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Research Hypothesis In Psychology: Types, & Examples

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

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A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

Some key points about hypotheses:

• A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
• It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
• A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
• Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
• For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
• Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.

Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

• Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.

• Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
• However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to Write a Hypothesis

• Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
• Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
• Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
• Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
• Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

• The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
• The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

More Examples

• Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
• Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
• Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
• Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
• Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
• Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
• Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
• Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

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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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A Practical Guide to Writing Quantitative and Qualitative Research Questions and Hypotheses in Scholarly Articles

Edward barroga.

1 Department of General Education, Graduate School of Nursing Science, St. Luke’s International University, Tokyo, Japan.

Glafera Janet Matanguihan

2 Department of Biological Sciences, Messiah University, Mechanicsburg, PA, USA.

The development of research questions and the subsequent hypotheses are prerequisites to defining the main research purpose and specific objectives of a study. Consequently, these objectives determine the study design and research outcome. The development of research questions is a process based on knowledge of current trends, cutting-edge studies, and technological advances in the research field. Excellent research questions are focused and require a comprehensive literature search and in-depth understanding of the problem being investigated. Initially, research questions may be written as descriptive questions which could be developed into inferential questions. These questions must be specific and concise to provide a clear foundation for developing hypotheses. Hypotheses are more formal predictions about the research outcomes. These specify the possible results that may or may not be expected regarding the relationship between groups. Thus, research questions and hypotheses clarify the main purpose and specific objectives of the study, which in turn dictate the design of the study, its direction, and outcome. Studies developed from good research questions and hypotheses will have trustworthy outcomes with wide-ranging social and health implications.

INTRODUCTION

Scientific research is usually initiated by posing evidenced-based research questions which are then explicitly restated as hypotheses. 1 , 2 The hypotheses provide directions to guide the study, solutions, explanations, and expected results. 3 , 4 Both research questions and hypotheses are essentially formulated based on conventional theories and real-world processes, which allow the inception of novel studies and the ethical testing of ideas. 5 , 6

It is crucial to have knowledge of both quantitative and qualitative research 2 as both types of research involve writing research questions and hypotheses. 7 However, these crucial elements of research are sometimes overlooked; if not overlooked, then framed without the forethought and meticulous attention it needs. Planning and careful consideration are needed when developing quantitative or qualitative research, particularly when conceptualizing research questions and hypotheses. 4

There is a continuing need to support researchers in the creation of innovative research questions and hypotheses, as well as for journal articles that carefully review these elements. 1 When research questions and hypotheses are not carefully thought of, unethical studies and poor outcomes usually ensue. Carefully formulated research questions and hypotheses define well-founded objectives, which in turn determine the appropriate design, course, and outcome of the study. This article then aims to discuss in detail the various aspects of crafting research questions and hypotheses, with the goal of guiding researchers as they develop their own. Examples from the authors and peer-reviewed scientific articles in the healthcare field are provided to illustrate key points.

DEFINITIONS AND RELATIONSHIP OF RESEARCH QUESTIONS AND HYPOTHESES

A research question is what a study aims to answer after data analysis and interpretation. The answer is written in length in the discussion section of the paper. Thus, the research question gives a preview of the different parts and variables of the study meant to address the problem posed in the research question. 1 An excellent research question clarifies the research writing while facilitating understanding of the research topic, objective, scope, and limitations of the study. 5

On the other hand, a research hypothesis is an educated statement of an expected outcome. This statement is based on background research and current knowledge. 8 , 9 The research hypothesis makes a specific prediction about a new phenomenon 10 or a formal statement on the expected relationship between an independent variable and a dependent variable. 3 , 11 It provides a tentative answer to the research question to be tested or explored. 4

Hypotheses employ reasoning to predict a theory-based outcome. 10 These can also be developed from theories by focusing on components of theories that have not yet been observed. 10 The validity of hypotheses is often based on the testability of the prediction made in a reproducible experiment. 8

Conversely, hypotheses can also be rephrased as research questions. Several hypotheses based on existing theories and knowledge may be needed to answer a research question. Developing ethical research questions and hypotheses creates a research design that has logical relationships among variables. These relationships serve as a solid foundation for the conduct of the study. 4 , 11 Haphazardly constructed research questions can result in poorly formulated hypotheses and improper study designs, leading to unreliable results. Thus, the formulations of relevant research questions and verifiable hypotheses are crucial when beginning research. 12

