele inherited for another gene.
Suppose that you want to know if the genes for pea texture (R = round, r = wrinkled) and color (Y = yellow, y = green) are linked. You perform a dihybrid cross between two heterozygous (RY / ry) pea plants. The hypotheses you’re testing with your experiment are:
You observe 100 peas:
To calculate the expected values, you can make a Punnett square. If the two genes are unlinked, the probability of each genotypic combination is equal.
| RY | ry | Ry | rY | |
| RY | RRYY | RrYy | RRYy | RrYY |
| ry | RrYy | rryy | Rryy | rrYy |
| Ry | RRYy | Rryy | RRyy | RrYy |
| rY | RrYY | rrYy | RrYy | rrYY |
The expected phenotypic ratios are therefore 9 round and yellow: 3 round and green: 3 wrinkled and yellow: 1 wrinkled and green.
From this, you can calculate the expected phenotypic frequencies for 100 peas:
| Phenotype | Observed | Expected |
| Round and yellow | 78 | 100 * (9/16) = 56.25 |
| Round and green | 6 | 100 * (3/16) = 18.75 |
| Wrinkled and yellow | 4 | 100 * (3/16) = 18.75 |
| Wrinkled and green | 12 | 100 * (1/16) = 6.21 |
| Phenotype | Observed | Expected | O − E | (O − E)2 | (O − E)2 / E |
| Round and yellow | 78 | 56.25 | 21.75 | 473.06 | 8.41 |
| Round and green | 6 | 18.75 | −12.75 | 162.56 | 8.67 |
| Wrinkled and yellow | 4 | 18.75 | −14.75 | 217.56 | 11.6 |
| Wrinkled and green | 12 | 6.21 | 5.79 | 33.52 | 5.4 |
Χ2 = 8.41 + 8.67 + 11.6 + 5.4 = 34.08
Since there are four groups (round and yellow, round and green, wrinkled and yellow, wrinkled and green), there are three degrees of freedom.
For a test of significance at α = .05 and df = 3, the Χ2 critical value is 7.82.
Χ2 = 34.08
Critical value = 7.82
The Χ2 value is greater than the critical value.
The Χ2 value is greater than the critical value, so we reject the null hypothesis that the population of offspring have an equal probability of inheriting all possible genotypic combinations. There is a significant difference between the observed and expected genotypic frequencies (p < .05).
The data supports the alternative hypothesis that the offspring do not have an equal probability of inheriting all possible genotypic combinations, which suggests that the genes are linked
You can use the chisq.test() function to perform a chi-square goodness of fit test in R. Give the observed values in the “x” argument, give the expected values in the “p” argument, and set “rescale.p” to true. For example:
chisq.test(x = c(22,30,23), p = c(25,25,25), rescale.p = TRUE)
You can use the CHISQ.TEST() function to perform a chi-square goodness of fit test in Excel. It takes two arguments, CHISQ.TEST(observed_range, expected_range), and returns the p value.
An abbreviation is a shortened version of an existing word, such as Dr. for Doctor. In contrast, an acronym uses the first letter of each word to create a wholly new word, such as UNESCO (an acronym for the United Nations Educational, Scientific and Cultural Organization).
As a rule of thumb, write the explanation in full the first time you use an acronym or abbreviation. You can then proceed with the shortened version. However, if the abbreviation is very common (like PC, USA, or DNA), then you can use the abbreviated version from the get-go.
Be sure to add each abbreviation in your list of abbreviations!
If you only used a few abbreviations in your thesis or dissertation, you don’t necessarily need to include a list of abbreviations.
If your abbreviations are numerous, or if you think they won’t be known to your audience, it’s never a bad idea to add one. They can also improve readability, minimizing confusion about abbreviations unfamiliar to your reader.
A list of abbreviations is a list of all the abbreviations that you used in your thesis or dissertation. It should appear at the beginning of your document, with items in alphabetical order, just after your table of contents.
Both correlations and chi-square tests can test for relationships between two variables. However, a correlation is used when you have two quantitative variables and a chi-square test of independence is used when you have two categorical variables.
Both chi-square tests and t tests can test for differences between two groups. However, a t test is used when you have a dependent quantitative variable and an independent categorical variable (with two groups). A chi-square test of independence is used when you have two categorical variables.
The two main chi-square tests are the chi-square goodness of fit test and the chi-square test of independence.
A chi-square distribution is a continuous probability distribution. The shape of a chi-square distribution depends on its degrees of freedom, k. The mean of a chi-square distribution is equal to its degrees of freedom (k) and the variance is 2k. The range is 0 to ∞.
As the degrees of freedom (k) increases, the chi-square distribution goes from a downward curve to a hump shape. As the degrees of freedom increases further, the hump goes from being strongly right-skewed to being approximately normal.
To find the quartiles of a probability distribution, you can use the distribution’s quantile function.
You can use the quantile() function to find quartiles in R. If your data is called “data”, then “quantile(data, prob=c(.25,.5,.75), type=1)” will return the three quartiles.
You can use the QUARTILE() function to find quartiles in Excel. If your data is in column A, then click any blank cell and type “=QUARTILE(A:A,1)” for the first quartile, “=QUARTILE(A:A,2)” for the second quartile, and “=QUARTILE(A:A,3)” for the third quartile.
It is important to find credible sources and use those that you can be sure are sufficiently scholarly.
In academic writing, the sources you cite should be credible and scholarly. Some of the main types of sources used are:
Scholarly sources are written by experts in their field and are typically subjected to peer review. They are intended for a scholarly audience, include a full bibliography, and use scholarly or technical language. For these reasons, they are typically considered credible sources.
Popular sources like magazines and news articles are typically written by journalists. These types of sources usually don’t include a bibliography and are written for a popular, rather than academic, audience. They are not always reliable and may be written from a biased or uninformed perspective, but they can still be cited in some contexts.
There are many types of sources commonly used in research. These include:
You’ll likely use a variety of these sources throughout the research process, and the kinds of sources you use will depend on your research topic and goals.
You usually shouldn’t cite tertiary sources as evidence in your research paper, but you can use them in the beginning stages of the research process to:
Use tertiary sources in your preliminary research to find relevant primary and secondary sources that you will engage with in more depth during the writing process.
What constitutes a tertiary source depends on your research question and how you use the source.
To determine whether a source is tertiary, ask:
Primary sources provide direct evidence about your research topic (photographs, personal letters, etc.).
Secondary sources interpret and comment on information from primary sources (academic books, journal articles, etc.).
Tertiary sources are reference works that identify and provide background information on primary and secondary sources. They do not provide original insights or analysis.
A tertiary source may list, summarize, or index primary and secondary sources or provide general information from a variety of sources. But it does not provide original interpretations or analysis.
Some examples of tertiary sources include:
Your list of tables and figures should go directly after your table of contents in your thesis or dissertation.
Lists of figures and tables are often not required, and aren’t particularly common. They specifically aren’t required for APA-Style, though you should be careful to follow their other guidelines for figures and tables.
If you have many figures and tables in your thesis or dissertation, include one may help you stay organized. Your educational institution may require them, so be sure to check their guidelines.
A list of figures and tables compiles all of the figures and tables that you used in your thesis or dissertation and displays them with the page number where they can be found.
The table of contents in a thesis or dissertation always goes between your abstract and your introduction.
You can use the PEARSON() function to calculate the Pearson correlation coefficient in Excel. If your variables are in columns A and B, then click any blank cell and type “PEARSON(A:A,B:B)”.
There is no function to directly test the significance of the correlation.
You can use the cor() function to calculate the Pearson correlation coefficient in R. To test the significance of the correlation, you can use the cor.test() function.
You should use the Pearson correlation coefficient when (1) the relationship is linear and (2) both variables are quantitative and (3) normally distributed and (4) have no outliers.
The Pearson correlation coefficient (r) is the most common way of measuring a linear correlation. It is a number between –1 and 1 that measures the strength and direction of the relationship between two variables.
This table summarizes the most important differences between normal distributions and Poisson distributions:
| Characteristic | Normal | Poisson |
|---|---|---|
| Continuous or discrete | Continuous | Discrete |
| Parameter | Mean (µ) and standard deviation (σ) | Lambda (λ) |
| Shape | Bell-shaped | Depends on λ |
| Symmetry | Symmetrical | Asymmetrical (right-skewed). As λ increases, the asymmetry decreases. |
| Range | −∞ to ∞ | 0 to ∞ |
When the mean of a Poisson distribution is large (>10), it can be approximated by a normal distribution.
In the Poisson distribution formula, lambda (λ) is the mean number of events within a given interval of time or space. For example, λ = 0.748 floods per year.
The e in the Poisson distribution formula stands for the number 2.718. This number is called Euler’s constant. You can simply substitute e with 2.718 when you’re calculating a Poisson probability. Euler’s constant is a very useful number and is especially important in calculus.
It can sometimes be hard to distinguish accurate from inaccurate sources, especially online. Published articles are not always credible and can reflect a biased viewpoint without providing evidence to support their conclusions.
Information literacy is important because it helps you to be aware of such unreliable content and to evaluate sources effectively, both in an academic context and more generally.
Information literacy refers to a broad range of skills, including the ability to find, evaluate, and use sources of information effectively.
Being information literate means that you:
The three types of skewness are:
Skewness and kurtosis are both important measures of a distribution’s shape.
A parenthetical citation in Chicago author-date style includes the author’s last name, the publication date, and, if applicable, the relevant page number or page range in parentheses. Include a comma after the year, but not after the author’s name.
For example: (Swan 2003, 6)
To automatically generate accurate Chicago references, you can use Scribbr’s free Chicago reference generator.
APA Style distinguishes between parenthetical and narrative citations.
In parenthetical citations, you include all relevant source information in parentheses at the end of the sentence or clause: “Parts of the human body reflect the principles of tensegrity (Levin, 2002).”
In narrative citations, you include the author’s name in the text itself, followed by the publication date in parentheses: “Levin (2002) argues that parts of the human body reflect the principles of tensegrity.”
In a parenthetical citation in MLA style, include the author’s last name and the relevant page number or range in parentheses.
For example: (Eliot 21)
A parenthetical citation gives credit in parentheses to a source that you’re quoting or paraphrasing. It provides relevant information such as the author’s name, the publication date, and the page number(s) cited.
How you use parenthetical citations will depend on your chosen citation style. It will also depend on the type of source you are citing and the number of authors.
APA does not permit the use of ibid. This is because APA in-text citations are parenthetical and there’s no need to shorten them further.
Ibid. may be used in Chicago footnotes or endnotes.
Write “Ibid.” alone when you are citing the same page number and source as the previous citation.
When you are citing the same source, but a different page number, use ibid. followed by a comma and the relevant page number(s). For example:
Only use ibid. if you are directing the reader to a previous full citation of a source.
Ibid. only refers to the previous citation. Therefore, you should only use ibid. directly after a citation that you want to repeat.
A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (“x affects y because …”).
A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study, the statistical hypotheses correspond logically to the research hypothesis.
The alternative hypothesis is often abbreviated as Ha or H1. When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).
The null hypothesis is often abbreviated as H0. When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).
You may acknowledge God in your dissertation acknowledgements, but be sure to follow academic convention by also thanking the members of academia, as well as family, colleagues, and friends who helped you.
When searching for sources in databases, think of specific keywords that are relevant to your topic, and consider variations on them or synonyms that might be relevant.
Once you have a clear idea of your research parameters and key terms, choose a database that is relevant to your research (e.g., Medline, JSTOR, Project MUSE).
Find out if the database has a “subject search” option. This can help to refine your search. Use Boolean operators to combine your keywords, exclude specific search terms, and search exact phrases to find the most relevant sources.
Proximity operators are specific words used alongside your chosen keywords that let you specify the proximity of one keyword in relation to another.
The most common proximity operators include NEAR (Nx), WITHIN (Wx), and SENTENCE.
Each proximity operator has a unique function. For example, Nx allows you to find sources that contain the specified keywords within a set number of words (x) of each other.
Boolean operators are specific words and symbols that you can use to expand or narrow your search parameters when using a database or search engine.
The most common Boolean operators are AND, OR, NOT or AND NOT, quotation marks “”, parentheses (), and asterisks *.
Each Boolean operator has a unique function. For example, the Boolean operator AND will provide search results containing both/all of your keywords.
A Boolean search uses specific words and symbols known as Boolean operators (e.g., AND, OR) alongside keywords to limit or expand search results. Boolean searches allow you to:
The t distribution was first described by statistician William Sealy Gosset under the pseudonym “Student.”
To calculate a confidence interval of a mean using the critical value of t, follow these four steps:
To test a hypothesis using the critical value of t, follow these four steps:
You can use the T.INV() function to find the critical value of t for one-tailed tests in Excel, and you can use the T.INV.2T() function for two-tailed tests.
=T.INV.2T(0.05,29)
You can use the qt() function to find the critical value of t in R. The function gives the critical value of t for the one-tailed test. If you want the critical value of t for a two-tailed test, divide the significance level by two.
qt(p = .025, df = 29)
Indirect quotation means reporting what someone said (or wrote) but not using their exact words. It’s similar to paraphrasing, but it only involves changing enough words to fit the statement into your sentence grammatically (e.g., changing the tense or the pronouns).
Since some of the words have changed, indirect quotations are not enclosed in quotation marks.
Quotes within quotes are punctuated differently to distinguish them from the surrounding quote.
Make sure to close both sets of quotes!
The use of single and double quotation marks when quoting differs between US and UK English. In US English, you must use double quotation marks. Single quotation marks are used for quotes within quotes.
In UK English, it’s most common to use single quotation marks, with double quotation marks for quotes within quotes, although the other way around is acceptable too.
Signal phrases can be used in various ways and can be placed at the beginning, middle, or end of a sentence.
To use signal phrases effectively, include:
Different citation styles require you to use specific verb tenses when using signal phrases.
Signal phrases allow you to give credit for an idea or quote to its author or originator. This helps you to:
A signal phrase is a group of words that ascribes a quote or idea to an outside source.
Signal phrases distinguish the cited idea or argument from your own writing and introduce important information including the source of the material that you are quoting, paraphrasing, or summarizing. For example:
“Cognitive psychologist Steven Pinker (1994) insists that humans possess an innate faculty for comprehending grammar.”
You can use the RSQ() function to calculate R² in Excel. If your dependent variable is in column A and your independent variable is in column B, then click any blank cell and type “RSQ(A:A,B:B)”.
You can use the summary() function to view the R² of a linear model in R. You will see the “R-squared” near the bottom of the output.
There are two formulas you can use to calculate the coefficient of determination (R²) of a simple linear regression.
Formula 1: 
Formula 2: 
The coefficient of determination (R²) is a number between 0 and 1 that measures how well a statistical model predicts an outcome. You can interpret the R² as the proportion of variation in the dependent variable that is predicted by the statistical model.
If you’re quoting from a text that paraphrases or summarizes other sources and cites them in parentheses, APA and Chicago both recommend retaining the citations as part of the quote. However, MLA recommends omitting citations within a quote:
Footnote or endnote numbers that appear within quoted text should be omitted in all styles.
If you want to cite an indirect source (one you’ve only seen quoted in another source), either locate the original source or use the phrase “as cited in” in your citation.
In scientific subjects, the information itself is more important than how it was expressed, so quoting should generally be kept to a minimum. In the arts and humanities, however, well-chosen quotes are often essential to a good paper.
In social sciences, it varies. If your research is mainly quantitative, you won’t include many quotes, but if it’s more qualitative, you may need to quote from the data you collected.
As a general guideline, quotes should take up no more than 5–10% of your paper. If in doubt, check with your instructor or supervisor how much quoting is appropriate in your field.
A literature review is a survey of credible sources on a topic, often used in dissertations, theses, and research papers. Literature reviews give an overview of knowledge on a subject, helping you identify relevant theories and methods, as well as gaps in existing research. Literature reviews are set up similarly to other academic texts, with an introduction, a main body, and a conclusion.
An annotated bibliography is a list of source references that has a short description (called an annotation) for each of the sources. It is often assigned as part of the research process for a paper.
To present information from other sources in academic writing, it’s best to paraphrase in most cases. This shows that you’ve understood the ideas you’re discussing and incorporates them into your text smoothly.
It’s appropriate to quote when:
To paraphrase effectively, don’t just take the original sentence and swap out some of the words for synonyms. Instead, try:
The main point is to ensure you don’t just copy the structure of the original text, but instead reformulate the idea in your own words.
“Et al.” is an abbreviation of the Latin term “et alia,” which means “and others.” It’s used in source citations to save space when there are too many authors to name them all.
Guidelines for using “et al.” differ depending on the citation style you’re following:
The key difference between observational studies and experimental designs is that a well-done observational study does not influence the responses of participants, while experiments do have some sort of treatment condition applied to at least some participants by random assignment.
An observational study is a great choice for you if your research question is based purely on observations. If there are ethical, logistical, or practical concerns that prevent you from conducting a traditional experiment, an observational study may be a good choice. In an observational study, there is no interference or manipulation of the research subjects, as well as no control or treatment groups.
To insert endnotes in Microsoft Word, follow the steps below:
If you need to change the type of notes used in a Word document from footnotes to endnotes, or the other way around, follow these steps:
To insert a footnote automatically in a Word document:
Footnotes are notes indicated in your text with numbers and placed at the bottom of the page. They’re used to provide:
Be sparing in your use of footnotes (other than citation footnotes), and consider whether the information you’re adding is relevant for the reader.
Footnotes appear at the bottom of the page they refer to. This is convenient for the reader but may cause your text to look cluttered if there are a lot of footnotes.
Endnotes appear all together at the end of the whole text. This may be less convenient for the reader but reduces clutter.
Both footnotes and endnotes are used in the same way: to cite sources or add extra information. You should usually choose one or the other to use in your text, not both.
An in-text citation is an acknowledgement you include in your text whenever you quote or paraphrase a source. It usually gives the author’s last name, the year of publication, and the page number of the relevant text. In-text citations allow the reader to look up the full source information in your reference list and see your sources for themselves.
Academic integrity means being honest, ethical, and thorough in your academic work. To maintain academic integrity, you should avoid misleading your readers about any part of your research and refrain from offenses like plagiarism and contract cheating, which are examples of academic misconduct.
Proofreading rates can be calculated in several different ways. You can set your rate:
A per-word rate is generally the most precise, since it closely reflects the amount of work you’ll have to do. But it can be confusing for clients to parse at a glance; one solution is to quote per 1,000 words so the numbers involved are clearer.
It’s often best to ask a variety of people to review your measurements. You can ask experts, such as other researchers, or laypeople, such as potential participants, to judge the face validity of tests.
While experts have a deep understanding of research methods, the people you’re studying can provide you with valuable insights you may have missed otherwise.
