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The Craft of Writing a Strong Hypothesis

Table of Contents

Writing a hypothesis is one of the essential elements of a scientific research paper. It needs to be to the point, clearly communicating what your research is trying to accomplish. A blurry, drawn-out, or complexly-structured hypothesis can confuse your readers. Or worse, the editor and peer reviewers.

A captivating hypothesis is not too intricate. This blog will take you through the process so that, by the end of it, you have a better idea of how to convey your research paper's intent in just one sentence.

What is a Hypothesis?

The first step in your scientific endeavor, a hypothesis, is a strong, concise statement that forms the basis of your research. It is not the same as a thesis statement , which is a brief summary of your research paper .

The sole purpose of a hypothesis is to predict your paper's findings, data, and conclusion. It comes from a place of curiosity and intuition . When you write a hypothesis, you're essentially making an educated guess based on scientific prejudices and evidence, which is further proven or disproven through the scientific method.

The reason for undertaking research is to observe a specific phenomenon. A hypothesis, therefore, lays out what the said phenomenon is. And it does so through two variables, an independent and dependent variable.

The independent variable is the cause behind the observation, while the dependent variable is the effect of the cause. A good example of this is “mixing red and blue forms purple.” In this hypothesis, mixing red and blue is the independent variable as you're combining the two colors at your own will. The formation of purple is the dependent variable as, in this case, it is conditional to the independent variable.

Different Types of Hypotheses‌

Types of hypotheses

Some would stand by the notion that there are only two types of hypotheses: a Null hypothesis and an Alternative hypothesis. While that may have some truth to it, it would be better to fully distinguish the most common forms as these terms come up so often, which might leave you out of context.

Apart from Null and Alternative, there are Complex, Simple, Directional, Non-Directional, Statistical, and Associative and casual hypotheses. They don't necessarily have to be exclusive, as one hypothesis can tick many boxes, but knowing the distinctions between them will make it easier for you to construct your own.

1. Null hypothesis

A null hypothesis proposes no relationship between two variables. Denoted by H 0 , it is a negative statement like “Attending physiotherapy sessions does not affect athletes' on-field performance.” Here, the author claims physiotherapy sessions have no effect on on-field performances. Even if there is, it's only a coincidence.

2. Alternative hypothesis

Considered to be the opposite of a null hypothesis, an alternative hypothesis is donated as H1 or Ha. It explicitly states that the dependent variable affects the independent variable. A good  alternative hypothesis example is “Attending physiotherapy sessions improves athletes' on-field performance.” or “Water evaporates at 100 °C. ” The alternative hypothesis further branches into directional and non-directional.

• Directional hypothesis: A hypothesis that states the result would be either positive or negative is called directional hypothesis. It accompanies H1 with either the ‘<' or ‘>' sign.
• Non-directional hypothesis: A non-directional hypothesis only claims an effect on the dependent variable. It does not clarify whether the result would be positive or negative. The sign for a non-directional hypothesis is ‘≠.'

3. Simple hypothesis

A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, “Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking.

4. Complex hypothesis

In contrast to a simple hypothesis, a complex hypothesis implies the relationship between multiple independent and dependent variables. For instance, “Individuals who eat more fruits tend to have higher immunity, lesser cholesterol, and high metabolism.” The independent variable is eating more fruits, while the dependent variables are higher immunity, lesser cholesterol, and high metabolism.

5. Associative and casual hypothesis

Associative and casual hypotheses don't exhibit how many variables there will be. They define the relationship between the variables. In an associative hypothesis, changing any one variable, dependent or independent, affects others. In a casual hypothesis, the independent variable directly affects the dependent.

6. Empirical hypothesis

Also referred to as the working hypothesis, an empirical hypothesis claims a theory's validation via experiments and observation. This way, the statement appears justifiable and different from a wild guess.

Say, the hypothesis is “Women who take iron tablets face a lesser risk of anemia than those who take vitamin B12.” This is an example of an empirical hypothesis where the researcher  the statement after assessing a group of women who take iron tablets and charting the findings.

7. Statistical hypothesis

The point of a statistical hypothesis is to test an already existing hypothesis by studying a population sample. Hypothesis like “44% of the Indian population belong in the age group of 22-27.” leverage evidence to prove or disprove a particular statement.

Characteristics of a Good Hypothesis

Writing a hypothesis is essential as it can make or break your research for you. That includes your chances of getting published in a journal. So when you're designing one, keep an eye out for these pointers:

• A research hypothesis has to be simple yet clear to look justifiable enough.
• It has to be testable — your research would be rendered pointless if too far-fetched into reality or limited by technology.
• It has to be precise about the results —what you are trying to do and achieve through it should come out in your hypothesis.
• A research hypothesis should be self-explanatory, leaving no doubt in the reader's mind.
• If you are developing a relational hypothesis, you need to include the variables and establish an appropriate relationship among them.
• A hypothesis must keep and reflect the scope for further investigations and experiments.

Separating a Hypothesis from a Prediction

Outside of academia, hypothesis and prediction are often used interchangeably. In research writing, this is not only confusing but also incorrect. And although a hypothesis and prediction are guesses at their core, there are many differences between them.

A hypothesis is an educated guess or even a testable prediction validated through research. It aims to analyze the gathered evidence and facts to define a relationship between variables and put forth a logical explanation behind the nature of events.

Predictions are assumptions or expected outcomes made without any backing evidence. They are more fictionally inclined regardless of where they originate from.

For this reason, a hypothesis holds much more weight than a prediction. It sticks to the scientific method rather than pure guesswork. "Planets revolve around the Sun." is an example of a hypothesis as it is previous knowledge and observed trends. Additionally, we can test it through the scientific method.

Whereas "COVID-19 will be eradicated by 2030." is a prediction. Even though it results from past trends, we can't prove or disprove it. So, the only way this gets validated is to wait and watch if COVID-19 cases end by 2030.

Finally, How to Write a Hypothesis

Quick tips on writing a hypothesis

1.  Be clear about your research question

A hypothesis should instantly address the research question or the problem statement. To do so, you need to ask a question. Understand the constraints of your undertaken research topic and then formulate a simple and topic-centric problem. Only after that can you develop a hypothesis and further test for evidence.

2. Carry out a recce

Once you have your research's foundation laid out, it would be best to conduct preliminary research. Go through previous theories, academic papers, data, and experiments before you start curating your research hypothesis. It will give you an idea of your hypothesis's viability or originality.

Making use of references from relevant research papers helps draft a good research hypothesis. SciSpace Discover offers a repository of over 270 million research papers to browse through and gain a deeper understanding of related studies on a particular topic. Additionally, you can use SciSpace Copilot , your AI research assistant, for reading any lengthy research paper and getting a more summarized context of it. A hypothesis can be formed after evaluating many such summarized research papers. Copilot also offers explanations for theories and equations, explains paper in simplified version, allows you to highlight any text in the paper or clip math equations and tables and provides a deeper, clear understanding of what is being said. This can improve the hypothesis by helping you identify potential research gaps.

3. Create a 3-dimensional hypothesis

Variables are an essential part of any reasonable hypothesis. So, identify your independent and dependent variable(s) and form a correlation between them. The ideal way to do this is to write the hypothetical assumption in the ‘if-then' form. If you use this form, make sure that you state the predefined relationship between the variables.

In another way, you can choose to present your hypothesis as a comparison between two variables. Here, you must specify the difference you expect to observe in the results.

4. Write the first draft

Now that everything is in place, it's time to write your hypothesis. For starters, create the first draft. In this version, write what you expect to find from your research.

Clearly separate your independent and dependent variables and the link between them. Don't fixate on syntax at this stage. The goal is to ensure your hypothesis addresses the issue.

5. Proof your hypothesis

After preparing the first draft of your hypothesis, you need to inspect it thoroughly. It should tick all the boxes, like being concise, straightforward, relevant, and accurate. Your final hypothesis has to be well-structured as well.

Research projects are an exciting and crucial part of being a scholar. And once you have your research question, you need a great hypothesis to begin conducting research. Thus, knowing how to write a hypothesis is very important.

Now that you have a firmer grasp on what a good hypothesis constitutes, the different kinds there are, and what process to follow, you will find it much easier to write your hypothesis, which ultimately helps your research.

Now it's easier than ever to streamline your research workflow with SciSpace Discover . Its integrated, comprehensive end-to-end platform for research allows scholars to easily discover, write and publish their research and fosters collaboration.

It includes everything you need, including a repository of over 270 million research papers across disciplines, SEO-optimized summaries and public profiles to show your expertise and experience.

If you found these tips on writing a research hypothesis useful, head over to our blog on Statistical Hypothesis Testing to learn about the top researchers, papers, and institutions in this domain.

Frequently Asked Questions (FAQs)

1. what is the definition of hypothesis.

According to the Oxford dictionary, a hypothesis is defined as “An idea or explanation of something that is based on a few known facts, but that has not yet been proved to be true or correct”.

2. What is an example of hypothesis?

The hypothesis is a statement that proposes a relationship between two or more variables. An example: "If we increase the number of new users who join our platform by 25%, then we will see an increase in revenue."

3. What is an example of null hypothesis?

A null hypothesis is a statement that there is no relationship between two variables. The null hypothesis is written as H0. The null hypothesis states that there is no effect. For example, if you're studying whether or not a particular type of exercise increases strength, your null hypothesis will be "there is no difference in strength between people who exercise and people who don't."

4. What are the types of research?

• Fundamental research

• Applied research

• Qualitative research

• Quantitative research

• Mixed research

• Exploratory research

• Longitudinal research

• Cross-sectional research

• Field research

• Laboratory research

• Fixed research

• Flexible research

• Action research

• Policy research

• Classification research

• Comparative research

• Causal research

• Inductive research

• Deductive research

5. How to write a hypothesis?

• Your hypothesis should be able to predict the relationship and outcome.

• Avoid wordiness by keeping it simple and brief.

• Your hypothesis should contain observable and testable outcomes.

• Your hypothesis should be relevant to the research question.

6. What are the 2 types of hypothesis?

• Null hypotheses are used to test the claim that "there is no difference between two groups of data".

• Alternative hypotheses test the claim that "there is a difference between two data groups".

7. Difference between research question and research hypothesis?

A research question is a broad, open-ended question you will try to answer through your research. A hypothesis is a statement based on prior research or theory that you expect to be true due to your study. Example - Research question: What are the factors that influence the adoption of the new technology? Research hypothesis: There is a positive relationship between age, education and income level with the adoption of the new technology.

8. What is plural for hypothesis?

The plural of hypothesis is hypotheses. Here's an example of how it would be used in a statement, "Numerous well-considered hypotheses are presented in this part, and they are supported by tables and figures that are well-illustrated."

9. What is the red queen hypothesis?

The red queen hypothesis in evolutionary biology states that species must constantly evolve to avoid extinction because if they don't, they will be outcompeted by other species that are evolving. Leigh Van Valen first proposed it in 1973; since then, it has been tested and substantiated many times.

10. Who is known as the father of null hypothesis?

The father of the null hypothesis is Sir Ronald Fisher. He published a paper in 1925 that introduced the concept of null hypothesis testing, and he was also the first to use the term itself.

11. When to reject null hypothesis?

You need to find a significant difference between your two populations to reject the null hypothesis. You can determine that by running statistical tests such as an independent sample t-test or a dependent sample t-test. You should reject the null hypothesis if the p-value is less than 0.05.

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How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis.

• Operationalization

Hypothesis Types

Hypotheses examples.

• Collecting Data

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process.

Consider a study designed to examine the relationship between sleep deprivation and test performance. The hypothesis might be: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

At a Glance

A hypothesis is crucial to scientific research because it offers a clear direction for what the researchers are looking to find. This allows them to design experiments to test their predictions and add to our scientific knowledge about the world. This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

• Forming a question
• Performing background research
• Creating a hypothesis
• Designing an experiment
• Collecting data
• Analyzing the results
• Drawing conclusions
• Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. At this point, researchers then begin to develop a testable hypothesis.

Unless you are creating an exploratory study, your hypothesis should always explain what you  expect  to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore numerous factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment  do not  support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk adage that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

• Is your hypothesis based on your research on a topic?
• Can your hypothesis be tested?
• Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the  journal articles you read . Many authors will suggest questions that still need to be explored.

How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

• Collect as many observations about a topic or problem as you can.
• Evaluate these observations and look for possible causes of the problem.
• Create a list of possible explanations that you might want to explore.
• After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method ,  falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that  if  something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

The Importance of Operational Definitions

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

Operational definitions are specific definitions for all relevant factors in a study. This process helps make vague or ambiguous concepts detailed and measurable.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in various ways. Clearly defining these variables and how they are measured helps ensure that other researchers can replicate your results.

Replicability

One of the basic principles of any type of scientific research is that the results must be replicable.

Replication means repeating an experiment in the same way to produce the same results. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. For example, how would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

To measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming others. The researcher might utilize a simulated task to measure aggressiveness in this situation.

Hypothesis Checklist

• Does your hypothesis focus on something that you can actually test?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate the variables?
• Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

• Simple hypothesis : This type of hypothesis suggests there is a relationship between one independent variable and one dependent variable.
• Complex hypothesis : This type suggests a relationship between three or more variables, such as two independent and dependent variables.
• Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
• Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
• Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative population sample and then generalizes the findings to the larger group.
• Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the  dependent variable  if you change the  independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

A few examples of simple hypotheses:

• "Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
• "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."​
• "Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."
• "Children who receive a new reading intervention will have higher reading scores than students who do not receive the intervention."

Examples of a complex hypothesis include:

• "People with high-sugar diets and sedentary activity levels are more likely to develop depression."
• "Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

Examples of a null hypothesis include:

• "There is no difference in anxiety levels between people who take St. John's wort supplements and those who do not."
• "There is no difference in scores on a memory recall task between children and adults."
• "There is no difference in aggression levels between children who play first-person shooter games and those who do not."

Examples of an alternative hypothesis:

• "People who take St. John's wort supplements will have less anxiety than those who do not."
• "Adults will perform better on a memory task than children."
• "Children who play first-person shooter games will show higher levels of aggression than children who do not." 

Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

Descriptive Research Methods

Descriptive research such as  case studies ,  naturalistic observations , and surveys are often used when  conducting an experiment is difficult or impossible. These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a  correlational study  can examine how the variables are related. This research method might be used to investigate a hypothesis that is difficult to test experimentally.

Experimental Research Methods

Experimental methods  are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually  cause  another to change.

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Thompson WH, Skau S. On the scope of scientific hypotheses .  R Soc Open Sci . 2023;10(8):230607. doi:10.1098/rsos.230607

Taran S, Adhikari NKJ, Fan E. Falsifiability in medicine: what clinicians can learn from Karl Popper [published correction appears in Intensive Care Med. 2021 Jun 17;:].  Intensive Care Med . 2021;47(9):1054-1056. doi:10.1007/s00134-021-06432-z

Eyler AA. Research Methods for Public Health . 1st ed. Springer Publishing Company; 2020. doi:10.1891/9780826182067.0004

Nosek BA, Errington TM. What is replication ?  PLoS Biol . 2020;18(3):e3000691. doi:10.1371/journal.pbio.3000691

Aggarwal R, Ranganathan P. Study designs: Part 2 - Descriptive studies .  Perspect Clin Res . 2019;10(1):34-36. doi:10.4103/picr.PICR_154_18

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Educational resources and simple solutions for your research journey

What is a Research Hypothesis: How to Write it, Types, and Examples

Any research begins with a research question and a research hypothesis . A research question alone may not suffice to design the experiment(s) needed to answer it. A hypothesis is central to the scientific method. But what is a hypothesis ? A hypothesis is a testable statement that proposes a possible explanation to a phenomenon, and it may include a prediction. Next, you may ask what is a research hypothesis ? Simply put, a research hypothesis is a prediction or educated guess about the relationship between the variables that you want to investigate.  

It is important to be thorough when developing your research hypothesis. Shortcomings in the framing of a hypothesis can affect the study design and the results. A better understanding of the research hypothesis definition and characteristics of a good hypothesis will make it easier for you to develop your own hypothesis for your research. Let’s dive in to know more about the types of research hypothesis , how to write a research hypothesis , and some research hypothesis examples .  

Table of Contents

What is a hypothesis ?  

A hypothesis is based on the existing body of knowledge in a study area. Framed before the data are collected, a hypothesis states the tentative relationship between independent and dependent variables, along with a prediction of the outcome.  

What is a research hypothesis ?  

Young researchers starting out their journey are usually brimming with questions like “ What is a hypothesis ?” “ What is a research hypothesis ?” “How can I write a good research hypothesis ?”   

A research hypothesis is a statement that proposes a possible explanation for an observable phenomenon or pattern. It guides the direction of a study and predicts the outcome of the investigation. A research hypothesis is testable, i.e., it can be supported or disproven through experimentation or observation.     

Characteristics of a good hypothesis  

Here are the characteristics of a good hypothesis :  

• Clearly formulated and free of language errors and ambiguity  
• Concise and not unnecessarily verbose  
• Has clearly defined variables  
• Testable and stated in a way that allows for it to be disproven  
• Can be tested using a research design that is feasible, ethical, and practical   
• Specific and relevant to the research problem  
• Rooted in a thorough literature search  
• Can generate new knowledge or understanding.  

How to create an effective research hypothesis  

A study begins with the formulation of a research question. A researcher then performs background research. This background information forms the basis for building a good research hypothesis . The researcher then performs experiments, collects, and analyzes the data, interprets the findings, and ultimately, determines if the findings support or negate the original hypothesis.  

Let’s look at each step for creating an effective, testable, and good research hypothesis :  

• Identify a research problem or question: Start by identifying a specific research problem.   
• Review the literature: Conduct an in-depth review of the existing literature related to the research problem to grasp the current knowledge and gaps in the field.   
• Formulate a clear and testable hypothesis : Based on the research question, use existing knowledge to form a clear and testable hypothesis . The hypothesis should state a predicted relationship between two or more variables that can be measured and manipulated. Improve the original draft till it is clear and meaningful.  
• State the null hypothesis: The null hypothesis is a statement that there is no relationship between the variables you are studying.   
• Define the population and sample: Clearly define the population you are studying and the sample you will be using for your research.  
• Select appropriate methods for testing the hypothesis: Select appropriate research methods, such as experiments, surveys, or observational studies, which will allow you to test your research hypothesis .  

Remember that creating a research hypothesis is an iterative process, i.e., you might have to revise it based on the data you collect. You may need to test and reject several hypotheses before answering the research problem.  

How to write a research hypothesis  

When you start writing a research hypothesis , you use an “if–then” statement format, which states the predicted relationship between two or more variables. Clearly identify the independent variables (the variables being changed) and the dependent variables (the variables being measured), as well as the population you are studying. Review and revise your hypothesis as needed.  

An example of a research hypothesis in this format is as follows:  

“ If [athletes] follow [cold water showers daily], then their [endurance] increases.”  

Population: athletes  

Independent variable: daily cold water showers  

Dependent variable: endurance  

You may have understood the characteristics of a good hypothesis . But note that a research hypothesis is not always confirmed; a researcher should be prepared to accept or reject the hypothesis based on the study findings.  

Research hypothesis checklist  

Following from above, here is a 10-point checklist for a good research hypothesis :  

• Testable: A research hypothesis should be able to be tested via experimentation or observation.  
• Specific: A research hypothesis should clearly state the relationship between the variables being studied.  
• Based on prior research: A research hypothesis should be based on existing knowledge and previous research in the field.  
• Falsifiable: A research hypothesis should be able to be disproven through testing.  
• Clear and concise: A research hypothesis should be stated in a clear and concise manner.  
• Logical: A research hypothesis should be logical and consistent with current understanding of the subject.  
• Relevant: A research hypothesis should be relevant to the research question and objectives.  
• Feasible: A research hypothesis should be feasible to test within the scope of the study.  
• Reflects the population: A research hypothesis should consider the population or sample being studied.  
• Uncomplicated: A good research hypothesis is written in a way that is easy for the target audience to understand.  

By following this research hypothesis checklist , you will be able to create a research hypothesis that is strong, well-constructed, and more likely to yield meaningful results.  

Types of research hypothesis  

Different types of research hypothesis are used in scientific research:  

1. Null hypothesis:

A null hypothesis states that there is no change in the dependent variable due to changes to the independent variable. This means that the results are due to chance and are not significant. A null hypothesis is denoted as H0 and is stated as the opposite of what the alternative hypothesis states.   

Example: “ The newly identified virus is not zoonotic .”  

2. Alternative hypothesis:

This states that there is a significant difference or relationship between the variables being studied. It is denoted as H1 or Ha and is usually accepted or rejected in favor of the null hypothesis.  

Example: “ The newly identified virus is zoonotic .”  

3. Directional hypothesis :

This specifies the direction of the relationship or difference between variables; therefore, it tends to use terms like increase, decrease, positive, negative, more, or less.   

Example: “ The inclusion of intervention X decreases infant mortality compared to the original treatment .”   

4. Non-directional hypothesis:

While it does not predict the exact direction or nature of the relationship between the two variables, a non-directional hypothesis states the existence of a relationship or difference between variables but not the direction, nature, or magnitude of the relationship. A non-directional hypothesis may be used when there is no underlying theory or when findings contradict previous research.  

Example, “ Cats and dogs differ in the amount of affection they express .”  

5. Simple hypothesis :

A simple hypothesis only predicts the relationship between one independent and another independent variable.  

Example: “ Applying sunscreen every day slows skin aging .”  

6 . Complex hypothesis :

A complex hypothesis states the relationship or difference between two or more independent and dependent variables.   

Example: “ Applying sunscreen every day slows skin aging, reduces sun burn, and reduces the chances of skin cancer .” (Here, the three dependent variables are slowing skin aging, reducing sun burn, and reducing the chances of skin cancer.)  

7. Associative hypothesis:  

An associative hypothesis states that a change in one variable results in the change of the other variable. The associative hypothesis defines interdependency between variables.  

Example: “ There is a positive association between physical activity levels and overall health .”  

8 . Causal hypothesis:

A causal hypothesis proposes a cause-and-effect interaction between variables.  

Example: “ Long-term alcohol use causes liver damage .”  

Note that some of the types of research hypothesis mentioned above might overlap. The types of hypothesis chosen will depend on the research question and the objective of the study.  

Research hypothesis examples  

Here are some good research hypothesis examples :  

“The use of a specific type of therapy will lead to a reduction in symptoms of depression in individuals with a history of major depressive disorder.”  

“Providing educational interventions on healthy eating habits will result in weight loss in overweight individuals.”  

“Plants that are exposed to certain types of music will grow taller than those that are not exposed to music.”  

“The use of the plant growth regulator X will lead to an increase in the number of flowers produced by plants.”  

Characteristics that make a research hypothesis weak are unclear variables, unoriginality, being too general or too vague, and being untestable. A weak hypothesis leads to weak research and improper methods.   

Some bad research hypothesis examples (and the reasons why they are “bad”) are as follows:  

“This study will show that treatment X is better than any other treatment . ” (This statement is not testable, too broad, and does not consider other treatments that may be effective.)  

“This study will prove that this type of therapy is effective for all mental disorders . ” (This statement is too broad and not testable as mental disorders are complex and different disorders may respond differently to different types of therapy.)  

“Plants can communicate with each other through telepathy . ” (This statement is not testable and lacks a scientific basis.)  

Importance of testable hypothesis  

If a research hypothesis is not testable, the results will not prove or disprove anything meaningful. The conclusions will be vague at best. A testable hypothesis helps a researcher focus on the study outcome and understand the implication of the question and the different variables involved. A testable hypothesis helps a researcher make precise predictions based on prior research.  

To be considered testable, there must be a way to prove that the hypothesis is true or false; further, the results of the hypothesis must be reproducible.  

Frequently Asked Questions (FAQs) on research hypothesis  

1. What is the difference between research question and research hypothesis ?  

A research question defines the problem and helps outline the study objective(s). It is an open-ended statement that is exploratory or probing in nature. Therefore, it does not make predictions or assumptions. It helps a researcher identify what information to collect. A research hypothesis , however, is a specific, testable prediction about the relationship between variables. Accordingly, it guides the study design and data analysis approach.