CHARACTERISTICS OF GOOD RESEARCH QUESTIONS AND HYPOTHESES

Excellent research questions are specific and focused. These integrate collective data and observations to confirm or refute the subsequent hypotheses. Well-constructed hypotheses are based on previous reports and verify the research context. These are realistic, in-depth, sufficiently complex, and reproducible. More importantly, these hypotheses can be addressed and tested. 13

There are several characteristics of well-developed hypotheses. Good hypotheses are 1) empirically testable 7 , 10 , 11 , 13 ; 2) backed by preliminary evidence 9 ; 3) testable by ethical research 7 , 9 ; 4) based on original ideas 9 ; 5) have evidenced-based logical reasoning 10 ; and 6) can be predicted. 11 Good hypotheses can infer ethical and positive implications, indicating the presence of a relationship or effect relevant to the research theme. 7 , 11 These are initially developed from a general theory and branch into specific hypotheses by deductive reasoning. In the absence of a theory to base the hypotheses, inductive reasoning based on specific observations or findings form more general hypotheses. 10

TYPES OF RESEARCH QUESTIONS AND HYPOTHESES

Research questions and hypotheses are developed according to the type of research, which can be broadly classified into quantitative and qualitative research. We provide a summary of the types of research questions and hypotheses under quantitative and qualitative research categories in Table 1 .

Research questions in quantitative research

In quantitative research, research questions inquire about the relationships among variables being investigated and are usually framed at the start of the study. These are precise and typically linked to the subject population, dependent and independent variables, and research design. 1 Research questions may also attempt to describe the behavior of a population in relation to one or more variables, or describe the characteristics of variables to be measured ( descriptive research questions ). 1 , 5 , 14 These questions may also aim to discover differences between groups within the context of an outcome variable ( comparative research questions ), 1 , 5 , 14 or elucidate trends and interactions among variables ( relationship research questions ). 1 , 5 We provide examples of descriptive, comparative, and relationship research questions in quantitative research in Table 2 .

Hypotheses in quantitative research

In quantitative research, hypotheses predict the expected relationships among variables. 15 Relationships among variables that can be predicted include 1) between a single dependent variable and a single independent variable ( simple hypothesis ) or 2) between two or more independent and dependent variables ( complex hypothesis ). 4 , 11 Hypotheses may also specify the expected direction to be followed and imply an intellectual commitment to a particular outcome ( directional hypothesis ) 4 . On the other hand, hypotheses may not predict the exact direction and are used in the absence of a theory, or when findings contradict previous studies ( non-directional hypothesis ). 4 In addition, hypotheses can 1) define interdependency between variables ( associative hypothesis ), 4 2) propose an effect on the dependent variable from manipulation of the independent variable ( causal hypothesis ), 4 3) state a negative relationship between two variables ( null hypothesis ), 4 , 11 , 15 4) replace the working hypothesis if rejected ( alternative hypothesis ), 15 explain the relationship of phenomena to possibly generate a theory ( working hypothesis ), 11 5) involve quantifiable variables that can be tested statistically ( statistical hypothesis ), 11 6) or express a relationship whose interlinks can be verified logically ( logical hypothesis ). 11 We provide examples of simple, complex, directional, non-directional, associative, causal, null, alternative, working, statistical, and logical hypotheses in quantitative research, as well as the definition of quantitative hypothesis-testing research in Table 3 .

Research questions in qualitative research

Unlike research questions in quantitative research, research questions in qualitative research are usually continuously reviewed and reformulated. The central question and associated subquestions are stated more than the hypotheses. 15 The central question broadly explores a complex set of factors surrounding the central phenomenon, aiming to present the varied perspectives of participants. 15

There are varied goals for which qualitative research questions are developed. These questions can function in several ways, such as to 1) identify and describe existing conditions ( contextual research question s); 2) describe a phenomenon ( descriptive research questions ); 3) assess the effectiveness of existing methods, protocols, theories, or procedures ( evaluation research questions ); 4) examine a phenomenon or analyze the reasons or relationships between subjects or phenomena ( explanatory research questions ); or 5) focus on unknown aspects of a particular topic ( exploratory research questions ). 5 In addition, some qualitative research questions provide new ideas for the development of theories and actions ( generative research questions ) or advance specific ideologies of a position ( ideological research questions ). 1 Other qualitative research questions may build on a body of existing literature and become working guidelines ( ethnographic research questions ). Research questions may also be broadly stated without specific reference to the existing literature or a typology of questions ( phenomenological research questions ), may be directed towards generating a theory of some process ( grounded theory questions ), or may address a description of the case and the emerging themes ( qualitative case study questions ). 15 We provide examples of contextual, descriptive, evaluation, explanatory, exploratory, generative, ideological, ethnographic, phenomenological, grounded theory, and qualitative case study research questions in qualitative research in Table 4 , and the definition of qualitative hypothesis-generating research in Table 5 .