Face validity is important because it’s a simple first step to measuring the overall validity of a test or technique. It’s a relatively intuitive, quick, and easy way to start checking whether a new measure seems useful at first glance.
Good face validity means that anyone who reviews your measure says that it seems to be measuring what it’s supposed to. With poor face validity, someone reviewing your measure may be left confused about what you’re measuring and why you’re using this method.
Face validity is about whether a test appears to measure what it’s supposed to measure. This type of validity is concerned with whether a measure seems relevant and appropriate for what it’s assessing only on the surface.
Statistical analyses are often applied to test validity with data from your measures. You test convergent validity and discriminant validity with correlations to see if results from your test are positively or negatively related to those of other established tests.
You can also use regression analyses to assess whether your measure is actually predictive of outcomes that you expect it to predict theoretically. A regression analysis that supports your expectations strengthens your claim of construct validity.
When designing or evaluating a measure, construct validity helps you ensure you’re actually measuring the construct you’re interested in. If you don’t have construct validity, you may inadvertently measure unrelated or distinct constructs and lose precision in your research.
Construct validity is often considered the overarching type of measurement validity, because it covers all of the other types. You need to have face validity, content validity, and criterion validity to achieve construct validity.
Construct validity is about how well a test measures the concept it was designed to evaluate. It’s one of four types of measurement validity, which includes construct validity, face validity, and criterion validity.
There are two subtypes of construct validity.
Naturalistic observation is a valuable tool because of its flexibility, external validity, and suitability for topics that can’t be studied in a lab setting.
The downsides of naturalistic observation include its lack of scientific control, ethical considerations, and potential for bias from observers and subjects.
Naturalistic observation is a qualitative research method where you record the behaviors of your research subjects in real world settings. You avoid interfering or influencing anything in a naturalistic observation.
You can think of naturalistic observation as “people watching” with a purpose.
A dependent variable is what changes as a result of the independent variable manipulation in experiments. It’s what you’re interested in measuring, and it “depends” on your independent variable.
In statistics, dependent variables are also called:
An independent variable is the variable you manipulate, control, or vary in an experimental study to explore its effects. It’s called “independent” because it’s not influenced by any other variables in the study.
Independent variables are also called:
As a rule of thumb, questions related to thoughts, beliefs, and feelings work well in focus groups. Take your time formulating strong questions, paying special attention to phrasing. Be careful to avoid leading questions, which can bias your responses.
Overall, your focus group questions should be:
A structured interview is a data collection method that relies on asking questions in a set order to collect data on a topic. They are often quantitative in nature. Structured interviews are best used when:
More flexible interview options include semi-structured interviews, unstructured interviews, and focus groups.
The interviewer effect is a type of bias that emerges when a characteristic of an interviewer (race, age, gender identity, etc.) influences the responses given by the interviewee.
There is a risk of an interviewer effect in all types of interviews, but it can be mitigated by writing really high-quality interview questions.
A semi-structured interview is a blend of structured and unstructured types of interviews. Semi-structured interviews are best used when:
An unstructured interview is the most flexible type of interview, but it is not always the best fit for your research topic.
Unstructured interviews are best used when:
The four most common types of interviews are:
Deductive reasoning is commonly used in scientific research, and it’s especially associated with quantitative research.
In research, you might have come across something called the hypothetico-deductive method. It’s the scientific method of testing hypotheses to check whether your predictions are substantiated by real-world data.
Deductive reasoning is a logical approach where you progress from general ideas to specific conclusions. It’s often contrasted with inductive reasoning, where you start with specific observations and form general conclusions.
Deductive reasoning is also called deductive logic.
Plagiarism is a form of theft, since it involves taking the words and ideas of others and passing them off as your own. As such, it’s academically dishonest and can have serious consequences.
Plagiarism also hinders the learning process, obscuring the sources of your ideas and usually resulting in bad writing. Even if you could get away with it, plagiarism harms your own learning.
There are many different types of inductive reasoning that people use formally or informally.
Here are a few common types:
Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down.
Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.
In inductive research, you start by making observations or gathering data. Then, you take a broad scan of your data and search for patterns. Finally, you make general conclusions that you might incorporate into theories.
Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning, where you proceed from general information to specific conclusions.
Inductive reasoning is also called inductive logic or bottom-up reasoning.
A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.
A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
Triangulation can help:
But triangulation can also pose problems:
There are four main types of triangulation:
Yes, APA language guidelines state that you should always use the serial comma (aka Oxford comma) in your writing.
This means including a comma before the word “and” at the end of a list of three or more items: “spelling, grammar, and punctuation.” Doing this consistently tends to make your lists less ambiguous.
Yes, it’s perfectly valid to write sentences in the passive voice. The APA language guidelines do caution against overusing the passive voice, because it can obscure your meaning or be needlessly long-winded. For this reason, default to the active voice in most cases.
The passive voice is most useful when the point of the sentence is just to state what was done, not to emphasize who did it. For example, “The projector was mounted on the wall” is better than “James and I mounted the projector on the wall” if it’s not particularly important who mounted the projector.
Yes, APA language guidelines encourage you to use the first-person pronouns “I” or “we” when referring to yourself or a group including yourself in your writing.
In APA Style, you should not refer to yourself in the third person. For example, do not refer to yourself as “the researcher” or “the author” but simply as “I” or “me.” Referring to yourself in the third person is still common practice in some academic fields, but APA Style rejects this convention.
Many academic fields use peer review, largely to determine whether a manuscript is suitable for publication. Peer review enhances the credibility of the published manuscript.
However, peer review is also common in non-academic settings. The United Nations, the European Union, and many individual nations use peer review to evaluate grant applications. It is also widely used in medical and health-related fields as a teaching or quality-of-care measure.
Peer assessment is often used in the classroom as a pedagogical tool. Both receiving feedback and providing it are thought to enhance the learning process, helping students think critically and collaboratively.
Peer review can stop obviously problematic, falsified, or otherwise untrustworthy research from being published. It also represents an excellent opportunity to get feedback from renowned experts in your field. It acts as a first defense, helping you ensure your argument is clear and that there are no gaps, vague terms, or unanswered questions for readers who weren’t involved in the research process.
Peer-reviewed articles are considered a highly credible source due to this stringent process they go through before publication.
In general, the peer review process follows the following steps:
Most online plagiarism checkers only have access to public databases, whose software doesn’t allow you to compare two documents for plagiarism.
However, in addition to our Plagiarism Checker, Scribbr also offers an Self-Plagiarism Checker. This is an add-on tool that lets you compare your paper with unpublished or private documents. This way you can rest assured that you haven’t unintentionally plagiarized or self-plagiarized.
Compare two sources for plagiarism
The observer-expectancy effect occurs when researchers influence the results of their own study through interactions with participants.
Researchers’ own beliefs and expectations about the study results may unintentionally influence participants through demand characteristics.
The observer-expectancy effect is often used synonymously with the Pygmalion or Rosenthal effect.
You can use several tactics to minimize observer bias.
It’s impossible to completely avoid observer bias in studies where data collection is done or recorded manually, but you can take steps to reduce this type of bias in your research.
Observer bias occurs when a researcher’s expectations, opinions, or prejudices influence what they perceive or record in a study. It usually affects studies when observers are aware of the research aims or hypotheses. This type of research bias is also called detection bias or ascertainment bias.
There are three main types of missing data.
Missing completely at random (MCAR) data are randomly distributed across the variable and unrelated to other variables.
Missing at random (MAR) data are not randomly distributed but they are accounted for by other observed variables.
Missing not at random (MNAR) data systematically differ from the observed values.
To tidy up your missing data, your options usually include accepting, removing, or recreating the missing data.
Missing data are important because, depending on the type, they can sometimes bias your results. This means your results may not be generalizable outside of your study because your data come from an unrepresentative sample.
Missing data, or missing values, occur when you don’t have data stored for certain variables or participants.
In any dataset, there’s usually some missing data. In quantitative research, missing values appear as blank cells in your spreadsheet.
Exploratory research is often used when the issue you’re studying is new or when the data collection process is challenging for some reason.
You can use exploratory research if you have a general idea or a specific question that you want to study but there is no preexisting knowledge or paradigm with which to study it.
Exploratory research is a methodology approach that explores research questions that have not previously been studied in depth. It is often used when the issue you’re studying is new, or the data collection process is challenging in some way.
Explanatory research is used to investigate how or why a phenomenon occurs. Therefore, this type of research is often one of the first stages in the research process, serving as a jumping-off point for future research.
Exploratory research aims to explore the main aspects of an under-researched problem, while explanatory research aims to explain the causes and consequences of a well-defined problem.
Explanatory research is a research method used to investigate how or why something occurs when only a small amount of information is available pertaining to that topic. It can help you increase your understanding of a given topic.
There are two steps to calculating the geometric mean:
Before calculating the geometric mean, note that:
The arithmetic mean is the most commonly used type of mean and is often referred to simply as “the mean.” While the arithmetic mean is based on adding and dividing values, the geometric mean multiplies and finds the root of values.
Even though the geometric mean is a less common measure of central tendency, it’s more accurate than the arithmetic mean for percentage change and positively skewed data. The geometric mean is often reported for financial indices and population growth rates.
The geometric mean is an average that multiplies all values and finds a root of the number. For a dataset with n numbers, you find the nth root of their product.
Outliers are extreme values that differ from most values in the dataset. You find outliers at the extreme ends of your dataset.
It’s best to remove outliers only when you have a sound reason for doing so.
Some outliers represent natural variations in the population, and they should be left as is in your dataset. These are called true outliers.
Other outliers are problematic and should be removed because they represent measurement errors, data entry or processing errors, or poor sampling.
You can choose from four main ways to detect outliers:
Outliers can have a big impact on your statistical analyses and skew the results of any hypothesis test if they are inaccurate.
These extreme values can impact your statistical power as well, making it hard to detect a true effect if there is one.
Clean data are valid, accurate, complete, consistent, unique, and uniform. Dirty data include inconsistencies and errors.
Dirty data can come from any part of the research process, including poor research design, inappropriate measurement materials, or flawed data entry.
Data cleaning takes place between data collection and data analyses. But you can use some methods even before collecting data.
For clean data, you should start by designing measures that collect valid data. Data validation at the time of data entry or collection helps you minimize the amount of data cleaning you’ll need to do.
After data collection, you can use data standardization and data transformation to clean your data. You’ll also deal with any missing values, outliers, and duplicate values.
Every dataset requires different techniques to clean dirty data, but you need to address these issues in a systematic way. You focus on finding and resolving data points that don’t agree or fit with the rest of your dataset.
These data might be missing values, outliers, duplicate values, incorrectly formatted, or irrelevant. You’ll start with screening and diagnosing your data. Then, you’ll often standardize and accept or remove data to make your dataset consistent and valid.
Data cleaning is necessary for valid and appropriate analyses. Dirty data contain inconsistencies or errors, but cleaning your data helps you minimize or resolve these.
Without data cleaning, you could end up with a Type I or II error in your conclusion. These types of erroneous conclusions can be practically significant with important consequences, because they lead to misplaced investments or missed opportunities.
Data cleaning involves spotting and resolving potential data inconsistencies or errors to improve your data quality. An error is any value (e.g., recorded weight) that doesn’t reflect the true value (e.g., actual weight) of something that’s being measured.
In this process, you review, analyze, detect, modify, or remove “dirty” data to make your dataset “clean.” Data cleaning is also called data cleansing or data scrubbing.
When writing your Common App essay, choose a prompt that sparks your interest and that you can connect to a unique personal story.
No matter which prompt you choose, admissions officers are more interested in your ability to demonstrate personal development, insight, or motivation for a certain area of study.
The Common App essay is your primary writing sample within the Common Application, a college application portal accepted by more than 900 schools. All your prospective schools that accept the Common App will read this essay to understand your character, background, and value as a potential student.
Since this essay is read by many colleges, avoid mentioning any college names or programs; instead, save tailored answers for the supplementary school-specific essays within the Common App.
Most importantly, your essay should be about you, not another person or thing. An insightful college admissions essay requires deep self-reflection, authenticity, and a balance between confidence and vulnerability.
Your essay shouldn’t be a résumé of your experiences but instead should tell a story that demonstrates your most important values and qualities.
Most institutions have an internal database of previously submitted student papers. Turnitin can check for self-plagiarism by comparing your paper against this database. If you’ve reused parts of an assignment you already submitted, it will flag any similarities as potential plagiarism.
Online plagiarism checkers don’t have access to your institution’s database, so they can’t detect self-plagiarism of unpublished work. If you’re worried about accidentally self-plagiarizing, you can use Scribbr’s Self-Plagiarism Checker to upload your unpublished documents and check them for similarities.
When revising your college essay, first check for big-picture issues regarding your message and content. Then, check for flow, tone, style, and clarity. Finally, focus on eliminating grammar and punctuation errors.
If your college essay goes over the word count limit, cut any sentences with tangents or irrelevant details. Delete unnecessary words that clutter your essay.
If you’re struggling to reach the word count for your college essay, add vivid personal stories or share your feelings and insight to give your essay more depth and authenticity.
If you’ve got to write your college essay fast, don’t panic. First, set yourself deadlines: you should spend about 10% of your remaining time on brainstorming, 10% on outlining, 40% writing, 30% revising, and 10% taking breaks in between stages.
Second, brainstorm stories and values based on your essay prompt.
Third, outline your essay based on the montage or narrative essay structure.
Fourth, write specific, personal, and unique stories that would be hard for other students to replicate.
Fifth, revise your essay and make sure it’s clearly written.
Last, if possible, get feedback from an essay coach. Scribbr essay editors can help you revise your essay in 12 hours or less.
If you have a small amount of attrition bias, you can use some statistical methods to try to make up for it.
Multiple imputation involves using simulations to replace the missing data with likely values. Alternatively, you can use sample weighting to make up for the uneven balance of participants in your sample.
To avoid attrition, applying some of these measures can help you reduce participant dropout by making it easy and appealing for participants to stay.
Attrition bias can skew your sample so that your final sample differs significantly from your original sample. Your sample is biased because some groups from your population are underrepresented.
With a biased final sample, you may not be able to generalize your findings to the original population that you sampled from, so your external validity is compromised.
Attrition bias is a threat to internal validity. In experiments, differential rates of attrition between treatment and control groups can skew results.
This bias can affect the relationship between your independent and dependent variables. It can make variables appear to be correlated when they are not, or vice versa.
Some attrition is normal and to be expected in research. However, the type of attrition is important because systematic bias can distort your findings. Attrition bias can lead to inaccurate results because it affects internal and/or external validity.
Attrition bias is the selective dropout of some participants who systematically differ from those who remain in the study.
Some groups of participants may leave because of bad experiences, unwanted side effects, or inadequate incentives for participation, among other reasons. Attrition is also called subject mortality, but it doesn’t always refer to participants dying!
Avoid swearing in a college essay, since admissions officers’ opinions of profanity will vary. In some cases, it might be okay to use a vulgar word, such as in dialogue or quotes that make an important point in your essay. However, it’s safest to try to make the same point without swearing.
If you have bad grades on your transcript, you may want to use your college admissions essay to explain the challenging circumstances that led to them. Make sure to avoid dwelling on the negative aspects and highlight how you overcame the situation or learned an important lesson.
However, some college applications offer an additional information section where you can explain your bad grades, allowing you to choose another meaningful topic for your college essay.
Here’s a brief list of college essay topics that may be considered cliché:
It’s easier to write a standout essay with a unique topic. However, it’s possible to make a common topic compelling with interesting story arcs, uncommon connections, and an advanced writing style.
Yes. The college application essay is less formal than other academic writing—though of course it’s not mandatory to use contractions in your essay.
In a college essay, you can be creative with your language. When writing about the past, you can use the present tense to make the reader feel as if they were there in the moment with you. But make sure to maintain consistency and when in doubt, default to the correct verb tense according to the time you’re writing about.
The college admissions essay gives admissions officers a different perspective on you beyond your academic achievements, test scores, and extracurriculars. It’s your chance to stand out from other applicants with similar academic profiles by telling a unique, personal, and specific story.
Use a standard font such as Times New Roman or Arial to avoid distracting the reader from your college essay’s content.
A college application essay is less formal than most academic writing. Instead of citing sources formally with in-text citations and a reference list, you can cite them informally in your text.
For example, “In her research paper on genetics, Quinn Roberts explores …”
There is no set number of paragraphs in a college admissions essay. College admissions essays can diverge from the traditional five-paragraph essay structure that you learned in English class. Just make sure to stay under the specified word count.
Most topics are acceptable for college essays if you can use them to demonstrate personal growth or a lesson learned. However, there are a few difficult topics for college essays that should be avoided. Avoid topics that are:
To write an effective diversity essay, include vulnerable, authentic stories about your unique identity, background, or perspective. Provide insight into how your lived experience has influenced your outlook, activities, and goals. If relevant, you should also mention how your background has led you to apply for this university and why you’re a good fit.
Many universities believe a student body composed of different perspectives, beliefs, identities, and backgrounds will enhance the campus learning and community experience.
Admissions officers are interested in hearing about how your unique background, identity, beliefs, culture, or characteristics will enrich the campus community, which is why they assign a diversity essay.
In addition to your main college essay, some schools and scholarships may ask for a supplementary essay focused on an aspect of your identity or background. This is sometimes called a diversity essay.
You can use humor in a college essay, but carefully consider its purpose and use it wisely. An effective use of humor involves unexpected, keen observations of the everyday, or speaks to a deeper theme. Humor shouldn’t be the main focus of the essay, but rather a tool to improve your storytelling.
Get a second opinion from a teacher, counselor, or essay coach on whether your essay’s humor is appropriate.
Though admissions officers are interested in hearing your story, they’re also interested in how you tell it. An exceptionally written essay will differentiate you from other applicants, meaning that admissions officers will spend more time reading it.
You can use literary devices to catch your reader’s attention and enrich your storytelling; however, focus on using just a few devices well, rather than trying to use as many as possible.
To decide on a good college essay topic, spend time thoughtfully answering brainstorming questions. If you still have trouble identifying topics, try the following two strategies:
You can also ask family, friends, or mentors to help you brainstorm topics, give feedback on your potential essay topics, or recall key stories that showcase your qualities.
Yes—admissions officers don’t expect everyone to have a totally unique college essay topic. But you must differentiate your essay from others by having a surprising story arc, an interesting insight, and/or an advanced writing style.
There are no foolproof college essay topics—whatever your topic, the key is to write about it effectively. However, a good topic
You can control demand characteristics by taking a few precautions in your research design and materials.
Use these measures:
Demand characteristics are a type of extraneous variable that can affect the outcomes of the study. They can invalidate studies by providing an alternative explanation for the results.