2. When to reject null hypothesis ?

A null hypothesis should be rejected when the evidence from a statistical test shows that it is unlikely to be true. This happens when the test statistic (e.g., p -value) is less than the defined significance level (e.g., 0.05). Rejecting the null hypothesis does not necessarily mean that the alternative hypothesis is true; it simply means that the evidence found is not compatible with the null hypothesis.  

3. How can I be sure my hypothesis is testable?  

A testable hypothesis should be specific and measurable, and it should state a clear relationship between variables that can be tested with data. To ensure that your hypothesis is testable, consider the following:  

• Clearly define the key variables in your hypothesis. You should be able to measure and manipulate these variables in a way that allows you to test the hypothesis.  
• The hypothesis should predict a specific outcome or relationship between variables that can be measured or quantified.   
• You should be able to collect the necessary data within the constraints of your study.  
• It should be possible for other researchers to replicate your study, using the same methods and variables.   
• Your hypothesis should be testable by using appropriate statistical analysis techniques, so you can draw conclusions, and make inferences about the population from the sample data.  
• The hypothesis should be able to be disproven or rejected through the collection of data.  

4. How do I revise my research hypothesis if my data does not support it?  

If your data does not support your research hypothesis , you will need to revise it or develop a new one. You should examine your data carefully and identify any patterns or anomalies, re-examine your research question, and/or revisit your theory to look for any alternative explanations for your results. Based on your review of the data, literature, and theories, modify your research hypothesis to better align it with the results you obtained. Use your revised hypothesis to guide your research design and data collection. It is important to remain objective throughout the process.  

5. I am performing exploratory research. Do I need to formulate a research hypothesis?  

As opposed to “confirmatory” research, where a researcher has some idea about the relationship between the variables under investigation, exploratory research (or hypothesis-generating research) looks into a completely new topic about which limited information is available. Therefore, the researcher will not have any prior hypotheses. In such cases, a researcher will need to develop a post-hoc hypothesis. A post-hoc research hypothesis is generated after these results are known.  

6. How is a research hypothesis different from a research question?

A research question is an inquiry about a specific topic or phenomenon, typically expressed as a question. It seeks to explore and understand a particular aspect of the research subject. In contrast, a research hypothesis is a specific statement or prediction that suggests an expected relationship between variables. It is formulated based on existing knowledge or theories and guides the research design and data analysis.

7. Can a research hypothesis change during the research process?

Yes, research hypotheses can change during the research process. As researchers collect and analyze data, new insights and information may emerge that require modification or refinement of the initial hypotheses. This can be due to unexpected findings, limitations in the original hypotheses, or the need to explore additional dimensions of the research topic. Flexibility is crucial in research, allowing for adaptation and adjustment of hypotheses to align with the evolving understanding of the subject matter.

8. How many hypotheses should be included in a research study?

The number of research hypotheses in a research study varies depending on the nature and scope of the research. It is not necessary to have multiple hypotheses in every study. Some studies may have only one primary hypothesis, while others may have several related hypotheses. The number of hypotheses should be determined based on the research objectives, research questions, and the complexity of the research topic. It is important to ensure that the hypotheses are focused, testable, and directly related to the research aims.

9. Can research hypotheses be used in qualitative research?

Yes, research hypotheses can be used in qualitative research, although they are more commonly associated with quantitative research. In qualitative research, hypotheses may be formulated as tentative or exploratory statements that guide the investigation. Instead of testing hypotheses through statistical analysis, qualitative researchers may use the hypotheses to guide data collection and analysis, seeking to uncover patterns, themes, or relationships within the qualitative data. The emphasis in qualitative research is often on generating insights and understanding rather than confirming or rejecting specific research hypotheses through statistical testing.

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How Do You Write a Hypothesis for a Research Paper: Tips and Examples

Crafting a well-defined hypothesis is a critical step in the research process, serving as the foundation for your study. A hypothesis not only guides your research design but also provides a clear focus for your investigation. In this article, we will explore the essential aspects of writing a strong hypothesis for a research paper, including its characteristics, formulation steps, types, and common pitfalls to avoid. Additionally, we will provide examples from various disciplines to illustrate what makes a hypothesis effective.

Key Takeaways

• A hypothesis is a testable statement that predicts the relationship between variables in your research.
• Clarity and precision are crucial for a strong hypothesis, ensuring that it is understandable and specific.
• A good hypothesis must be testable and falsifiable, meaning it can be supported or refuted through experimentation or observation.
• Formulating a hypothesis involves identifying a research problem, conducting a literature review, and clearly stating the expected outcome.
• Avoid common pitfalls such as overly complex hypotheses, vague language, and lack of testability to ensure your hypothesis is effective.

Understanding the Role of a Hypothesis in Research

Defining a hypothesis.

A hypothesis is a testable prediction about the relationship between two or more variables. It serves as a navigational tool in the research process, directing what you aim to predict and how. Crafting a thesis statement is crucial in the writing process, guiding research and shaping arguments.

Purpose and Importance of a Hypothesis

In research, a hypothesis serves as the cornerstone for your empirical study. It not only lays out what you aim to investigate but also provides a structured approach for your data collection and analysis. Flexibility and clarity are key for effective statements.

Hypothesis vs. Prediction

A hypothesis is an attempt at explaining a phenomenon or the relationships between phenomena/variables in the real world. While hypotheses are sometimes called “educated guesses,” they should be based on previous observations, existing theories, scientific evidence, and logic. A hypothesis is not a prediction; rather, predictions are based on clearly formulated hypotheses.

Key Characteristics of a Strong Hypothesis

A robust hypothesis is essential for guiding your research effectively. Firstly, clarity and precision are paramount . Your hypothesis should be specific and unambiguous, providing a clear understanding of the expected relationship between variables. This ensures that your research question is well-defined and comprehensible.

Testability and falsifiability are also crucial. A hypothesis must be testable, allowing you to analyze data through empirical means, such as observation or experimentation, to assess if there is significant support for the hypothesis. Additionally, it should be falsifiable, meaning that it can be proven wrong through evidence.

Lastly, relevance to the research question is vital. Your hypothesis should be grounded in existing research or theoretical frameworks, ensuring its applicability and significance to the field of study. This connection to prior research not only strengthens your hypothesis but also aligns it with the broader academic discourse.

Steps to Formulate a Hypothesis for a Research Paper

Identifying the research problem.

The first step in formulating a hypothesis is to clearly identify the research problem. This involves understanding the phenomenon or the relationships between variables that you wish to explore. A well-defined research problem sets the stage for a focused and effective hypothesis.

Conducting a Literature Review

Before you can formulate a hypothesis, it's essential to conduct a thorough literature review. This helps you understand what has already been studied and where gaps in the research exist. By reviewing existing literature, you can ensure that your hypothesis is both original and relevant.

Formulating the Hypothesis

Once you have identified the research problem and reviewed the literature, you can begin to formulate your hypothesis . A strong hypothesis should be clear, testable, and directly related to the research question. It often helps to frame your hypothesis as an 'if-then' statement, which clearly outlines the expected relationship between variables.

Types of Hypotheses in Research

Understanding the various types of hypotheses is crucial for crafting effective research. Each type serves a unique purpose and can significantly influence the direction and outcomes of your study. All hypotheses contrast with the null hypothesis , which posits that no significant relationship exists between the variables under investigation.

Common Pitfalls to Avoid When Writing a Hypothesis

When crafting a hypothesis for your research paper, it's crucial to steer clear of common mistakes that can undermine your work. Avoiding these pitfalls will help you create a robust and testable hypothesis that can withstand academic scrutiny.

Examples of Well-Written Hypotheses

In this section, we will explore various examples of well-crafted hypotheses to help you understand what makes a hypothesis strong and effective. By examining these examples, you can gain insights into the essential components that contribute to a robust hypothesis.

Testing and Refining Your Hypothesis

Once you have formulated your hypothesis, the next crucial step is to test and refine it. This process ensures that your hypothesis is robust and reliable, ultimately contributing to the validity of your research findings.

Testing and refining your hypothesis is a crucial step in your thesis journey. It ensures that your research is on the right track and that your findings are valid. To make this process easier, our Thesis Action Plan offers a structured approach to help you navigate through each stage with confidence. Don't let uncertainty hold you back. Visit our website to learn more and claim your special offer now !

Crafting a well-defined hypothesis is a critical step in the research process, serving as the foundation upon which your entire study is built. A clear and concise hypothesis not only guides your research design and methodology but also provides a focal point for data collection and analysis. By following the tips and examples provided in this article, researchers can develop robust hypotheses that are both testable and meaningful. Remember, a strong hypothesis is characterized by its specificity, clarity, and relevance to the research question. As you embark on your research journey, take the time to refine your hypothesis, as it will significantly impact the quality and credibility of your study. With careful consideration and thoughtful formulation, your hypothesis can pave the way for insightful and impactful research findings.

Frequently Asked Questions

What is a hypothesis in a research paper.

A hypothesis in a research paper is a statement that predicts the relationship between variables. It serves as a tentative explanation for an observation, phenomenon, or scientific problem that can be tested by further investigation.

How do I formulate a strong hypothesis?

To formulate a strong hypothesis, ensure it is clear, precise, testable, and relevant to your research question. Conducting a thorough literature review can help you identify gaps in existing knowledge and formulate a hypothesis that addresses those gaps.

What is the difference between a hypothesis and a prediction?

A hypothesis is a testable statement about the relationship between two or more variables, while a prediction is a specific outcome that you expect to observe if the hypothesis is true. Predictions are often derived from hypotheses.

What are the types of hypotheses in research?

The main types of hypotheses in research are the null hypothesis, alternative hypothesis, directional hypothesis, and non-directional hypothesis. Each type serves a different purpose in statistical testing and research design.

Why is testability important in a hypothesis?

Testability is crucial in a hypothesis because it allows researchers to use empirical methods to determine whether the hypothesis is supported or refuted by the data. A hypothesis must be testable to be scientifically valid.

Can a hypothesis be revised?

Yes, a hypothesis can be revised based on new data, insights, or changes in the research focus. Revising a hypothesis is a common part of the scientific process as researchers refine their questions and methods.

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How to Write a Research Hypothesis: Good & Bad Examples

What is a research hypothesis?

A research hypothesis is an attempt at explaining a phenomenon or the relationships between phenomena/variables in the real world. Hypotheses are sometimes called “educated guesses”, but they are in fact (or let’s say they should be) based on previous observations, existing theories, scientific evidence, and logic. A research hypothesis is also not a prediction—rather, predictions are ( should be) based on clearly formulated hypotheses. For example, “We tested the hypothesis that KLF2 knockout mice would show deficiencies in heart development” is an assumption or prediction, not a hypothesis. 

The research hypothesis at the basis of this prediction is “the product of the KLF2 gene is involved in the development of the cardiovascular system in mice”—and this hypothesis is probably (hopefully) based on a clear observation, such as that mice with low levels of Kruppel-like factor 2 (which KLF2 codes for) seem to have heart problems. From this hypothesis, you can derive the idea that a mouse in which this particular gene does not function cannot develop a normal cardiovascular system, and then make the prediction that we started with. 

What is the difference between a hypothesis and a prediction?

You might think that these are very subtle differences, and you will certainly come across many publications that do not contain an actual hypothesis or do not make these distinctions correctly. But considering that the formulation and testing of hypotheses is an integral part of the scientific method, it is good to be aware of the concepts underlying this approach. The two hallmarks of a scientific hypothesis are falsifiability (an evaluation standard that was introduced by the philosopher of science Karl Popper in 1934) and testability —if you cannot use experiments or data to decide whether an idea is true or false, then it is not a hypothesis (or at least a very bad one).

So, in a nutshell, you (1) look at existing evidence/theories, (2) come up with a hypothesis, (3) make a prediction that allows you to (4) design an experiment or data analysis to test it, and (5) come to a conclusion. Of course, not all studies have hypotheses (there is also exploratory or hypothesis-generating research), and you do not necessarily have to state your hypothesis as such in your paper. 

But for the sake of understanding the principles of the scientific method, let’s first take a closer look at the different types of hypotheses that research articles refer to and then give you a step-by-step guide for how to formulate a strong hypothesis for your own paper.

Types of Research Hypotheses

Hypotheses can be simple , which means they describe the relationship between one single independent variable (the one you observe variations in or plan to manipulate) and one single dependent variable (the one you expect to be affected by the variations/manipulation). If there are more variables on either side, you are dealing with a complex hypothesis. You can also distinguish hypotheses according to the kind of relationship between the variables you are interested in (e.g., causal or associative ). But apart from these variations, we are usually interested in what is called the “alternative hypothesis” and, in contrast to that, the “null hypothesis”. If you think these two should be listed the other way round, then you are right, logically speaking—the alternative should surely come second. However, since this is the hypothesis we (as researchers) are usually interested in, let’s start from there.

Alternative Hypothesis

If you predict a relationship between two variables in your study, then the research hypothesis that you formulate to describe that relationship is your alternative hypothesis (usually H1 in statistical terms). The goal of your hypothesis testing is thus to demonstrate that there is sufficient evidence that supports the alternative hypothesis, rather than evidence for the possibility that there is no such relationship. The alternative hypothesis is usually the research hypothesis of a study and is based on the literature, previous observations, and widely known theories. 

Null Hypothesis

The hypothesis that describes the other possible outcome, that is, that your variables are not related, is the null hypothesis ( H0 ). Based on your findings, you choose between the two hypotheses—usually that means that if your prediction was correct, you reject the null hypothesis and accept the alternative. Make sure, however, that you are not getting lost at this step of the thinking process: If your prediction is that there will be no difference or change, then you are trying to find support for the null hypothesis and reject H1. 

Directional Hypothesis

While the null hypothesis is obviously “static”, the alternative hypothesis can specify a direction for the observed relationship between variables—for example, that mice with higher expression levels of a certain protein are more active than those with lower levels. This is then called a one-tailed hypothesis. 

Another example for a directional one-tailed alternative hypothesis would be that 

H1: Attending private classes before important exams has a positive effect on performance. 

Your null hypothesis would then be that

H0: Attending private classes before important exams has no/a negative effect on performance.

Nondirectional Hypothesis

A nondirectional hypothesis does not specify the direction of the potentially observed effect, only that there is a relationship between the studied variables—this is called a two-tailed hypothesis. For instance, if you are studying a new drug that has shown some effects on pathways involved in a certain condition (e.g., anxiety) in vitro in the lab, but you can’t say for sure whether it will have the same effects in an animal model or maybe induce other/side effects that you can’t predict and potentially increase anxiety levels instead, you could state the two hypotheses like this:

H1: The only lab-tested drug (somehow) affects anxiety levels in an anxiety mouse model.

You then test this nondirectional alternative hypothesis against the null hypothesis:

H0: The only lab-tested drug has no effect on anxiety levels in an anxiety mouse model.

How to Write a Hypothesis for a Research Paper

Now that we understand the important distinctions between different kinds of research hypotheses, let’s look at a simple process of how to write a hypothesis.

Writing a Hypothesis Step:1

Ask a question, based on earlier research. Research always starts with a question, but one that takes into account what is already known about a topic or phenomenon. For example, if you are interested in whether people who have pets are happier than those who don’t, do a literature search and find out what has already been demonstrated. You will probably realize that yes, there is quite a bit of research that shows a relationship between happiness and owning a pet—and even studies that show that owning a dog is more beneficial than owning a cat ! Let’s say you are so intrigued by this finding that you wonder: 

What is it that makes dog owners even happier than cat owners? 

Let’s move on to Step 2 and find an answer to that question.

Writing a Hypothesis Step 2:

Formulate a strong hypothesis by answering your own question. Again, you don’t want to make things up, take unicorns into account, or repeat/ignore what has already been done. Looking at the dog-vs-cat papers your literature search returned, you see that most studies are based on self-report questionnaires on personality traits, mental health, and life satisfaction. What you don’t find is any data on actual (mental or physical) health measures, and no experiments. You therefore decide to make a bold claim come up with the carefully thought-through hypothesis that it’s maybe the lifestyle of the dog owners, which includes walking their dog several times per day, engaging in fun and healthy activities such as agility competitions, and taking them on trips, that gives them that extra boost in happiness. You could therefore answer your question in the following way:

Dog owners are happier than cat owners because of the dog-related activities they engage in.

Now you have to verify that your hypothesis fulfills the two requirements we introduced at the beginning of this resource article: falsifiability and testability . If it can’t be wrong and can’t be tested, it’s not a hypothesis. We are lucky, however, because yes, we can test whether owning a dog but not engaging in any of those activities leads to lower levels of happiness or well-being than owning a dog and playing and running around with them or taking them on trips.  

Writing a Hypothesis Step 3:

Make your predictions and define your variables. We have verified that we can test our hypothesis, but now we have to define all the relevant variables, design our experiment or data analysis, and make precise predictions. You could, for example, decide to study dog owners (not surprising at this point), let them fill in questionnaires about their lifestyle as well as their life satisfaction (as other studies did), and then compare two groups of active and inactive dog owners. Alternatively, if you want to go beyond the data that earlier studies produced and analyzed and directly manipulate the activity level of your dog owners to study the effect of that manipulation, you could invite them to your lab, select groups of participants with similar lifestyles, make them change their lifestyle (e.g., couch potato dog owners start agility classes, very active ones have to refrain from any fun activities for a certain period of time) and assess their happiness levels before and after the intervention. In both cases, your independent variable would be “ level of engagement in fun activities with dog” and your dependent variable would be happiness or well-being . 

Examples of a Good and Bad Hypothesis

Let’s look at a few examples of good and bad hypotheses to get you started.

Good Hypothesis Examples

Bad Hypothesis Examples

Tips for Writing a Research Hypothesis

If you understood the distinction between a hypothesis and a prediction we made at the beginning of this article, then you will have no problem formulating your hypotheses and predictions correctly. To refresh your memory: We have to (1) look at existing evidence, (2) come up with a hypothesis, (3) make a prediction, and (4) design an experiment. For example, you could summarize your dog/happiness study like this:

(1) While research suggests that dog owners are happier than cat owners, there are no reports on what factors drive this difference. (2) We hypothesized that it is the fun activities that many dog owners (but very few cat owners) engage in with their pets that increases their happiness levels. (3) We thus predicted that preventing very active dog owners from engaging in such activities for some time and making very inactive dog owners take up such activities would lead to an increase and decrease in their overall self-ratings of happiness, respectively. (4) To test this, we invited dog owners into our lab, assessed their mental and emotional well-being through questionnaires, and then assigned them to an “active” and an “inactive” group, depending on… 

Note that you use “we hypothesize” only for your hypothesis, not for your experimental prediction, and “would” or “if – then” only for your prediction, not your hypothesis. A hypothesis that states that something “would” affect something else sounds as if you don’t have enough confidence to make a clear statement—in which case you can’t expect your readers to believe in your research either. Write in the present tense, don’t use modal verbs that express varying degrees of certainty (such as may, might, or could ), and remember that you are not drawing a conclusion while trying not to exaggerate but making a clear statement that you then, in a way, try to disprove . And if that happens, that is not something to fear but an important part of the scientific process.

Similarly, don’t use “we hypothesize” when you explain the implications of your research or make predictions in the conclusion section of your manuscript, since these are clearly not hypotheses in the true sense of the word. As we said earlier, you will find that many authors of academic articles do not seem to care too much about these rather subtle distinctions, but thinking very clearly about your own research will not only help you write better but also ensure that even that infamous Reviewer 2 will find fewer reasons to nitpick about your manuscript. 

Perfect Your Manuscript With Professional Editing

Now that you know how to write a strong research hypothesis for your research paper, you might be interested in our free AI Proofreader , Wordvice AI, which finds and fixes errors in grammar, punctuation, and word choice in academic texts. Or if you are interested in human proofreading , check out our English editing services , including research paper editing and manuscript editing .

On the Wordvice academic resources website , you can also find many more articles and other resources that can help you with writing the other parts of your research paper , with making a research paper outline before you put everything together, or with writing an effective cover letter once you are ready to submit.

15 Hypothesis Examples

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

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A hypothesis is defined as a testable prediction , and is used primarily in scientific experiments as a potential or predicted outcome that scientists attempt to prove or disprove (Atkinson et al., 2021; Tan, 2022).

In my types of hypothesis article, I outlined 13 different hypotheses, including the directional hypothesis (which makes a prediction about an effect of a treatment will be positive or negative) and the associative hypothesis (which makes a prediction about the association between two variables).

This article will dive into some interesting examples of hypotheses and examine potential ways you might test each one.

Hypothesis Examples

1. “inadequate sleep decreases memory retention”.

Field: Psychology

Type: Causal Hypothesis A causal hypothesis explores the effect of one variable on another. This example posits that a lack of adequate sleep causes decreased memory retention. In other words, if you are not getting enough sleep, your ability to remember and recall information may suffer.

How to Test:

To test this hypothesis, you might devise an experiment whereby your participants are divided into two groups: one receives an average of 8 hours of sleep per night for a week, while the other gets less than the recommended sleep amount.

During this time, all participants would daily study and recall new, specific information. You’d then measure memory retention of this information for both groups using standard memory tests and compare the results.

Should the group with less sleep have statistically significant poorer memory scores, the hypothesis would be supported.

Ensuring the integrity of the experiment requires taking into account factors such as individual health differences, stress levels, and daily nutrition.

Relevant Study: Sleep loss, learning capacity and academic performance (Curcio, Ferrara & De Gennaro, 2006)

2. “Increase in Temperature Leads to Increase in Kinetic Energy”

Field: Physics

Type: Deductive Hypothesis The deductive hypothesis applies the logic of deductive reasoning – it moves from a general premise to a more specific conclusion. This specific hypothesis assumes that as temperature increases, the kinetic energy of particles also increases – that is, when you heat something up, its particles move around more rapidly.

This hypothesis could be examined by heating a gas in a controlled environment and capturing the movement of its particles as a function of temperature.

You’d gradually increase the temperature and measure the kinetic energy of the gas particles with each increment. If the kinetic energy consistently rises with the temperature, your hypothesis gets supporting evidence.

Variables such as pressure and volume of the gas would need to be held constant to ensure validity of results.

3. “Children Raised in Bilingual Homes Develop Better Cognitive Skills”

Field: Psychology/Linguistics

Type: Comparative Hypothesis The comparative hypothesis posits a difference between two or more groups based on certain variables. In this context, you might propose that children raised in bilingual homes have superior cognitive skills compared to those raised in monolingual homes.

Testing this hypothesis could involve identifying two groups of children: those raised in bilingual homes, and those raised in monolingual homes.

Cognitive skills in both groups would be evaluated using a standard cognitive ability test at different stages of development. The examination would be repeated over a significant time period for consistency.

If the group raised in bilingual homes persistently scores higher than the other, the hypothesis would thereby be supported.

The challenge for the researcher would be controlling for other variables that could impact cognitive development, such as socio-economic status, education level of parents, and parenting styles.

Relevant Study: The cognitive benefits of being bilingual (Marian & Shook, 2012)

4. “High-Fiber Diet Leads to Lower Incidences of Cardiovascular Diseases”

Field: Medicine/Nutrition

Type: Alternative Hypothesis The alternative hypothesis suggests an alternative to a null hypothesis. In this context, the implied null hypothesis could be that diet has no effect on cardiovascular health, which the alternative hypothesis contradicts by suggesting that a high-fiber diet leads to fewer instances of cardiovascular diseases.

To test this hypothesis, a longitudinal study could be conducted on two groups of participants; one adheres to a high-fiber diet, while the other follows a diet low in fiber.

After a fixed period, the cardiovascular health of participants in both groups could be analyzed and compared. If the group following a high-fiber diet has a lower number of recorded cases of cardiovascular diseases, it would provide evidence supporting the hypothesis.

Control measures should be implemented to exclude the influence of other lifestyle and genetic factors that contribute to cardiovascular health.

Relevant Study: Dietary fiber, inflammation, and cardiovascular disease (King, 2005)

5. “Gravity Influences the Directional Growth of Plants”

Field: Agronomy / Botany

Type: Explanatory Hypothesis An explanatory hypothesis attempts to explain a phenomenon. In this case, the hypothesis proposes that gravity affects how plants direct their growth – both above-ground (toward sunlight) and below-ground (towards water and other resources).

The testing could be conducted by growing plants in a rotating cylinder to create artificial gravity.

Observations on the direction of growth, over a specified period, can provide insights into the influencing factors. If plants consistently direct their growth in a manner that indicates the influence of gravitational pull, the hypothesis is substantiated.