These cues may nudge participants to consciously or unconsciously change their responses, and they pose a threat to both internal and external validity. You can’t be sure that your independent variable manipulation worked, or that your findings can be applied to other people or settings.
In research, demand characteristics are cues that might indicate the aim of a study to participants. These cues can lead to participants changing their behaviors or responses based on what they think the research is about.
Demand characteristics are common problems in psychology experiments and other social science studies because they can cause a bias in your research findings.
Unlike a five-paragraph essay, your admissions essay should not end by summarizing the points you’ve already made. It’s better to be creative and aim for a strong final impression.
You should also avoid stating the obvious (for example, saying that you hope to be accepted).
There are a few strategies you can use for a memorable ending to your college essay:
The best technique will depend on your topic choice, essay outline, and writing style. You can write several endings using different techniques to see which works best.
Research misconduct means making up or falsifying data, manipulating data analyses, or misrepresenting results in research reports. It’s a form of academic fraud.
These actions are committed intentionally and can have serious consequences; research misconduct is not a simple mistake or a point of disagreement but a serious ethical failure.
Anonymity means you don’t know who the participants are, while confidentiality means you know who they are but remove identifying information from your research report. Both are important ethical considerations.
You can only guarantee anonymity by not collecting any personally identifying information—for example, names, phone numbers, email addresses, IP addresses, physical characteristics, photos, or videos.
You can keep data confidential by using aggregate information in your research report, so that you only refer to groups of participants rather than individuals.
Research ethics matter for scientific integrity, human rights and dignity, and collaboration between science and society. These principles make sure that participation in studies is voluntary, informed, and safe.
Ethical considerations in research are a set of principles that guide your research designs and practices. These principles include voluntary participation, informed consent, anonymity, confidentiality, potential for harm, and results communication.
Scientists and researchers must always adhere to a certain code of conduct when collecting data from others.
These considerations protect the rights of research participants, enhance research validity, and maintain scientific integrity.
College deadlines vary depending on the schools you’re applying to and your application plan:
Depending on your prospective schools’ requirements, you may need to submit scores for the SAT or ACT as part of your college application.
Some schools now no longer require students to submit test scores; however, you should still take the SAT or ACT and aim to get a high score to strengthen your application package.
Aim to take the SAT or ACT in the spring of your junior year to give yourself enough time to retake it in the fall of your senior year if necessary.
Apply early for federal student aid and application fee waivers. You can also look for scholarships from schools, corporations, and charitable foundations.
To maximize your options, you should aim to apply to about eight schools:
The college admissions essay accounts for roughly 25% of the weight of your application.
At highly selective schools, there are four qualified candidates for every spot. While your academic achievements are important, your college admissions essay can help you stand out from other applicants with similar profiles.
In general, for your college application you will need to submit all of the following:
Different colleges may have specific requirements, so make sure you check exactly what’s expected in the application guidance.
You should start thinking about your college applications the summer before your junior year to give you sufficient time for college visits, taking standardized tests, applying for financial aid, writing essays, and collecting application material.
Yes, but make sure your essay directly addresses the prompt, respects the word count, and demonstrates the organization’s values.
If you plan ahead, you can save time by writing one scholarship essay for multiple prompts with similar questions. In a scholarship tracker spreadsheet, you can group or color-code overlapping essay prompts; then, write a single essay for multiple scholarships. Sometimes, you can even reuse or adapt your main college essay.
You can start applying for scholarships as early as your junior year. Continue applying throughout your senior year.
Invest time in applying for various scholarships, especially local ones with small dollar amounts, which are likely easier to win and more reflective of your background and interests. It will be easier for you to write an authentic and compelling essay if the scholarship topic is meaningful to you.
You can find scholarships through your school counselor, community network, or an internet search.
A scholarship essay requires you to demonstrate your values and qualities while answering the prompt’s specific question.
After researching the scholarship organization, identify a personal experience that embodies its values and exemplifies how you will be a successful student.
A standout college essay has several key ingredients:
While timelines will differ depending on the student, plan on spending at least 1–3 weeks brainstorming and writing the first draft of your college admissions essay, and at least 2–4 weeks revising across multiple drafts. Don’t forget to save enough time for breaks between each writing and editing stage.
You should already begin thinking about your essay the summer before your senior year so that you have plenty of time to try out different topics and get feedback on what works.
Your college essay accounts for about 25% of your application’s weight. It may be the deciding factor in whether you’re accepted, especially for competitive schools where most applicants have exceptional grades, test scores, and extracurricular track records.
In most cases, quoting other people isn’t a good way to start your college essay. Admissions officers want to hear your thoughts about yourself, and quotes often don’t achieve that. Unless a quote truly adds something important to your essay that it otherwise wouldn’t have, you probably shouldn’t include it.
Cliché openers in a college essay introduction are usually general and applicable to many students and situations. Most successful introductions are specific: they only work for the unique essay that follows.
The key to a strong college essay introduction is not to give too much away. Try to start with a surprising statement or image that raises questions and compels the reader to find out more.
The introduction of your college essay is the first thing admissions officers will read and therefore your most important opportunity to stand out. An excellent introduction will keep admissions officers reading, allowing you to tell them what you want them to know.
Yes, reusing your own work without acknowledgment is considered self-plagiarism. This can range from re-submitting an entire assignment to reusing passages or data from something you’ve turned in previously without citing them.
Self-plagiarism often has the same consequences as other types of plagiarism. If you want to reuse content you wrote in the past, make sure to check your university’s policy or consult your professor.
If you are reusing content or data you used in a previous assignment, make sure to cite yourself. You can cite yourself just as you would cite any other source: simply follow the directions for that source type in the citation style you are using.
Keep in mind that reusing your previous work can be considered self-plagiarism, so make sure you ask your professor or consult your university’s handbook before doing so.
If your college essay goes over the word count limit, cut any sentences with tangents or irrelevant details. Delete unnecessary words that clutter your essay.
You can speed up this process by shortening and smoothing your writing with a paraphrasing tool. After that, you can use the summarizer to shorten it even more.
If you’re struggling to reach the word count for your college essay, add vivid personal stories or share your feelings and insight to give your essay more depth and authenticity.
Most college application portals specify a word count range for your essay, and you should stay within 10% of the upper limit to write a developed and thoughtful essay.
You should aim to stay under the specified word count limit to show you can follow directions and write concisely. However, don’t write too little, as it may seem like you are unwilling or unable to write a detailed and insightful narrative about yourself.
If no word count is specified, we advise keeping your essay between 400 and 600 words.
In your application essay, admissions officers are looking for particular features: they want to see context on your background, positive traits that you could bring to campus, and examples of you demonstrating those qualities.
Colleges want to be able to differentiate students who seem similar on paper. In the college application essay, they’re looking for a way to understand each applicant’s unique personality and experiences.
You don’t need a title for your college admissions essay, but you can include one if you think it adds something important.
Your college essay’s format should be as simple as possible:
There are no set rules for how to structure a college application essay, but these are two common structures that work:
Avoid the five-paragraph essay structure that you learned in high school.
Campus visits are always helpful, but if you can’t make it in person, the college website will have plenty of information for you to explore. You should look through the course catalog and even reach out to current faculty with any questions about the school.
Colleges set a “Why this college?” essay because they want to see that you’ve done your research. You must prove that you know what makes the school unique and can connect that to your own personal goals and academic interests.
Depending on your writing, you may go through several rounds of revision. Make sure to put aside your essay for a little while after each editing stage to return with a fresh perspective.
Teachers and guidance counselors can help you check your language, tone, and content. Ask for their help at least one to two months before the submission deadline, as many other students will also want their help.
Friends and family are a good resource to check for authenticity. It’s best to seek help from family members with a strong writing or English educational background, or from older siblings and cousins who have been through the college admissions process.
If possible, get help from an essay coach or editor; they’ll have specialized knowledge of college admissions essays and be able to give objective expert feedback.
When revising your college essay, first check for big-picture issues regarding message, flow, tone, style, and clarity. Then, focus on eliminating grammar and punctuation errors.
Include specific, personal details and use your authentic voice to shed a new perspective on a common human experience.
Through specific stories, you can weave your achievements and qualities into your essay so that it doesn’t seem like you’re bragging from a resume.
When writing about yourself, including difficult experiences or failures can be a great way to show vulnerability and authenticity, but be careful not to overshare, and focus on showing how you matured from the experience.
First, spend time reflecting on your core values and character. You can start with these questions:
However, you should do a comprehensive brainstorming session to fully understand your values. Also consider how your values and goals match your prospective university’s program and culture. Then, brainstorm stories that illustrate the fit between the two.
In a college application essay, you can occasionally bend grammatical rules if doing so adds value to the storytelling process and the essay maintains clarity.
However, use standard language rules if your stylistic choices would otherwise distract the reader from your overall narrative or could be easily interpreted as unintentional errors.
Write concisely and use the active voice to maintain a quick pace throughout your essay and make sure it’s the right length. Avoid adding definitions unless they provide necessary explanation.
Use first-person “I” statements to speak from your perspective. Use appropriate word choices that show off your vocabulary but don’t sound like you used a thesaurus. Avoid using idioms or cliché expressions by rewriting them in a creative, original way.
If you’re an international student applying to a US college and you’re comfortable using American idioms or cultural references, you can. But instead of potentially using them incorrectly, don’t be afraid to write in detail about yourself within your own culture.
Provide context for any words, customs, or places that an American admissions officer might be unfamiliar with.
College application essays are less formal than other kinds of academic writing. Use a conversational yet respectful tone, as if speaking with a teacher or mentor. Be vulnerable about your feelings, thoughts, and experiences to connect with the reader.
Aim to write in your authentic voice, with a style that sounds natural and genuine. You can be creative with your word choice, but don’t use elaborate vocabulary to impress admissions officers.
Admissions officers use college admissions essays to evaluate your character, writing skills, and ability to self-reflect. The essay is your chance to show what you will add to the academic community.
The college essay may be the deciding factor in your application, especially for competitive schools where most applicants have exceptional grades, test scores, and extracurriculars.
Some colleges also require supplemental essays about specific topics, such as why you chose that specific college. Scholarship essays are often required to obtain financial aid.
Common knowledge does not need to be cited. However, you should be extra careful when deciding what counts as common knowledge.
Common knowledge encompasses information that the average educated reader would accept as true without needing the extra validation of a source or citation.
Common knowledge should be widely known, undisputed and easily verified. When in doubt, always cite your sources.
Plagiarism has serious consequences, and can indeed be illegal in certain scenarios.
While most of the time plagiarism in an undergraduate setting is not illegal, plagiarism or self-plagiarism in a professional academic setting can lead to legal action, including copyright infringement and fraud. Many scholarly journals do not allow you to submit the same work to more than one journal, and if you do not credit a co-author, you could be legally defrauding them.
Even if you aren’t breaking the law, plagiarism can seriously impact your academic career. While the exact consequences of plagiarism vary by institution and severity, common consequences include: a lower grade, automatically failing a course, academic suspension or probation, or even expulsion.
Accidental plagiarism is one of the most common examples of plagiarism. Perhaps you forgot to cite a source, or paraphrased something a bit too closely. Maybe you can’t remember where you got an idea from, and aren’t totally sure if it’s original or not.
These all count as plagiarism, even though you didn’t do it on purpose. When in doubt, make sure you’re citing your sources. Also consider running your work through a plagiarism checker tool prior to submission, which work by using advanced database software to scan for matches between your text and existing texts.
Scribbr’s Plagiarism Checker takes less than 10 minutes and can help you turn in your paper with confidence.
Self-plagiarism means recycling work that you’ve previously published or submitted as an assignment. It’s considered academic dishonesty to present something as brand new when you’ve already gotten credit and perhaps feedback for it in the past.
If you want to refer to ideas or data from previous work, be sure to cite yourself.
If you’re concerned that you may have self-plagiarized, Scribbr’s Self-Plagiarism Checker can help you turn in your paper with confidence. It compares your work to unpublished or private documents that you upload, so you can rest assured that you haven’t unintentionally plagiarized.
Incremental plagiarism means inserting quotes, passages, or excerpts from other works into your assignment without properly citing the original source.
Even if the vast majority of the text is yours, including any content that isn’t without citing it is plagiarism.
Consider using a plagiarism checker yourself before submitting your work. Plagiarism checkers work by scanning your document, comparing it to a database of webpages and publications, and highlighting passages that appear similar to other texts.
Scribbr’s Plagiarism Checker takes less than 10 minutes and can help you turn in your paper with confidence.
Patchwork plagiarism (aka mosaic plagiarism) means copying phrases, passages, or ideas from various existing sources and combining them to create a new text. While this type of plagiarism is more insidious than simply copy-pasting directly from a source, plagiarism checkers like Turnitin’s can still easily detect it.
To avoid plagiarism in any form, remember to cite your sources. Also consider running your work through a plagiarism checker tool prior to submission, which work by using advanced database software to scan for matches between your text and existing texts.
Scribbr’s Plagiarism Checker takes less than 10 minutes and can help you turn in your paper with confidence.
Verbatim plagiarism means copying text from a source and pasting it directly into your own document without giving proper credit.
Even if you delete a few words or replace them with synonyms, it still counts as verbatim plagiarism.
To use an author’s exact words, quote the original source by putting the copied text in quotation marks and including an in-text citation.
If you’re worried abotu plagiarism, consider running your work through a plagiarism checker tool prior to submission, which work by using advanced database software to scan for matches between your text and existing texts.
Scribbr’s Plagiarism Checker takes less than 10 minutes and can help you turn in your paper with confidence.
Global plagiarism means taking an entire work written by someone else and passing it off as your own. This can mean getting someone else to write an essay or assignment for you, or submitting a text you found online as your own work.
Global plagiarism is the most serious type of plagiarism because it involves deliberately and directly lying about the authorship of a work. It can have severe consequences.
To ensure you aren’t accidentally plagiarizing, consider running your work through plagiarism checker tool prior to submission. These tools work by using advanced database software to scan for matches between your text and existing texts.
Scribbr’s Plagiarism Checker takes less than 10 minutes and can help you turn in your paper with confidence.
Plagiarism can be detected by your professor or readers if the tone, formatting, or style of your text is different in different parts of your paper, or if they’re familiar with the plagiarized source.
Many universities also use plagiarism detection software like Turnitin’s, which compares your text to a large database of other sources, flagging any similarities that come up.
It can be easier than you think to commit plagiarism by accident. Consider using a plagiarism checker prior to submitting your paper to ensure you haven’t missed any citations.
Some examples of plagiarism include:
The most surefire way to avoid plagiarism is to always cite your sources. When in doubt, cite!
If you’re concerned about plagiarism, consider running your work through a plagiarism checker tool prior to submission. Scribbr’s Plagiarism Checker takes less than 10 minutes and can help you turn in your paper with confidence.
Plagiarism means presenting someone else’s work as your own without giving proper credit to the original author. In academic writing, plagiarism involves using words, ideas, or information from a source without including a citation.
Plagiarism can have serious consequences, even when it’s done accidentally. To avoid plagiarism, it’s important to keep track of your sources and cite them correctly.
A credible source should pass the CRAAP test and follow these guidelines:
The CRAAP test is an acronym to help you evaluate the credibility of a source you are considering using. It is an important component of information literacy.
The CRAAP test has five main components:
Peer review is a process of evaluating submissions to an academic journal. Utilizing rigorous criteria, a panel of reviewers in the same subject area decide whether to accept each submission for publication. For this reason, academic journals are often considered among the most credible sources you can use in a research project– provided that the journal itself is trustworthy and well-regarded.
Academic dishonesty can be intentional or unintentional, ranging from something as simple as claiming to have read something you didn’t to copying your neighbor’s answers on an exam.
You can commit academic dishonesty with the best of intentions, such as helping a friend cheat on a paper. Severe academic dishonesty can include buying a pre-written essay or the answers to a multiple-choice test, or falsifying a medical emergency to avoid taking a final exam.
Consequences of academic dishonesty depend on the severity of the offense and your institution’s policy. They can range from a warning for a first offense to a failing grade in a course to expulsion from your university.
For those in certain fields, such as nursing, engineering, or lab sciences, not learning fundamentals properly can directly impact the health and safety of others. For those working in academia or research, academic dishonesty impacts your professional reputation, leading others to doubt your future work.
Academic dishonesty refers to deceitful or misleading behavior in an academic setting. Academic dishonesty can occur intentionally or unintentionally, and varies in severity.
It can encompass paying for a pre-written essay, cheating on an exam, or committing plagiarism. It can also include helping others cheat, copying a friend’s homework answers, or even pretending to be sick to miss an exam.
Academic dishonesty doesn’t just occur in a classroom setting, but also in research and other academic-adjacent fields.
In multistage sampling, you can use probability or non-probability sampling methods.
For a probability sample, you have to conduct probability sampling at every stage.
You can mix it up by using simple random sampling, systematic sampling, or stratified sampling to select units at different stages, depending on what is applicable and relevant to your study.
Multistage sampling can simplify data collection when you have large, geographically spread samples, and you can obtain a probability sample without a complete sampling frame.
But multistage sampling may not lead to a representative sample, and larger samples are needed for multistage samples to achieve the statistical properties of simple random samples.
These are four of the most common mixed methods designs:
Triangulation in research means using multiple datasets, methods, theories and/or investigators to address a research question. It’s a research strategy that can help you enhance the validity and credibility of your findings.
Triangulation is mainly used in qualitative research, but it’s also commonly applied in quantitative research. Mixed methods research always uses triangulation.
In multistage sampling, or multistage cluster sampling, you draw a sample from a population using smaller and smaller groups at each stage.
This method is often used to collect data from a large, geographically spread group of people in national surveys, for example. You take advantage of hierarchical groupings (e.g., from state to city to neighborhood) to create a sample that’s less expensive and time-consuming to collect data from.
No, the steepness or slope of the line isn’t related to the correlation coefficient value. The correlation coefficient only tells you how closely your data fit on a line, so two datasets with the same correlation coefficient can have very different slopes.
To find the slope of the line, you’ll need to perform a regression analysis.
Correlation coefficients always range between -1 and 1.
The sign of the coefficient tells you the direction of the relationship: a positive value means the variables change together in the same direction, while a negative value means they change together in opposite directions.
The absolute value of a number is equal to the number without its sign. The absolute value of a correlation coefficient tells you the magnitude of the correlation: the greater the absolute value, the stronger the correlation.
These are the assumptions your data must meet if you want to use Pearson’s r:
In MLA style, footnotes or endnotes can be used to provide additional information that would interrupt the flow of your text.
This can be further examples or developments of ideas you only briefly discuss in the text. You can also use notes to provide additional sources or explain your citation practice.
You don’t have to use any notes at all; only use them to provide relevant information that complements your arguments or helps the reader to understand them.
No, you should use parenthetical MLA in-text citations to cite sources. Footnotes or endnotes can be used to add extra information that doesn’t fit into your main text, but they’re not needed for citations.
If you need to cite a lot of sources at the same point in the text, though, placing these citations in a note can be a good way to avoid cluttering your text.
Quantitative research designs can be divided into two main categories:
Qualitative research designs tend to be more flexible. Common types of qualitative design include case study, ethnography, and grounded theory designs.
A well-planned research design helps ensure that your methods match your research aims, that you collect high-quality data, and that you use the right kind of analysis to answer your questions, utilizing credible sources. This allows you to draw valid, trustworthy conclusions.
The priorities of a research design can vary depending on the field, but you usually have to specify:
A research design is a strategy for answering your research question. It defines your overall approach and determines how you will collect and analyze data.
To apply a hanging indent to your reference list or Works Cited list in Word or Google Docs, follow the steps below.
Microsoft Word:
Google Docs:
When the hanging indent is applied, for each reference, every line except the first is indented. This helps the reader see where one entry ends and the next begins.
According to MLA format guidelines, the Works Cited page(s) should look like this:
The MLA Works Cited lists every source that you cited in your paper. Each entry contains the author, title, and publication details of the source.
Questionnaires can be self-administered or researcher-administered.
Self-administered questionnaires can be delivered online or in paper-and-pen formats, in person or through mail. All questions are standardized so that all respondents receive the same questions with identical wording.
Researcher-administered questionnaires are interviews that take place by phone, in-person, or online between researchers and respondents. You can gain deeper insights by clarifying questions for respondents or asking follow-up questions.
You can organize the questions logically, with a clear progression from simple to complex, or randomly between respondents. A logical flow helps respondents process the questionnaire easier and quicker, but it may lead to bias. Randomization can minimize the bias from order effects.
Closed-ended, or restricted-choice, questions offer respondents a fixed set of choices to select from. These questions are easier to answer quickly.
Open-ended or long-form questions allow respondents to answer in their own words. Because there are no restrictions on their choices, respondents can answer in ways that researchers may not have otherwise considered.
A questionnaire is a data collection tool or instrument, while a survey is an overarching research method that involves collecting and analyzing data from people using questionnaires.
No, in an MLA annotated bibliography, you can write short phrases instead of full sentences to keep your annotations concise. You can still choose to use full sentences instead, though.
Use full sentences in your annotations if your instructor requires you to, and always use full sentences in the main text of your paper.
Usually, no title page is needed in an MLA paper. A header is generally included at the top of the first page instead. The exceptions are when:
In those cases, you should use a title page instead of a header, listing the same information but on a separate page.
The third variable and directionality problems are two main reasons why correlation isn’t causation.
The third variable problem means that a confounding variable affects both variables to make them seem causally related when they are not.
The directionality problem is when two variables correlate and might actually have a causal relationship, but it’s impossible to conclude which variable causes changes in the other.
Correlation describes an association between variables: when one variable changes, so does the other. A correlation is a statistical indicator of the relationship between variables.
Causation means that changes in one variable brings about changes in the other (i.e., there is a cause-and-effect relationship between variables). The two variables are correlated with each other, and there’s also a causal link between them.
While causation and correlation can exist simultaneously, correlation does not imply causation. In other words, correlation is simply a relationship where A relates to B—but A doesn’t necessarily cause B to happen (or vice versa). Mistaking correlation for causation is a common error and can lead to false cause fallacy.
Controlled experiments establish causality, whereas correlational studies only show associations between variables.
In general, correlational research is high in external validity while experimental research is high in internal validity.
A correlation is usually tested for two variables at a time, but you can test correlations between three or more variables.
A correlation coefficient is a single number that describes the strength and direction of the relationship between your variables.
Different types of correlation coefficients might be appropriate for your data based on their levels of measurement and distributions. The Pearson product-moment correlation coefficient (Pearson’s r) is commonly used to assess a linear relationship between two quantitative variables.
A correlational research design investigates relationships between two variables (or more) without the researcher controlling or manipulating any of them. It’s a non-experimental type of quantitative research.
A correlation reflects the strength and/or direction of the association between two or more variables.
When an online source (e.g. web page, blog post) doesn’t list a publication date, you should instead list an access date.
Unlike a publication date, this appears at the end of your MLA Works Cited entry, after the URL, e.g. “A Complete Guide to MLA Style.” Scribbr, www.scribbr.com/category/mla/. Accessed 28 Mar. 2021.
For offline sources with no publication date shown, don’t use an access date—just leave out the date.
The level of detail you provide in a publication date in your Works Cited list depends on the type of source and the information available. Generally, follow the lead of the source—if it gives the full date, give the full date; if it gives just the year, so should you.
Books usually list the year, whereas web pages tend to give a full date. For journal articles, give the year, month and year, or season and year, depending on what information is available. Check our citation examples if you’re unsure about a particular source type.
In an MLA Works Cited list, the names of months with five or more letters are abbreviated to the first three letters, followed by a period. For example, abbreviate Feb., Mar., Apr., but not June, July.
In the main text, month names should never be abbreviated.
In your MLA Works Cited list, dates are always written in day-month-year order, with the month abbreviated if it’s five or more letters long, e.g. 5 Mar. 2018.
In the main text, you’re free to use either day-month-year or month-day-year order, as long as you use one or the other consistently. Don’t abbreviate months in the main text, and use numerals for dates, e.g. 5 March 2018 or March 5, 2018.
In the US, most graduate school applications require you to include:
Some programs may ask you to write a personal statement in addition to, or instead of, a statement of purpose. You may also be asked to an interview.
Always carefully read the application instructions for the specific program you’re applying to.
Some source types, such as books and journal articles, may contain footnotes (or endnotes) with additional information. The following rules apply when citing information from a note in an MLA in-text citation:
The director should always be listed in the author position in a Chicago film citation, followed by the label “director.” Other contributors to the film (actors, cinematographers, writers, composers, producers, etc.) may be listed after the film title, e.g., “Featuring Willem Dafoe and Robert Pattinson. Cinematography by Jarin Blaschke.”
Only the contributors relevant to your discussion of the film should be added. You might mention actors whose performances are discussed in detail, or the composer if the use of music in the film is examined. It’s also fine to mention no contributors other than the director, if none are relevant to your discussion.
In Chicago style, when a source does not include page numbers but you still want to point the reader to a specific point within it, an alternative locator should be used in your Chicago footnote or Chicago in-text citation. With audiovisual sources (e.g., films, videos, podcasts, songs), this is a timestamp, e.g. 1:15:28.
Webpages are usually short enough that no specific locator is needed. However, for a particularly long web page, you can use a subheading from the page, in quotation marks, e.g., “Citing Sources with Notes.”
Note that page numbers should be left out of newspaper citations, even when they are available. This is because page numbers can vary between different editions of a newspaper.
To automatically generate accurate Chicago references, you can use Scribbr’s free Chicago reference generator.
The purpose of a lab report is to demonstrate your understanding of the scientific method with a hands-on lab experiment. Course instructors will often provide you with an experimental design and procedure. Your task is to write up how you actually performed the experiment and evaluate the outcome.
In contrast, a research paper requires you to independently develop an original argument. It involves more in-depth research and interpretation of sources and data.
A lab report is usually shorter than a research paper.
The sections of a lab report can vary between scientific fields and course requirements, but it usually contains the following:
A lab report conveys the aim, methods, results, and conclusions of a scientific experiment. Lab reports are commonly assigned in science, technology, engineering, and mathematics (STEM) fields.
Random error is almost always present in scientific studies, even in highly controlled settings. While you can’t eradicate it completely, you can reduce random error by taking repeated measurements, using a large sample, and controlling extraneous variables.
You can avoid systematic error through careful design of your sampling, data collection, and analysis procedures. For example, use triangulation to measure your variables using multiple methods; regularly calibrate instruments or procedures; use random sampling and random assignment; and apply masking (blinding) where possible.
Systematic error is generally a bigger problem in research.
With random error, multiple measurements will tend to cluster around the true value. When you’re collecting data from a large sample, the errors in different directions will cancel each other out.
Systematic errors are much more problematic because they can skew your data away from the true value. This can lead you to false conclusions (Type I and II errors) about the relationship between the variables you’re studying.
Random and systematic error are two types of measurement error.
Random error is a chance difference between the observed and true values of something (e.g., a researcher misreading a weighing scale records an incorrect measurement).
Systematic error is a consistent or proportional difference between the observed and true values of something (e.g., a miscalibrated scale consistently records weights as higher than they actually are).
On graphs, the explanatory variable is conventionally placed on the x-axis, while the response variable is placed on the y-axis.
The term “explanatory variable” is sometimes preferred over “independent variable” because, in real world contexts, independent variables are often influenced by other variables. This means they aren’t totally independent.
Multiple independent variables may also be correlated with each other, so “explanatory variables” is a more appropriate term.
The difference between explanatory and response variables is simple:
In a controlled experiment, all extraneous variables are held constant so that they can’t influence the results. Controlled experiments require:
Depending on your study topic, there are various other methods of controlling variables.
In Chicago style, when you don’t just refer to an image but actually include it in your (research) paper, the image should be formatted as a figure. Place the figure before or after the first paragraph where it is mentioned. Refer to figures by their numbers in the text (e.g., “see fig. 1”).
Below the figure, place a caption providing the figure number followed by a period (e.g., “Figure 1.”), a reference to the source (if you didn’t create the image yourself), and any relevant information to help the reader understand the image (if needed).
The caption is single-spaced and left-aligned, and followed by a blank line before the continuation of the main text.
To automatically generate accurate Chicago references, you can use Scribbr’s free Chicago reference generator.
There are 4 main types of extraneous variables:
An extraneous variable is any variable that you’re not investigating that can potentially affect the dependent variable of your research study.
A confounding variable is a type of extraneous variable that not only affects the dependent variable, but is also related to the independent variable.
According to the APA guidelines, you should report enough detail on inferential statistics so that your readers understand your analyses.
Report the following for each hypothesis test:
You should also present confidence intervals and estimates of effect sizes where relevant.
The number of decimal places to report depends on what you’re reporting. Generally, you should aim to round numbers while retaining precision. It’s best to present fewer decimal digits to aid easy understanding.
Use one decimal place for:
Use two decimal places for:
For a published interview (whether in video, audio, or print form), you should always include a citation, just as you would for any other source.
For an interview you conducted yourself, formally or informally, you often don’t need a citation and can just refer to it in the text or in a footnote, since the reader won’t be able to look them up anyway. MLA, however, still recommends including citations for your own interviews.
The main elements included in a newspaper interview citation across APA, MLA, and Chicago style are the names of the interviewer and interviewee, the interview title, the publication date, the name of the newspaper, and a URL (for online sources).
The information is presented differently in different citation styles. One key difference is that APA advises listing the interviewer in the author position, while MLA and Chicago advise listing the interviewee first.
In a factorial design, multiple independent variables are tested.
If you test two variables, each level of one independent variable is combined with each level of the other independent variable to create different conditions.
Within-subjects designs have many potential threats to internal validity, but they are also very statistically powerful.
Advantages:
Disadvantages:
Most medical school programs interview candidates, as do many (though not all) leading law and business schools.
In research programs, it depends—PhDs in business usually do, while those in economics normally do not, for example.
Some schools interview everyone, while others only interview their top candidates. Look at the websites of the schools you’re applying to for more information on whether they conduct interviews.
In addition to thinking about your answers for the most commonly asked grad school interview questions, you should reach out to former and current students to ask their advice on preparing and what sort of questions will be asked.
Look back through your resume and come up with anecdotes that you could use for common questions, particularly those that ask about obstacles that you overcame. If you’re applying for a research program, ensure that you can talk about the previous research experience you’ve had.
You should also read as much research in your field as possible. Research the faculty at the schools you’re applying to and read some of their papers. Come up with a few questions that you could ask them.
Graduate schools often ask questions about why you are interested in this particular program and what you will contribute.
Try to stay away from cliche answers like “this is a good program” or “I got good grades in undergrad” and focus instead on the unique strengths of the program or what you will bring to the table. Understand what the program is looking for and come up with anecdotes that demonstrate why you are a good fit for them.
Different types of programs may also focus on different questions:
The elements included in a newspaper article citation across APA, MLA, and Chicago style are the author name, the article title, the publication date, the newspaper name, and the URL if the article was accessed online.
In APA and MLA, the page numbers of the article appear in place of the URL if the article was accessed in print. No page numbers are used in Chicago newspaper citations.
Untitled sources (e.g. some images) are usually cited using a short descriptive text in place of the title. In APA Style, this description appears in brackets: [Chair of stained oak]. In MLA and Chicago styles, no brackets are used: Chair of stained oak.
For social media posts, which are usually untitled, quote the initial words of the post in place of the title: the first 160 characters in Chicago, or the first 20 words in APA. E.g. Biden, J. [@JoeBiden]. “The American Rescue Plan means a $7,000 check for a single mom of four. It means more support to safely.”
MLA recommends quoting the full post for something short like a tweet, and just describing the post if it’s longer.
The main elements included in image citations across APA, MLA, and Chicago style are the name of the image’s creator, the image title, the year (or more precise date) of publication, and details of the container in which the image was found (e.g. a museum, book, website).
In APA and Chicago style, it’s standard to also include a description of the image’s format (e.g. “Photograph” or “Oil on canvas”). This sort of information may be included in MLA too, but is not mandatory.
The main elements included in a lecture citation across APA, MLA, and Chicago style are the name of the speaker, the lecture title, the date it took place, the course or event it was part of, and the institution it took place at.
For transcripts or recordings of lectures/speeches, other details like the URL, the name of the book or website, and the length of the recording may be included instead of information about the event and institution.
The main elements included in a YouTube video citation across APA, MLA, and Chicago style are the name of the author/uploader, the title of the video, the publication date, and the URL.
The format in which this information appears is different for each style.
All styles also recommend using timestamps as a locator in the in-text citation or Chicago footnote.
While a between-subjects design has fewer threats to internal validity, it also requires more participants for high statistical power than a within-subjects design.
Advantages:
Disadvantages:
Yes. Between-subjects and within-subjects designs can be combined in a single study when you have two or more independent variables (a factorial design). In a mixed factorial design, one variable is altered between subjects and another is altered within subjects.
In a between-subjects design, every participant experiences only one condition, and researchers assess group differences between participants in various conditions.
In a within-subjects design, each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.
The word “between” means that you’re comparing different conditions between groups, while the word “within” means you’re comparing different conditions within the same group.
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Each annotation in an annotated bibliography is usually between 50 and 200 words long. Longer annotations may be divided into paragraphs.
The content of the annotation varies according to your assignment. An annotation can be descriptive, meaning it just describes the source objectively; evaluative, meaning it assesses its usefulness; or reflective, meaning it explains how the source will be used in your own research.
Any credible sources on your topic can be included in an annotated bibliography. The exact sources you cover will vary depending on the assignment, but you should usually focus on collecting journal articles and scholarly books. When in doubt, utilize the CRAAP test!
An annotated bibliography is an assignment where you collect sources on a specific topic and write an annotation for each source. An annotation is a short text that describes and sometimes evaluates the source.
The elements included in journal article citations across APA, MLA, and Chicago style are the name(s) of the author(s), the title of the article, the year of publication, the name of the journal, the volume and issue numbers, the page range of the article, and, when accessed online, the DOI or URL.
In MLA and Chicago style, you also include the specific month or season of publication alongside the year, when this information is available.
Random assignment is used in experiments with a between-groups or independent measures design. In this research design, there’s usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable.
In general, you should always use random assignment in this type of experimental design when it is ethically possible and makes sense for your study topic.
To implement random assignment, assign a unique number to every member of your study’s sample.
Then, you can use a random number generator or a lottery method to randomly assign each number to a control or experimental group. You can also do so manually, by flipping a coin or rolling a dice to randomly assign participants to groups.
Random selection, or random sampling, is a way of selecting members of a population for your study’s sample.
In contrast, random assignment is a way of sorting the sample into control and experimental groups.
Random sampling enhances the external validity or generalizability of your results, while random assignment improves the internal validity of your study.
In experimental research, random assignment is a way of placing participants from your sample into different groups using randomization. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group.
The main elements included in website citations across APA, MLA, and Chicago style are the author, the date of publication, the page title, the website name, and the URL. The information is presented differently in each style.
“Controlling for a variable” means measuring extraneous variables and accounting for them statistically to remove their effects on other variables.
Researchers often model control variable data along with independent and dependent variable data in regression analyses and ANCOVAs. That way, you can isolate the control variable’s effects from the relationship between the variables of interest.
Control variables help you establish a correlational or causal relationship between variables by enhancing internal validity.
If you don’t control relevant extraneous variables, they may influence the outcomes of your study, and you may not be able to demonstrate that your results are really an effect of your independent variable.
A control variable is any variable that’s held constant in a research study. It’s not a variable of interest in the study, but it’s controlled because it could influence the outcomes.
Including mediators and moderators in your research helps you go beyond studying a simple relationship between two variables for a fuller picture of the real world. They are important to consider when studying complex correlational or causal relationships.
Mediators are part of the causal pathway of an effect, and they tell you how or why an effect takes place. Moderators usually help you judge the external validity of your study by identifying the limitations of when the relationship between variables holds.
If something is a mediating variable:
A confounder is a third variable that affects variables of interest and makes them seem related when they are not. In contrast, a mediator is the mechanism of a relationship between two variables: it explains the process by which they are related.
A mediator variable explains the process through which two variables are related, while a moderator variable affects the strength and direction of that relationship.
When you want to cite a specific passage in a source without page numbers (e.g. an e-book or website), all the main citation styles recommend using an alternate locator in your in-text citation. You might use a heading or chapter number, e.g. (Smith, 2016, ch. 1)
In APA Style, you can count the paragraph numbers in a text to identify a location by paragraph number. MLA and Chicago recommend that you only use paragraph numbers if they’re explicitly marked in the text.
For audiovisual sources (e.g. videos), all styles recommend using a timestamp to show a specific point in the video when relevant.
The abbreviation “et al.” (Latin for “and others”) is used to shorten citations of sources with multiple authors.
“Et al.” is used in APA in-text citations of sources with 3+ authors, e.g. (Smith et al., 2019). It is not used in APA reference entries.
Use “et al.” for 3+ authors in MLA in-text citations and Works Cited entries.
Use “et al.” for 4+ authors in a Chicago in-text citation, and for 10+ authors in a Chicago bibliography entry.
Check if your university or course guidelines specify which citation style to use. If the choice is left up to you, consider which style is most commonly used in your field.
Other more specialized styles exist for certain fields, such as Bluebook and OSCOLA for law.
The most important thing is to choose one style and use it consistently throughout your text.
The main elements included in all book citations across APA, MLA, and Chicago style are the author, the title, the year of publication, and the name of the publisher. A page number is also included in in-text citations to highlight the specific passage cited.