It is crucial to ensure that other growth-influencing factors, such as light and water, are uniformly distributed so that only gravity influences the directional growth.

6. “The Implementation of Gamified Learning Improves Students’ Motivation”

Field: Education

Type: Relational Hypothesis The relational hypothesis describes the relation between two variables. Here, the hypothesis is that the implementation of gamified learning has a positive effect on the motivation of students.

To validate this proposition, two sets of classes could be compared: one that implements a learning approach with game-based elements, and another that follows a traditional learning approach.

The students’ motivation levels could be gauged by monitoring their engagement, performance, and feedback over a considerable timeframe.

If the students engaged in the gamified learning context present higher levels of motivation and achievement, the hypothesis would be supported.

Control measures ought to be put into place to account for individual differences, including prior knowledge and attitudes towards learning.

Relevant Study: Does educational gamification improve students’ motivation? (Chapman & Rich, 2018)

7. “Mathematics Anxiety Negatively Affects Performance”

Field: Educational Psychology

Type: Research Hypothesis The research hypothesis involves making a prediction that will be tested. In this case, the hypothesis proposes that a student’s anxiety about math can negatively influence their performance in math-related tasks.

To assess this hypothesis, researchers must first measure the mathematics anxiety levels of a sample of students using a validated instrument, such as the Mathematics Anxiety Rating Scale.

Then, the students’ performance in mathematics would be evaluated through standard testing. If there’s a negative correlation between the levels of math anxiety and math performance (meaning as anxiety increases, performance decreases), the hypothesis would be supported.

It would be crucial to control for relevant factors such as overall academic performance and previous mathematical achievement.

8. “Disruption of Natural Sleep Cycle Impairs Worker Productivity”

Field: Organizational Psychology

Type: Operational Hypothesis The operational hypothesis involves defining the variables in measurable terms. In this example, the hypothesis posits that disrupting the natural sleep cycle, for instance through shift work or irregular working hours, can lessen productivity among workers.

To test this hypothesis, you could collect data from workers who maintain regular working hours and those with irregular schedules.

Measuring productivity could involve examining the worker’s ability to complete tasks, the quality of their work, and their efficiency.

If workers with interrupted sleep cycles demonstrate lower productivity compared to those with regular sleep patterns, it would lend support to the hypothesis.

Consideration should be given to potential confounding variables such as job type, worker age, and overall health.

9. “Regular Physical Activity Reduces the Risk of Depression”

Field: Health Psychology

Type: Predictive Hypothesis A predictive hypothesis involves making a prediction about the outcome of a study based on the observed relationship between variables. In this case, it is hypothesized that individuals who engage in regular physical activity are less likely to suffer from depression.

Longitudinal studies would suit to test this hypothesis, tracking participants’ levels of physical activity and their mental health status over time.

The level of physical activity could be self-reported or monitored, while mental health status could be assessed using standard diagnostic tools or surveys.

If data analysis shows that participants maintaining regular physical activity have a lower incidence of depression, this would endorse the hypothesis.

However, care should be taken to control other lifestyle and behavioral factors that could intervene with the results.

Relevant Study: Regular physical exercise and its association with depression (Kim, 2022)

10. “Regular Meditation Enhances Emotional Stability”

Type: Empirical Hypothesis In the empirical hypothesis, predictions are based on amassed empirical evidence . This particular hypothesis theorizes that frequent meditation leads to improved emotional stability, resonating with numerous studies linking meditation to a variety of psychological benefits.

Earlier studies reported some correlations, but to test this hypothesis directly, you’d organize an experiment where one group meditates regularly over a set period while a control group doesn’t.

Both groups’ emotional stability levels would be measured at the start and end of the experiment using a validated emotional stability assessment.

If regular meditators display noticeable improvements in emotional stability compared to the control group, the hypothesis gains credit.

You’d have to ensure a similar emotional baseline for all participants at the start to avoid skewed results.

11. “Children Exposed to Reading at an Early Age Show Superior Academic Progress”

Type: Directional Hypothesis The directional hypothesis predicts the direction of an expected relationship between variables. Here, the hypothesis anticipates that early exposure to reading positively affects a child’s academic advancement.

A longitudinal study tracking children’s reading habits from an early age and their consequent academic performance could validate this hypothesis.

Parents could report their children’s exposure to reading at home, while standardized school exam results would provide a measure of academic achievement.

If the children exposed to early reading consistently perform better acadically, it gives weight to the hypothesis.

However, it would be important to control for variables that might impact academic performance, such as socioeconomic background, parental education level, and school quality.

12. “Adopting Energy-efficient Technologies Reduces Carbon Footprint of Industries”

Field: Environmental Science

Type: Descriptive Hypothesis A descriptive hypothesis predicts the existence of an association or pattern related to variables. In this scenario, the hypothesis suggests that industries adopting energy-efficient technologies will resultantly show a reduced carbon footprint.

Global industries making use of energy-efficient technologies could track their carbon emissions over time. At the same time, others not implementing such technologies continue their regular tracking.

After a defined time, the carbon emission data of both groups could be compared. If industries that adopted energy-efficient technologies demonstrate a notable reduction in their carbon footprints, the hypothesis would hold strong.

In the experiment, you would exclude variations brought by factors such as industry type, size, and location.

13. “Reduced Screen Time Improves Sleep Quality”

Type: Simple Hypothesis The simple hypothesis is a prediction about the relationship between two variables, excluding any other variables from consideration. This example posits that by reducing time spent on devices like smartphones and computers, an individual should experience improved sleep quality.

A sample group would need to reduce their daily screen time for a pre-determined period. Sleep quality before and after the reduction could be measured using self-report sleep diaries and objective measures like actigraphy, monitoring movement and wakefulness during sleep.

If the data shows that sleep quality improved post the screen time reduction, the hypothesis would be validated.

Other aspects affecting sleep quality, like caffeine intake, should be controlled during the experiment.

Relevant Study: Screen time use impacts low‐income preschool children’s sleep quality, tiredness, and ability to fall asleep (Waller et al., 2021)

14. Engaging in Brain-Training Games Improves Cognitive Functioning in Elderly

Field: Gerontology

Type: Inductive Hypothesis Inductive hypotheses are based on observations leading to broader generalizations and theories. In this context, the hypothesis deduces from observed instances that engaging in brain-training games can help improve cognitive functioning in the elderly.

A longitudinal study could be conducted where an experimental group of elderly people partakes in regular brain-training games.

Their cognitive functioning could be assessed at the start of the study and at regular intervals using standard neuropsychological tests.

If the group engaging in brain-training games shows better cognitive functioning scores over time compared to a control group not playing these games, the hypothesis would be supported.

15. Farming Practices Influence Soil Erosion Rates

Type: Null Hypothesis A null hypothesis is a negative statement assuming no relationship or difference between variables. The hypothesis in this context asserts there’s no effect of different farming practices on the rates of soil erosion.

Comparing soil erosion rates in areas with different farming practices over a considerable timeframe could help test this hypothesis.

If, statistically, the farming practices do not lead to differences in soil erosion rates, the null hypothesis is accepted.

However, if marked variation appears, the null hypothesis is rejected, meaning farming practices do influence soil erosion rates. It would be crucial to control for external factors like weather, soil type, and natural vegetation.

The variety of hypotheses mentioned above underscores the diversity of research constructs inherent in different fields, each with its unique purpose and way of testing.

While researchers may develop hypotheses primarily as tools to define and narrow the focus of the study, these hypotheses also serve as valuable guiding forces for the data collection and analysis procedures, making the research process more efficient and direction-focused.

Hypotheses serve as a compass for any form of academic research. The diverse examples provided, from Psychology to Educational Studies, Environmental Science to Gerontology, clearly demonstrate how certain hypotheses suit specific fields more aptly than others.

It is important to underline that although these varied hypotheses differ in their structure and methods of testing, each endorses the fundamental value of empiricism in research. Evidence-based decision making remains at the heart of scholarly inquiry, regardless of the research field, thus aligning all hypotheses to the core purpose of scientific investigation.

Testing hypotheses is an essential part of the scientific method . By doing so, researchers can either confirm their predictions, giving further validity to an existing theory, or they might uncover new insights that could potentially shift the field’s understanding of a particular phenomenon. In either case, hypotheses serve as the stepping stones for scientific exploration and discovery.

Atkinson, P., Delamont, S., Cernat, A., Sakshaug, J. W., & Williams, R. A. (2021).  SAGE research methods foundations . SAGE Publications Ltd.

Curcio, G., Ferrara, M., & De Gennaro, L. (2006). Sleep loss, learning capacity and academic performance.  Sleep medicine reviews ,  10 (5), 323-337.

Kim, J. H. (2022). Regular physical exercise and its association with depression: A population-based study short title: Exercise and depression.  Psychiatry Research ,  309 , 114406.

King, D. E. (2005). Dietary fiber, inflammation, and cardiovascular disease.  Molecular nutrition & food research ,  49 (6), 594-600.

Marian, V., & Shook, A. (2012, September). The cognitive benefits of being bilingual. In Cerebrum: the Dana forum on brain science (Vol. 2012). Dana Foundation.

Tan, W. C. K. (2022). Research Methods: A Practical Guide For Students And Researchers (Second Edition) . World Scientific Publishing Company.

Waller, N. A., Zhang, N., Cocci, A. H., D’Agostino, C., Wesolek‐Greenson, S., Wheelock, K., … & Resnicow, K. (2021). Screen time use impacts low‐income preschool children’s sleep quality, tiredness, and ability to fall asleep. Child: care, health and development, 47 (5), 618-626.

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7 Types of Research Hypothesis: Examples, Significance and Step-By-Step Guide

Introduction.

In any research study, a research hypothesis plays a crucial role in guiding the investigation and providing a clear direction for the research. It is an essential component of a thesis as it helps to frame the research question and determine the methodology to be used.

This article will provide a detailed analysis of research hypotheses in a thesis, highlighting their significance and qualities. It will also explore different types of research hypotheses and provide illustrative examples. Additionally, a step-by-step guide to developing research hypotheses and methods for testing and validating them will be discussed. By the end of this article, readers will have a comprehensive understanding of research hypotheses and their role in a thesis.

Understanding Research Hypotheses in a Thesis

A research hypothesis is a statement of expectation or prediction that will be tested by research. In a thesis, a research hypothesis is formulated to address the research question or problem statement . It serves as a tentative answer or explanation to the research question. The research hypothesis guides the direction of the study and helps in determining the research design and methodology.

The research hypothesis is typically based on existing theories, previous research findings, or observations. It is formulated after a thorough review of the literature and understanding of the research area. A well-defined research hypothesis provides a clear focus for the study and helps in generating testable predictions. By testing the research hypothesis, researchers aim to gather evidence to support or reject the hypothesis. This process contributes to the advancement of knowledge in the field and helps in drawing meaningful conclusions.

Significance of Research Hypotheses in a Thesis

One of the key significance of research hypotheses is that they help in organizing and structuring the research study. By formulating a hypothesis, the researcher defines the specific research question and identifies the variables that will be investigated. This helps in narrowing down the scope of the study and ensures that the research is focused and targeted.

Moreover, research hypotheses provide a framework for data collection and analysis. They guide the researcher in selecting appropriate research methods , tools, and techniques to gather relevant data. The hypotheses also help in determining the statistical tests and analysis techniques that will be used to analyze the collected data.

Another significance of research hypotheses is that they contribute to the advancement of knowledge in a particular field. By formulating hypotheses and conducting research to test them, researchers are able to generate new insights, theories, and explanations. This contributes to the existing body of knowledge and helps in expanding the understanding of a specific phenomenon or topic.

Furthermore, research hypotheses are important for establishing the validity and reliability of the research findings. By formulating clear and testable hypotheses, researchers can ensure that their study is based on sound scientific principles. The hypotheses provide a basis for evaluating the accuracy and generalizability of the research results.

In addition, research hypotheses are essential for making informed decisions and recommendations based on the research findings. They help in drawing conclusions and making predictions about the relationship between variables. This information can be used to inform policy decisions, develop interventions, or guide future research in the field.

Qualities of an Effective Research Hypothesis in a Thesis

An effective research hypothesis in a thesis possesses several key qualities that contribute to its strength and validity. These qualities are essential for ensuring that the hypothesis can be tested and validated through empirical research. The following are some of the qualities that make a research hypothesis effective:

1. Specificity: A good research hypothesis is specific and clearly defines the variables and the relationship between them. It provides a clear direction for the research and allows for precise testing of the hypothesis.

2. Testability: An effective hypothesis in research is testable, meaning that it can be empirically examined and either supported or refuted through data analysis. It should be possible to design experiments or collect data that can provide evidence for or against the hypothesis.

3. Clarity: A research hypothesis should be written in clear and concise language. It should avoid ambiguity and ensure that the intended meaning is easily understood by the readers. Clear language helps in communicating the hypothesis effectively and facilitates its evaluation.

4. Falsifiability: A strong research hypothesis is falsifiable, which means that it is possible to prove it wrong. It should be formulated in a way that allows for the possibility of obtaining evidence that contradicts the hypothesis. This is important for the scientific process as it encourages critical thinking and the exploration of alternative explanations.

5. Relevance: An effective research hypothesis is relevant to the research question and the overall objectives of the study. It should address a significant gap in knowledge or contribute to the existing body of literature. A relevant hypothesis adds value to the research and increases its significance.

6. Novelty: A good research hypothesis is original and innovative. It should propose a new idea or approach that has not been extensively explored before. Novelty in the hypothesis increases the potential for new discoveries and contributes to the advancement of knowledge in the field.

7. Coherence: An effective research hypothesis should be coherent and consistent with existing theories, concepts, and empirical evidence. It should align with the current understanding of the topic and build upon previous research. Coherence ensures that the hypothesis is grounded in a solid foundation and enhances its credibility.

8. Measurability: A research hypothesis should be measurable, meaning that it can be quantitatively or qualitatively assessed. It should be possible to collect data or evidence that can be used to evaluate the hypothesis. Measurability allows for objective testing and increases the reliability of the research findings.

By incorporating these qualities into the formulation of a research hypothesis, researchers can enhance the validity and reliability of their study.

Different Types of Research Hypotheses in a Thesis

In a thesis, there are several different types of research hypotheses that can be used to test the relationship between variables. These hypotheses provide a framework for the research and guide the direction of the study. Understanding the different types of research hypotheses is essential for conducting a comprehensive and effective thesis.

Null Hypothesis

The null hypothesis is a statement that suggests there is no significant relationship between the variables being studied. It assumes that any observed differences or relationships are due to chance or random variation. The null hypothesis is denoted as H0 and is often used as a starting point for hypothesis testing.

Alternative Hypothesis

The alternative hypothesis, also known as the research hypothesis, is a statement that suggests there is a significant relationship between the variables being studied. It contradicts the null hypothesis and proposes that the observed differences or relationships are not due to chance.

Directional Hypothesis

A directional hypothesis is a specific type of alternative hypothesis that predicts the direction of the relationship between variables. It states that there is a positive or negative relationship between the variables, indicating the direction of the effect.

Non-Directional Hypothesis

In contrast to a directional hypothesis, a non-directional hypothesis does not predict the direction of the relationship between variables. It simply states that there is a relationship between the variables without specifying the direction of the effect.

Statistical Hypothesis

A statistical hypothesis is a hypothesis that is formulated based on statistical analysis. It involves using statistical tests to determine the likelihood of the observed data occurring under the null hypothesis.

Associative Hypothesis

An associative hypothesis suggests that there is a relationship between variables, but it does not imply causation. It indicates that changes in one variable are associated with changes in another variable.

Causal Hypothesis

A causal hypothesis proposes a cause-and-effect relationship between variables. It suggests that changes in one variable directly cause changes in another variable.

These different types of research hypotheses provide researchers with various options to explore and test the relationships between variables in a thesis. The choice of hypothesis depends on the research question, the nature of the variables, and the available data.

Illustrative Examples of Research Hypotheses in a Thesis

To better understand research hypotheses in a thesis, let’s explore some illustrative examples. These examples will demonstrate how hypotheses are formulated and tested in different research studies.

Example 1: Hypothesis for a study on the effects of exercise on weight loss:

Null Hypothesis (H0): There is no significant difference in weight loss between individuals who engage in regular exercise and those who do not.

Alternative Hypothesis (H1): Individuals who engage in regular exercise will experience greater weight loss compared to those who do not exercise.

Example 2: Hypothesis for a study on the impact of social media on self-esteem:

Null Hypothesis (H0): There is no significant relationship between social media usage and self-esteem levels.

Alternative Hypothesis (H1): Increased social media usage is associated with lower self-esteem levels.

Example 3: Hypothesis for a study on the effectiveness of a new teaching method in improving student performance:

Null Hypothesis (H0): There is no significant difference in student performance between the traditional teaching method and the new teaching method.

Alternative Hypothesis (H1): The new teaching method leads to improved student performance compared to the traditional teaching method.

These examples highlight the structure of research hypotheses, where the null hypothesis represents no effect or relationship, while the alternative hypothesis suggests the presence of an effect or relationship. It is important to note that these hypotheses are testable and can be analyzed using appropriate statistical methods.

Step-by-Step Guide to Developing Research Hypotheses in a Thesis

Developing a research hypothesis is a crucial step in the process of conducting a thesis. In this section, we will provide a step-by-step guide to developing research hypotheses in a thesis.

Step 1: Identify the Research Topic

The first step in developing a research hypothesis is to clearly identify the research topic. This involves understanding the research problem and determining the specific area of study.

Step 2: Conduct Preliminary Research

Once the research topic is identified, it is important to conduct preliminary research to gather relevant information. This helps in understanding the existing knowledge and identifying any gaps or areas that need further investigation.

Step 3: Formulate the Research Question

Based on the preliminary research, formulate a clear and concise research question. The research question should be specific and focused, addressing the research problem identified in step 1.

Step 4: Define the Variables

Identify the variables that will be studied in the research. Variables are the factors or concepts that are being measured or manipulated in the study. It is important to clearly define the variables to ensure the research hypothesis is specific and testable.

Step 5: Predict the Relationship and Outcome

The research hypothesis should propose a link between the variables and predict the expected outcome. It should clearly state the expected relationship between the variables and the anticipated result.

Step 6: Ensure Clarity and Conciseness

A good research hypothesis should be simple and concise, avoiding wordiness. It should be clear and free from ambiguity or assumptions about the readers’ knowledge. The hypothesis should also be observable and measurable.

Step 7: Validate the Hypothesis

Before finalizing the research hypothesis, it is important to validate it. This can be done through further research, literature review , or consultation with experts in the field. Validating the hypothesis ensures its relevance and novelty.

By following these step-by-step guidelines, researchers can develop effective research hypotheses for their theses. A well-developed hypothesis provides a solid foundation for the research and helps in generating meaningful results.

Methods for Testing and Validating Research Hypotheses in a Thesis

Hypothesis testing is a formal procedure for investigating our ideas about the world. It allows you to statistically test your predictions. The usual process is to make a hypothesis, create an experiment to test it, run the experiment, draw a conclusion, and then allow other researchers to replicate the study to validate the findings. There are several methods for testing and validating research hypotheses in a thesis.

Experimental Research

One common method is experimental research, where researchers manipulate variables and measure their effects on the dependent variable.

Observational Research

Another method is observational research, where researchers observe and record data without manipulating variables. This method is often used when it is not feasible or ethical to conduct experiments.

Survey Research

Survey research is another method that involves collecting data from a sample of individuals using questionnaires or interviews . This method is useful for studying attitudes, opinions, and behaviors.

Conducting Meta-analysis

In addition to these methods, researchers can also use existing data or conduct meta-analyses to test and validate research hypotheses. Existing data can be obtained from sources such as government databases, previous studies, or publicly available datasets. Meta-analysis involves combining the results of multiple studies to determine the overall effect size and to test the generalizability of findings across different populations and contexts. Once the data is collected, researchers can use statistical analysis techniques to analyze the data and test the research hypotheses. Common statistical tests include t-tests, analysis of variance (ANOVA), regression analysis, and chi-square tests.

The choice of statistical test depends on the research design, the type of data collected, and the specific research hypotheses being tested. It is important to note that testing and validating research hypotheses is an iterative process. Researchers may need to refine their hypotheses, modify their research design, or collect additional data based on the initial findings. By using rigorous methods for testing and validating research hypotheses, researchers can ensure the reliability and validity of their findings, contributing to the advancement of knowledge in their field.

In conclusion, research hypotheses are essential components of a thesis that guide the research process and contribute to the advancement of knowledge in a particular field. By formulating clear and testable hypotheses, researchers can make meaningful contributions to their field and address important research questions. It is important for researchers to carefully develop and validate their hypotheses to ensure the credibility and reliability of their findings.

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Hypothesis: Basic Research Guidelines & Examples

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A hypothesis refers to a simple statement that predicts the findings of a research study. Basically, researchers develop propositions to provide tentative answers to research questions that address different aspects of a study objective. In writing, a scholar must use existing theories and knowledge to create a valid assumption. Besides, a researcher focuses on testing supposed claims through different methods, like experiments, observations, and statistical analysis of obtained data. In practice, the findings from a study can either support or refute a premise under examination. Then, when writing a suggestion, scholars should conduct adequate research on a specific topic, brainstorm for ideas, draft an assertion, revise a draft claim, and write a final sentence in simple language. Moreover, these steps lead to a valid development of accurate and precise propositions that identify relationships between independent and dependent variables. In practice, one should rely on a cause-and-effect theory when developing a hypothesis.

General Aspects

A good hypothesis suggests a sentence as a statement that gives a particular prediction about the findings of a research study. Basically, people make a specific hypothesis, which acts as a tentative answer to a research question. However, a proposition may lack scientific or scholarly proof. Then, a reasonable claim must address different aspects of a question under analysis. In writing, people must base their propositions on existing theories and knowledge. Besides, such a statement has to be testable through various methods, like experiments, observations, and statistical analysis. In practice, the findings from a study can either support or refute a working thesis. Therefore, writing a study assumption refers to a simple and clear statement that tries to predict the results of research.

What Is a Hypothesis and Its Purpose

According to its definition, a hypothesis is a testable statement or prediction about a specific phenomenon or a relationship between two or more variables, forming a unique basis for scientific investigation. In principle, such a statement is formulated based on observations, existing knowledge, and theoretical frameworks. For example, the main purpose of writing a hypothesis is to establish a specific direction for a particular study, enabling researchers to design experiments and collect data in a structured manner (Reichardt, 2022). Moreover, by testing a defined assertion through experimentation and analysis, people can determine whether their predictions hold true, contributing to a broader understanding of a discussed topic. This process of hypothesis testing is fundamental to a scientific method, as it allows for a particular validation, refinement, or rejection of theoretical concepts (Dillard & Flenner, 2021). In turn, the length of a hypothesis depends on academic levels and scopes of research, while general writing guidelines are:

High School

• Length: 1 sentence
• Word Count: 10-15 words
• Detail: A simple, clear, and testable statement about a specific relationship between variables.
• Example: “If plants are watered with different types of liquids, then the growth rate will vary.”

College (Undergraduate)

• Word Count: 15-30 words
• Detail: More detailed, specifying defined variables and expected outcomes with writing some contextual background.
• Example: “Students who study in a quiet environment will perform better on exams than those who study in a noisy environment due to fewer distractions and improved concentration.”

University (Advanced Undergraduate or Honors Thesis)

• Word Count: 20-35 words
• Detail: Includes specific variables, a rationale based on preliminary research, and a clear expected outcome.
• Example: “Exposure to natural light in the workplace will increase employee productivity compared to artificial lighting, as natural light has been shown to improve mood and energy levels.”

Master’s Thesis

• Length: 1-2 sentences
• Word Count: 25-40 words
• Detail: Detailed and precise writing, including variables, expected relationship, and grounding in existing literature or theoretical framework.
• Example: “Implementing a flipped classroom model in undergraduate biology courses will result in higher student engagement and academic performance, as this model promotes active learning and individualized instruction, which have been positively correlated with student outcomes in previous studies.”

Ph.D. Dissertation

• Length: 2-4 sentences (or more, if necessary)
• Word Count: 30-70+ words
• Detail: Highly detailed, specifying complex relationships between multiple variables, grounded in extensive literature review and theoretical framework, with writing about clear and expected outcomes.
• Example: “Incorporating machine learning algorithms into predictive models for climate change will significantly improve an overall accuracy of long-term weather forecasts. This assumption is based on a premise that machine learning can identify innovative patterns in large datasets that traditional statistical methods may miss, thus providing more reliable predictions of climatic phenomena.”