In Chicago style and in the 6th edition of APA Style, the location of the publisher is also included, e.g. London: Penguin.
There are various ways to improve power:
A power analysis is a calculation that helps you determine a minimum sample size for your study. It’s made up of four main components. If you know or have estimates for any three of these, you can calculate the fourth component.
Some students apply to graduate school straight from undergrad, but it’s also common to go back to school later in life. The ideal time to do so depends on various financial, personal, and career considerations. Graduate school is a big commitment, so you should apply at a time when you can devote your full attention to it.
Your career path may also determine when you should apply. In some career fields, you can easily progress without a graduate degree, while in others—such as medicine, business, and law—it’s virtually impossible to move up the career ladder without a specific graduate degree.
Most graduate school applications for American graduate programs are due in December or January for a September start.
Some types of programs, especially law school, are rolling applications, meaning that the earlier you apply, the earlier you’ll hear back. In this case, you should aim to apply as early as possible to maximize your chances.
Medical school follows a completely separate timeline with much earlier deadlines. If you’re applying for medical school, you should speak to advisors at your university for more information.
A good starting point to aim for is about 18 months before you would start the program, or 6–9 months before the applications are due.
In the first few months of the process, research programs and study for any standardized exams you might need.
You can then begin writing your personal statements and statements of purpose, as well as contacting people to write your letters of recommendation. Ensure that you give recommenders plenty of time to complete their letters (ideally around 2–4 months).
Null and alternative hypotheses are used in statistical hypothesis testing. The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
Statistical analysis is the main method for analyzing quantitative research data. It uses probabilities and models to test predictions about a population from sample data.
No, including a URL is optional in APA Style reference entries for legal sources (e.g. court cases, laws). It can be useful to do so to aid the reader in retrieving the source, but it’s not required, since the other information included should be enough to locate it.
Generally, you should identify a law in an APA reference entry by its location in the United States Code (U.S.C.).
But if the law is either spread across various sections of the code or not featured in the code at all, include the public law number in addition to information on the source you accessed the law in, e.g.:
You should report methods using the past tense, even if you haven’t completed your study at the time of writing. That’s because the methods section is intended to describe completed actions or research.
In your APA methods section, you should report detailed information on the participants, materials, and procedures used.
For a stronger conclusion paragraph, avoid including:
Your conclusion should leave the reader with a strong, decisive impression of your work.
Your essay’s conclusion should contain:
The conclusion may also reflect on the broader implications of your argument, showing how your ideas could applied to other contexts or debates.
The conclusion paragraph of an essay is usually shorter than the introduction. As a rule, it shouldn’t take up more than 10–15% of the text.
With APA legal citations, it’s recommended to cite all the reporters (publications reporting cases) in which a court case appears. To cite multiple reporters, just separate them with commas in your reference entry. This is called parallel citation.
Don’t repeat the name of the case, court, or year; just list the volume, reporter, and page number for each citation. For example:
In APA Style, when you’re citing a recent court case that has not yet been reported in print and thus doesn’t have a specific page number, include a series of three underscores (___) where the page number would usually appear:
If you cite multiple Shakespeare plays throughout your paper, the MLA in-text citation begins with an abbreviated version of the title (as shown here), e.g. (Oth. 1.2.4). Each play should have its own Works Cited entry (even if they all come from the same collection).
If you cite only one Shakespeare play in your paper, you should include a Works Cited entry for that play, and your in-text citations should start with the author’s name, e.g. (Shakespeare 1.1.4).
No, do not use page numbers in your MLA in-text citations of Shakespeare plays. Instead, specify the act, scene, and line numbers of the quoted material, separated by periods, e.g. (Shakespeare 3.2.20–25).
This makes it easier for the reader to find the relevant passage in any edition of the text.
The risk of making a Type II error is inversely related to the statistical power of a test. Power is the extent to which a test can correctly detect a real effect when there is one.
To (indirectly) reduce the risk of a Type II error, you can increase the sample size or the significance level to increase statistical power.
The risk of making a Type I error is the significance level (or alpha) that you choose. That’s a value that you set at the beginning of your study to assess the statistical probability of obtaining your results (p value).
The significance level is usually set at 0.05 or 5%. This means that your results only have a 5% chance of occurring, or less, if the null hypothesis is actually true.
To reduce the Type I error probability, you can set a lower significance level.
In statistics, a Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s actually false.
When an article (e.g. in a newspaper) appears on non-consecutive pages (e.g. starting on page 1 and continuing on page 6), you should use “pp.” in your Works Cited entry, since it’s on multiple pages, but MLA recommends just listing the first page followed by a plus sign, e.g. pp. 1+.
In an MLA style Works Cited entry for a newspaper, you can cite a local newspaper in the same way as you would a national one, except that you may have to add the name of the city in square brackets to clarify what newspaper you mean, e.g. The Gazette [Montreal].
Do not add the city name in brackets if it’s already part of the newspaper’s name, e.g. Dallas Observer.
In statistics, power refers to the likelihood of a hypothesis test detecting a true effect if there is one. A statistically powerful test is more likely to reject a false negative (a Type II error).
If you don’t ensure enough power in your study, you may not be able to detect a statistically significant result even when it has practical significance. Your study might not have the ability to answer your research question.
While statistical significance shows that an effect exists in a study, practical significance shows that the effect is large enough to be meaningful in the real world.
Statistical significance is denoted by p-values whereas practical significance is represented by effect sizes.
There are dozens of measures of effect sizes. The most common effect sizes are Cohen’s d and Pearson’s r. Cohen’s d measures the size of the difference between two groups while Pearson’s r measures the strength of the relationship between two variables.
Effect size tells you how meaningful the relationship between variables or the difference between groups is.
A large effect size means that a research finding has practical significance, while a small effect size indicates limited practical applications.
In APA style, statistics can be presented in the main text or as tables or figures. To decide how to present numbers, you can follow APA guidelines:
Since these are general guidelines, use your own judgment and feedback from others for effective presentation of numbers.
In an APA results section, you should generally report the following:
Using descriptive and inferential statistics, you can make two types of estimates about the population: point estimates and interval estimates.
Both types of estimates are important for gathering a clear idea of where a parameter is likely to lie.
Standard error and standard deviation are both measures of variability. The standard deviation reflects variability within a sample, while the standard error estimates the variability across samples of a population.
The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean. It tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population.
Like most style guides, APA recommends listing the book of the Bible you’re citing in your APA in-text citation, in combination with chapter and verse numbers. For example:
Books of the Bible may be abbreviated to save space; a list of standard abbreviations can be found here. Page numbers are not used in Bible citations.
Yes, in the 7th edition of APA Style, versions of the Bible are treated much like other books; you should include the edition you used in your reference list.
Previously, in the 6th edition of the APA manual, it was recommended to just use APA 6 in-text citations to refer to the Bible, and omit it from the reference list.
MLA recommends citing the original source wherever possible, rather than the source in which it is quoted or reproduced.
If this isn’t possible, cite the secondary source and use “qtd. in” (quoted in) in your MLA in-text citation. For example: (qtd. in Smith 233)
If a source is reproduced in full within another source (e.g. an image within a PowerPoint or a poem in an article), give details of the original source first, then include details of the secondary source as a container. For example:
When you want to cite a PowerPoint or lecture notes from a lecture you viewed in person in MLA, check whether they can also be accessed online; if so, this is the best version to cite, as it allows the reader to access the source.
If the material is not available online, use the details of where and when the presentation took place.
When you need to highlight a specific moment in a video or audio source, use a timestamp in your APA in-text citation. Just include the timestamp from the start of the part you’re citing. For example:
In an MLA song citation, you need to give some sort of container to indicate how you accessed the song. If this is a physical or downloaded album, the Works Cited entry should list the album name, distributor, year, and format.
However, if you listened to the song on a streaming service, you can just list the site as a container, including a URL. In this case, including the album details is optional; you may add this information if it is relevant to your discussion or if it will help the reader access the song.
To figure out whether a given number is a parameter or a statistic, ask yourself the following:
If the answer is yes to both questions, the number is likely to be a parameter. For small populations, data can be collected from the whole population and summarized in parameters.
If the answer is no to either of the questions, then the number is more likely to be a statistic.
In the US, the graduate school application process is similar whether you’re applying for a master’s or a PhD. Both require letters of recommendation, a statement of purpose or personal statement, a resume or CV, and transcripts. Programs in the US and Canada usually also require a certain type of standardized test—often the GRE.
Outside the US, PhD programs usually also require applicants to write a research proposal, because students are expected to begin dissertation research in the first year of their PhD.
A master’s degree usually has a higher upfront cost, but it also allows you to start earning a higher salary more quickly. The exact cost depends on the country and the school: private universities usually cost more than public ones, and European degrees usually cost less than North American ones. There are limited possibilities for financial aid.
PhDs often waive tuition fees and offer a living stipend in exchange for a teaching or research assistantship. However, they take many years to complete, during which time you earn very little.
This depends on the country. In the United States, you can generally go directly to a PhD with only a bachelor’s degree, as a master’s program is included as part of the doctoral program.
Elsewhere, you generally need to graduate from a research-intensive master’s degree before continuing to the PhD.
This varies by country. In the United States, PhDs usually take between 5–7 years: 2 years of coursework followed by 3–5 years of independent research work to produce a dissertation.
In the rest of the world, students normally have a master’s degree before beginning the PhD, so they proceed directly to the research stage and complete a PhD in 3–5 years.
A PhD, which is short for philosophiae doctor (doctor of philosophy in Latin), is the highest university degree that can be obtained. In a PhD, students spend 3–5 years writing a dissertation, which aims to make a significant, original contribution to current knowledge.
A PhD is intended to prepare students for a career as a researcher, whether that be in academia, the public sector, or the private sector.
A master’s is a 1- or 2-year graduate degree that can prepare you for a variety of careers.
All master’s involve graduate-level coursework. Some are research-intensive and intend to prepare students for further study in a PhD; these usually require their students to write a master’s thesis. Others focus on professional training for a specific career.
To avoid plagiarism when summarizing an article or other source, follow these two rules:
A summary is always much shorter than the original text. The length of a summary can range from just a few sentences to several paragraphs; it depends on the length of the article you’re summarizing, and on the purpose of the summary.
A summary is a short overview of the main points of an article or other source, written entirely in your own words. Want to make your life super easy? Try our free text summarizer today!
Whenever you refer to an image created by someone else in your text, you should include a citation leading the reader to the image you’re discussing.
If you include the image directly in your text as a figure, the details of the source appear in the figure’s caption. If you don’t, just include an MLA in-text citation wherever you mention the image, and an entry in the Works Cited list giving full details.
The main guidelines for formatting a paper in Chicago style are to:
To automatically generate accurate Chicago references, you can use Scribbr’s free Chicago reference generator.
The main guidelines for formatting a paper in MLA style are as follows:
To format a paper in APA Style, follow these guidelines:
To include a direct quote in APA, follow these rules:
A block quote is a long quote formatted as a separate “block” of text. Instead of using quotation marks, you place the quote on a new line, and indent the entire quote to mark it apart from your own words.
The rules for when to apply block quote formatting depend on the citation style:
In academic writing, there are three main situations where quoting is the best choice:
Don’t overuse quotes; your own voice should be dominant. If you just want to provide information from a source, it’s usually better to paraphrase or summarize.
Every time you quote a source, you must include a correctly formatted in-text citation. This looks slightly different depending on the citation style.
For example, a direct quote in APA is cited like this: “This is a quote” (Streefkerk, 2020, p. 5).
Every in-text citation should also correspond to a full reference at the end of your paper.
A quote is an exact copy of someone else’s words, usually enclosed in quotation marks and credited to the original author or speaker.
APA doesn’t require you to include a list of tables or a list of figures. However, it is advisable to do so if your text is long enough to feature a table of contents and it includes a lot of tables and/or figures.
A list of tables and list of figures appear (in that order) after your table of contents, and are presented in a similar way.
Copyright information can usually be found wherever the table or figure was published. For example, for a diagram in a journal article, look on the journal’s website or the database where you found the article. Images found on sites like Flickr are listed with clear copyright information.
If you find that permission is required to reproduce the material, be sure to contact the author or publisher and ask for it.
If you adapt or reproduce a table or figure from another source, you should include that source in your APA reference list. You should also include copyright information in the note for the table or figure, and include an APA in-text citation when you refer to it.
Tables and figures you created yourself, based on your own data, are not included in the reference list.
An APA in-text citation is placed before the final punctuation mark in a sentence.
In an APA in-text citation, you use the phrase “as cited in” if you want to cite a source indirectly (i.e., if you cannot find the original source).
Parenthetical citation: (Brown, 1829, as cited in Mahone, 2018)
Narrative citation: Brown (1829, as cited in Mahone, 2018) states that…
On the reference page, you only include the secondary source (Mahone, 2018).
Popular word processors like Microsoft Word and Google Docs can order lists in alphabetical order, but they don’t follow the APA Style alphabetization guidelines.
If you use Scribbr’s APA Citation Generator to create citations, references are ordered automatically based on the APA guidelines, taking into account all the exceptions.
Order numerals as though they were spelled out:
Read more about alphabetizing the APA reference page.
It’s best to ask in person if possible, so first reach out and request a meeting to discuss your graduate school plans.
Let the potential recommender know which programs you’re applying to, and ask if they feel they can provide a strong letter of recommendation. A lukewarm recommendation can be the kiss of death for an application, so make sure your letter writers are enthusiastic about recommending you and your work!
Always remember to remain polite. Your recommenders are doing you a favor by taking the time to write a letter in support of your graduate school goals.
This depends on the program that you are applying for. Generally, for professional programs like business and policy school, you should ask managers who can speak to your future leadership potential and ability to succeed in your chosen career path.
However, in other graduate programs, you should mostly ask your former professors or research supervisors to write your recommendation letters, unless you have worked in a job that corresponds closely with your chosen field (e.g., as a full-time research assistant).
Choose people who know your work well and can speak to your ability to succeed in the program that you are applying to.
Remember, it is far more important to choose someone who knows you well than someone well-known. You may have taken classes with more prominent professors, but if they haven’t worked closely with you, they probably can’t write you a strong letter.
No, it’s not appropriate to present new arguments or evidence in the conclusion. While you might be tempted to save a striking argument for last, research papers follow a more formal structure than this.
All your findings and arguments should be presented in the body of the text (more specifically in the results and discussion sections if you are following a scientific structure). The conclusion is meant to summarize and reflect on the evidence and arguments you have already presented, not introduce new ones.
The conclusion of a research paper has several key elements you should make sure to include:
In MLA Style, you should cite a specific chapter or work within a book in two situations:
If you cite multiple chapters or works from the same book, include a separate Works Cited entry for each chapter.
Yes, if relevant you can and should include APA in-text citations in your appendices. Use author-date citations as you do in the main text.
Any sources cited in your appendices should appear in your reference list. Do not create a separate reference list for your appendices.
Appendices in an APA Style paper appear right at the end, after the reference list and after your tables and figures if you’ve also included these at the end.
An appendix contains information that supplements the reader’s understanding of your research but is not essential to it. For example:
Something is only worth including as an appendix if you refer to information from it at some point in the text (e.g. quoting from an interview transcript). If you don’t, it should probably be removed.
The arithmetic mean is the most commonly used mean. It’s often simply called the mean or the average. But there are some other types of means you can calculate depending on your research purposes:
You can find the mean, or average, of a data set in two simple steps:
This method is the same whether you are dealing with sample or population data or positive or negative numbers.
An essay is a focused piece of writing that explains, argues, describes, or narrates.
In high school, you may have to write many different types of essays to develop your writing skills.
Academic essays at college level are usually argumentative: you develop a clear thesis about your topic and make a case for your position using evidence, analysis and interpretation.
The “hook” is the first sentence of your essay introduction. It should lead the reader into your essay, giving a sense of why it’s interesting.
To write a good hook, avoid overly broad statements or long, dense sentences. Try to start with something clear, concise and catchy that will spark your reader’s curiosity.
Your essay introduction should include three main things, in this order:
The length of each part depends on the length and complexity of your essay.
The median is the most informative measure of central tendency for skewed distributions or distributions with outliers. For example, the median is often used as a measure of central tendency for income distributions, which are generally highly skewed.
Because the median only uses one or two values, it’s unaffected by extreme outliers or non-symmetric distributions of scores. In contrast, the mean and mode can vary in skewed distributions.
To find the median, first order your data. Then calculate the middle position based on n, the number of values in your data set.
.
and 
.A data set can often have no mode, one mode or more than one mode – it all depends on how many different values repeat most frequently.
Your data can be:
To find the mode:
Then you simply need to identify the most frequently occurring value.
There are three key steps in systematic sampling:
Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval – for example, by selecting every 15th person on a list of the population. If the population is in a random order, this can imitate the benefits of simple random sampling.
Let’s say you’re writing a five-paragraph essay about the environmental impacts of dietary choices. Here are three examples of topic sentences you could use for each of the three body paragraphs:
Each of these sentences expresses one main idea – by listing them in order, we can see the overall structure of the essay at a glance. Each paragraph will expand on the topic sentence with relevant detail, evidence, and arguments.
The topic sentence usually comes at the very start of the paragraph.
However, sometimes you might start with a transition sentence to summarize what was discussed in previous paragraphs, followed by the topic sentence that expresses the focus of the current paragraph.
Topic sentences help keep your writing focused and guide the reader through your argument.
In an essay or paper, each paragraph should focus on a single idea. By stating the main idea in the topic sentence, you clarify what the paragraph is about for both yourself and your reader.
A topic sentence is a sentence that expresses the main point of a paragraph. Everything else in the paragraph should relate to the topic sentence.
The interquartile range is the best measure of variability for skewed distributions or data sets with outliers. Because it’s based on values that come from the middle half of the distribution, it’s unlikely to be influenced by outliers.
The two most common methods for calculating interquartile range are the exclusive and inclusive methods.
The exclusive method excludes the median when identifying Q1 and Q3, while the inclusive method includes the median as a value in the data set in identifying the quartiles.
For each of these methods, you’ll need different procedures for finding the median, Q1 and Q3 depending on whether your sample size is even- or odd-numbered. The exclusive method works best for even-numbered sample sizes, while the inclusive method is often used with odd-numbered sample sizes.
While the range gives you the spread of the whole data set, the interquartile range gives you the spread of the middle half of a data set.
Don’t feel that you have to write the introduction first. The introduction is often one of the last parts of the research paper you’ll write, along with the conclusion.
This is because it can be easier to introduce your paper once you’ve already written the body; you may not have the clearest idea of your arguments until you’ve written them, and things can change during the writing process.
The way you present your research problem in your introduction varies depending on the nature of your research paper. A research paper that presents a sustained argument will usually encapsulate this argument in a thesis statement.
A research paper designed to present the results of empirical research tends to present a research question that it seeks to answer. It may also include a hypothesis—a prediction that will be confirmed or disproved by your research.
The introduction of a research paper includes several key elements:
and your problem statement
Homoscedasticity, or homogeneity of variances, is an assumption of equal or similar variances in different groups being compared.
This is an important assumption of parametric statistical tests because they are sensitive to any dissimilarities. Uneven variances in samples result in biased and skewed test results.
Statistical tests such as variance tests or the analysis of variance (ANOVA) use sample variance to assess group differences of populations. They use the variances of the samples to assess whether the populations they come from significantly differ from each other.
Yes, you can create a stratified sample using multiple characteristics, but you must ensure that every participant in your study belongs to one and only one subgroup. In this case, you multiply the numbers of subgroups for each characteristic to get the total number of groups.
For example, if you were stratifying by location with three subgroups (urban, rural, or suburban) and marital status with five subgroups (single, divorced, widowed, married, or partnered), you would have 3 x 5 = 15 subgroups.
You should use stratified sampling when your sample can be divided into mutually exclusive and exhaustive subgroups that you believe will take on different mean values for the variable that you’re studying.
Using stratified sampling will allow you to obtain more precise (with lower variance) statistical estimates of whatever you are trying to measure.
For example, say you want to investigate how income differs based on educational attainment, but you know that this relationship can vary based on race. Using stratified sampling, you can ensure you obtain a large enough sample from each racial group, allowing you to draw more precise conclusions.
In stratified sampling, researchers divide subjects into subgroups called strata based on characteristics that they share (e.g., race, gender, educational attainment).
Once divided, each subgroup is randomly sampled using another probability sampling method.
The thesis statement is essential in any academic essay or research paper for two main reasons:
Without a clear thesis statement, an essay can end up rambling and unfocused, leaving your reader unsure of exactly what you want to say.
The thesis statement should be placed at the end of your essay introduction.
Follow these four steps to come up with a thesis statement:
A thesis statement is a sentence that sums up the central point of your paper or essay. Everything else you write should relate to this key idea.
An essay isn’t just a loose collection of facts and ideas. Instead, it should be centered on an overarching argument (summarized in your thesis statement) that every part of the essay relates to.
The way you structure your essay is crucial to presenting your argument coherently. A well-structured essay helps your reader follow the logic of your ideas and understand your overall point.
The structure of an essay is divided into an introduction that presents your topic and thesis statement, a body containing your in-depth analysis and arguments, and a conclusion wrapping up your ideas.
The structure of the body is flexible, but you should always spend some time thinking about how you can organize your essay to best serve your ideas.
Variance is the average squared deviations from the mean, while standard deviation is the square root of this number. Both measures reflect variability in a distribution, but their units differ:
Although the units of variance are harder to intuitively understand, variance is important in statistical tests.
The empirical rule, or the 68-95-99.7 rule, tells you where most of the values lie in a normal distribution:
The empirical rule is a quick way to get an overview of your data and check for any outliers or extreme values that don’t follow this pattern.
In a normal distribution, data are symmetrically distributed with no skew. Most values cluster around a central region, with values tapering off as they go further away from the center.
The measures of central tendency (mean, mode, and median) are exactly the same in a normal distribution.
The standard deviation is the average amount of variability in your data set. It tells you, on average, how far each score lies from the mean.
In normal distributions, a high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean.
In a thesis or dissertation, the discussion is an in-depth exploration of the results, going into detail about the meaning of your findings and citing relevant sources to put them in context.
The conclusion is more shorter and more general: it concisely answers your main research question and makes recommendations based on your overall findings.
In the discussion, you explore the meaning and relevance of your research results, explaining how they fit with existing research and theory. Discuss:
The results chapter or section simply and objectively reports what you found, without speculating on why you found these results. The discussion interprets the meaning of the results, puts them in context, and explains why they matter.
In qualitative research, results and discussion are sometimes combined. But in quantitative research, it’s considered important to separate the objective results from your interpretation of them.
Results are usually written in the past tense, because they are describing the outcome of completed actions.
The results chapter of a thesis or dissertation presents your research results concisely and objectively.
In quantitative research, for each question or hypothesis, state:
In qualitative research, for each question or theme, describe:
Don’t interpret or speculate in the results chapter.
No. Because the range formula subtracts the lowest number from the highest number, the range is always zero or a positive number.
In statistics, the range is the spread of your data from the lowest to the highest value in the distribution. It is the simplest measure of variability.
Cluster sampling is more time- and cost-efficient than other probability sampling methods, particularly when it comes to large samples spread across a wide geographical area.
However, it provides less statistical certainty than other methods, such as simple random sampling, because it is difficult to ensure that your clusters properly represent the population as a whole.
There are three types of cluster sampling: single-stage, double-stage and multi-stage clustering. In all three types, you first divide the population into clusters, then randomly select clusters for use in your sample.
Cluster sampling is a probability sampling method in which you divide a population into clusters, such as districts or schools, and then randomly select some of these clusters as your sample.
The clusters should ideally each be mini-representations of the population as a whole.
While central tendency tells you where most of your data points lie, variability summarizes how far apart your points from each other.
Data sets can have the same central tendency but different levels of variability or vice versa. Together, they give you a complete picture of your data.
Variability is most commonly measured with the following descriptive statistics:
Variability tells you how far apart points lie from each other and from the center of a distribution or a data set.
Variability is also referred to as spread, scatter or dispersion.
The vast majority of essays written at university are some sort of argumentative essay. Almost all academic writing involves building up an argument, though other types of essay might be assigned in composition classes.
Essays can present arguments about all kinds of different topics. For example:
At high school and in composition classes at university, you’ll often be told to write a specific type of essay, but you might also just be given prompts.
Look for keywords in these prompts that suggest a certain approach: The word “explain” suggests you should write an expository essay, while the word “describe” implies a descriptive essay. An argumentative essay might be prompted with the word “assess” or “argue.”
While interval and ratio data can both be categorized, ranked, and have equal spacing between adjacent values, only ratio scales have a true zero.
For example, temperature in Celsius or Fahrenheit is at an interval scale because zero is not the lowest possible temperature. In the Kelvin scale, a ratio scale, zero represents a total lack of thermal energy.
In rhetorical analysis, a claim is something the author wants the audience to believe. A support is the evidence or appeal they use to convince the reader to believe the claim. A warrant is the (often implicit) assumption that links the support with the claim.
Logos appeals to the audience’s reason, building up logical arguments. Ethos appeals to the speaker’s status or authority, making the audience more likely to trust them. Pathos appeals to the emotions, trying to make the audience feel angry or sympathetic, for example.
Collectively, these three appeals are sometimes called the rhetorical triangle. They are central to rhetorical analysis, though a piece of rhetoric might not necessarily use all of them.
The term “text” in a rhetorical analysis essay refers to whatever object you’re analyzing. It’s frequently a piece of writing or a speech, but it doesn’t have to be. For example, you could also treat an advertisement or political cartoon as a text.
The goal of a rhetorical analysis is to explain the effect a piece of writing or oratory has on its audience, how successful it is, and the devices and appeals it uses to achieve its goals.
Unlike a standard argumentative essay, it’s less about taking a position on the arguments presented, and more about exploring how they are constructed.
A critical value is the value of the test statistic which defines the upper and lower bounds of a confidence interval, or which defines the threshold of statistical significance in a statistical test. It describes how far from the mean of the distribution you have to go to cover a certain amount of the total variation in the data (i.e. 90%, 95%, 99%).
If you are constructing a 95% confidence interval and are using a threshold of statistical significance of p = 0.05, then your critical value will be identical in both cases.
The t-distribution gives more probability to observations in the tails of the distribution than the standard normal distribution (a.k.a. the z-distribution).
In this way, the t-distribution is more conservative than the standard normal distribution: to reach the same level of confidence or statistical significance, you will need to include a wider range of the data.
A t-score (a.k.a. a t-value) is equivalent to the number of standard deviations away from the mean of the t-distribution.
The t-score is the test statistic used in t-tests and regression tests. It can also be used to describe how far from the mean an observation is when the data follow a t-distribution.
The t-distribution is a way of describing a set of observations where most observations fall close to the mean, and the rest of the observations make up the tails on either side. It is a type of normal distribution used for smaller sample sizes, where the variance in the data is unknown.
The t-distribution forms a bell curve when plotted on a graph. It can be described mathematically using the mean and the standard deviation.
If properly implemented, simple random sampling is usually the best sampling method for ensuring both internal and external validity. However, it can sometimes be impractical and expensive to implement, depending on the size of the population to be studied,
If you have a list of every member of the population and the ability to reach whichever members are selected, you can use simple random sampling.
The American Community Survey is an example of simple random sampling. In order to collect detailed data on the population of the US, the Census Bureau officials randomly select 3.5 million households per year and use a variety of methods to convince them to fill out the survey.
Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population. Each member of the population has an equal chance of being selected. Data is then collected from as large a percentage as possible of this random subset.
You should try to follow your outline as you write your essay. However, if your ideas change or it becomes clear that your structure could be better, it’s okay to depart from your essay outline. Just make sure you know why you’re doing so.
If you have to hand in your essay outline, you may be given specific guidelines stating whether you have to use full sentences. If you’re not sure, ask your supervisor.
When writing an essay outline for yourself, the choice is yours. Some students find it helpful to write out their ideas in full sentences, while others prefer to summarize them in short phrases.
You will sometimes be asked to hand in an essay outline before you start writing your essay. Your supervisor wants to see that you have a clear idea of your structure so that writing will go smoothly.
Even when you do not have to hand it in, writing an essay outline is an important part of the writing process. It’s a good idea to write one (as informally as you like) to clarify your structure for yourself whenever you are working on an essay.
In statistics, ordinal and nominal variables are both considered categorical variables.
Even though ordinal data can sometimes be numerical, not all mathematical operations can be performed on them.
Ordinal data has two characteristics:
However, unlike with interval data, the distances between the categories are uneven or unknown.
To automatically insert a table of contents in Microsoft Word, follow these steps:
Make sure to update your table of contents if you move text or change headings. To update, simply right click and select Update Field.
All level 1 and 2 headings should be included in your table of contents. That means the titles of your chapters and the main sections within them.
The contents should also include all appendices and the lists of tables and figures, if applicable, as well as your reference list.
Do not include the acknowledgements or abstract in the table of contents.
Nominal and ordinal are two of the four levels of measurement. Nominal level data can only be classified, while ordinal level data can be classified and ordered.
Nominal data is data that can be labelled or classified into mutually exclusive categories within a variable. These categories cannot be ordered in a meaningful way.
For example, for the nominal variable of preferred mode of transportation, you may have the categories of car, bus, train, tram or bicycle.
If your confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.
If your confidence interval for a correlation or regression includes zero, that means that if you run your experiment again there is a good chance of finding no correlation in your data.
In both of these cases, you will also find a high p-value when you run your statistical test, meaning that your results could have occurred under the null hypothesis of no relationship between variables or no difference between groups.
If you want to calculate a confidence interval around the mean of data that is not normally distributed, you have two choices:
The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.
Any normal distribution can be converted into the standard normal distribution by turning the individual values into z-scores. In a z-distribution, z-scores tell you how many standard deviations away from the mean each value lies.
The z-score and t-score (aka z-value and t-value) show how many standard deviations away from the mean of the distribution you are, assuming your data follow a z-distribution or a t-distribution.
These scores are used in statistical tests to show how far from the mean of the predicted distribution your statistical estimate is. If your test produces a z-score of 2.5, this means that your estimate is 2.5 standard deviations from the predicted mean.
The predicted mean and distribution of your estimate are generated by the null hypothesis of the statistical test you are using. The more standard deviations away from the predicted mean your estimate is, the less likely it is that the estimate could have occurred under the null hypothesis.
To calculate the confidence interval, you need to know:
Then you can plug these components into the confidence interval formula that corresponds to your data. The formula depends on the type of estimate (e.g. a mean or a proportion) and on the distribution of your data.
The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way.
The confidence interval consists of the upper and lower bounds of the estimate you expect to find at a given level of confidence.
For example, if you are estimating a 95% confidence interval around the mean proportion of female babies born every year based on a random sample of babies, you might find an upper bound of 0.56 and a lower bound of 0.48. These are the upper and lower bounds of the confidence interval. The confidence level is 95%.
The abstract appears on its own page in the thesis or dissertation, after the title page and acknowledgements but before the table of contents.
The abstract is the very last thing you write. You should only write it after your research is complete, so that you can accurately summarize the entirety of your thesis, dissertation or research paper.
An abstract for a thesis or dissertation is usually around 200–300 words. There’s often a strict word limit, so make sure to check your university’s requirements.
In a thesis or dissertation, the acknowledgements should usually be no longer than one page. There is no minimum length.
The acknowledgements are generally included at the very beginning of your thesis, directly after the title page and before the abstract.
Yes, it’s important to thank your supervisor(s) in the acknowledgements section of your thesis or dissertation.
Even if you feel your supervisor did not contribute greatly to the final product, you must acknowledge them, if only for a very brief thank you. If you do not include your supervisor, it may be seen as a snub.
In the acknowledgements of your thesis or dissertation, you should first thank those who helped you academically or professionally, such as your supervisor, funders, and other academics.
Then you can include personal thanks to friends, family members, or anyone else who supported you during the process.
Comparisons in essays are generally structured in one of two ways:
It’s also possible to combine both methods, for example by writing a full paragraph on each of your topics and then a final paragraph contrasting the two according to a specific metric.
Your subjects might be very different or quite similar, but it’s important that there be meaningful grounds for comparison. You can probably describe many differences between a cat and a bicycle, but there isn’t really any connection between them to justify the comparison.
You’ll have to write a thesis statement explaining the central point you want to make in your essay, so be sure to know in advance what connects your subjects and makes them worth comparing.
Some essay prompts include the keywords “compare” and/or “contrast.” In these cases, an essay structured around comparing and contrasting is the appropriate response.
Comparing and contrasting is also a useful approach in all kinds of academic writing: You might compare different studies in a literature review, weigh up different arguments in an argumentative essay, or consider different theoretical approaches in a theoretical framework.
Quasi-experimental design is most useful in situations where it would be unethical or impractical to run a true experiment.
Quasi-experiments have lower internal validity than true experiments, but they often have higher external validity as they can use real-world interventions instead of artificial laboratory settings.
A quasi-experiment is a type of research design that attempts to establish a cause-and-effect relationship. The main difference with a true experiment is that the groups are not randomly assigned.
The key difference is that a narrative essay is designed to tell a complete story, while a descriptive essay is meant to convey an intense description of a particular place, object, or concept.
Narrative and descriptive essays both allow you to write more personally and creatively than other kinds of essays, and similar writing skills can apply to both.
If you’re not given a specific prompt for your descriptive essay, think about places and objects you know well, that you can think of interesting ways to describe, or that have strong personal significance for you.
The best kind of object for a descriptive essay is one specific enough that you can describe its particular features in detail—don’t choose something too vague or general.
The mean is the most frequently used measure of central tendency because it uses all values in the data set to give you an average.
For data from skewed distributions, the median is better than the mean because it isn’t influenced by extremely large values.
The mode is the only measure you can use for nominal or categorical data that can’t be ordered.
The measures of central tendency you can use depends on the level of measurement of your data.
Measures of central tendency help you find the middle, or the average, of a data set.
The 3 most common measures of central tendency are the mean, median and mode.
If you’re not given much guidance on what your narrative essay should be about, consider the context and scope of the assignment. What kind of story is relevant, interesting, and possible to tell within the word count?
The best kind of story for a narrative essay is one you can use to reflect on a particular theme or lesson, or that takes a surprising turn somewhere along the way.
Don’t worry too much if your topic seems unoriginal. The point of a narrative essay is how you tell the story and the point you make with it, not the subject of the story itself.
Narrative essays are usually assigned as writing exercises at high school or in university composition classes. They may also form part of a university application.
When you are prompted to tell a story about your own life or experiences, a narrative essay is usually the right response.
The majority of the essays written at university are some sort of argumentative essay. Unless otherwise specified, you can assume that the goal of any essay you’re asked to write is argumentative: To convince the reader of your position using evidence and reasoning.
In composition classes you might be given assignments that specifically test your ability to write an argumentative essay. Look out for prompts including instructions like “argue,” “assess,” or “discuss” to see if this is the goal.
At college level, you must properly cite your sources in all essays, research papers, and other academic texts (except exams and in-class exercises).
Add a citation whenever you quote, paraphrase, or summarize information or ideas from a source. You should also give full source details in a bibliography or reference list at the end of your text.
The exact format of your citations depends on which citation style you are instructed to use. The most common styles are APA, MLA, and Chicago.
Some variables have fixed levels. For example, gender and ethnicity are always nominal level data because they cannot be ranked.
However, for other variables, you can choose the level of measurement. For example, income is a variable that can be recorded on an ordinal or a ratio scale:
If you have a choice, the ratio level is always preferable because you can analyze data in more ways. The higher the level of measurement, the more precise your data is.
The level at which you measure a variable determines how you can analyze your data.
Depending on the level of measurement, you can perform different descriptive statistics to get an overall summary of your data and inferential statistics to see if your results support or refute your hypothesis.
Levels of measurement tell you how precisely variables are recorded. There are 4 levels of measurement, which can be ranked from low to high:
No. The p-value only tells you how likely the data you have observed is to have occurred under the null hypothesis.
If the p-value is below your threshold of significance (typically p < 0.05), then you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.
The alpha value, or the threshold for statistical significance, is arbitrary – which value you use depends on your field of study.
In most cases, researchers use an alpha of 0.05, which means that there is a less than 5% chance that the data being tested could have occurred under the null hypothesis.
P-values are usually automatically calculated by the program you use to perform your statistical test. They can also be estimated using p-value tables for the relevant test statistic.
P-values are calculated from the null distribution of the test statistic. They tell you how often a test statistic is expected to occur under the null hypothesis of the statistical test, based on where it falls in the null distribution.
If the test statistic is far from the mean of the null distribution, then the p-value will be small, showing that the test statistic is not likely to have occurred under the null hypothesis.
A p-value, or probability value, is a number describing how likely it is that your data would have occurred under the null hypothesis of your statistical test.
The test statistic you use will be determined by the statistical test.
You can choose the right statistical test by looking at what type of data you have collected and what type of relationship you want to test.
The test statistic will change based on the number of observations in your data, how variable your observations are, and how strong the underlying patterns in the data are.
For example, if one data set has higher variability while another has lower variability, the first data set will produce a test statistic closer to the null hypothesis, even if the true correlation between two variables is the same in either data set.
The formula for the test statistic depends on the statistical test being used.