Note: Some writing components of a hypothesis can be added, deleted, or combined with each other, and such a statement is usually 1 sentence long. For example, the three main parts of a hypothesis statement are an independent variable, a dependent variable, and a predicted relationship between them (Lund, 2021). In a research paper, a standard hypothesis is typically found in an introduction section, where such a statement outlines an expected relationship between variables and sets a particular stage for an entire study. Further on, a hypothesis is a testable prediction about a unique relationship between variables, while a research question is a broad query that guides an entire investigation into a specific topic (Misra et al., 2021). Moreover, there is a direct relationship between a hypothesis and research objectives, as the former provides a specific, testable prediction that aligns with and helps to achieve broader goals outlined by the latter. In writing, a basic checklist to evaluate an overall effectiveness of any hypothesis includes ensuring a research assertion is a clear, specific, and testable statement that is based on existing knowledge and covers both independent and dependent variables (Rubin & Donkin, 2022). Finally, to start a hypothesis, people begin by writing an “If” statement that clearly identifies an independent variable, followed by a “then” statement predicting a specific outcome or effect on a dependent variable.

Independent and Dependent Variables

A hypothesis in some studies must contain independent and dependent variables. Basically, hypothesis testing is a statistical method that people use to determine a specific connection between suggestions and their alternative outcomes to understand what is true or not and write about them. For example. experimental and correlational studies examine relationships between two or more variables (Sharang, 2020). In turn, independent elements refer to factors people can control or change. Besides, this aspect refers to factors scholars observe or measure for their writing. Then, a null hypothesis of experimental and correlational studies must predict relationships between dependent and independent variables. Moreover, such predictions should not be guesses but should contain evidence from research studies.

There are different types of hypotheses people can develop for writing their studies. In this case, common types of hypotheses include:

• A simple hypothesis refers to predictions of relationships between independent and dependent variables.
• A complex hypothesis predicts relationships between two or more independent and dependent variables.
• An empirical hypothesis is a working prediction that exists when a person tests a specific theory by using observations and experiments. Basically, this type of assertion goes through some trial and error methods to obtain the necessary findings and write about them. In some instances, people may change some aspects around other elements.
• A null hypothesis , denoted as H 0 , exists when a person believes a relationship does not exist between independent and dependent variables. Basically, this statement may exist when an individual lacks adequate information to make a scientific prediction. Besides, inferences made from the findings attempt to disapprove or discredit a null theory.
• An alternative hypothesis , denoted as H 1 , attempts to disapprove a null proposition. In this case, people attempt to discover or affirm an alternative proposition.
• A logical hypothesis refers to a proposed explanation of a concept that contains limited evidence. In writing, investigators intend to turn a reasonable assumption into an empirical claim. Besides, they put theories or postulate them to a particular testing process.
• A statistical hypothesis is a claim related to studies that examine a section of a specific population. In this case, people identify a sample population and study their behaviors related to a given research question. 

Steps on How to Write a Good Hypothesis

To write a good hypothesis, people clearly define specific independent and dependent variables and formulate a testable prediction about a particular relationship between them, often structured as an “If [independent variable], then [dependent variable]” statement. As such, researchers should focus on developing and writing reasonable assertation statements for their studies. For example, one should consider different factors that relate to existing studies or theories (Sharang, 2020). In writing, some predictions should pertain to research data and provide tentative answers to study questions. Hence, the following are essential writing steps a person should consider when developing a proposition.

Step 1: Researching

A first step in developing a hypothesis is to research and gather details related to writing an intended topic. Basically, researching allows a scholar to gain more knowledge concerning issues and factors and how variables change. For example, to form a hypothesis sentence, people start wording by identifying independent and dependent variables, reviewing existing literature, and then creating a clear, testable prediction that outlines an expected relationship between defined elements (Reichardt, 2022). Besides, this step will enable people to become familiar with the expected results. As a result, an entire writing process influences a relevant theory’s development.

Step 2: Asking Questions

A person should develop research questions before developing a main claim. For instance, investigators should create scientific questions that relate to studied and identified elements (Dillard & Flenner, 2021). In writing, brainstorming enhances a particular ability to determine relationships between independent and dependent variables. Basically, successful scholars remain focused on writing about one cause-and-effect theory to ensure they develop accurate ideas for a prediction. Therefore, a second writing step in developing a proposition is to brainstorm questions that reveal a specific relationship between independent and dependent elements. 

Step 3: Use Clear Language

Scholars should use simple and clear language when developing any suggestion for writing a study. For instance, one should draft concise predictions that answer developed research questions (Sharang, 2020). In practice, one should write a hypothesis in a particular form of a direct proposition that an action leads to a specific result. Futher on, the three main words that should be in a hypothesis statement are “if,” “then,” and “because.” Moreover, a person should not state a supposition as a question but as an affirmative statement that predicts outcomes from a particular course of action. Therefore, a third step in developing a new theory involves selecting a simple language for writing scientific predictions. 

Step 4. Revising a Statement

A scholar should revise a draft hypothesis to ensure writing any prediction makes a testable thesis through research and experimentation. For instance, a person should review a prediction to ensure such a sentence captures relationships between at least two elements (Dillard & Flenner, 2021). Hence, a scholar must revise a drafted proposition to ensure this statement captures a testable relationship between independent and dependent variables. In writing, some examples of sentence starters for beginning a hypothesis statement are:

• If [independent variable] is introduced or modified, then we anticipate [dependent variable] will exhibit a measurable change in terms of … .
• It is hypothesized that a particular presence or alteration of [independent element] will significantly affect [dependent element] by causing … .
• We predict that variations in [independent aspect] will result in corresponding changes in [dependent aspect], specifically in key aspects of … .
• A formulated assumption posits that altering [independent variable] will lead to observable differences in [dependent variable], particularly in relation to … .
• Based on existing theories and previous research, it is expected that modifying [independent element] will impact [dependent element] by … .
• We hypothesize an increase or decrease in [independent aspect], which will have a direct influence on [dependent aspect], leading to … .
• It is proposed that a particular manipulation of [independent variable] will result in [specific outcome] within [dependent variable] due to a specific mechanism of … .
• If [independent element] is systematically varied, then [dependent element] will demonstrate a change characterized by … .
• A current premise suggests that specific changes in [independent aspect] will cause predictable alterations in [dependent aspect], which can be measured by … .
• We expect that, by introducing [independent variable], there will be a significant impact on [dependent variable], as evidenced by changes in … .

• Research question – How does divorce affect sociological development among young children?
• H 0 – Challenges that lead to divorce hurt young children’s social development, which affects their ability to interact with other people. 
• H 1 – Most children manage to cope with domestic challenges that lead to divorce, enabling them to realize healthy sociological development.
• Research question – How did tenebrism influence baroque art during the 16 th and 17 th centuries?
• H 0 – A particular origin of tenebrism had a positive impact on a dynamic appearance of baroque art.
• H 1 – Baroque art emerged as a unique art that did not have any form of external influence.
• Research question – To what extent does geological activity affect the Earth?
• H 0 – A specific movement of tectonic plates beneath the Earth’s surface results in volcanic eruptions and faults that lead to mountains and lift valleys.  
• H 1 – Mountains and valleys are natural features with little connection with geological activities like a particular movement of tectonic plates beneath the Earth’s surface.
• Research question – Do animals have rights and welfare in society?
• H 0 – Wild and domestic animals are living creatures with a right to care and protection by humans.
• H 1 – Wild and domestic animals are subordinate to humans, which implies they do not have a right to care and protection.  
• Research question – Does a specific consumption of genetically modified plants cause health complications in humans?
• H 0 – Genetically modified foods are safe for human consumption and do not pose any possible health risks.
• H 1 – Genetically modified foods interfere with healthy cell development, which leads to health complications.

Indigenous Studies

• Research question – What role does culture play among Indigenous communities?
• H 0 – Cultural practices among Aboriginals promote their identity and contribute to the members’ overall well-being.
• H 1 – cultural practices among Aboriginals do not significantly contribute to an overall quality of their lives.
• Research question – Does fascism exist in the twenty-first century?
• H 0 – Established forms of democracy in the twenty-first century do not allow political leaders to implement all the fascism elements.
• H 1 – Some political leaders in the twenty-first century adopt radical policies that promote a particular existence of fascism.
• Research question – Do neutrons have mass?
• H 0 – Neutrons are small particles that have masses.
• H 1 – Neutrons are small particles whose weight remains insignificant.

Health Studies

• Research question – How do evidence-based treatment approaches enhance an overall quality of current treatments?
• H 0 – Evidence-based treatment methods allow doctors to gather adequate and accurate information about patients, which helps them to tailor treatment and care approaches to meet people’s needs.
• H 1 – Evidence-based approaches do not enhance an overall quality of current treatments since they lead to inconsistency in the care and medications given to a patient.

Environmental Studies

• Research question – To what extent do human activities contribute to global warming?
• H 0 – Most human activities release greenhouse gases into the atmosphere, which results in a particular rise in average temperatures.
• H 1 – Most human activities release insignificant amounts of greenhouse gases into the atmosphere, contributing to global warming.

What to Include

Common Mistakes

• Being Too Vague: A hypothesis statement must be specific and clearly define corresponding variables and expected outcomes.
• Not Being Testable: A prediction should be formulated in a way that can be empirically tested through experiments or observations.
• Lack of Clarity: Avoid writing in ambiguous language since a scientific assertion should be clear and straightforward.
• Being Too Complex: Keep a statement focused on a single relationship between variables to avoid confusion.
• Ignoring Prior Research: Writing a good premise is based on existing knowledge and theories, while ignoring these concepts can lead to redundant or invalid studies.
• Using Subjective Terms: Avoid writing terms that are open to interpretation because any prediction should be objective and measurable.
• Making Assumptions: Do not assume outcomes without evidence since any assertion should be based on logical reasoning.
• Not Aligning With a Research Question: Ensure a formulated prediction directly addresses a study question posed.
• Being Too Broad: Writing a hypothesis statement should be narrow enough to be manageable within a specific scope of research.
• Neglecting to Include Variables: Clearly identify and define both independent and dependent variables in a given assertion.

Writing Tips

In its simple definition, a basic hypothesis gives a specific prediction about the findings of a research paper or study. Basically, people develop scientific predictions to provide tentative answers to study questions (Reichardt, 2022). In turn, some of the factors one must consider when writing an assumption statement include:

• conduct adequate research on a specific topic;
• brainstorm for ideas;
• draft a statement;
• revise a draft proposition;
• write a final assertion in simple language.

A hypothesis is a statement predicting a specific outcome of a research study, which is based on existing theories, literature, and knowledge. Basically, writing such a statement includes independent and dependent variables and must be testable through experiments, observations, or statistical analysis. Further on, common types of hypotheses include simple, complex, empirical, null, alternative, logical, and statistical writing formats. To develop a good hypothesis, one should research a specific topic, ask relevant questions, use clear language, and revise a formulated statement to ensure its writing captures a direct relationship between variables. Finally, accurate assumptions help in identifying cause-and-effect relationships in research.

Dillard, A., & Flenner, J. (2021). Crush hypothesis testing . Happy Hypotenuse Publishing.

Lund, T. (2021). Research problems and hypotheses in empirical research. Scandinavian Journal of Educational Research , 66 (7), 1183–1193. https://doi.org/10.1080/00313831.2021.1982765

Misra, D. P., Gasparyan, A. Y., Zimba, O., Yessirkepov, M., Agarwal, V., & Kitas, G. D. (2021). Formulating hypotheses for different study designs. Journal of Korean Medical Science , 36 (50), 1–9. https://doi.org/10.3346/jkms.2021.36.e338

Reichardt, C. S. (2022). The method of multiple hypotheses: A guide for professional and academic researchers . Routledge, Taylor & Francis Group.

Rubin, M., & Donkin, C. (2022). Exploratory hypothesis tests can be more compelling than confirmatory hypothesis tests. Philosophical Psychology , 1–29. https://doi.org/10.1080/09515089.2022.2113771

Sharang, S. (2020). Research methodology techniques: Understanding how to write, present and defend any research report . Stephen Sharang.

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15 Examples of Hypothesis to Inform Your Research Project

by  Antony W

August 5, 2024

What first comes to your mind when someone mentions the word hypothesis? For many students, terms such as prediction, dependent variables, and independent variables come to mind.

Primarily, a hypothesis is a statement derived from a research question, subject to debate, and can be proven or disapproved based on scientific research methods such as objective   observations, lab experiments, and statistical analysis.

A hypothesis predicts an outcome based on evidence, knowledge, or theories and it forms the initial point of an investigation.

You already know how to write a hypothesis .

You also know about hypothesis vs research question .

If you haven’t looked at the two in detail, we suggest that you look at the two posts for more insights.

In this lesson, we’ll look at some examples of hypothesis to help you understand how you can formulate your own.

Let’s get started.

Can You Prove a Hypothesis?

Credit: CrazyEgg

Since a hypothesis is an assumption of an expected result from a scientific experiment, you can’t prove it to be correct.

You can only reject or support it depending on the results that you get from the experiment.

It’s important to avoid references that try to prove a theory with 100% certainty when formulating a hypothesis because there may exist solid evidence that refutes the theory.

What’s the Purpose of a Hypothesis?

Credit: PublicHealthNotes

A hypothesis describes a research study in correct terms and provides a basis that you can use to evaluate and prove the validity or invalidity of a specific research.

Because hypothesis helps to analyze the scientific validity of research methodologies, researchers can assume an almost accurate probability of the progress of failure of a research.

Moreover, it’s only by formulating a hypothesis that a researcher can easily establish a relationship between a theory and a research question.

Example of Hypothesis

Credit: Study.com

To make things easier for you, we’ll give you examples for each type of hypothesis. So whether you’re struggling to formulate a concrete hypothesis or you need some ideas to add to your checklist, this guide is for you.

1. Simple Hypothesis

The hypothesis predicts the outcome between an independent (cause) and a dependent variable (effect).

• Getting 6 to 8 hours of sleep can improve a student’s alertness in class
• Excessive consumption of alcohol can cause liver disease
• Smoking cigarette can cause lung cancer
• Drinking a lot of sugary beverages can cause obesity

2. Complex Hypothesis

A complex hypothesis gives a relationship between two or more independent and dependent variables.

• Obese persons who continue to eat oily foods are likely to accumulate high cholesterol and develop heart complications
• Individuals who live in cities and smoke have a higher chance of developing respiratory disease and suffer from cancer
• Overweight adults who want to live long are more likely to lose weight

3. Directional Hypothesis

This kind of a hypothesis gives a researcher or student the direction he or she should follow to determine the relationship between a dependent and an independent variable.

• Boys perform better than girls in school
• The prediction that health decreases as stress decreases

4. Non-directional Hypothesis

It’s the opposite of a directional hypothesis, which means it doesn’t show the nature of the relationship between dependent and independent variables.

• The likelihood that there will be a difference between the performance of boys and girls

5. Associative and Causal Hypothesis

An associative and causal hypothesis uses statistical information to analyze a sample population from a specific area.

• 13% of the US population are poor
• The current rate of divorce in the US stands at the rate of 80% because of irreconcilable differences
• Nearly 40% of the Savannah population lives past the age of 60

6. Null Hypothesis

A null hypothesis exists where there’s no relationship between two variable. A researcher can also formulate a null hypothesis if they don’t have the information to state a scientific hypothesis.

• There is no significant change in an individual’s work habit if they get more than 6 hours of sleep
• There’s no significant change in health status if you drink root beer
• Age doesn’t have an effect on someone’s ability to write Math assignments

7. Alternative Hypothesis

Researchers use an alternative hypothesis (H1) to try to disprove the null hypothesis (H0). In other words, they try to come up with a reasonable alternative that they can use in the place of th null hypothesis.

• Your health can increase if you drink green tea instead of root beer
• Your work habits can improve if you get six hours of sleep instead of nine
• You can improve the growth of plant if you use water rich in vitamins instead of distilled water

Null Hypothesis vs Alternative Hypothesis

The table below shows the difference between a null hypothesis and an alternate hypothesis.

8.  Logical Hypothesis

A logical hypothesis is a proposed assumption or explanation with limited evidence.

• Creatures that live in the bottom of an ocean use aerobic respiration instead of anaerobic respiration
• Cactus experience successful growth rates than tulips on planet Mars

9. Empirical Hypothesis

By putting a theory to the test, and changing around independent variable, and using observations and experiments, a researcher comes up with an empirical hypothesis also known as a working hypothesis. An empirical hypothesis ceases to be just an idea, assumption or notion.

• A woman to takes vitamin E grows her hair faster than a woman who takes vitamin K

Note that until you’re able to test a theory for an extended period, the evidence for any claim can only remain logical.

About the author 

Antony W is a professional writer and coach at Help for Assessment. He spends countless hours every day researching and writing great content filled with expert advice on how to write engaging essays, research papers, and assignments.

Research Hypothesis: The Essential Requirements and Guidelines

Table of contents

• 1.1 Research Question vs Hypothesis
• 1.2 Null Hypothesis
• 1.3 Alternative Hypothesis
• 2 Hypothesis Essential Requirements
• 3 How to Formulate an Effective Research Hypothesis
• 4 Research Hypothesis Examples

Writing research requires students to have a deep knowledge not only of the subject but also of the requirements for the project. There are a lot of structural units that form an integral part of research writing.

Knowing the right methods and carrying out background research will lead you to discoveries. In this article, we will talk about such a technique as a research hypothesis. We will analyze in detail the features of using a good research hypothesis, its types, and meanings, the peculiarities of independent and dependent variables, as well as the connection with the research topic.

This article will guide you as you write your paper and give you the key techniques to follow all the requirements.

What is a Hypothesis in Research?

Let’s start by clarifying the term “ research hypothesis “. This is a kind of assumption or idea that the author of the study puts forward for further investigation. A hypothesis requires proof and is not true until confirmatory experiments have been carried out.

In the context of the research project, a hypothesis is necessary for the presentation of the expected directions and results of the work. This idea must be clearly stated to follow a logical chain and help to write your research and do further experiments. The ultimate goal of your research is to confirm or disprove the hypothesis. Not to be confused with the research question.

Let’s list the main types of hypotheses and find out the differences they may present for academic research:

• Null hypothesis
• Alternative hypothesis
• Simple hypothesis
• Complex hypothesis
• Statistical hypothesis
• Empirical hypothesis
• Causal hypothesis
• Directional hypothesis
• Associative hypothesis
• Logical hypothesis

Being aware that there are different kinds of research hypotheses will help you build your own with less effort. Many researchers adhere to the approach that there are only two varieties: Null hypothesis and Alternative hypothesis. However, we will consider what the essence of the most commonly used methods is.

The Null hypotheses is a statement with two or more variables. The Null hypothesis proposes that there is no connection between those variables. This type of inference is very often used in the course of scientific research in the fields of statistics, medicine, biology and many other sciences. The Alternative hypothesis states the opposite information to the Null Hypothesis, and aims to prove that there is a relationship between two variables.

A Simple hypothesis presents a correlation between only two variables, a single dependent variable and a single independent variable. While the Complex hypothesis states the presence of a connection between several dependent variables and independent variables.

Research Question vs Hypothesis

The differences between these two critical techniques for writing a good research paper  should be explained so that you have no doubts. A research question  is a question that is raised in the course of observations and which the researcher seeks to answer.

While a hypothesis is an assumption that must be proven or refuted in the course of the study, these two concepts are different by nature, the research question has an inquisitive function, while a research hypothesis predicts the outcome of the experiment.

Null Hypothesis

Now we will take a closer look at the most used, basic scientific method. Null hypothesis states that there is no interconnection between the two variables that are being studied. To formulate the Null Hypothesis, you need to present your testable prediction about relevant variables as a negative statement.

The original hypothesis might state that the variables do not have differences, there is no influence of factors, there is no effect, the characteristics of which are equal to zero, with no statistical significance.

The purpose of scientific experiments is to disprove the Null Hypothesis, that is, to prove the positive relationship between independent and dependent variables. For example, you are a scientist in the field of mental health, and you face the necessity of writing a psychology research paper .

Studying a popular theory and presenting a null hypothesis: When a teenager uses social media, it will not impact their self-esteem. Alfred your aim is to carry out a comprehensive, thorough investigation to prove or disprove this prediction.

Alternative Hypothesis

Let’s now talk about the opposite of the Null Hypothesis, which is the Alternative Hypothesis. This kind of inference is the opposite idea to the one supported by the Null Hypothesis. It is also sometimes called an experimental hypothesis, as it reveals the subject of future scientific research.

The essence of this hypothesis involves proposing the relationship between two variables, more precisely one variable influences the independent variable. The experimental hypothesis predicts how exactly the outcome may be affected during experimental manipulations.

At the same time the Alternative hypothesis can be divided into two groups: Directional hypothesis and Non-directional hypothesis.

Hypothesis Essential Requirements

A good research hypothesis sets the direction for your further research study. If you manage to formulate it correctly, then this will give a significant impetus to experiments.

However, if the basis of your scientific research paper is not specifically or vaguely explained, then your experiments may go into a dead corner. To avoid such problems, let’s look at what an effective research hypothesis should look like.

• Researchers must write a hypothesis based on the theme of the goals and objectives of the work. The formulation of the hypothesis should be competent, concise, and specific.
• The scientific hypothesis should be formulated in such a way that the stated problems could be studied, proved, or refuted in the course of the work.
• Your hypothesis must include at least one dependent variable and one independent variable.
• A non-testable hypothesis is a blind corner to your research study. The purpose of creating a hypothesis is to further study it, which is why only the testable hypothesis can underlie your work.
• It is crucial that the hypothesis states the object of the studies in a non-ambiguous way so as not to mislead the reader. Your testable statement should correspond with the research question.
• Prior research stands at the base of a strong research hypothesis. Researchers need to be knowledgeable in the field of studies, as there is a significant difference between just a guess and a working hypothesis.
• Your hypothesis should be the result of a study of existing theories. To do this, you need to study the variables involved and make precise predictions, having previously identified problematic issues suitable for study.

By following these guidelines, you will be able to accurately formulate a compelling hypothesis that will serve as a reliable core and help you write a research paper fundamentally. It will also be very helpful to study a few examples of good research hypotheses in order to have a better understanding of the issue.

How to Formulate an Effective Research Hypothesis

A hypothesis is an effective methodological tool that helps us structure our work. That is why it is very important to pay attention to the correct formulation and designation of a strong hypothesis.

Preliminary research is also required before formulating your assumptions. General knowledge of the field of study will help you accurately identify problems in the subject of study. Namely, this is the basis for the construction of supporting assumptions.

A hypothesis itself is a scientific method in the form of an assumption that is formed based on a theory. Therefore, the key to successful research is the choice of a reliable experimental and theoretical base. Brilliant research is based on previous and no less brilliant research. Therefore, your assumptions must come from evidence-based sources. Otherwise, they may lead to false results.

To formulate a hypothesis, you need to study the research problem. This means that preliminary research is indispensable, and it is precisely what a hypothesis begins with. If you find it challenging to manage the study on your own, you can opt for research paper help from professional writers.

It is necessary that your predictions correspond to the object of study, do not create contradictions between existing and received knowledge, and are also testable. Be careful not to use banal facts as a basis for building a hypothesis, otherwise, you will severely limit the field for experiments.

In the course of conducting previous research, you will be able to highlight certain factors in the theory that need additional observation. Perhaps these phenomena deviate from the general vector of the functioning of the theory.

Talking about variables, they should be well elaborated, to avoid any misconceptions. Find out what your independent variable would be, it is the one you are about to substitute to get new research data. Then figure out what you’d dependent variable stands for, which is what the research measures. Subsequently, you have to determine what kind of relationship exists between them.

Once you have identified the necessary factors, you are ready to begin formulating your hypothesis. Or if you still struggle to start the research, then it may be useful for you to resort to writing service professional help. This should be done in such a way that the hypothesis explains the cause of the problem. Then you have to test your assumptions by conducting an experiment or by looking for correlations between the dependent variable and independent variable.

As difficult as it may be to formulate a good hypothesis, this is a key step to successful, structured work. Any knowledge comes through a long process of learning theory and then reconciling skills in practice. That is why we are confident in your abilities, and we wish you success in creating a research hypothesis. We hope this article has become informative for you and clarified the key concepts necessary for a good scientific hypothesis.

Research Hypothesis Examples

Here are examples that illustrate how hypotheses can shape research across various disciplines.

Increased exposure to sunlight will result in higher rates of photosynthesis in spinach plants. Individuals with a higher level of emotional intelligence will have more successful personal relationships. Access to higher education will decrease income inequality within a society. An increase in temperature will result in an increase in the average kinetic energy of gas molecules. Increasing the concentration of a reactant in a chemical reaction will increase the rate of reaction. The presence of a black hole at the center of a galaxy will affect the motion of stars within the galaxy. Changes in the Earth’s magnetic field will result in changes in the frequency and intensity of earthquakes. The introduction of non-native species to an ecosystem will disrupt the food chain and result in decreased biodiversity. The use of written language will result in the development of more complex societies. An increase in the minimum wage will result in decreased unemployment rates within a society.

For additional inspiration, you can find more samples of student’s hypotheses in research.

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How To Write A Research Paper

How To Write A Hypothesis

How To Write a Hypothesis in a Research Paper | Steps & Examples

13 min read

Published on: Aug 5, 2021

Last updated on: Mar 5, 2024

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Imagine spending hours conducting experiments, only to realize that your hypothesis is unclear or poorly constructed.

This can lead to wasted time, resources, and a lack of meaningful results.

Fortunately, by mastering the art of hypothesis writing, you can ensure that your research paper is focused and structured. 

This comprehensive guide will provide you with step-by-step instructions and examples to write a hypothesis effectively.

By the end of this guide, you will have all the knowledge to write hypotheses that drive impactful scientific research.

On This Page On This Page -->

What is a Hypothesis?

A hypothesis is a tentative explanation or prediction that can be tested through scientific investigation. 

It is like a roadmap that guides researchers in their quest for answers. By formulating a hypothesis, researchers make educated guesses about the relationship between variables or phenomena.

Think of a hypothesis as a detective's hunch. Just like a detective forms a theory about a crime based on evidence, a researcher develops a hypothesis based on existing knowledge and observations. 

Now that we have a basic understanding of what a hypothesis is, let's delve into the process of writing one effectively.

Variables in Hypothesis

In hypotheses, variables play a crucial role as they represent the factors that are being studied and tested. 

Let's explore two types of variables commonly found in hypotheses:

1. Independent Variable: This variable is manipulated or controlled by the researcher. It is the factor believed to have an effect on the dependent variable. Here's an example:

Hypothesis: "Increasing study time (independent variable) leads to improved test scores (dependent variable) in students."

In this hypothesis, the independent variable is the study time, which the researcher can manipulate to observe its impact on the test scores.

2. Dependent Variable: This variable is the outcome or response that is measured or observed as a result of the changes in the independent variable. Here's an example:

Hypothesis: "Exposure to sunlight (independent variable) affects plant growth (dependent variable)."

In this hypothesis, the dependent variable is plant growth, which is expected to be influenced by the independent variable, sunlight exposure. The researcher measures or observes the changes in plant growth based on the different levels of sunlight exposure.

Research Question vs Hypothesis

A research question is an inquiry that defines the focus and direction of a research study. A hypothesis, on the other hand, is a tentative statement that suggests a relationship between variables or predicts the outcome of a research study.

Hypothesis vs. Prediction

The difference between a hypothesis and a prediction is slight, but it's critical to understand. 

Hypotheses are a great way to explain why something happens based on scientific methods. A prediction is a statement that says something will happen based on what has been observed.

A hypothesis is a statement with variables. A prediction is a statement that says what will happen in the future.

Theory vs. Hypothesis

The theory and hypothesis have some differences between them.

• A hypothesis is the explanation of a phenomenon that will be supported through scientific methods. 
• A theory is a well-substantiated and already-tested explanation backed by evidence.  

To turn a hypothesis into a theory, you need to test it in different situations and with strong evidence. Theories can also be used to make predictions about something that is not understood. Once you have predictions, you can turn them into hypotheses that can be tested.

How to Develop a Hypothesis Step by Step?

Developing a hypothesis is an important step in scientific research, as it sets the foundation for designing experiments and testing theories. 

Let's explore the step-by-step process of developing a hypothesis, using the example of studying the effects of exercise on sleep quality.

Step 1. Ask a Question

To begin, ask a specific question that focuses on the relationship between variables. In our example, the question could be: "Does regular exercise have a positive impact on sleep quality?"

Step 2. Do Background Research

Before formulating your hypothesis, conduct preliminary research to gather existing knowledge on the topic. 

Review scientific studies, articles, and relevant literature to understand the current understanding of exercise and its potential effects on sleep quality. This research will provide a foundation for formulating your hypothesis.

Step 3. Develop Your Hypothesis

Based on your question and preliminary research, formulate a hypothesis that predicts the expected relationship between variables. In our example, the hypothesis could be: 

"Regular exercise has a positive influence on sleep quality, resulting in improved sleep duration and reduced sleep disturbances."

Step 4. Refine Your Hypothesis

Refine your hypothesis by making it more specific and testable. Specify the variables involved and the anticipated outcomes in clear terms. For instance: 

"Engaging in moderate-intensity aerobic exercise for at least 30 minutes, three times a week, will lead to an increase in total sleep time and a decrease in the frequency of sleep disruptions."

Step 5. Express Your Hypothesis in Three Forms

To ensure comprehensiveness, phrase your hypothesis in three different ways: as a simple statement, as a positive correlation, and as a negative correlation. This will cover different perspectives and potential outcomes. 

Using our example:

• Simple Statement: "Regular exercise positively affects sleep quality."
• Positive Correlation: "As the frequency of regular exercise increases, sleep quality improves."
• Negative Correlation: "A lack of regular exercise is associated with poorer sleep quality."

Step 6. Construct a Null Hypothesis

In addition to the main hypothesis, it is important to write a null hypothesis. The null hypothesis assumes that there is no significant relationship between the variables being studied. 

The example below shows how to state the null hypothesis in a research paper: 

By following these steps, you can develop a well-structured and testable hypothesis that serves as a guiding framework for your scientific research.

Types of Research Hypotheses with Examples

Hypotheses come in various forms, depending on the nature of the research and the relationship between variables. 

Here are seven common types of hypotheses along with examples:

• Simple Hypothesis: A straightforward statement about the expected relationship between variables.

Example: "Increasing fertilizer dosage will lead to higher crop yields."

• Complex Hypothesis: A hypothesis that suggests a more intricate relationship between multiple variables.

Example: "The interaction of genetic factors and environmental stressors contributes to the development of certain mental disorders."

• Directional Hypothesis: A hypothesis that predicts the specific direction of the relationship between variables.

Example: "As temperature decreases, the viscosity of the liquid will increase."

• Non-Directional Hypothesis: A hypothesis that suggests a relationship between variables without specifying the direction.

Example: "There is a correlation between caffeine consumption and anxiety levels."

• Null Hypothesis: A hypothesis that assumes no significant relationship between variables.

Example: "There is no difference in exam performance between students who study in silence and students who listen to music."

• Alternative Hypothesis: A hypothesis that contradicts or offers an alternative explanation to the null hypothesis.

Example: "There is a significant difference in weight loss between individuals following a low-carb diet and those following a low-fat diet."

• Associative Hypothesis: A hypothesis that suggests a relationship between variables without implying causality.

Example: "There is a correlation between exercise frequency and cardiovascular health."

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What Makes a Good Hypothesis? 5 Key Elements

Crafting a good hypothesis is essential for conducting effective scientific research. A well-formed hypothesis sets the stage for meaningful experiments. 

Here are some key characteristics that make a hypothesis strong:

1. Testable and Specific

A good hypothesis should be testable through observation or experimentation. It should be formulated in a way that allows researchers to gather data and evidence to support or refute it. 

When writing a research hypothesis, it is crucial to structure it in a manner that suggests clear ways to measure or observe the variables involved.

2. Grounded in Existing Knowledge

A strong hypothesis is built upon a foundation of existing knowledge and understanding of the topic. By connecting your hypothesis to previous findings, you ensure that your research contributes to the broader scientific knowledge. 

This incorporation of existing knowledge aligns with the concept of research hypotheses, where hypotheses are framed based on the understanding of the subject from previous studies.

3. Falsifiable

A good hypothesis must be falsifiable, meaning that it can be proven false if it is indeed false. This principle is important because it allows for rigorous testing and prevents researchers from making claims that are impossible to verify or disprove. 

This aligns with the idea of statistical hypothesis, where hypotheses need to be formulated in a way that allows statistical testing to determine their validity.

4. Clearly Defines Variables

A well-formulated hypothesis clearly identifies the independent and dependent variables involved in the research. It specifies the relationship between two variables and states what researchers expect to find during the study. 

The clarity in defining variables is a crucial aspect of developing logical hypotheses.

5. Supported by Logic and Reasoning

A good hypothesis is logical and based on sound reasoning. It should be supported by evidence and a plausible rationale. The relationship between two variables proposed in the hypothesis should be grounded in a solid understanding of cause-and-effect relationships and theories.

A strong hypothesis, whether it is a research hypothesis, statistical hypothesis, or logical hypothesis, encompasses these key elements. By incorporating these elements you lay the groundwork for a robust and meaningful research study.

Hypothesis Examples 

Here are a few more examples for you to look at and get a better understanding!

How to Write a Hypothesis in Research

Research Question: "Does exposure to violent video games increase aggressive behavior in adolescents?"

Hypothesis 1: "Adolescents who are exposed to violent video games will display higher levels of aggressive behavior compared to those who are not exposed."

Hypothesis 2: "There is a positive correlation between the amount of time spent playing violent video games and the level of aggressive behavior exhibited by adolescents."

How to Write a Hypothesis for a Lab Report:

Lab Experiment: Testing the effect of different fertilizers on plant growth.

Hypothesis 1: "Plants treated with fertilizer A will exhibit greater growth in terms of height and leaf count compared to plants treated with fertilizer B."

Hypothesis 2: "There is a significant difference in the growth rate of plants when exposed to different types of fertilizers."

How to Write a Hypothesis in a Report:

Report Topic: Investigating the impact of social media usage on self-esteem.

Hypothesis 1: "Individuals who spend more time on social media will report lower levels of self-esteem compared to those who spend less time on social media."

Hypothesis 2: "There is an inverse relationship between the frequency of social media use and self-esteem levels among individuals."

Example of Hypothesis in a Research Proposal:

Crafting hypotheses in a research proposal is pivotal for outlining the research aims and guiding the investigative process. Here's an example of a hypothesis within a research proposal:

Research Proposal Topic: Investigating the impact of social media usage on adolescents' self-esteem levels.

Hypothesis: "Adolescents who spend more time on social media platforms will have lower self-esteem levels compared to those who spend less time on social media."

How To Write a Hypothesis Psychology

Research Topic: Investigating the impact of mindfulness meditation on reducing symptoms of anxiety in college students.

Hypothesis 1: "College students who regularly practice mindfulness meditation will report lower levels of anxiety compared to those who do not engage in mindfulness practices."

Hypothesis 2: "There will be a significant decrease in anxiety scores among college students who undergo a structured mindfulness meditation program compared to a control group receiving no intervention."

How to Write a Hypothesis for a Research Paper:

 Research Paper Topic: Examining the effect of mindfulness meditation on stress reduction.

Hypothesis 1: "Participating in regular mindfulness meditation practice will result in a significant decrease in perceived stress levels among participants."

Hypothesis 2: "There is a positive association between the frequency of mindfulness meditation practice and the reduction of stress levels in individuals."

How to Write a Hypothesis for Qualitative Research:

Qualitative Research Topic: Exploring the experiences of first-time mothers during the postpartum period.

Hypothesis 1: "First-time mothers will report feelings of increased anxiety and stress during the early weeks of the postpartum period."

Hypothesis 2: "There will be a common theme of adjustment challenges among first-time mothers in their narratives about the postpartum experience."

Good and Bad Hypothesis Example

Below are examples of good and bad hypotheses, along with their corresponding research question and hypothesis examples:

In conclusion, a well-crafted hypothesis sets the stage for designing experiments, collecting data, and drawing meaningful conclusions. 

By following the steps of formulating a hypothesis, researchers can ensure that their investigations are grounded in solid reasoning. AI essay writing tools can be a great help in getting ideas.

However, If you need assistance with essay writing, consider leveraging the services of CollegeEssay.org. Our team of experienced writers is dedicated to delivering high-quality, customized essays that meet your requirements and deadlines. 

Don't hesitate to visit CollegeEssay.org and benefit from our professional essay writing service . Contact us today and say goodbye to your academic paper-writing worries.

Frequently Asked Questions

What are the 3 required parts of a hypothesis.

The three main parts of the hypothesis are: 

• Problem 
• Proposed solution 
• Result 

What are 5 characteristics of a good hypothesis?

The main five characteristics of a good hypothesis are: 

• Clarity 
• Relevant to problem 
• Consistency 
• Specific 
• Testability 

What should not be characteristic of a hypothesis?

Complexity should not be a good characteristic of a hypothesis. 

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How to Write a Good Hypothesis in a Research Paper

What is a hypothesis in a research paper.

Every research has many parts, but its vital part is the proper hypothesis construction. A hypothesis represents a question, which includes an expected or predicted research result. When there’s no hypothesis, the base for an experiment or research is missing. With that said, it’s essential to carefully build the hypothesis. Such writing projects require patience, thoroughness, and persistence. Here, you’ll learn what is a hypothesis in research and how to write a hypothesis for a research paper and construct it clearly.

Characteristics of a Great Hypothesis

When you start learning how to write hypothesis, it’s crucial to understand what makes it good.

• It should be concise, precise, and clear
• It should be testable
• It should be focused on one problem only
• All great hypotheses aren’t contradictory
• It should be stated simply and clearly. That way, everyone can understand it with ease.

All this may sound too complex. At the start, everything seems complicated and confusing. But most beginnings are like that. Learning other things, including writing an  appendix for a research paper are tricky, but once you get into it, it becomes easier. Learning new things, especially of scientific nature, requires effort and patience.

Before you start working on hypotheses, there’re several questions every researcher should ask, including:

• Is the language used for the scientific reports clear?
• How can the thesis be tested? In what ways?
• Which explanations should be explored?
• Does the theory include different variables, dependent and independent?
• Is the idea in conflict with any nature laws?

Every question is equally important. These point to the complexity of the work. For many students, a scientific study is too complicated, more complex than learning how to write a  method section for a research paper or learning how to conclude a subject. But diving into it often turns into a fun journey.

Make sure to provide answers for all the above. If something is missing or doesn’t seem suitable, it means you’ll have to make appropriate changes.

General Types of the Research Hypothesis

There’re several general hypothesis types to explore, and those are:

• Simple — This type foresees the relation between a single independent variable and a dependent one.
• Complex — Focuses on foreseeing the connection between two or more independent variables and two or more dependent ones.
• Directional — It focuses on giving an explanation of the expected outcome direction.
• Non-directional — It doesn’t explain the expected direction of the result.
• Associative — It points out how the change in one of the variables affects the other.
• Causal — It shows how the manipulation of an independent variable affects the dependent one.
• Null — It points out there’s no relation between variables.
• Alternative — It shows the relationship between variables and identifies the expected research result.

Learning how to distinguish all these types takes time. With proper understanding, the entire study becomes easier. However, some students turn to professional help, and you can do the same — simply buy your research paper online because experienced researchers create them. These researchers possess the knowledge and skills to deliver exceptional work.

Keep in mind that one theory can fall into one of the types mentioned above or into several types. All the definitions previously listed are created to be simple and understandable for beginners.

Main Steps: How to Write the Hypothesis Section of a Research Paper

Here’re the footsteps on how to write a hypothesis in a research paper that you should follow:

• First, ask a  question , for example: “How does exercise affect sleep?”
• Start collecting data — take experiments, conduct interviews, and explore academic journals. Gather information from many sources and different sides.
• Create the answer to the previously asked question: “Exercise decreases insomnia, along with other sleep issues and complaints, and its effects are similar to results sleeping pills are providing.”
• Create the hypothesis — It should include variables, outcomes, and who or what is studied. “If a person regularly exercises, they will have better sleep quality and sleep complaints will reduce.”
• Clarify the hypothesis by exploring the difference or connection between the two groups.
• Null hypothesis creation — Finally, formulate a hypothesis — null (that points out there’s no evidence that supports differences) or alternative (showing proof there’re differences).

The process is complex and requires time, effort, and exploration. It’s tricky even for experienced people. That is why many students turn to  custom writing service where professionals provide all the work at affordable prices, following the format and other requirements of scientific research.

When you start working on your assignment, ensure to follow all the steps we’ve listed. That way, you’ll ensure nothing is missing.

How to Create a Strong Hypothesis for the Research Paper?

Creating a solid hypothesis requires several things, and those are:

• First, state the issue — the topic needs to be clearly defined.
• If possible, use the statement that has the If and Then components. In other words, if some specific action is taking place, then the particular result is anticipated.
• Variables need to be detected. In the example above, the variables are exercise and sleep.

Learning how to write a null hypothesis in a research paper isn’t easy. There’re many parts to understand, but carefully following a  guide to writing a research paper can be very helpful. Give yourself time and be patient until you figure it out.

As you may notice, there are a couple of crucial steps to follow. One of the key factors is to follow the guide and ensure that you are clear and concise.

Hypothesis Examples

Before you start working on study articles, here’re some hypothesis samples that’ll help you get a better understanding of how things work:

• Brushing the teeth every day prevents the formation of cavities.
• Eating broccoli and berries boosts the metabolism.
• Students that don’t skip breakfast perform better in school than those who do skip breakfast.
• When fertilizing the garden, the plants will grow more quicker.
• When taking adequate breaks, employees’ work performance increases.

When you don’t have enough time for a proper study and data collection, there’s an option to  pay for writing a research paper that many students use, even the top researchers. Everyone needs a break at times. Plus, these services are affordable and tailored to match the budget of a student.

We’ve created the examples above so every student that is new to this type of work can get familiar with the basics. At first glance, getting it all seems like a lot. But as you keep exploring the examples, things will get easier.

All researches require a lot of effort, especially when you are a beginner. Creating a hypothesis and developing an entire essay about a particular question isn’t always easy. You have a lot of analysis in front of you, some experiments, data collection, and more. Even though a tremendous amount of work is required, completing statistical analysis and the project altogether is pretty fun. Remember, if you are busy, professionals can do it for you.

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• A Research Guide
• Research Paper Guide

How to Write a Hypothesis for a Research Paper

• What is a hypothesis
• Purpose of a hypothesis
• What makes a good hypothesis

Hypothesis vs. prediction

• Step-by-step guide
• What is the format of a hypothesis
• Hypothesis examples

What is a hypothesis?

“A hypothesis is a work in progress where you draw questions about a topic you want to research. The question devices should be used in the research ahead on the topic. The questions should also be taken from an issue that you understand best. You can read about the topic or discover other forms of literature to help you know more about the topic you want to draw a hypothesis from. First, think of what will happen, then draw a hypothesis from what you think will happen. You get to experiment with what happens when you later research your hypothesis.”

What is the purpose of the hypothesis?

What makes a good hypothesis.

• First, a reasonable hypothesis has cause and effect. As in the example above, if a person regularly practices yoga, he becomes calm. The condition or cause is yoga. The result is calmness. Further in the study, you can test this dependence. Here are some other research hypothesis examples: if a person drinks two cups of coffee in a row, his pressure rises two times. You can also explore this dependency further. Or watching movies in Spanish every day improves your language skills.
• The second sign of a reasonable hypothesis is the ability to test it. If you cannot conduct an experiment or check the literature, then such a hypothesis is worth rewriting.
• The third thing that should be in a reasonable hypothesis is data dependency. A theory that says that if you change the condition, the result will change. For example, you will feel overwhelmed if you sleep 2 hours a day. When the condition changes, for example, if you sleep 10 hours a day, the result will change, and you will feel rested.
• The hypothesis assumes the answer to a question. It is based on experiments that facts may dispute. Hypothesis gives you variables that can contradict themselves. They can only be disputed by the scientific facts of the experiments conducted. For instance, a hypothesis can be drawn from looking into the relationship between exercising and not Gettysburg obese. They test the clues of answers you have before getting the facts.
• A prediction is when someone concludes their little knowledge of the topic without research. Predictions may be based on facts you don’t know more about. Thus, the hypothesis is a knowledgeable guess.

How to write a hypothesis for a research paper: main steps

Select a topic that interests you, read existing research on the selected topic.

Analyze the information you have gathered from all the materials you have used

Come up with queries after reading about the topic and its literature, come up with important clues on what you think the answers to your questions might be, get a simple hypothesis topic in the paper, what is the format of a hypothesis, and how do you use it.

• Research the question you asked. The information can be found in books and articles online on websites. In libraries and schools. Research and get your findings from combined sources. The information may contain unknown parts of the study. This will help you in drawing research questions.
• Create a hypothesis that gives the possible answers to the questions you formulated from your research and reading more. You will use your hypothesis to experiment to determine if the hypothesis statement you draw does not contain a null hypothesis.
• Construct an experiment structure to check your hypothesis. This experiment uses scientific methods to search for the use of machines to conclude. This information can be found using methods like observation and interviewing people to get information from them. You can also use questionnaires to get information that is not biased. The information should give you the results of the population that shared their information.
• Study your results, then conclude. The conclusions are drawn from the information obtained from the scientific methods used. The information is analyzed, and comparisons are made. They are compared to the hypothesis you drew earlier. This information is used to form a hypothesis.
• Give your findings to your teacher or whoever it may concern. After a study, the findings should be presented. It could be done during class discussions, presentations, or further library research. Use this finding to nullify your hypothesis.

Some of the hypothesis examples and types of hypothesis in research

• Why is the percentage of obese women more than that of men? This is a question you ask yourself when you are interested in a topic and want to study it.
• A lack of exercise in the body causes obesity.
• Most women find it hard to exercise.
• Men exercise more than women.
• Eating junk foods without exercising may cause obesity.
• Why do you think a lack of exercising the body may cause obesity? Because of a lack of exercise, the baby may accumulate fat.
• Why do women find it hard to exercise? Because women are believed to be soft creatures that need lots of care.
• Why do men exercise more than women? Because they feel masculinity is defined by how strong you might be.
• Why does eating junk foods without exercising have the possibility of being obese? Because junk foods cause fat to build up in the body. Without burning the fat exercising, it will build up and may cause obesity
• Reading magazines and newspapers
• Use of questionnaires
• Interviewing people
• Observation of people’s behavior
• Telephone calls
• The data collected should be used to analyze and conclude. Most people might be giving the same information on the topic which you are researching. You will draw your conclusions based on the data you have gathered. The conclusion should not be biased. It should be accurate and comprehensive.
• Your results on the findings and conclusion should be presented and communicated to your supervisors or the parties concerned. It can be presented like a class presentation or a group discussion and also further library research. In your group discussion, discuss your findings. Many people in the group may have also had other conclusions about the topic you researched. Some may respond positively, but that doesn’t mean it affects your conclusion.

• Writing a Research Paper
• Research Paper Title
• Research Paper Sources
• Research Paper Problem Statement
• Research Paper Thesis Statement
• Hypothesis for a Research Paper
• Research Question
• Research Paper Outline
• Research Paper Summary
• Research Paper Prospectus
• Research Paper Proposal
• Research Paper Format
• Research Paper Styles
• AMA Style Research Paper
• MLA Style Research Paper
• Chicago Style Research Paper
• APA Style Research Paper
• Research Paper Structure
• Research Paper Cover Page
• Research Paper Abstract
• Research Paper Introduction
• Research Paper Body Paragraph
• Research Paper Literature Review
• Research Paper Background
• Research Paper Methods Section
• Research Paper Results Section
• Research Paper Discussion Section
• Research Paper Conclusion
• Research Paper Appendix
• Research Paper Bibliography
• APA Reference Page
• Annotated Bibliography
• Bibliography vs Works Cited vs References Page
• Research Paper Types
• What is Qualitative Research

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• Knowledge Base
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• 10 Research Question Examples to Guide Your Research Project

10 Research Question Examples to Guide your Research Project

Published on October 30, 2022 by Shona McCombes . Revised on October 19, 2023.