Generally, the test statistic is calculated as the pattern in your data (i.e. the correlation between variables or difference between groups) divided by the variance in the data (i.e. the standard deviation).
An argumentative essay tends to be a longer essay involving independent research, and aims to make an original argument about a topic. Its thesis statement makes a contentious claim that must be supported in an objective, evidence-based way.
An expository essay also aims to be objective, but it doesn’t have to make an original argument. Rather, it aims to explain something (e.g., a process or idea) in a clear, concise way. Expository essays are often shorter assignments and rely less on research.
An expository essay is a common assignment in high-school and university composition classes. It might be assigned as coursework, in class, or as part of an exam.
Sometimes you might not be told explicitly to write an expository essay. Look out for prompts containing keywords like “explain” and “define.” An expository essay is usually the right response to these prompts.
An expository essay is a broad form that varies in length according to the scope of the assignment.
Expository essays are often assigned as a writing exercise or as part of an exam, in which case a five-paragraph essay of around 800 words may be appropriate.
You’ll usually be given guidelines regarding length; if you’re not sure, ask.
Blinding is important to reduce research bias (e.g., observer bias, demand characteristics) and ensure a study’s internal validity.
If participants know whether they are in a control or treatment group, they may adjust their behavior in ways that affect the outcome that researchers are trying to measure. If the people administering the treatment are aware of group assignment, they may treat participants differently and thus directly or indirectly influence the final results.
Blinding means hiding who is assigned to the treatment group and who is assigned to the control group in an experiment.
The 3 main types of descriptive statistics concern the frequency distribution, central tendency, and variability of a dataset.
Descriptive statistics summarize the characteristics of a data set. Inferential statistics allow you to test a hypothesis or assess whether your data is generalizable to the broader population.
A true experiment (a.k.a. a controlled experiment) always includes at least one control group that doesn’t receive the experimental treatment.
However, some experiments use a within-subjects design to test treatments without a control group. In these designs, you usually compare one group’s outcomes before and after a treatment (instead of comparing outcomes between different groups).
For strong internal validity, it’s usually best to include a control group if possible. Without a control group, it’s harder to be certain that the outcome was caused by the experimental treatment and not by other variables.
An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not. They should be identical in all other ways.
Individual Likert-type questions are generally considered ordinal data, because the items have clear rank order, but don’t have an even distribution.
Overall Likert scale scores are sometimes treated as interval data. These scores are considered to have directionality and even spacing between them.
The type of data determines what statistical tests you should use to analyze your data.
A Likert scale is a rating scale that quantitatively assesses opinions, attitudes, or behaviors. It is made up of 4 or more questions that measure a single attitude or trait when response scores are combined.
To use a Likert scale in a survey, you present participants with Likert-type questions or statements, and a continuum of items, usually with 5 or 7 possible responses, to capture their degree of agreement.
In scientific research, concepts are the abstract ideas or phenomena that are being studied (e.g., educational achievement). Variables are properties or characteristics of the concept (e.g., performance at school), while indicators are ways of measuring or quantifying variables (e.g., yearly grade reports).
The process of turning abstract concepts into measurable variables and indicators is called operationalization.
There are various approaches to qualitative data analysis, but they all share five steps in common:
The specifics of each step depend on the focus of the analysis. Some common approaches include textual analysis, thematic analysis, and discourse analysis.
There are five common approaches to qualitative research:
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses, by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.
When an online source does not list a publication date, replace it with an access date in your Chicago footnotes and your bibliography:
If you are using author-date in-text citations, or if the source was not accessed online, replace the date with “n.d.”
To automatically generate accurate Chicago references, you can use Scribbr’s free Chicago reference generator.
Operationalization means turning abstract conceptual ideas into measurable observations.
For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioral avoidance of crowded places, or physical anxiety symptoms in social situations.
Before collecting data, it’s important to consider how you will operationalize the variables that you want to measure.
When conducting research, collecting original data has significant advantages:
However, there are also some drawbacks: data collection can be time-consuming, labor-intensive and expensive. In some cases, it’s more efficient to use secondary data that has already been collected by someone else, but the data might be less reliable.
Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organizations.
There are several methods you can use to decrease the impact of confounding variables on your research: restriction, matching, statistical control and randomization.
In restriction, you restrict your sample by only including certain subjects that have the same values of potential confounding variables.
In matching, you match each of the subjects in your treatment group with a counterpart in the comparison group. The matched subjects have the same values on any potential confounding variables, and only differ in the independent variable.
In statistical control, you include potential confounders as variables in your regression.
In randomization, you randomly assign the treatment (or independent variable) in your study to a sufficiently large number of subjects, which allows you to control for all potential confounding variables.
A confounding variable is closely related to both the independent and dependent variables in a study. An independent variable represents the supposed cause, while the dependent variable is the supposed effect. A confounding variable is a third variable that influences both the independent and dependent variables.
Failing to account for confounding variables can cause you to wrongly estimate the relationship between your independent and dependent variables.
To ensure the internal validity of your research, you must consider the impact of confounding variables. If you fail to account for them, you might over- or underestimate the causal relationship between your independent and dependent variables, or even find a causal relationship where none exists.
Yes, but including more than one of either type requires multiple research questions.
For example, if you are interested in the effect of a diet on health, you can use multiple measures of health: blood sugar, blood pressure, weight, pulse, and many more. Each of these is its own dependent variable with its own research question.
You could also choose to look at the effect of exercise levels as well as diet, or even the additional effect of the two combined. Each of these is a separate independent variable.
To ensure the internal validity of an experiment, you should only change one independent variable at a time.
No. The value of a dependent variable depends on an independent variable, so a variable cannot be both independent and dependent at the same time. It must be either the cause or the effect, not both!
You want to find out how blood sugar levels are affected by drinking diet soda and regular soda, so you conduct an experiment.
Determining cause and effect is one of the most important parts of scientific research. It’s essential to know which is the cause – the independent variable – and which is the effect – the dependent variable.
In non-probability sampling, the sample is selected based on non-random criteria, and not every member of the population has a chance of being included.
Common non-probability sampling methods include convenience sampling, voluntary response sampling, purposive sampling, snowball sampling, and quota sampling.
Probability sampling means that every member of the target population has a known chance of being included in the sample.
Probability sampling methods include simple random sampling, systematic sampling, stratified sampling, and cluster sampling.
Using careful research design and sampling procedures can help you avoid sampling bias. Oversampling can be used to correct undercoverage bias.
Some common types of sampling bias include self-selection bias, nonresponse bias, undercoverage bias, survivorship bias, pre-screening or advertising bias, and healthy user bias.
Sampling bias is a threat to external validity – it limits the generalizability of your findings to a broader group of people.
Sampling bias occurs when some members of a population are systematically more likely to be selected in a sample than others.
A sampling error is the difference between a population parameter and a sample statistic.
A statistic refers to measures about the sample, while a parameter refers to measures about the population.
Populations are used when a research question requires data from every member of the population. This is usually only feasible when the population is small and easily accessible.
Samples are used to make inferences about populations. Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.
You must include an MLA in-text citation every time you quote or paraphrase from a source (e.g. a book, movie, website, or article).
There are seven threats to external validity: selection bias, history, experimenter effect, Hawthorne effect, testing effect, aptitude-treatment and situation effect.
The two types of external validity are population validity (whether you can generalize to other groups of people) and ecological validity (whether you can generalize to other situations and settings).
The external validity of a study is the extent to which you can generalize your findings to different groups of people, situations, and measures.
Cross-sectional studies cannot establish a cause-and-effect relationship or analyze behavior over a period of time. To investigate cause and effect, you need to do a longitudinal study or an experimental study.
Cross-sectional studies are less expensive and time-consuming than many other types of study. They can provide useful insights into a population’s characteristics and identify correlations for further research.
Sometimes only cross-sectional data is available for analysis; other times your research question may only require a cross-sectional study to answer it.
Longitudinal studies can last anywhere from weeks to decades, although they tend to be at least a year long.
The 1970 British Cohort Study, which has collected data on the lives of 17,000 Brits since their births in 1970, is one well-known example of a longitudinal study.
Longitudinal studies are better to establish the correct sequence of events, identify changes over time, and provide insight into cause-and-effect relationships, but they also tend to be more expensive and time-consuming than other types of studies.
Longitudinal studies and cross-sectional studies are two different types of research design. In a cross-sectional study you collect data from a population at a specific point in time; in a longitudinal study you repeatedly collect data from the same sample over an extended period of time.
| Longitudinal study | Cross-sectional study |
|---|---|
| Repeated observations | Observations at a single point in time |
| Observes the same group multiple times | Observes different groups (a “cross-section”) in the population |
| Follows changes in participants over time | Provides snapshot of society at a given point |
There are eight threats to internal validity: history, maturation, instrumentation, testing, selection bias, regression to the mean, social interaction and attrition.
Internal validity is the extent to which you can be confident that a cause-and-effect relationship established in a study cannot be explained by other factors.
If you’ve gone over the word limit set for your assignment, shorten your sentences and cut repetition and redundancy during the editing process. If you use a lot of long quotes, consider shortening them to just the essentials.
If you need to remove a lot of words, you may have to cut certain passages. Remember that everything in the text should be there to support your argument; look for any information that’s not essential to your point and remove it.
To make this process easier and faster, you can use a paraphrasing tool. With this tool, you can rewrite your text to make it simpler and shorter. If that’s not enough, you can copy-paste your paraphrased text into the summarizer. This tool will distill your text to its core message.
Revising, proofreading, and editing are different stages of the writing process.
In statistics, model selection is a process researchers use to compare the relative value of different statistical models and determine which one is the best fit for the observed data.
The Akaike information criterion is one of the most common methods of model selection. AIC weights the ability of the model to predict the observed data against the number of parameters the model requires to reach that level of precision.
AIC model selection can help researchers find a model that explains the observed variation in their data while avoiding overfitting.
In statistics, a model is the collection of one or more independent variables and their predicted interactions that researchers use to try to explain variation in their dependent variable.
You can test a model using a statistical test. To compare how well different models fit your data, you can use Akaike’s information criterion for model selection.
The Akaike information criterion is calculated from the maximum log-likelihood of the model and the number of parameters (K) used to reach that likelihood. The AIC function is 2K – 2(log-likelihood).
Lower AIC values indicate a better-fit model, and a model with a delta-AIC (the difference between the two AIC values being compared) of more than -2 is considered significantly better than the model it is being compared to.
The Akaike information criterion is a mathematical test used to evaluate how well a model fits the data it is meant to describe. It penalizes models which use more independent variables (parameters) as a way to avoid over-fitting.
AIC is most often used to compare the relative goodness-of-fit among different models under consideration and to then choose the model that best fits the data.
If you adapt or reproduce a table or figure from another source, you should include that source in your APA reference list. You should also acknowledge the original source in the note or caption for the table or figure.
Tables and figures you created yourself, based on your own data, are not included in the reference list.
APA doesn’t require you to include a list of tables or a list of figures. However, it is advisable to do so if your text is long enough to feature a table of contents and it includes a lot of tables and/or figures.
A list of tables and list of figures appear (in that order) after your table of contents, and are presented in a similar way.
In an APA Style paper, use a table or figure when it’s a clearer way to present important data than describing it in your main text. This is often the case when you need to communicate a large amount of information.
Before including a table or figure in your text, always reflect on whether it’s useful to your readers’ understanding:
If the data you need to present only contains a few relevant numbers, try summarizing it in the text (potentially including full data in an appendix). If describing the data makes your text overly long and difficult to read, a table or figure may be the best option.
A factorial ANOVA is any ANOVA that uses more than one categorical independent variable. A two-way ANOVA is a type of factorial ANOVA.
Some examples of factorial ANOVAs include:
In ANOVA, the null hypothesis is that there is no difference among group means. If any group differs significantly from the overall group mean, then the ANOVA will report a statistically significant result.
Significant differences among group means are calculated using the F statistic, which is the ratio of the mean sum of squares (the variance explained by the independent variable) to the mean square error (the variance left over).
If the F statistic is higher than the critical value (the value of F that corresponds with your alpha value, usually 0.05), then the difference among groups is deemed statistically significant.
The only difference between one-way and two-way ANOVA is the number of independent variables. A one-way ANOVA has one independent variable, while a two-way ANOVA has two.
All ANOVAs are designed to test for differences among three or more groups. If you are only testing for a difference between two groups, use a t-test instead.
Multiple linear regression is a regression model that estimates the relationship between a quantitative dependent variable and two or more independent variables using a straight line.
Linear regression most often uses mean-square error (MSE) to calculate the error of the model. MSE is calculated by:
Linear regression fits a line to the data by finding the regression coefficient that results in the smallest MSE.
Simple linear regression is a regression model that estimates the relationship between one independent variable and one dependent variable using a straight line. Both variables should be quantitative.
For example, the relationship between temperature and the expansion of mercury in a thermometer can be modeled using a straight line: as temperature increases, the mercury expands. This linear relationship is so certain that we can use mercury thermometers to measure temperature.
A regression model is a statistical model that estimates the relationship between one dependent variable and one or more independent variables using a line (or a plane in the case of two or more independent variables).
A regression model can be used when the dependent variable is quantitative, except in the case of logistic regression, where the dependent variable is binary.
The literature review usually comes near the beginning of your thesis or dissertation. After the introduction, it grounds your research in a scholarly field and leads directly to your theoretical framework or methodology.
There are several reasons to conduct a literature review at the beginning of a research project:
Writing the literature review shows your reader how your work relates to existing research and what new insights it will contribute.
A literature review is a survey of scholarly sources (such as books, journal articles, and theses) related to a specific topic or research question.
It is often written as part of a thesis, dissertation, or research paper, in order to situate your work in relation to existing knowledge.
The sections in your graduate school resume depend on two things: your experience, and the focus of the program you’re applying to.
Always start with your education. If you have more than one degree, list the most recent one first.
The title and order of the other sections depend on what you want to emphasize. You might include things like:
The resume should aim for a balance between two things: giving a snapshot of what you’ve done with your life so far, and showing that you’re a good candidate for graduate study.
A resume is typically shorter than a CV, giving only the most relevant professional and educational highlights.
An academic CV should give full details of your education and career, including lists of publications and presentations, certifications, memberships, grants, and research projects. Because it is more comprehensive, it’s acceptable for an academic CV to be many pages long.
Note that, outside of the US, resume and CV are often used interchangeably.
No, don’t include your high school courses and grades. The education section should only detail your college education.
If you want to discuss aspects of high school in your graduate school application, you can include this in your personal statement.
A resume for a graduate school application is typically no more than 1–2 pages long.
Note, however, that if you are asked to submit a CV (curriculum vitae), you should give comprehensive details of all your academic experience. An academic CV can be much longer than a normal resume.
Always carefully check the instructions and adhere to any length requirements for each application.
A one-sample t-test is used to compare a single population to a standard value (for example, to determine whether the average lifespan of a specific town is different from the country average).
A paired t-test is used to compare a single population before and after some experimental intervention or at two different points in time (for example, measuring student performance on a test before and after being taught the material).
A t-test measures the difference in group means divided by the pooled standard error of the two group means.
In this way, it calculates a number (the t-value) illustrating the magnitude of the difference between the two group means being compared, and estimates the likelihood that this difference exists purely by chance (p-value).
Your choice of t-test depends on whether you are studying one group or two groups, and whether you care about the direction of the difference in group means.
If you are studying one group, use a paired t-test to compare the group mean over time or after an intervention, or use a one-sample t-test to compare the group mean to a standard value. If you are studying two groups, use a two-sample t-test.
If you want to know only whether a difference exists, use a two-tailed test. If you want to know if one group mean is greater or less than the other, use a left-tailed or right-tailed one-tailed test.
A t-test is a statistical test that compares the means of two samples. It is used in hypothesis testing, with a null hypothesis that the difference in group means is zero and an alternate hypothesis that the difference in group means is different from zero.
MLA Style is the second most used citation style (after APA). It is mainly used by students and researchers in humanities fields such as literature, languages, and philosophy.
If information about your source is not available, you can either leave it out of the MLA citation or replace it with something else, depending on the type of information.
A standard MLA Works Cited entry is structured as follows:
Only include information that is available for and relevant to your source.
In mixed methods research, you use both qualitative and quantitative data collection and analysis methods to answer your research question.
The research methods you use depend on the type of data you need to answer your research question.
Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test. Significance is usually denoted by a p-value, or probability value.
Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis.
When the p-value falls below the chosen alpha value, then we say the result of the test is statistically significant.
A test statistic is a number calculated by a statistical test. It describes how far your observed data is from the null hypothesis of no relationship between variables or no difference among sample groups.
The test statistic tells you how different two or more groups are from the overall population mean, or how different a linear slope is from the slope predicted by a null hypothesis. Different test statistics are used in different statistical tests.
Statistical tests commonly assume that:
If your data does not meet these assumptions you might still be able to use a nonparametric statistical test, which have fewer requirements but also make weaker inferences.
Avoid citing sources in your abstract. There are two reasons for this:
There are some circumstances where you might need to mention other sources in an abstract: for example, if your research responds directly to another study or focuses on the work of a single theorist. In general, though, don’t include citations unless absolutely necessary.
An abstract is a concise summary of an academic text (such as a journal article or dissertation). It serves two main purposes:
Abstracts are often indexed along with keywords on academic databases, so they make your work more easily findable. Since the abstract is the first thing any reader sees, it’s important that it clearly and accurately summarizes the contents of your paper.
In an APA Style paper, the abstract is placed on a separate page after the title page (page 2).
An APA abstract is around 150–250 words long. However, always check your target journal’s guidelines and don’t exceed the specified word count.
Yes. MLA style uses title case, which means that all principal words (nouns, pronouns, verbs, adjectives, adverbs, and some conjunctions) are capitalized.
This applies to titles of sources as well as the title of, and subheadings in, your paper. Use MLA capitalization style even when the original source title uses different capitalization.
The title of an article is not italicized in MLA style, but placed in quotation marks. This applies to articles from journals, newspapers, websites, or any other publication. Use italics for the title of the source where the article was published. For example:
Use the same formatting in the Works Cited entry and when referring to the article in the text itself.
In MLA style, book titles appear in italics, with all major words capitalized. If there is a subtitle, separate it from the main title with a colon and a space (even if no colon appears in the source). For example:
The format is the same in the Works Cited list and in the text itself. However, when you mention the book title in the text, you don’t have to include the subtitle.
The title of a part of a book—such as a chapter, or a short story or poem in a collection—is not italicized, but instead placed in quotation marks.
The DOI is usually clearly visible when you open a journal article on an academic database. It is often listed near the publication date, and includes “doi.org” or “DOI:”. If the database has a “cite this article” button, this should also produce a citation with the DOI included.