The research question is one of the most important parts of your research paper , thesis or dissertation . It’s important to spend some time assessing and refining your question before you get started.

The exact form of your question will depend on a few things, such as the length of your project, the type of research you’re conducting, the topic , and the research problem . However, all research questions should be focused, specific, and relevant to a timely social or scholarly issue.

Once you’ve read our guide on how to write a research question , you can use these examples to craft your own.

Note that the design of your research question can depend on what method you are pursuing. Here are a few options for qualitative, quantitative, and statistical research questions.

Other interesting articles

If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

Methodology

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

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6 Week 5 Introduction to Hypothesis Testing Reading

An introduction to hypothesis testing.

What are you interested in learning about? Perhaps you’d like to know if there is a difference in average final grade between two different versions of a college class? Does the Fort Lewis women’s soccer team score more goals than the national Division II women’s average? Which outdoor sport do Fort Lewis students prefer the most?  Do the pine trees on campus differ in mean height from the aspen trees? For all of these questions, we can collect a sample, analyze the data, then make a statistical inference based on the analysis.  This means determining whether we have enough evidence to reject our null hypothesis (what was originally assumed to be true, until we prove otherwise). The process is called hypothesis testing .

A really good Khan Academy video to introduce the hypothesis test process: Khan Academy Hypothesis Testing . As you watch, please don’t get caught up in the calculations, as we will use SPSS to do these calculations.  We will also use SPSS p-values, instead of the referenced Z-table, to make statistical decisions.

The Six-Step Process

Hypothesis testing requires very specific, detailed steps.  Think of it as a mathematical lab report where you have to write out your work in a particular way.  There are six steps that we will follow for ALL of the hypothesis tests that we learn this semester.

1. Research Question

All hypothesis tests start with a research question.  This is literally a question that includes what you are trying to prove, like the examples earlier:  Which outdoor sport do Fort Lewis students prefer the most? Is there sufficient evidence to show that the Fort Lewis women’s soccer team scores more goals than the national Division 2 women’s average?

In this step, besides literally being a question, you’ll want to include:

• mention of your variable(s)
• wording specific to the type of test that you’ll be conducting (mean, mean difference, relationship, pattern)
• specific wording that indicates directionality (are you looking for a ‘difference’, are you looking for something to be ‘more than’ or ‘less than’ something else, or are you comparing one pattern to another?)

Consider this research question: Do the pine trees on campus differ in mean height from the aspen trees?

• The wording of this research question clearly mentions the variables being studied. The independent variable is the type of tree (pine or aspen), and these trees are having their heights compared, so the dependent variable is height.
• ‘Mean’ is mentioned, so this indicates a test with a quantitative dependent variable.
• The question also asks if the tree heights ‘differ’. This specific word indicates that the test being performed is a two-tailed (i.e. non-directional) test. More about the meaning of one/two-tailed will come later.

2. Statistical Hypotheses

A statistical hypothesis test has a null hypothesis, the status quo, what we assume to be true.  Notation is H 0, read as “H naught”.  The alternative hypothesis is what you are trying to prove (mentioned in your research question), H 1 or H A .  All hypothesis tests must include a null and an alternative hypothesis.  We also note which hypothesis test is being done in this step.

The notation for your statistical hypotheses will vary depending on the type of test that you’re doing. Writing statistical hypotheses is NOT the same as most scientific hypotheses. You are not writing sentences explaining what you think will happen in the study. Here is an example of what statistical hypotheses look like using the research question: Do the pine trees on campus differ in mean height from the aspen trees?

3. Decision Rule

In this step, you state which alpha value you will use, and when appropriate, the directionality, or tail, of the test.  You also write a statement: “I will reject the null hypothesis if p < alpha” (insert actual alpha value here).  In this introductory class, alpha is the level of significance, how willing we are to make the wrong statistical decision, and it will be set to 0.05 or 0.01.

Example of a Decision Rule:

Let alpha=0.01, two-tailed. I will reject the null hypothesis if p<0.01.

4. Assumptions, Analysis and Calculations

Quite a bit goes on in this step.  Assumptions for the particular hypothesis test must be done.  SPSS will be used to create appropriate graphs, and test output tables. Where appropriate, calculations of the test’s effect size will also be done in this step.

All hypothesis tests have assumptions that we hope to meet. For example, tests with a quantitative dependent variable consider a histogram(s) to check if the distribution is normal, and whether there are any obvious outliers. Each hypothesis test has different assumptions, so it is important to pay attention to the specific test’s requirements.

Required SPSS output will also depend on the test.

5. Statistical Decision

It is in Step 5 that we determine if we have enough statistical evidence to reject our null hypothesis.  We will consult the SPSS p-value and compare to our chosen alpha (from Step 3: Decision Rule).

Put very simply, the p -value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample. The p -value can also be thought of as the probability that the results (from the sample) that we are seeing are solely due to chance. This concept will be discussed in much further detail in the class notes.

Based on this numerical comparison between the p-value and alpha, we’ll either reject or retain our null hypothesis.  Note: You may NEVER ‘accept’ the null hypothesis. This is because it is impossible to prove a null hypothesis to be true.

Retaining the null means that you just don’t have enough evidence to prove your alternative hypothesis to be true, so you fall back to your null. (You retain the null when p is greater than or equal to alpha.)

Rejecting the null means that you did find enough evidence to prove your alternative hypothesis as true. (You reject the null when p is less than alpha.)

Example of a Statistical Decision:

Retain the null hypothesis, because p=0.12 > alpha=0.01.

The p-value will come from SPSS output, and the alpha will have already been determined back in Step 3. You must be very careful when you compare the decimal values of the p-value and alpha. If, for example, you mistakenly think that p=0.12 < alpha=0.01, then you will make the incorrect statistical decision, which will likely lead to an incorrect interpretation of the study’s findings.

6. Interpretation

The interpretation is where you write up your findings. The specifics will vary depending on the type of hypothesis test you performed, but you will always include a plain English, contextual conclusion of what your study found (i.e. what it means to reject or retain the null hypothesis in that particular study).  You’ll have statistics that you quote to support your decision.  Some of the statistics will need to be written in APA style citation (the American Psychological Association style of citation).  For some hypothesis tests, you’ll also include an interpretation of the effect size.

Some hypothesis tests will also require an additional (non-Parametric) test after the completion of your original test, if the test’s assumptions have not been met. These tests are also call “Post-Hoc tests”.

As previously stated, hypothesis testing is a very detailed process. Do not be concerned if you have read through all of the steps above, and have many questions (and are possibly very confused). It will take time, and a lot of practice to learn and apply these steps!

This Reading is just meant as an overview of hypothesis testing. Much more information is forthcoming in the various sets of Notes about the specifics needed in each of these steps. The Hypothesis Test Checklist will be a critical resource for you to refer to during homeworks and tests.

Student Course Learning Objectives

4.  Choose, administer and interpret the correct tests based on the situation, including identification of appropriate sampling and potential errors

c. Choose the appropriate hypothesis test given a situation

d. Describe the meaning and uses of alpha and p-values

e. Write the appropriate null and alternative hypotheses, including whether the alternative should be one-sided or two-sided

f. Determine and calculate the appropriate test statistic (e.g. z-test, multiple t-tests, Chi-Square, ANOVA)

g. Determine and interpret effect sizes.

h. Interpret results of a hypothesis test

• Use technology in the statistical analysis of data
• Communicate in writing the results of statistical analyses of data

Attributions

Adapted from “Week 5 Introduction to Hypothesis Testing Reading” by Sherri Spriggs and Sandi Dang is licensed under CC BY-NC-SA 4.0 .

Math 132 Introduction to Statistics Readings Copyright © by Sherri Spriggs is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

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What Is a Research Paper and How Should You Write One?

Updated 02 Sep 2024

Students face tons of assignments at schools and higher education institutions. Among all the different academic written assignments’ types, research paper writing is often considered to be one of the most challenging and complex. Is it really that stressful and hard to handle? The answer depends not on the subject you are studying, but more on your personal abilities to comprehend your knowledge. What is the goal for such a task, what is a research paper, and how to write it? In this article, our expert writers provide you with the answers.

Defining the Term: What Is a Research Paper Exactly?

A research essay is a large scientific work. The main goal of this project, regardless of the subject, is defining a particular issue and providing new ways to solve it that can be used to further investigate the problem. So, what is the accurate research paper definition? Unlike regular essays, such projects imply thinking out of the box. Here are the major features that distinguish research papers from other academic tasks.

• More extensive in volume than other written assignments.
• Needs extensive investigation on a particular problem.
• Often requires conducting experiments along with further results’ analysis.
• Insights should be based on your own thoughts, as well as experiments.
• Purpose implies finding some novel solutions or approaches.
• Everything should be supported by solid, verifiable evidence.
• Findings should be good enough to serve as a basis for further study.

Basically, if you want to define a research paper, you would be speaking about academic work done completely independently. In such a project, you are supposed to present your own view on things you investigate. This is where students usually face difficulties, so many of them prefer seeking for alternative ways to get cheap custom research papers.

How Does a Research Paper Differ from a Research Proposal?

One should understand the difference between a proposal and a paper before the actual writing process begins, as these are different tasks. As its name implies, a proposal is a rationale for conducting research to be approved by an instructor. It should explain the purpose of future projects and what new aspects of knowledge it brings into the academic studies’ field. A research proposal’s specific structure should explain a methodology that appears to be the most sufficient for its purposes and anticipated outcomes. Unlike a research paper, a proposal must have a more extensive literature review section as it serves as the ground for rationale and ensures originality of suggested topic. You may ask yourself is this ethical to pay someone to write my research paper? The answer is we won't judge you, but instead, we'll provide you reliable help.

Structure of the Research Paper

The general layout usually depends on the requested formatting style and specific instructions. Speaking about what to include in a paper in terms of obligatory sections, one can observe the following parts in any project:

• Research paper introduction

It should include a general background narrowed down to a specific problem under study and explain why you conduct the study. The purpose is embodied in a research question and original main argument. The key idea in this section is to provide a reader with a proper road map and a clear vision of the topic that goes from a broad perspective to a narrow one.

This is the longest part of your text that is essential for good research paper. A previously developed and presented narrow theme should be thoroughly discussed here following standard academic requirements for coherent papers. Each paragraph in this section is a mini-research paper since you first develop a specific claim related to the particular aspect of the main thesis statement, provide evidence gathered during literature search that proves the mentioned claim, present your own interpretation and ability to analyze facts, and, finally, wrap everything up with a concluding sentence that also brings the next point of discussion for subsequent paragraphs.

A general description of all outcomes and a summary of all main points of discussion will help your reader grasp the meaning of the entire paper. This section presupposes careful writing for you not to omit anything important as such drawbacks undermine your hard work’s quality.

These are basic requirements for a perfect academic paper, irrespective of its specific type and content as the readability and coherence of a written paper represent that one honed his or her writing skills. Every instructor highly appreciates these abilities.

Main Types of Research Papers

What is the key to getting the highest assessment? The main things that can help with research paper include understanding the task, its objectives and in-depth knowledge of the chosen topic. There are several common types of this kind of academic work. Each type is widely used in different educational institutions for different disciplines. Thus, understanding their peculiarities is important to grasp how to write a successful research paper:

• Compare and contrast: Describes the same issue from two different perspectives.
• Cause and effect: Should present a logical chain of causes and effects related to the chosen problem or subject.
• Persuasive/Argumentative: Discusses several sides of a particular issue and provides arguments in favor of one chosen side.
• Analytical writing demonstrates your best qualities, as such a task asks you to create a piece with deep analysis of various opinions regarding the same issue.
• Experiment: Students experiment and share their results.
• Report: Outlines previously conducted studies.
• Overview: Focuses on one, usually extensive scholarly study, so that the following tips on  how to write a research summary would be extremely useful.
• Survey: Student conducts a survey among chosen participants, analyzes findings, and develops conclusions.
• Problem-solution: Presents a problem and ways to resolve it.
• Communication research paper: Dedicated to developing one’s ability to produce reasonable arguments.

Usually, all these projects are rather lengthy, so that a 5-page research paper is a minimum requirement in most cases. It is a misconception that instructors demand long writing without a reason as it is impossible to cover complex study areas, including all needed sections, and meeting requirements in just a page or two.

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Layouts, References, and Citations: Stages of Writing a Research Paper

Many first-year students feel quite at a loss about how to start a research paper. The first piece of advice: divide your project into small clear stages to know how to write a research paper step by step.

Stage 1: How to Write an Outline for a Research Paper

Before starting your project, read your guidelines thoroughly. Have a clear understanding of required work’s volume. Remember that division on clear sections is a representative feature of a good paper. Each of the research paper's steps has a purpose.

A typical outline contains:

• A separate title page (Your topic with all requested credentials);
• Abstract (Short summary of your work, no new information here);
• Introduction/Literature review (Presents what was written before in this area);
• Methods section (Describes how exactly your study was conducted and instruments for analysis);
• Results (Obtained during your experiment, analysis, etc.);
• Discussion (Your interpretation of results);
• Conclusion (Summarizing paper);
• References (All used sources listed here);
• Appendixes (Include tables or any other additional information that is needed for more complete understanding).

The above-mentioned parts are usually grouped into bigger sections – for example, methods, results, and discussion are referred to as the body of the completed paper.

Read Also:  Chemistry Research Topics That Will Knock You Off Your Feet

Stage 2: Developing the Perfect Topic

Choosing a perfect topic is crucial. Whether you need History, Physics or  Biology research topics , instructors may provide a list of ready-made problems so you can choose or give freedom to develop your own topic. An idea’s originality and necessity to bring something new in the study area is a key element in definition of research paper. There is an opportunity to come across some knowledge gaps even among  research paper topics  already discussed before by other scholars. In any case, you should think  about  whether a question you want to research is interesting, allows gathering necessary information, and developing a structured argument.

Stage 3: Searching for Sources

Preliminary research is necessary as you need to have a general understanding of a topic under study before looking closely at your own specific aspect so that you know how to set up a research paper. Use information available online, especially on credible websites located on .edu, .gov, .org domains, to find more about background information.

The next step implies gathering good reliable sources to develop a literature review. Rely only on online university libraries and digital databases of scholarly journals and other academic credible sources like JSTOR. Google Scholar search engine is helpful to find publications that are recent and relevant to your research.

Stage 4: Thesis Statement is the Central Point of Structure

In a piece as huge and complex as a research essay, the choice of a study focus is just a start. While reviewing literature you need to keep in mind the main claim and central idea of the paper in progress as well as the answer you expect to find. This claim is expected in the form of a thesis statement and the entire paper should aim at proving it.

Stage 5: Going on a Quest: Researching and Experimenting

That is the most time-consuming part of the project. During this step, you delve into gathered literature, conduct experiments, and analyze obtained results. Remember the initial outline and general structure so that gathered information will be located in the proper sections.

Stage 6: Compose and Write a Paper as Scholars Do

Now you have to write it all down and produce a research paper. Transform your notes into a coherent, logical text that defends your point. Style of such papers is very formal with lots of specific terms. Make sure facts from reliable sources support every statement made in your work.

Stage 7: Formatting, Editing, and Proofreading

What you have written in your first Word document is not a real paper yet – it is just a first draft. Then, you would have to sit down, re-read it multiple times, edit typos and style and format it according to the style requested by the instructor. Remember that typos and formatting mistakes are unacceptable as they undermine even perfectly researched and structured papers. Follow these three steps to ensure effective polishing: read your paper aloud, ask someone else to read it to have a fresh perspective, and use spell check software.

How to Write a Research Paper That Will Be Really Convincing

Analytical skills and the ability to logically expressing one’s thoughts in a formal manner are as crucial in academic writing as knowledge of the study area. Thankfully, there are many ways to optimize the process and finish task properly and on time:

• Plan your work and set deadlines for each part of the assignment. It is easier to focus on small, separate portions day by day than write a paper in a rush before your deadline.
• Discuss your thesis statement with the instructor. Together, you will make the thesis concise and focused on the point you are going to disclose in your writing.
• Think about the intended audience of your research essay before starting to write it: whether it is a general audience that does not know much about the topic or community of scholars. Both writing style and structure of writing differ significantly depending on the audience.
• Always take notes so that all important details are included and nothing is omitted.
• Be careful with sources as all of them must be reliable to give solid evidence.
• Add proper citations with page numbers for all facts that you collect during research. This will help you to avoid wasting time looking over all sources again while formatting the paper.
• You don’t know how to type a research paper? Indeed, the scope of work is immense, so a developing detailed written outline with all main arguments will be extremely helpful in the early writing stages as you keep the whole picture in mind.
• Think about the word count to be allocated to each part. Students often devote a large part of their papers to a background, leaving not enough space for their own analysis, which affects the quality of their argument.
• Do not work completely alone. Work together with your peers and show your first draft to the instructor for useful feedback.
• Leave enough time for final proofreading and formatting of the completed task. Be warned that this process takes more time than you usually expect. Overlooking small mistakes while rushing is plausible.

Checklist: Have I met all requirements of what is a research essay?

• Is my topic focused on discussing something new in my chosen field of study?
• Is there enough information available in this particular field?
• Have I utilized only reliable and academic sources?
• Is it possible to gather evidence and find proper answers to my research question and prove my claim?
• Have I included all the requested components mentioned in the outline? Is the research paper structure clear?
• Did I cite all facts and data taken from outside sources so that any plagiarism issues are effectively prevented?
• Did I summarize all my findings in a concise conclusion?
• Have I polished the paper before submission?

The Importance of Proper Formatting

This aspect of the research paper writing process depends not only on the general educational institution’s requirements or specific instructor’s guidelines but also on the chosen subject and field. Details about formatting demands are the last among research paper tips. The main demand for a student who wants to know how to format a research paper is to follow all features of the chosen style attentively. Do not mix different styles in one paper:

APA : Usually used in Medicine, Psychological and Social sciences;

MLA: Widely used in the Humanities;

Harvard: There is no particular study area that uses only this style, but it occurs more often in Social sciences and the Humanities;

Chicago/Turabian style citation generator is useful for formatting research papers in Business and History studies’ fields;

IEEE: Became standard for specialists in Engineering, Computer, and Information science;

ASA: Required for publications in the field of Sociology;

AMA: Prevalent in Healthcare, Nursing, and Medicine fields of study;

CSE: This style is obligatory for those who study Life sciences, especially Biology;

APSA: Students majoring in Political Science should know all details of this style.

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Is there a way to get help.

Choosing a topic, researching, conducting experiments, using formal language, checking if all formatting requirements are met - the whole process of writing a research paper may appear overwhelming, sometimes even scary. One might think: “How can I write my paper perfectly if it takes years to become a great writer?” And the answer is positive since there are quality services that provide around-the-clock assistance of native-speaking writers with graduate degrees who can help you solve all academic writing issues. Learning is easier if someone can provide experienced backup with the research and writing process itself.

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What a Thesis Paper is and How to Write One

From choosing a topic and conducting research to crafting a strong argument, writing a thesis paper can be a rewarding experience.

It can also be a challenging experience. If you've never written a thesis paper before, you may not know where to start. You may not even be sure exactly what a thesis paper is. But don't worry; the right support and resources can help you navigate this writing process.

What is a Thesis Paper?

A thesis paper is a type of academic essay that you might write as a graduation requirement for certain bachelor's, master's or honors programs. Thesis papers present your own original research or analysis on a specific topic related to your field.

“In some ways, a thesis paper can look a lot like a novella,” said Shana Chartier , director of information literacy at Southern New Hampshire University (SNHU). “It’s too short to be a full-length novel, but with the standard size of 40-60 pages (for a bachelor’s) and 60-100 pages (for a master’s), it is a robust exploration of a topic, explaining one’s understanding of a topic based on personal research.”

Chartier has worked in academia for over 13 years and at SNHU for nearly eight. In her role as an instructor and director, Chartier has helped to guide students through the writing process, like editing and providing resources.

Chartier has written and published academic papers such as "Augmented Reality Gamifies the Library: A Ride Through the Technological Frontier" and "Going Beyond the One-Shot: Spiraling Information Literacy Across Four Years." Both of these academic papers required Chartier to have hands-on experience with the subject matter. Like a thesis paper, they also involved hypothesizing and doing original research to come to a conclusion.

“When writing a thesis paper, the importance of staying organized cannot be overstated,” said Chartier. “Mapping out each step of the way, making firm and soft deadlines... and having other pairs of eyes on your work to ensure academic accuracy and clean editing are crucial to writing a successful paper.”

How Do I Choose a Topic For My Thesis Paper?

What your thesis paper is for will determine some of the specific requirements and steps you might take, but the first step is usually the same: Choosing a topic.

“Choosing a topic can be daunting," said Rochelle Attari , a peer tutor at SNHU. "But if (you) stick with a subject (you're) interested in... choosing a topic is much more manageable.”

Similar to a thesis, Attari recently finished the capstone  for her bachelor’s in psychology . Her bachelor’s concentration is in forensics, and her capstone focused on the topic of using a combined therapy model for inmates who experience substance abuse issues to reduce recidivism.

“The hardest part was deciding what I wanted to focus on,” Attari said. “But once I nailed down my topic, each milestone was more straightforward.”

In her own writing experience, Attari said brainstorming was an important step when choosing her topic. She recommends writing down different ideas on a piece of paper and doing some preliminary research on what’s already been written on your topic.

By doing this exercise, you can narrow or broaden your ideas until you’ve found a topic you’re excited about. " Brainstorming is essential when writing a paper and is not a last-minute activity,” Attari said.

How Do I Structure My Thesis Paper?

Thesis papers tend to have a standard format with common sections as the building blocks.

While the structure Attari describes below will work for many theses, it’s important to double-check with your program to see if there are any specific requirements. Writing a thesis for a Master of Fine Arts, for example, might actually look more like a fiction novel.

According to Attari, a thesis paper is often structured with the following major sections:

Introduction

• Literature review
• Methods, results

Now, let’s take a closer look at what each different section should include.

Your introduction is your opportunity to present the topic of your thesis paper. In this section, you can explain why that topic is important. The introduction is also the place to include your thesis statement, which shows your stance in the paper.

Attari said that writing an introduction can be tricky, especially when you're trying to capture your reader’s attention and state your argument.

“I have found that starting with a statement of truth about a topic that pertains to an issue I am writing about typically does the trick,” Attari said. She demonstrated this advice in an example introduction she wrote for a paper on the effects of daylight in Alaska:

In the continental United States, we can always count on the sun rising and setting around the same time each day, but in Alaska, during certain times of the year, the sun rises and does not set for weeks. Research has shown that the sun provides vitamin D and is an essential part of our health, but little is known about how daylight twenty-four hours a day affects the circadian rhythm and sleep.

In the example Attari wrote, she introduces the topic and informs the reader what the paper will cover. Somewhere in her intro, she said she would also include her thesis statement, which might be:

Twenty-four hours of daylight over an extended period does not affect sleep patterns in humans and is not the cause of daytime fatigue in northern Alaska .

Literature Review

In the literature review, you'll look at what information is already out there about your topic. “This is where scholarly articles  about your topic are essential,” said Attari. “These articles will help you find the gap in research that you have identified and will also support your thesis statement."

Telling your reader what research has already been done will help them see how your research fits into the larger conversation. Most university libraries offer databases of scholarly/peer-reviewed articles that can be helpful in your search.

In the methods section of your thesis paper, you get to explain how you learned what you learned. This might include what experiment you conducted as a part of your independent research.

“For instance,” Attari said, “if you are a psychology major and have identified a gap in research on which therapies are effective for anxiety, your methods section would consist of the number of participants, the type of experiment and any other particulars you would use for that experiment.”

In this section, you'll explain the results of your study. For example, building on the psychology example Attari outlined, you might share self-reported anxiety levels for participants trying different kinds of therapies. To help you communicate your results clearly, you might include data, charts, tables or other visualizations.

The discussion section of your thesis paper is where you will analyze and interpret the results you presented in the previous section. This is where you can discuss what your findings really mean or compare them to the research you found in your literature review.

The discussion section is your chance to show why the data you collected matters and how it fits into bigger conversations in your field.

The conclusion of your thesis paper is your opportunity to sum up your argument and leave your reader thinking about why your research matters.

Attari breaks the conclusion down into simple parts. “You restate the original issue and thesis statement, explain the experiment's results and discuss possible next steps for further research,” she said.

Find Your Program

Resources to help write your thesis paper.

While your thesis paper may be based on your independent research, writing it doesn’t have to be a solitary process. Asking for help and using the resources that are available to you can make the process easier.

If you're writing a thesis paper, some resources Chartier encourages you to use are:

• Citation Handbooks: An online citation guide or handbook can help you ensure your citations are correct. APA , MLA and Chicago styles have all published their own guides.
• Citation Generators: There are many citation generator tools that help you to create citations. Some — like RefWorks — even let you directly import citations from library databases as you research.
• Your Library's Website: Many academic and public libraries allow patrons to access resources like databases or FAQs. Some FAQs at the SNHU library that might be helpful in your thesis writing process include “ How do I read a scholarly article? ” or “ What is a research question and how do I develop one? ”

It can also be helpful to check out what coaching or tutoring options are available through your school. At SNHU, for example, the Academic Support Center offers writing and grammar workshops , and students can access 24/7 tutoring and 1:1 sessions with peer tutors, like Attari.

"Students can even submit their papers and receive written feedback... like revisions and editing suggestions," she said.

If you are writing a thesis paper, there are many resources available to you. It's a long paper, but with the right mindset and support, you can successfully navigate the process.

“Pace yourself,” said Chartier. “This is a marathon, not a sprint. Setting smaller goals to get to the big finish line can make the process seem less daunting, and remember to be proud of yourself and celebrate your accomplishment once you’re done. Writing a thesis is no small task, and it’s important work for the scholarly community.”

A degree can change your life. Choose your program  from 200+ SNHU degrees that can take you where you want to go.

Meg Palmer ’18 is a writer and scholar by trade who loves reading, riding her bike and singing in a barbershop quartet. She earned her bachelor’s degree in English, language and literature at Southern New Hampshire University (SNHU) and her master’s degree in writing, rhetoric and discourse at DePaul University (’20). While attending SNHU, she served as the editor-in-chief of the campus student newspaper, The Penmen Press, where she deepened her passion for writing. Meg is an adjunct professor at Johnson and Wales University, where she teaches first year writing, honors composition, and public speaking. Connect with her on LinkedIn .

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About southern new hampshire university.

SNHU is a nonprofit, accredited university with a mission to make high-quality education more accessible and affordable for everyone.

Founded in 1932, and online since 1995, we’ve helped countless students reach their goals with flexible, career-focused programs . Our 300-acre campus in Manchester, NH is home to over 3,000 students, and we serve over 135,000 students online. Visit our about SNHU  page to learn more about our mission, accreditations, leadership team, national recognitions and awards.

A Good check on the Bayes factor

• Original Manuscript
• Open access
• Published: 04 September 2024

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You have full access to this open access article

• Nikola Sekulovski   ORCID: orcid.org/0000-0001-7032-1684 1 ,
• Maarten Marsman   ORCID: orcid.org/0000-0001-5309-7502 1 &
• Eric-Jan Wagenmakers   ORCID: orcid.org/0000-0003-1596-1034 1  

Bayes factor hypothesis testing provides a powerful framework for assessing the evidence in favor of competing hypotheses. To obtain Bayes factors, statisticians often require advanced, non-standard tools, making it important to confirm that the methodology is computationally sound. This paper seeks to validate Bayes factor calculations by applying two theorems attributed to Alan Turing and Jack Good. The procedure entails simulating data sets under two hypotheses, calculating Bayes factors, and assessing whether their expected values align with theoretical expectations. We illustrate this method with an ANOVA example and a network psychometrics application, demonstrating its efficacy in detecting calculation errors and confirming the computational correctness of the Bayes factor results. This structured validation approach aims to provide researchers with a tool to enhance the credibility of Bayes factor hypothesis testing, fostering more robust and trustworthy scientific inferences.

Avoid common mistakes on your manuscript.

Introduction

The Bayes factor (Kass & Raftery, 1995 ; Jeffreys, 1935 ) serves as a valuable tool for testing scientific hypotheses by comparing the relative predictive adequacy of two competing statistical models. In recent decades, there has been a surge in the adoption of Bayes factors as a tool for hypothesis testing (e.g., in psychology, Heck et al., 2023 ; van de Schoot et al., 2017 ). This increasing trend towards Bayesian hypothesis testing and model comparison has been catalyzed by a growing critique of traditional frequentist null hypothesis significance testing methods (e.g., Wasserstein and Lazar, 2016 ; Wagenmakers, 2007 ; Cohen, 1994 ; Wagenmakers et al., 2018b ; Benjamin et al., 2018 ; for an early critique see Edwards et al., 1963 ). In addition, the emergence of user-friendly software packages (e.g., JASP Team, 2023 ; Morey and Rouder, 2022 ; Gu et al., 2021 ) and associated tutorial articles have played a crucial role in making the benefits of the Bayesian framework more accessible to applied researchers (e.g., van Doorn et al., 2021 ; Rouder et al., 2012 ; Hoijtink et al., 2019 ; Marsman and Wagenmakers, 2017 ; Wagenmakers et al., 2018b ; Wagenmakers et al., 2018a ). Overall, this upswing in Bayesian methodology has ushered in a new era of statistical analysis, offering researchers valuable alternatives to traditional approaches.

Although Bayes factors have gained popularity in scientific practice, calculating them can be challenging, especially when comparing the relative likelihood of two complex models, such as hierarchical or nonlinear models with a large number of parameters. In such cases, Bayes factors often need to be approximated using various numerical (sampling) techniques such as bridge sampling (Gronau et al., 2017 ) or path sampling (Zhou et al., 2012 ); for a general introduction to stochastic sampling in Bayesian inference see Gamerman and Lopes ( 2006 ). These techniques often require the user to specify proposal distributions or tune certain parameters within the sampler, which may lead to inaccuracies. There are also state-of-the-art sampling methods designed to obtain joint posterior probabilities over many models; some notable examples of these transdimensional methods are Reversible Jump MCMC (Green, 1995 ), MCMC with mixtures of mutually singular distributions (Gottardo & Raftery, 2008 ) and the product space method (Lodewyckx et al., 2011 ; Carlin & Chib, 1995 ). These methods, even though very powerful, are quite complex to implement in software and therefore error-prone. Therefore, despite their utility, the use of these numerical techniques can introduce errors, such as the one highlighted by Tsukamura and Okada ( 2023 ), who pointed out a common coding error when computing Bayes factors in certain settings in the Stan programming language (Stan Development Team, 2023 ). Recently, Schad and Vasishth ( 2024 ) showed that Bayes factor estimates can be biased in some commonly used factorial designs.

In addition to the potential inaccuracies of existing approac-hes, ongoing research is constantly advancing the methods used to compute Bayes factors; a recent development by Kim and Rockova ( 2023 ) introduces a deep learning estimator as an addition to the toolkit of techniques available for computing Bayes factors. While the diversity of computational approaches is crucial, it is important to note that the complexity of these tools can lead to inaccuracies in Bayes factor calculations in applied research contexts. Thus, the development of appropriate controls and checks becomes imperative.

Schad et al. ( 2022 ) highlight five key considerations that warrant attention when computing Bayes factors, two of which are (i) the Bayes factor estimates for complex statistical models can be unstable, and (ii) the Bayes factor estimates can be biased. Therefore, Schad et al. ( 2022 ) propose a structured approach based on simulation-based calibration, which was originally developed as a method to validate the computational correctness of applied Bayesian inference more generally, and use it to verify the accuracy of Bayes factor calculations (see Talts et al., 2018 ; Cook et al., 2006 ; Geweke, 2004 ). Their method is based on the idea that that the marginal expected posterior model probability is equal to the prior model probability. We provide a more detailed description of the method proposed by Schad et al. ( 2022 ) in one of the following sections.

Before proposing another formal Bayes factor check in the spirit of the one by Schad et al. ( 2022 ), we would like to mention two other methods that, while not explicitly described as Bayes factor checks, can be used for this purpose. For the first method, suppose a researcher is interested in computing the Bayes factor for the relative adequacy of two complex (possibly non-nested) models, \(\mathcal {H}_1\) and \(\mathcal {H}_{\text {2}}\) , and has already chosen a numerical method implemented in some software for computing \(\text {BF}_{12}\) . To check that the calculation has been carried out correctly, they can construct nested versions of each of the models by selecting a single parameter and setting it to its maximum likelihood estimate (MLE) value, which would act as a surrogate oracle null model. They can then use the Savage–Dickey density ratio (Dickey & Lientz, 1970 ; Wagenmakers et al., 2010 ) to compute \(\text {BF}_{\text {ou}}\) – the Bayes factor in favor of the oracle null over the unconstrained model – for both \(\mathcal {H}_1\) and \(\mathcal {H}_{\text {2}}\) . When both models have Savage–Dickey \(\text {BF}_{\text {ou}}\) ’s that match the \(\text {BF}_{\text {ou}}\) ’s obtained from the method under scrutiny, then this gives the researcher reason to believe that \(\text {BF}_{12}\) has been computed correctly. A similar approach has been implemented by Gronau et al. ( 2020 ) for computing the marginal likelihood in evidence accumulation models, achieved by introducing a Warp-III bridge sampling algorithm. A second method to check the Bayes factor is pragmatic and can be used whenever multiple computational methods are available for a specific application. The idea is that one can use all methods – if they agree, they will mutually reinforce the conclusion and provide evidence that the Bayes factor has been calculated correctly. Furthermore, a Bayes factor can be computed for this agreement. Given that the probability of two correct methods yielding the same outcome is 1, the Bayes factor is calculated as 1 divided by the probability of a chance agreement between two methods, assuming at least one is incorrect. Since the probability of two methods converging on the same wrong value is very small, the Bayes factor provides very strong evidence that both methods are correct.

In this paper, we draw attention to two theorems by Alan Turing and Jack Good (e.g., Good, 1950 , 1985 , 1994 ), which they proposed could be used to verify the computation of Bayes factors. We introduce a structured approach to perform this verification, aiming to revive and highlight an idea that, until now, has not received the attention it deserves.

The remainder of this paper is structured as follows. In the next section, we provide an overview of the material in Good ( 1985 ), where we discuss the theorems, introduce key concepts, and establish notation. Following this, we present a simple binomial model to illustrate the conditions under which these theorems apply. Next, we outline the workflow for the Bayes factor check tool and offer two numerical examples to demonstrate its application-one employing an ANOVA design and the other utilizing a complex psychometric network model. We conclude the paper by comparing the strengths and limitations of this method, as well as highlighting potential avenues for improvement.

Theoretical background

The weight of evidence.

Good ( 1985 ) points out that the concept of weight of evidence , which is used in many areas (e.g., in science, medicine, law, and daily life), is a function of the probabilities of the data under two hypotheses (see also Good, 1950 , 1965 , 1979 , 1994 , 1995 ). Formally, this relation takes the form

where \(\mathcal {W}(\mathcal {H}_1:\text {data})\) denotes the weight of evidence in favor of the hypothesis \(\mathcal {H}_1\) provided by the evidence (data), while \(p(\text {data} \mid \mathcal {H}_\cdot )\) denote the probabilities of the data under each of the hypotheses (i.e., what is usually called the marginal likelihood of the data). Good ( 1985 ) further points out that this function should be mathematically independent of \(p(\mathcal {H}_\cdot )\) , known as the prior probability of a hypothesis, but that \(p(\mathcal {H}_\cdot \mid \text {data})\) (i.e., the posterior probability) should depend both on the weight of evidence and the prior probability. This relationship can therefore be expressed as

Thus, the Bayes factor can be interpreted as the factor by which the initial odds are multiplied to give the final odds, or as the ratio of the posterior odds for \(\mathcal {H}_1\) to its prior odds. When \(\mathcal {H}_1\) and \(\mathcal {H}_2\) are simple (point) hypotheses the Bayes factor is equal to the likelihood ratio (Royall, 2017 ). Good defined the weight of evidence as the logarithm of the Bayes factor (Good, 1950 , 1985 , 1994 ), because it is additive and symmetric (e.g., \(\log (\text {BF} = 10) = 2.3\) and \(\log (\text {BF} = {1}/{10}) = -2.3\) , the average of which is 0). In contrast, the Bayes factor scale is not symmetric – the average of a Bayes factor of 10 and 1/10 is larger than 1. In writing about an appropriate metric for the weight of evidence, Good ( 1985 ) draws attention to a counterintuitive theorem about the Bayes factor, and suggested it may be used to check whether a particular procedure computes Bayes factors correctly. The theorem states that “the expected (Bayes) factor in favor of the false hypothesis is 1” . Good attributed this paradoxical insight to Alan Turing, whose team at Bletchley Park decrypted German naval messages during World War II (cf. Zabell, 2023 ).

In the following subsection, we first introduce Turing’s theorem. We then present another related theorem proposed by Good, which shows the relationship between higher-order moments of Bayes factors.

Moments of the Bayes factor

Theorem 1: the expected (bayes) factor in favor of the false hypothesis equals 1. – alan turing.

Suppose the possible outcomes of an experiment are \(E_1, E_2,...,E_M\) , where \(\mathcal {H}_t\) is the true hypothesis and \(\mathcal {H}_f\) is the false hypothesis. Footnote 1 Taking the expectation of the Bayes factor in favor of one of the hypotheses simply means calculating the weighted average of that Bayes factor where the weights are provided by the probability of the evidence given the true hypothesis (i.e., \(p(\text {E} \mid \mathcal {H}_t)\) ). Then the expected Bayes factor in favor of \(\mathcal {H}_f\) is given by

\(\square \)

The theorem states that the expected Bayes factor against the truth is 1, regardless of sample size. For example, consider a binomial experiment with \(n = 2\) trials and k successes, where \(\mathcal {H}_0\text {: } \theta = {1}/{2}\) and \(\mathcal {H}_1\text {: } \theta \sim \text {Beta}(\alpha =1\text {, }\beta =1)\) . There are three possible outcomes for this experiment, \(E_1\text {: } k = 0\) , \(E_2\text {: } k = 1\) , and \(E_3\text {: } k = 2\) . It follows from the beta-binomial distribution that the probability is the same for each possible outcome under \(\mathcal {H}_1\) , which in this case is 1/3 \(\forall \ E_i\) . Under \(\mathcal {H}_0\) the probability of \(E_1\) and \(E_3\) is 1/4 and for \(E_2\) is 1/2. Assuming that \(\mathcal {H}_1\) is the correct hypotheses we have

As a Bayes factor of 1 indicates the complete absence of evidence, this theorem is paradoxical; intuition suggests that – especially for large sample sizes – the average Bayes factor against the truth should be much smaller than 1. As mentioned in the previous subsection, unlike the weight of evidence, the Bayes factor is not symmetric. For example, the mean of \(\text {BF}_{10} = {1}/{10}\) and \(\text {BF}_{10} = 10\) is 5.05 and not 1, whereas the mean of \(\log ({1}/{10})\) and \(\log (10)\) is 0. This theorem implies that the sampling distribution of the Bayes factor is skewed to the right. Therefore, Good ( 1985 ) suggests that the Bayes factor is likely to have a (roughly) log-normal distribution while the weight of evidence has a (roughly) normal distribution (see also, Good, 1994 ). Finally, Good ( 1985 ) shows that the expected weight of evidence in favor of the truth (i.e., \(\mathcal {W}(\mathcal {H}_t: \text {data})\) ) is non-negative and vanishes when the weight of evidence is 0. This again illustrates that the weight of evidence is additive and its expected value is more meaningful than that of the Bayes factor.

Until now, Theorem 1 has been used almost exclusively to establish the universal bound on obtaining misleading evidence (e.g., Royall, 2000 ; Sanborn and Hills, 2014 ). The universal bound states that the probability of obtaining a Bayes factor greater than or equal to \({1}/{\alpha }\) in favor of the false hypothesis is less than or equal to some threshold \(\alpha \) . For example, the probability of obtaining a Bayes factor of 100 in favor of the false hypothesis is less than or equal to \(1\%\) . This is related to the fact that a Bayes factor in favor of the false hypothesis is related to a non-negative test martingale where the expected value of the martingale at any point t is 1. Footnote 2 That is, the test martingale measures the evidence against a hypothesis \(\mathcal {H}\) , and its inverse at some point t is a Bayes factor in favor of \(\mathcal {H}\) (see e.g., Shafer et al., 2011 ; Grünwald et al., 2020 ). Footnote 3 These properties have also been used independently in sequential analysis by Abraham Wald (Wald, 1945 ). Since the concept of a martingale (Ville, 1939 ) predates the work of Good and Turing, this suggests that they were not the first to be (at least implicitly) aware of this theorem. However, Jack Good was apparently the first to propose that the theorem may be used to verify the computation of the Bayes factor (Good, 1985 , p. 255). This paper implements Good’s idea.

Theorem 1 shows that the first moment of the Bayes factor under the false hypothesis is equal to 1. This is the main result; however, Good ( 1985 ) shows that Theorem 1 is a special case of another theorem which shows the equivalence between higher-order moments of Bayes factors; we turn to this theorem next.

Theorem 2: Equivalence of moments for Bayes factors under \(\mathcal {H}_1\) and \(\mathcal {H}_2 \) . – Jack Good

The second theorem generalizes the first and states that

The theorem can be expressed as

Using the product law of exponents, the right-hand side of the equation above can be rewritten as

which immediately proves the result.

This theorem states that the \(k^{th}\) moment of the Bayes factor in favor of \(\mathcal {H}_1\) about the origin, given that \(\mathcal {H}_1\) is true is equal to the \((k+1)^{st}\) moment of the Bayes factor in favor of \(\mathcal {H}_1\) given that \(\mathcal {H}_2\) is true. Here we refer to the raw moments, that is the moments about the origin and not to the central moments (such as the variance, which is the second moment about the mean). When \(k = 0\) , this result reduces to that of the first theorem.

Considering the binomial example from earlier with \(n = 2\) and hypotheses \(\mathcal {H}_0\text {: } \theta = {1}/{2}\) and \(\mathcal {H}_1\text {: } \theta \sim \text {Beta}(\alpha = 1\text {, } \beta = 1)\) one can see that

Numerical illustrations

Consider a sequence of n coin tosses that forms the basis of a test of the null hypothesis \(\mathcal {H}_0\text {: } \theta = {1}/{2}\) against the alternative hypothesis \(\mathcal {H}_1\text {: } \theta \sim \text {Uniform}(0,1)\) , where \(\theta \) represents the probability of the coin landing heads. Footnote 4 Additionally, in the last part of this section, we consider a restricted (directional) hypothesis \(\mathcal {H}_{\text {r}}\text {: } \theta > {1}/{2}\) . We simulated a total of \(m = 100{,}000\) data sets either under \(\mathcal {H}_0\) , \(\mathcal {H}_1\) or \(\mathcal {H}_{\text {r}}\) for sample sizes of \(n = \{10, 50, 100\}\) . For each simulation setting, we averaged the \(m = 2, \dots , 100{,}000\) Bayes factors in favor of the wrong hypothesis. The code to reproduce the examples in this paper is publicly available in an OSF repository at https://osf.io/438vy/ .

The average Bayes factor in favor of the null hypothesis quickly converges to 1 for synthetic data sets generated under the alternative hypothesis. The figure depicts the average \(\text {BF}_{01}\) as a function of the number of synthetic data sets m generated under \(\mathcal {H}_1\) , for \(n = 10, 50, 100\) ; the black solid line is for \(n = 10\) , the red dashed line is for \(n = 50\) , and the green dotted line is for \(n = 100\) . The left panel plots the cumulative mean across \(m = 100{,}000\) data sets; the right panel zooms in on the first \(m = 1{,}000\) iterations

The average Bayes factor in favor of the alternative hypothesis does not converge to 1 as n increases for the synthetic data sets generated under the null hypothesis. The figure depicts the average \(\text {BF}_{10}\) as a function of the number of synthetic data sets m generated under \(\mathcal {H}_0\) , for \(n = 10, 50, 100\) ; the black solid line is for \(n = 10\) , the red dashed line is for \(n = 50\) , and the green dotted line is for \(n = 100\)

Illustration of Theorem 1

Figure 1 illustrates the situation where \(\mathcal {H}_1\) is true and plots the mean Bayes factor in favor of \(\mathcal {H}_0\) , that is, the average \(\text {BF}_{01}\) . For all three values of n , the average \(\text {BF}_{01}\) quickly stabilizes towards 1. There is a slightly larger instability in the mean for larger sample sizes n ; however, the results quickly converge as m increases.

Figure 2 illustrates the situation where \(\mathcal {H}_0\) is true and plots the mean Bayes factor in favor of \(\mathcal {H}_1\) , that is, the average \(\text {BF}_{10}\) calculated for the data sets simulated under \(\mathcal {H}_0\) . It is immediately evident that for larger sample size n , the mean \(\text {BF}_{10}\) becomes unstable and moves away from 1. As m increases, the average appears to stabilize on values different from 1. This observation suggests that under \(\mathcal {H}_0\) , with a large sample size, a very large number of iterations would be necessary to obtain a mean \(\text {BF}_{10}\) that approaches 1. This phenomenon arises because, under \(\mathcal {H}_0\) , there exist rare outcomes that produce extreme \(\text {BF}_{10}\) values, a situation that does not occur with \(\text {BF}_{01}\) when \(\mathcal {H}_1\) is the true hypothesis. The chance of encountering these extreme results under \(\mathcal {H}_0\) , which in turn yields extreme \(\text {BF}_{10}\) values, becomes less probable as the sample size n increases. Consequently, in this scenario the mean \(\text {BF}_{10}\) does not quickly converge to 1. We conclude that the Turing–Good theorems exhibit more robust performance in practice when the true hypothesis is not a point null hypothesis (i.e., when the more complicated hypothesis is true).

When the encompassing hypothesis is true, the average Bayes factor in favor of the restricted hypothesis rapidly converges to 1, whereas for when the restricted hypothesis is true the average Bayes factor in favor of the encompassing hypothesis does not converge to 1 when the sample size is large. The left panel shows the average \(\text {BF}_{\text {re}}\) as a function of the number of synthetic data sets m generated under \(\mathcal {H}_{\text {e}}\) , for \(n = 10, 50, 100\) ; the black solid line is for \(n = 10\) , the red dashed line is for \(n = 50\) , and the green dotted line is for \(n = 100\) . The right panel shows the average \(\text {BF}_{\text {er}}\) as a function of the number of synthetic data sets m generated under \(\mathcal {H}_{\text {r}}\) , for \(n = 10, 50, 100\)

Illustration of Theorem 2

To illustrate the second theorem, we compare the first moment of the Bayes factor in favor of the true hypothesis with the second raw moment in favor of the false hypothesis. We first calculated these moments analytically for \(n = \{10, 50, 100\}\) with \(\mathcal {H}_0\text {: } \theta = {1}/{2}\) and \(\mathcal {H}_1\text {: } \theta \sim \text {Uniform}(0,1)\) . We then calculated the same moments for the Bayes factors based on the synthetic data. We calculated the second raw moments for the Bayes factors using the following formula:

The results are summarized in Table 1 .

The eighth column of Table 1 shows that, on average, the evidence for \(\mathcal {H}_0\) increases with the sample size n . Comparing the seventh and eighth columns (shaded in gray) confirms that the mean of \(\text {BF}_{01}\) when \(\mathcal {H}_0\) is true is approximately equal to the second raw moment of \(\text {BF}_{01}\) when \(\mathcal {H}_1\) is true, regardless of sample size.

When the restricted hypothesis is true, the Bayes factor in favor of the null hypothesis rapidly converges to 1, whereas when the null hypothesis is true the Bayes factor in favor of the restricted hypothesis does not converge to 1 when the sample size is large. The left panel shows the average \(\text {BF}_{\text {0r}}\) as a function of the number of synthetic data sets m generated under \(\mathcal {H}_{\text {r}}\) , for \(n = 10, 50, 100\) ; the black solid line is for \(n = 10\) , the red dashed line is for \(n = 50\) , and the green dotted line is for \(n = 100\) . The right panel shows the average \(\text {BF}_{\text {r0}}\) as a function of the number of synthetic data sets m generated under \(\mathcal {H}_0\) , for \(n = 10, 50, 100\)

The sixth column of Table 1 shows that the expected evidence in favor of \(\mathcal {H}_1\) becomes extreme as n increases; contrasting this with the second moment of \(\text {BF}_{10}\) when \(\mathcal {H}_0\) shows that the values are equal for \(n = 10\) , but as n increases these values diverge. These instabilities are due to the same reasons highlighted in the previous subsection. Note, however, that the theorems still hold in this situation, and for a very large number of iterations m the moments are expected to eventually converge. This is supported by the analytical solutions presented in columns 2 through 6. However, the results computed from the synthetic data suggest that in practice, when dealing with a point null hypothesis, one should compute the first moment from the data generated under \(\mathcal {H}_0\) and compare it with the second raw moment computed from the data generated under \(\mathcal {H}_1\) .