If you can’t find the DOI, you can search on Crossref using information like the author, the article title, and the journal name.
In MLA style citations, format a DOI as a link, including “https://doi.org/” at the start and then the unique numerical code of the article.
DOIs are used mainly when citing journal articles in MLA.
A DOI is a unique identifier for a digital document. DOIs are important in academic citation because they are more permanent than URLs, ensuring that your reader can reliably locate the source.
Journal articles and ebooks can often be found on multiple different websites and databases. The URL of the page where an article is hosted can be changed or removed over time, but a DOI is linked to the specific document and never changes.
A confounding variable, also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.
A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.
In your research design, it’s important to identify potential confounding variables and plan how you will reduce their impact.
Discrete and continuous variables are two types of quantitative variables:
Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).
Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).
You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results.
You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause, while a dependent variable is the effect.
In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable. For example, in an experiment about the effect of nutrients on crop growth:
Defining your variables, and deciding how you will manipulate and measure them, is an important part of experimental design.
The MLA Handbook is currently in its 9th edition, published in 2021.
This quick guide to MLA style explains the latest guidelines for citing sources and formatting papers according to MLA.
The fastest and most accurate way to create MLA citations is by using Scribbr’s MLA Citation Generator.
Search by book title, page URL, or journal DOI to automatically generate flawless citations, or cite manually using the simple citation forms.
MLA recommends using 12-point Times New Roman, since it’s easy to read and installed on every computer. Other standard fonts such as Arial or Georgia are also acceptable. If in doubt, check with your supervisor which font you should be using.
Experimental design means planning a set of procedures to investigate a relationship between variables. To design a controlled experiment, you need:
When designing the experiment, you decide:
Experimental design is essential to the internal and external validity of your experiment.
Internal validity is the degree of confidence that the causal relationship you are testing is not influenced by other factors or variables.
External validity is the extent to which your results can be generalized to other contexts.
The validity of your experiment depends on your experimental design.
In APA Style, all sources that are not retrievable for the reader are cited as personal communications. In other words, if your source is private or inaccessible to the audience of your paper, it’s a personal communication.
Common examples include conversations, emails, messages, letters, and unrecorded interviews or performances.
Interviews you conducted yourself are not included in your reference list, but instead cited in the text as personal communications.
Published or recorded interviews are included in the reference list. Cite them in the usual format of the source type (for example, a newspaper article, website or YouTube video).
When you quote or paraphrase a specific passage from a source, you need to indicate the location of the passage in your APA in-text citation. If there are no page numbers (e.g. when citing a website) but the text is long, you can instead use section headings, paragraph numbers, or a combination of the two:
(Caulfield, 2019, Linking section, para. 1).
Section headings can be shortened if necessary. Kindle location numbers should not be used in ebook citations, as they are unreliable.
If you are referring to the source as a whole, it’s not necessary to include a page number or other marker.
APA Style usually does not require an access date. You never need to include one when citing journal articles, e-books, or other stable online sources.
However, if you are citing a website or online article that’s designed to change over time, it’s a good idea to include an access date. In this case, write it in the following format at the end of the reference: Retrieved October 19, 2020, from https://www.uva.nl/en/about-the-uva/about-the-university/about-the-university.html
The 7th edition APA Manual, published in October 2019, is the most current edition. However, the 6th edition, published in 2009, is still used by many universities and journals.
The American Psychological Association anticipates that most people will start using the 7th edition in the spring of 2020 or thereafter.
It’s best to ask your supervisor or check the website of the journal you want to publish in to see which APA guidelines you should follow.
If you’re citing from an edition other than the first (e.g. a 2nd edition or revised edition), the edition appears in the reference, abbreviated in parentheses after the book’s title (e.g. 2nd ed. or Rev. ed.).
In the 7th edition of the APA manual, no location information is required for publishers. The 6th edition previously required you to include the city and state where the publisher was located, but this is no longer the case.
When a book’s chapters are written by different authors, you should cite the specific chapter you are referring to.
When all the chapters are written by the same author (or group of authors), you should usually cite the entire book, but some styles include exceptions to this.
In an APA reference list, journal article citations include only the year of publication, not the exact date, month, or season.
The inclusion of volume and issue numbers makes a more specific date unnecessary.
In an APA journal citation, if a DOI (digital object identifier) is available for an article, always include it.
If an article has no DOI, and you accessed it through a database or in print, just omit the DOI.
If an article has no DOI, and you accessed it through a website other than a database (for example, the journal’s own website), include a URL linking to the article.
Include the DOI at the very end of the APA reference entry. If you’re using the 6th edition APA guidelines, the DOI is preceded by the label “doi:”. In the 7th edition, the DOI is preceded by ‘https://doi.org/’.
Hawi, N. S., & Samaha, M. (2016). The relations among social media addiction, self-esteem, and life satisfaction in university students. Social Science Computer Review, 35(5), 576–586. https://doi.org/10.1177/0894439316660340
Reliability and validity are both about how well a method measures something:
If you are doing experimental research, you also have to consider the internal and external validity of your experiment.
A sample is a subset of individuals from a larger population. Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.
In statistics, sampling allows you to test a hypothesis about the characteristics of a population.
Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.
Quantitative methods allow you to systematically measure variables and test hypotheses. Qualitative methods allow you to explore concepts and experiences in more detail.
In a scientific paper, the methodology always comes after the introduction and before the results, discussion and conclusion. The same basic structure also applies to a thesis, dissertation, or research proposal.
Depending on the length and type of document, you might also include a literature review or theoretical framework before the methodology.
Methodology refers to the overarching strategy and rationale of your research project. It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.
Methods are the specific tools and procedures you use to collect and analyze data (for example, experiments, surveys, and statistical tests).
In shorter scientific papers, where the aim is to report the findings of a specific study, you might simply describe what you did in a methods section.
In a longer or more complex research project, such as a thesis or dissertation, you will probably include a methodology section, where you explain your approach to answering the research questions and cite relevant sources to support your choice of methods.
If you’re applying to multiple graduate school programs, you should tailor your personal statement to each application.
Some applications provide a prompt or question. In this case, you might have to write a new personal statement from scratch: the most important task is to respond to what you have been asked.
If there’s no prompt or guidelines, you can re-use the same idea for your personal statement – but change the details wherever relevant, making sure to emphasize why you’re applying to this specific program.
If the application also includes other essays, such as a statement of purpose, you might have to revise your personal statement to avoid repeating the same information.
The typical length of a personal statement for graduate school applications is between 500 and 1,000 words.
Different programs have different requirements, so always check if there’s a minimum or maximum length and stick to the guidelines. If there is no recommended word count, aim for no more than 1-2 pages.
A statement of purpose is usually more formal, focusing on your academic or professional goals. It shouldn’t include anything that isn’t directly relevant to the application.
A personal statement can often be more creative. It might tell a story that isn’t directly related to the application, but that shows something about your personality, values, and motivations.
However, both types of document have the same overall goal: to demonstrate your potential as a graduate student and show why you’re a great match for the program.
Chicago format doesn’t require you to use any specific font, as long as you choose something readable. A good standard choice is 12 pt Times New Roman.
Both present the exact same information; the only difference is the placement of the year in source citations:
There are also other types of bibliography that work as stand-alone texts, such as a Chicago annotated bibliography.
Turabian style is a version of Chicago style designed specifically for students and researchers. It follows most Chicago conventions, but also adds extra guidelines for formatting research papers, theses and dissertations.
More information can be found in A Manual for Writers of Research Papers, Theses, and Dissertations by Kate L. Turabian, now in its ninth edition.
Footnotes appear at the bottom of the relevant page. Endnotes appear in a list at the end of the text, just before the reference list or bibliography. Don’t mix footnotes and endnotes in the same document: choose one or the other and use them consistently.
In Chicago notes and bibliography style, you can use either footnotes or endnotes, and citations follow the same format in either case.
In APA and MLA style, footnotes or endnotes are not used for citations, but they can be used to provide additional information.
In Chicago author-date style, your text must include a reference list. It appears at the end of your paper and gives full details of every source you cited.
In notes and bibliography style, you use Chicago style footnotes to cite sources; a bibliography is optional but recommended. If you don’t include one, be sure to use a full note for the first citation of each source.
In Chicago notes and bibliography style, the usual standard is to use a full note for the first citation of each source, and short notes for any subsequent citations of the same source.
However, your institution’s guidelines may differ from the standard rule. In some fields, you’re required to use a full note every time, whereas in some other fields you can use short notes every time, as long as all sources are listed in your bibliography. If you’re not sure, check with your instructor.
When a source has four or more authors, your in-text citation or Chicago footnote should give only the first author’s name followed by “et al.” (Latin for “and others”). This makes your citations more concise.
In your bibliography or reference list, when a source has more than 10 authors, list the first seven followed by “et al.” Otherwise, list every author.
Page numbers should be included in your Chicago in-text citations when:
When you’re referring to the overall argument or general content of a source, it’s unnecessary to include page numbers.
To create a correctly formatted block quote in Microsoft Word, follow these steps:
Do not put quotation marks around the quote, and make sure to include an MLA in-text citation after the period at the end.
To format a block quote in MLA:
Then continue your text on a new line (not indented).
In MLA style, if you quote more than four lines from a source, use MLA block quote formatting.
If you are quoting poetry, use block quote formatting for any quote longer than three lines.
An MLA in-text citation should always include the author’s last name, either in the introductory text or in parentheses after a quote.
If line numbers or page numbers are included in the original source, add these to the citation.
If you are discussing multiple poems by the same author, make sure to also mention the title of the poem (shortened if necessary). The title goes in quotation marks.
In the list of Works Cited, start with the poet’s name and the poem’s title in quotation marks. The rest of the citation depends on where the poem was published.
If you read the poem in a book or anthology, follow the format of an MLA book chapter citation. If you accessed the poem online, follow the format of an MLA website citation.
Only use line numbers in an MLA in-text citation if the lines are numbered in the original source. If so, write “lines” in the first citation of the poem, and only the numbers in subsequent citations.
If there are no line numbers in the source, you can use page numbers instead. If the poem appears on only one page of a book (or on a website), don’t include a number in the citation.
To quote poetry in MLA style, introduce the quote and use quotation marks as you would for any other source quotation.
If the quote includes line breaks, mark these using a forward slash with a space on either side. Use two slashes to indicate a stanza break.
If the quote is longer than three lines, set them off from the main text as an MLA block quote. Reproduce the line breaks, punctuation, and formatting of the original.
When citing a webpage or online article, the APA in-text citation consists of the author’s last name and year of publication. For example: (Worland & Williams, 2015). Note that the author can also be an organization. For example: (American Psychological Association, 2019).
If you’re quoting you should also include a locator. Since web pages don’t have page numbers, you can use one of the following options:
Always include page numbers in the APA in-text citation when quoting a source. Don’t include page numbers when referring to a work as a whole – for example, an entire book or journal article.
If your source does not have page numbers, you can use an alternative locator such as a timestamp, chapter heading or paragraph number.
The abbreviation “et al.” (meaning “and others”) is used to shorten APA in-text citations with three or more authors. Here’s how it works:
Only include the first author’s last name, followed by “et al.”, a comma and the year of publication, for example (Taylor et al., 2018).
Whether you’re publishing a blog, submitting a research paper, or even just writing an important email, there are a few techniques you can use to make sure it’s error-free:
If you want to be confident that an important text is error-free, it might be worth choosing a professional proofreading service instead.
Editing and proofreading are different steps in the process of revising a text.
Editing comes first, and can involve major changes to content, structure and language. The first stages of editing are often done by authors themselves, while a professional editor makes the final improvements to grammar and style (for example, by improving sentence structure and word choice).
Proofreading is the final stage of checking a text before it is published or shared. It focuses on correcting minor errors and inconsistencies (for example, in punctuation and capitalization). Proofreaders often also check for formatting issues, especially in print publishing.
The cost of proofreading depends on the type and length of text, the turnaround time, and the level of services required. Most proofreading companies charge per word or page, while freelancers sometimes charge an hourly rate.
For proofreading alone, which involves only basic corrections of typos and formatting mistakes, you might pay as little as $0.01 per word, but in many cases, your text will also require some level of editing, which costs slightly more.
It’s often possible to purchase combined proofreading and editing services and calculate the price in advance based on your requirements.
There are many different routes to becoming a professional proofreader or editor. The necessary qualifications depend on the field – to be an academic or scientific proofreader, for example, you will need at least a university degree in a relevant subject.
For most proofreading jobs, experience and demonstrated skills are more important than specific qualifications. Often your skills will be tested as part of the application process.
To learn practical proofreading skills, you can choose to take a course with a professional organization such as the Society for Editors and Proofreaders. Alternatively, you can apply to companies that offer specialized on-the-job training programmes, such as the Scribbr Academy.
Articles in newspapers and magazines can be primary or secondary depending on the focus of your research.
In historical studies, old articles are used as primary sources that give direct evidence about the time period. In social and communication studies, articles are used as primary sources to analyze language and social relations (for example, by conducting content analysis or discourse analysis).
If you are not analyzing the article itself, but only using it for background information or facts about your topic, then the article is a secondary source.
A fictional movie is usually a primary source. A documentary can be either primary or secondary depending on the context.
If you are directly analyzing some aspect of the movie itself – for example, the cinematography, narrative techniques, or social context – the movie is a primary source.
If you use the movie for background information or analysis about your topic – for example, to learn about a historical event or a scientific discovery – the movie is a secondary source.
Whether it’s primary or secondary, always properly cite the movie in the citation style you are using. Learn how to create an MLA movie citation or an APA movie citation.
To determine if a source is primary or secondary, ask yourself:
Some types of source are nearly always primary: works of art and literature, raw statistical data, official documents and records, and personal communications (e.g. letters, interviews). If you use one of these in your research, it is probably a primary source.
Primary sources are often considered the most credible in terms of providing evidence for your argument, as they give you direct evidence of what you are researching. However, it’s up to you to ensure the information they provide is reliable and accurate.
Always make sure to properly cite your sources to avoid plagiarism.
Common examples of secondary sources include academic books, journal articles, reviews, essays, and textbooks.
Anything that summarizes, evaluates or interprets primary sources can be a secondary source. If a source gives you an overview of background information or presents another researcher’s ideas on your topic, it is probably a secondary source.
Common examples of primary sources include interview transcripts, photographs, novels, paintings, films, historical documents, and official statistics.
Anything you directly analyze or use as first-hand evidence can be a primary source, including qualitative or quantitative data that you collected yourself.
APA Style papers should be written in a font that is legible and widely accessible. For example:
The same font and font size is used throughout the document, including the running head, page numbers, headings, and the reference page. Text in footnotes and figure images may be smaller and use single line spacing.
The easiest way to set up APA format in Word is to download Scribbr’s free APA format template for student papers or professional papers.
Alternatively, you can watch Scribbr’s 5-minute step-by-step tutorial or check out our APA format guide with examples.
You need an APA in-text citation and reference entry. Each source type has its own format; for example, a webpage citation is different from a book citation.
Use Scribbr’s free APA Citation Generator to generate flawless citations in seconds or take a look at our APA citation examples.
APA format is widely used by professionals, researchers, and students in the social and behavioral sciences, including fields like education, psychology, and business.
Be sure to check the guidelines of your university or the journal you want to be published in to double-check which style you should be using.
Yes, page numbers are included on all pages, including the title page, table of contents, and reference page. Page numbers should be right-aligned in the page header.
To insert page numbers in Microsoft Word or Google Docs, click ‘Insert’ and then ‘Page number’.
The Scribbr Citation Generator is developed using the open-source Citation Style Language (CSL) project and Frank Bennett’s citeproc-js. It’s the same technology used by dozens of other popular citation tools, including Mendeley and Zotero.
You can find all the citation styles and locales used in the Scribbr Citation Generator in our publicly accessible repository on Github.
If you’ve correctly cited all the sources you used, then you do not need to use a plagiarism checker before submitting your paper to your instructor. However, it is very easy to commit plagiarism accidentally, even if you’ve been very careful. To ensure that you didn’t forget to cite anything, then you should use a plagiarism checker yourself.
A plagiarism checker works by using advanced database software to scan for matches between your text and existing texts.
To help you decide which checker to use, we conducted in-depth research comparing popular plagiarism checkers to find out which one is best.
Paraphrasing without crediting the original author is a form of plagiarism, because you’re presenting someone else’s ideas as if they were your own.
However, paraphrasing is not plagiarism if you correctly cite the source. This means including an in-text citation and a full reference, formatted according to your required citation style.
As well as citing, make sure that any paraphrased text is completely rewritten in your own words.
Plagiarism means using someone else’s words or ideas and passing them off as your own. Paraphrasing means putting someone else’s ideas in your own words.
So when does paraphrasing count as plagiarism?
Yes, Scribbr offers a limited free version of its plagiarism checker in partnership with Turnitin. It uses Turnitin’s industry-leading plagiarism detection technology and has access to most content databases.
If you’re a university representative, you can contact the sales department of Turnitin.
If you’ve properly paraphrased or quoted and correctly cited the source, you are not committing plagiarism.
However, the word correctly is vital. In order to avoid plagiarism, you must adhere to the guidelines of your citation style (e.g. APA or MLA).
You can use the Scribbr Plagiarism Checker to make sure you haven’t missed any citations, while our Citation Checker ensures you’ve properly formatted your citations in APA style.
The accuracy depends on the plagiarism checker you use. Per our in-depth research, Scribbr is the most accurate plagiarism checker. Many free plagiarism checkers fail to detect all plagiarism or falsely flag text as plagiarism.
Plagiarism checkers work by using advanced database software to scan for matches between your text and existing texts. Their accuracy is determined by two factors: the algorithm (which recognizes the plagiarism) and the size of the database (with which your document is compared).
The consequences of plagiarism vary depending on the type of plagiarism and the context in which it occurs. For example, submitting a whole paper by someone else will have the most severe consequences, while accidental citation errors are considered less serious.
If you’re a student, then you might fail the course, be suspended or expelled, or be obligated to attend a workshop on plagiarism. It depends on whether it’s your first offense or you’ve done it before.
As an academic or professional, plagiarizing seriously damages your reputation. You might also lose your research funding or your job, and you could even face legal consequences for copyright infringement.
Our team helps students graduate by offering:
Scribbr specializes in editing study-related documents. We proofread:
The Scribbr Plagiarism Checker is powered by elements of Turnitin’s Similarity Checker, namely the plagiarism detection software and the Internet Archive and Premium Scholarly Publications content databases.
The Scribbr Citation Generator is developed using the open-source Citation Style Language (CSL) project and Frank Bennett’s citeproc-js. It’s the same technology used by dozens of other popular citation tools, including Mendeley and Zotero.
You can find all the citation styles and locales used in the Scribbr Citation Generator in our publicly accessible repository on Github.