It is also possible to compare, for example, the second and third raw moments. In the results from the simulation, the second raw moments of \(\text {BF}_{01}\) for the data sets generated under \(\mathcal {H}_0\) are 4.28, 19, and 37.32, for \(n = 10, 50\) , and 100, respectively. And the third raw moments of \(\text {BF}_{01}\) for the data sets generated under \(\mathcal {H}_1\) are 4.3, 18.8 and 37.1. These results illustrate that the second theorem holds for higher-order moments in general.

Directional hypotheses

In this subsection, we examine how the Bayes factor behaves when one of the hypotheses under consideration is a directional (i.e., inequality constrained or restricted) hypothesis. Hypotheses that consist of a combination of inequality and equality constraints among the parameters are known as informative hypotheses (Hoijtink, 2011 ). Informative hypotheses allow researchers to express their substantive theory and expectations and have become popular in recent years; therefore, it is important to also consider how inequality constrained hypotheses perform under the two theorems.

We make use of the restricted hypothesis \(\mathcal {H}_{\text {r}}: \theta > {1}/{2}\) , which we specify as \(\mathcal {H}_{\text {r}}: \theta \sim \text {Uniform}(0.5, 1)\) . This is equivalent to setting a truncated Beta distribution from 0.5 to 1 for the probability \(\theta \) . We then compare \(\mathcal {H}_{\text {r}}\) with the alternative hypothesis ( \(\mathcal {H}_1\) ) and the null hypothesis ( \(\mathcal {H}_0\) ) from the previous subsections. In line with previous literature (e.g., Klugkist et al., 2005 ), we rename the alternative hypothesis ( \(\mathcal {H}_1\) ) to the encompassing hypothesis and denote it as \(\mathcal {H}_{\text {e}}\) , as both \(\mathcal {H}_0\) and \(\mathcal {H}_{\text {r}}\) are nested under this encompassing hypothesis.

Figure 3 illustrates the situation of comparing \(\mathcal {H}_{\text {e}}\) and \(\mathcal {H}_{\text {r}}\) . In the left plot, the average \(\text {BF}_{\text {re}}\) when \(\mathcal {H}_{\text {e}}\) is the true hypothesis quickly stabilizes towards 1 for all three sample size values. Note also that the initial fluctuations are all greater than 1; this is because half of the outcomes expected under \(\mathcal {H}_{\text {e}}\) are also plausible under \(\mathcal {H}_{\text {r}}\) . The right panel of Fig. 3 illustrates the reverse situation, where \(\mathcal {H}_{\text {r}}\) is the true hypothesis. As can be seen, the Bayes factor now does not quickly converge to 1 for larger sample sizes, because under \(\mathcal {H}_{\text {r}}\) , outcomes that produce large \(\text {BF}_{\text {er}}\) ’s are highly improbable; similar to the case when considering \(\text {BF}_{10}\) when \(\mathcal {H}_0\) is true (cf. Figure 2 ).

Figure 4 illustrates the situation of comparing \(\mathcal {H}_0\) with \(\mathcal {H}_{\text {r}}\) . In the left panel, the average \(\text {BF}_{0r}\) when \(\mathcal {H}_{\text {r}}\) is the true hypothesis approaches 1 for all three sample size values; note, however, that for \(n = 100\) it takes a considerable number of iterations for the average \(\text {BF}_{\text {0r}}\) to converge to 1. The right panel of Fig. 4 illustrates the situation when \(\mathcal {H}_0\) is the true hypothesis; as was the case in Fig. 2 , when the point (null) hypothesis is the true hypothesis, for a finite number of iterations, the average Bayes factor in favor of the false hypothesis does not converge to 1 as the sample size increases. Again, this is due to the fact that under \(\mathcal {H}_0\) very few outcomes produce large \(\text {BF}_{\text {r0}}\) .

Examining the third and fourth columns of Table 2 , we see that the second raw moment of \(\text {BF}_{\text {re}}\) when \(\mathcal {H}_{\text {e}}\) is true is equal to the mean of \(\text {BF}_{\text {re}}\) when \(\mathcal {H}_{\text {r}}\) is true. A similar observation can be made when comparing the sixth and ninth columns. This illustrates that the second theorem also holds for inequality-constrained hypotheses. However, if we compare the mean of \(\text {BF}_{\text {er}}\) when \(\mathcal {H}_{\text {e}}\) is true with the second moment of \(\text {BF}_{\text {er}}\) when \(\mathcal {H}_0\) is true, we observe that these values diverge, especially as the sample size increases. The same divergence occurs when we compare the mean of \(\text {BF}_{12}\) when \(\mathcal {H}_1\) is true with the second moment of \(\text {BF}_{12}\) when \(\mathcal {H}_0\) is true (cf. Table 1 ).

These results illustrate that both theorems are applicable to directional hypotheses and can be used as a general method for checking Bayes factors. Furthermore, generalizing from all the examples, the first theorem shows more robust performance when the more general (encompassing) hypothesis is true. For the second theorem, the (more) specific hypothesis should be set to true, and the average Bayes factor in favor of the more specific hypothesis should be compared with the second moment of the Bayes factor in favor of the more specific hypothesis when the more general hypothesis is true.

An exception to the rule

In the philosophy of science, a universal generalization is a hypothesis stating that a parameter or characteristic is true for the entire population without exceptions (e.g., all ravens are black). So for the binomial example, this would be equivalent to \(\mathcal {H}_0\text {: } \theta = 1\) . The two theorems do not hold in this situation, since they require that the true hypothesis (in this case \(\mathcal {H}_0\) ) must assign a non-zero prior mass to all events that are considered plausible under the false hypothesis. In other words, both hypotheses must assign non-zero mass to the same sample space.

A formal approach for checking the Bayes factor calculation

In their method for checking the calculation of the Bayes factor, Schad et al. ( 2022 ) recommend simulating multiple data sets from statistical models (with predefined prior model probabilities) and then obtaining Bayes factors and posterior model probabilities using the same method that is to be used to calculate the Bayes factor(s) on the empirical data. This method represents a structured approach based on simulation-based calibration (Geweke, 2004 ; Cook et al., 2006 ). The idea is based on the fact that the expected posterior model probability should equal the prior model probability (see e.g., Skyrms, 1997 ; Goldstein, 1983 ; Huttegger, 2017 ). Therefore, if the average posterior model probability across the simulated data sets is equal to the prior model probability, then the calculation of the Bayes factor (and the posterior model probability) should be considered accurate.

For the correctly specified calculation the average \(\text {BF}_{01}\) rapidly converges to 1, whereas for the misspecified calculation, it does not. The figure depicts average \(\text {BF}_{01}\) calculated for the data generated under \(\mathcal {H}_1\) as a function of the number of synthetic data sets m . The Bayes factor is calculated using two different values for the scale of the scaled inverse chi-squared distribution

In this paper, we follow the approach by Schad et al. ( 2022 ) and propose a new method for checking the Bayes factor, based on Turing and Good’s theorems described in the previous sections. The check (steps 1-4) assumes that if the calculation of the Bayes factor is executed correctly and if all the assumptions are met, then its expected value in favor of the wrong hypothesis should be (approximately) equal to 1. Additionally, it is possible to extend this check by comparing higher-order moments (steps 5-6). After collecting the data and selecting the appropriate analysis, the proposed methodology can be summarized as follows:

Specify two rival models; since the prior can be seen as an integral part of the model (e.g., Vanpaemel, 2010 ; Vanpaemel and Lee, 2012 ), this step includes the assignment of prior distributions to the model parameters.

Calculate the Bayes factor based on the observed data using the computational methodology of interest.

Select one of the models to generate simulated data from – we strongly recommend this to be the more complex model; in nested models, one should therefore simulate from the alternative hypothesis and not from the null hypothesis.

Sample data from the prior predictive distribution. This could, for example, be done by selecting a parameter (vector) from the joint prior distribution and use this to generate a synthetic data set of the same length as the observed data (although it could be any length in principle).

Compute the Bayes factor in favor of the false hypothesis over the true hypothesis for the synthetic data set, using the same computational technique used for the observed data (step 2).

Repeat steps b-c m times, yielding m Bayes factors in favor of the false hypothesis.

Calculate the average Bayes factor in favor of the false hypothesis across the m Bayes factors obtained in the previous step. If this mean value is close to 1 for a sufficiently large number of simulations m , this provides strong evidence that the Bayes factor calculation has been executed correctly. Then one can confidently report the value obtained in step 2.

Additionally, simulate data as described in step 3, but this time set the other hypothesis under consideration (e.g., \(\mathcal {H}_0\) ) to true. Calculate the Bayes factor in favor of the true hypothesis. Repeat this step m times and calculate the average Bayes factor in favor of the true hypothesis.

Compare the mean Bayes factor from step 5 with the second moment of the Bayes factor in favor of the wrong hypothesis based on the data generated in step 3. If these two values are approximately equal, this provides additional evidence that the Bayes factor calculation was performed correctly.

This step-by-step approach helps validate the Bayes factor calculations and ensures that the results obtained are reliable. More specifically, if the Bayes factor calculation is done correctly, we should be confident that there were no issues with the calculation of the Bayes factor. In the following two subsections, we illustrate these steps with two concrete examples.

Note that the purpose of the following examples-one using a simple Bayes factor for an intervention effect in an ANOVA design, and another using a transdimensional Bayes factor for the inclusion of an edge in a graphical model-is to demonstrate how to perform the proposed check. A comprehensive review of the performance of various software packages in calculating Bayes factors is beyond the scope of this paper.

Example 1: A Bayes factor test for an intervention effect in one-way ANOVA

Consider a one-way ANOVA model where the standard alternative hypothesis ( \(\mathcal {H}_1\) ), which states that not all means between the 3 groups are equal, is tested against the null hypothesis ( \(\mathcal {H}_0\) ), which states that the means are equal. The model can be expressed as

where \(y_i\) is the value of the dependent variable for participant i , \(\alpha \) is the intercept, \(x_i\) is the factor variable denoting the group membership, \(\beta \) is the parameter representing the effect of the experimental manipulation, and \(\epsilon _i\) is the residual term normally distributed around 0 with variance \(\sigma ^2\) . To calculate the Bayes factor on the empirical data one can use the default settings in the R package BayesFactor (Morey & Rouder, 2022 ). The function anovaBF assigns Jeffreys priors to the intercept and residual variance, and a normal prior to the main effect

where g is given an independent scaled inverse-chi-squared hyperprior with 1 degree of freedom. The interested reader is referred to Rouder et al. ( 2012 ) for the details of the prior specifications. We now illustrate how the check can be performed for the current example.

Suppose we have collected data from 150 participants (50 participants in each of the 3 groups) and we wish to test \(\mathcal {H}_1\) versus \(\mathcal {H}_0\) . We simulate \(m = 200{,}000\) data sets under \(\mathcal {H}_1\) by sampling the parameter \(\beta \) from its prior distribution, employing the same default specification as used in the package (i.e., applying a scaled inverse-chi-squared hyperprior for g with a scale of 1/2 and Jeffreys priors on \(\alpha \) and \(\sigma ^2\) with a value of \(\sigma ^2 = 0.5\) ). Additionally, we generate m datasets under \(\mathcal {H}_0\) by setting \(\beta = 0\) . In both cases, we calculate the Bayes factors using the default settings as described above. To illustrate what happens when the Bayes factor calculation is misspecified, we re-calculate the Bayes factor for the data generated under \(\mathcal {H}_1\) by altering the default value for the scale of the inverse chi-squared distribution. Specifically, we change the scale from medium to ultrawide , corresponding to values of 1/2 and 1, respectively. For the Bayes factors calculated on the data sets where \(\mathcal {H}_1\) is true, approximately 0.28% of the Bayes factors calculations failed due to computational difficulties.

Figure 5 depicts the cumulative mean for \(\text {BF}_{01}\) when \(\mathcal {H}_1\) is true. Notably, for the Bayes factors calculated using the default settings of the package, which precisely mirror how the data was generated, the average \(\text {BF}_{01}\) rapidly converges to 1. However, when there is a discrepancy between the data and the Bayes factor calculation, which for the purpose of this example was achieved by altering the scale of the inverse chi-squared hyperprior from 1/2 to 1, we notice that the average Bayes factor deviates significantly from 1. It eventually stabilizes at a value of approximately 3.16, illustrating the sensitivity of the Bayes factor when its calculation is misspecified.

For the second set of synthetic data generated under \(\mathcal {H}_0\) , we calculate the average \(\text {BF}_{01}\) , which yields a value of 8.18, which we can compare with the second raw moment of \(\text {BF}_{01}\) from the data sets where the alternative hypothesis is true, which yields a value of 8.15. This result provides additional proof that the calculation of the Bayes factor was done correctly.

Example 2: A Bayes factor test for conditional independence in a Markov random field model

Network psychometrics is a relatively new subdiscipline in which psychological constructs (e.g., intelligence, mental disorders) are conceptualized as complex systems of behavioral and cognitive factors (Marsman & Rhemtulla, 2022 ; Borsboom & Cramer, 2013 ). Psychometric network analysis is then used to infer the structure of such systems from multivariate psychological data (Borsboom et al., 2021 ). These analyses use graphical models known as Markov Random Fields (MRFs, Kindermann and Snell, 1980 ; Rozanov, 1982 ) in which psychological variables assume the role of the network nodes. The edges of the network express the direct influence of one variable on another given the remaining network variables, that is, that they are conditionally dependent , and the absence of an edge implies that the two variables are conditionally independent (Lauritzen, 2004 ). The Bayesian approach to analyzing these graphical models (Mohammadi & Wit, 2015 ; Marsman et al., 2015 ; Marsman, 2022 ; Marsman et al., 2023 ; Williams, 2021 ; Williams & Mulder, 2020 ) allows researchers to quantify the evidence in the data for the presence or absence of edges, and thus to formally test for conditional (in)dependence (see Sekulovski et al., 2024 , for an overview of three Bayesian methods for testing conditional independence).

Sekulovski et al. ( 2024 ) discuss two types of Bayes factor tests for conditional independence. In one test, the predictive success of a particular network structure with the relationship of interest is compared against the same network structure with the relationship of interest removed. One problem with testing for conditional independence in this way is that even for relatively small networks, there are many possible structures to consider, and as Sekulovski et al. ( 2024 ) have shown, Bayes factor tests for conditional independence can be highly sensitive to the choice of that network structure. In the second Bayes factor test, we use Bayesian model averaging (BMA, Hoeting et al., 1999 ; Hinne et al., 2020 ) and contrast the predictive success of all structures with the relationship of interest against the predictive success of all structures without that relationship. This is known as the inclusion Bayes factor (Marsman, 2022 ; Marsman et al., 2023 ). Sekulovski et al. ( 2024 ) showed that the inclusion Bayes factor is robust to variations in the structures underlying the rest of the network. However, the BMA methods for psychometric network analysis required to estimate the inclusion Bayes factor are much more complex and thus more prone to the computational problems identified above. For an accessible introduction to BMA with a specific example on network models, see Hinne et al. ( 2020 ) and for an accessible introduction to BMA analysis of psychometric network models, see Huth et al. ( 2023 ) and Sekulovski et al. ( 2024 ).

The average \(\text {BF}_{01}\) converges to 1. The figure depicts the average inclusion \(\text {BF}_{01}\) calculated for the data generated under \(\mathcal {H}_1\) as a function of the number of synthetic data sets m

In this paper, we scrutinize the Bayesian edge selection method developed by Marsman et al. ( 2023 ) for analyzing MRF models for binary and ordinal data, and which can be used to estimate the inclusion Bayes factor. This method, implemented in the R package bgms (Marsman et al., 2023 ), stipulates a discrete spike and slab prior distribution on the edge weights of the MRF, and models the inclusion and exclusion of pairwise relations in the model with an edge indicator ( \(\gamma \) ), which when present designates the corresponding edge weight a diffuse prior and when absent sets it to 0. That is, for a single edge weight \(\theta _{ij}\) , between variables i and j , the prior distribution can be expressed as

The transdimensional Markov chain Monte Carlo method proposed by Gottardo and Raftery ( 2008 ) is used to simulate from the multivariate posterior distribution of the MRF’s parameters and edge indicators. The output of this approach can be used to compute the inclusion Bayes factor which is defined as

Since the inclusion Bayes factor is an extension of the classical Bayes factor presented in Eq.  1 and involves a much more complex calculation, we wish to verify that its computation is performed correctly using the newly proposed methodology. Therefore, we simulated \(m = 30{,}000\) datasets with \(p = 5\) binary variables and \(N = 500\) observations each. We focus on testing whether the first two variables are conditionally independent, that is, we compare \(\mathcal {H}_0\text {: } \theta _{12} = 0\) with \(\mathcal {H}_1\text {: } \theta _{12} \ne 0\) . For the case where \(\mathcal {H}_1\) is true, we simulated data where all ten possible edges have an edge weight value of \(\theta _{ij} = 0.5\) . Additionally, for the case where \(\mathcal {H}_0\) is true, we simulated a second set of data by setting the focal edge weight parameter \(\theta _{12}\) to 0 and leaving the values of the nine remaining edge weights unchanged. We estimated the graphical model for each simulated data set using the R package bgms . We used a unit information prior for \(f_{slab}\) ; a Dirac measure at 0 for \(f_{spike}\) , and an independent Bernoulli distribution for each \(\gamma _{ij}\) with a prior inclusion probability of 1/2 (see Sekulovski et al., 2024 , for a detailed analysis of the prior distributions for these models). Under this prior specification, the prior inclusion odds are equal to 1. In cases where the posterior inclusion probability was equal to 1, we obtained undefined values for the inclusion Bayes factor (i.e., 1/0). For the data sets where \(\mathcal {H}_1\) was true, there were 9,345 Bayes factors with undefined values (31%), and for the data sets where \(\mathcal {H}_0\) was true, there were 53 undefined values (0.2%). To work around this problem, we set all undefined values to 1 + the highest observed finite value of the inclusion Bayes factor.

Figure 6 shows the cumulative mean of the inclusion \(\text {BF}_{01}\) when \(\mathcal {H}_1\) is true (i.e., there is an edge between variables 1 and 2). As the number of simulations increases, the mean inclusion \(\text {BF}_{01}\) stabilizes around 1 (1.01 at the last iteration), indicating that the inclusion Bayes factor obtained with this approach was computed correctly. In addition, we computed the mean \(\text {BF}_{01}\) when \(\mathcal {H}_0\) is true, which was 11.5, and compared it to the second moment of \(\text {BF}_{01}\) when \(\mathcal {H}_1\) is true, which was 9.96. These values are not equal. However, we suspect that the reason for this is twofold: first, the sample size N in each of the simulated data sets was quite large, and second, since the calculation of this Bayes factor is more involved, it probably takes many more iterations m to be sure that the moments are equal. Estimating these models takes much more time than estimating other more standard statistical models, so it was not computationally feasible to do more than \(m = 30{,}000\) repetitions under each of the hypotheses. In addition, we must consider the sampling variability of the simulated data sets. In other words, due to variability, not all of the simulated data sets will show support for the hypothesis under which they were simulated, further reducing the number of “effective” data sets. These reasons also justify the choice to recode the undefined inclusion Bayes factor values as we did, rather than omitting them altogether.

This paper presents a structured approach to checking the accuracy of Bayes factor calculations based on the theorems of Turing and Good. The approach provides researchers with a general and practical method for confirming that their Bayes factor results are reliable. Application to two concrete examples demonstrated the effectiveness of this approach in verifying the correctness of Bayes factor calculations. In particular, if the method of calculating the Bayes factor is consistent with the data generation process, the mean Bayes factor in favor of the false hypothesis converges to approximately 1, in accordance with the first theorem. Furthermore, comparing the first and second moments of the Bayes factors under different hypotheses provides additional evidence for correct calculations. However, as we have seen in the second example when dealing with more complex models, the second theorem requires many more iterations. Due to the variability of the second moment, one can only be sure that the second theorem approximately holds for a finite number of simulations. Therefore, we recommend that researchers focus primarily on the first theorem and perform the additional check based on the second theorem whenever practically possible. This would also make the check less computationally expensive since it would only require simulating data under one of the hypotheses.

Finally, we have demonstrated that for practical applications of the first theorem, it is best to simulate under the more general hypothesis and take the average Bayes factor in favor of the more specific hypothesis. For the second theorem, the optimal approach can be summarized as follows. First, compute the mean Bayes factor in favor of the more specific hypothesis for data where that hypothesis is true. Second, compare this to the second raw moment in favor of the more specific hypothesis computed on data simulated under the more general hypothesis.

Limitations & Possible extensions

While the proposed approach provides a practical way to validate Bayes factor calculations, it is not without limitations. In cases with large sample sizes, or when dealing with highly complex models, the convergence of the values for the higher-order moments may require a significant number of iterations. In such cases, as we have seen, the second moments may not match very closely. In situations where Bayes factors are used for comparing highly complex models, different methods of checking their calculation might be more appropriate, such as the method proposed by Schad et al. ( 2022 ).

However, for certain Bayes factors, particularly those based on Bayesian model averaging (BMA), such as the inclusion Bayes factor for including an edge in a graphical model or a predictor in linear regression, the method proposed in this paper can be straightforwardly applied to verify these calculations. This is because the other two methods are more suitable for checking classical (i.e., non-BMA) Bayes factors, which compare two competing statistical models (see, Sekulovski et al., 2024 , for a discussion of the difference between these two Bayes factors)

One of the reviewers of the paper suggested that the check proposed in this paper could be incorporated as an additional step within the approach proposed by Schad et al. ( 2022 ). This would mean that at the start of the simulation exercise, we would have to (a) assign prior probabilities to two competing models and then randomly select one of those models, (b) simulate synthetic data under the sampled model, (c) compute the Bayes factor and the posterior model probability, and then repeat these steps m times. Then, step 4 would be split into two, where we filter out the data sets generated by only one of the models, and filter out the associated Bayes factors. For each resulting set of Bayes factors, we would compute the mean in favor of the false hypothesis, where we expect both means to be approximately equal to one.

Providing a structured and systematic way to evaluate Bayes factor calculations helps to increase the credibility and rigor of Bayesian hypothesis testing in applied research. The proposed methods serve as a valuable tool for researchers working with Bayes factors, providing a means to validate their results and ensure the robustness of their statistical inferences. We encourage researchers to consider this approach when using Bayes factors in their analyses, thereby fostering greater confidence in the validity of their conclusions.

Code Availability

The data and materials for all simulation examples are available at the OSF repository https://osf.io/438vy/ .

Availability of data and materials

Not applicable.

We use E and ‘data’ interchangeably.

A martingale is a sequence of random variables where the conditional expected value of the next value, given all prior values, equals the current value. For instance, consider a coin flip game where a player starts with 100 euros, winning one euro for heads and losing one euro for tails; in this scenario, the expected amount of money after each flip remains equal to the player’s current amount. Consequently, regardless of the number of flips, the expected future value is always equal to the present value, exemplifying the martingale property.

It should be noted that the marginal Bayes factor (i.e., a Bayes factor not conditioned on the false hypothesis) is not a martingale.

Note that the specification of \(\mathcal {H}_0\) and \(\mathcal {H}_1\) is the same as in the binomial example from the previous section with \(n = 2\) .

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Acknowledgements

The authors would like to thank Wolf Vanpaemel for providing the idea and example script for merging the Good check with the check proposed by Schad et al. ( 2022 ), as well as two other reviewers and the Associate Editor for their comments on earlier versions of the manuscript.

NS and MM were supported by the European Union (ERC, BAYESIAN P-NETS, #101040876). Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.

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Sekulovski, N., Marsman, M. & Wagenmakers, EJ. A Good check on the Bayes factor. Behav Res (2024). https://doi.org/10.3758/s13428-024-02491-4

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