Qualitative studies usually pose at least one central research question and several subquestions starting with How or What . These research questions use exploratory verbs such as explore or describe . These also focus on one central phenomenon of interest, and may mention the participants and research site. 15

Hypotheses in qualitative research

Hypotheses in qualitative research are stated in the form of a clear statement concerning the problem to be investigated. Unlike in quantitative research where hypotheses are usually developed to be tested, qualitative research can lead to both hypothesis-testing and hypothesis-generating outcomes. 2 When studies require both quantitative and qualitative research questions, this suggests an integrative process between both research methods wherein a single mixed-methods research question can be developed. 1

FRAMEWORKS FOR DEVELOPING RESEARCH QUESTIONS AND HYPOTHESES

Research questions followed by hypotheses should be developed before the start of the study. 1 , 12 , 14 It is crucial to develop feasible research questions on a topic that is interesting to both the researcher and the scientific community. This can be achieved by a meticulous review of previous and current studies to establish a novel topic. Specific areas are subsequently focused on to generate ethical research questions. The relevance of the research questions is evaluated in terms of clarity of the resulting data, specificity of the methodology, objectivity of the outcome, depth of the research, and impact of the study. 1 , 5 These aspects constitute the FINER criteria (i.e., Feasible, Interesting, Novel, Ethical, and Relevant). 1 Clarity and effectiveness are achieved if research questions meet the FINER criteria. In addition to the FINER criteria, Ratan et al. described focus, complexity, novelty, feasibility, and measurability for evaluating the effectiveness of research questions. 14

The PICOT and PEO frameworks are also used when developing research questions. 1 The following elements are addressed in these frameworks, PICOT: P-population/patients/problem, I-intervention or indicator being studied, C-comparison group, O-outcome of interest, and T-timeframe of the study; PEO: P-population being studied, E-exposure to preexisting conditions, and O-outcome of interest. 1 Research questions are also considered good if these meet the “FINERMAPS” framework: Feasible, Interesting, Novel, Ethical, Relevant, Manageable, Appropriate, Potential value/publishable, and Systematic. 14

As we indicated earlier, research questions and hypotheses that are not carefully formulated result in unethical studies or poor outcomes. To illustrate this, we provide some examples of ambiguous research question and hypotheses that result in unclear and weak research objectives in quantitative research ( Table 6 ) 16 and qualitative research ( Table 7 ) 17 , and how to transform these ambiguous research question(s) and hypothesis(es) into clear and good statements.

a These statements were composed for comparison and illustrative purposes only.

b These statements are direct quotes from Higashihara and Horiuchi. 16

a This statement is a direct quote from Shimoda et al. 17

The other statements were composed for comparison and illustrative purposes only.

CONSTRUCTING RESEARCH QUESTIONS AND HYPOTHESES

To construct effective research questions and hypotheses, it is very important to 1) clarify the background and 2) identify the research problem at the outset of the research, within a specific timeframe. 9 Then, 3) review or conduct preliminary research to collect all available knowledge about the possible research questions by studying theories and previous studies. 18 Afterwards, 4) construct research questions to investigate the research problem. Identify variables to be accessed from the research questions 4 and make operational definitions of constructs from the research problem and questions. Thereafter, 5) construct specific deductive or inductive predictions in the form of hypotheses. 4 Finally, 6) state the study aims . This general flow for constructing effective research questions and hypotheses prior to conducting research is shown in Fig. 1 .

Research questions are used more frequently in qualitative research than objectives or hypotheses. 3 These questions seek to discover, understand, explore or describe experiences by asking “What” or “How.” The questions are open-ended to elicit a description rather than to relate variables or compare groups. The questions are continually reviewed, reformulated, and changed during the qualitative study. 3 Research questions are also used more frequently in survey projects than hypotheses in experiments in quantitative research to compare variables and their relationships.

Hypotheses are constructed based on the variables identified and as an if-then statement, following the template, ‘If a specific action is taken, then a certain outcome is expected.’ At this stage, some ideas regarding expectations from the research to be conducted must be drawn. 18 Then, the variables to be manipulated (independent) and influenced (dependent) are defined. 4 Thereafter, the hypothesis is stated and refined, and reproducible data tailored to the hypothesis are identified, collected, and analyzed. 4 The hypotheses must be testable and specific, 18 and should describe the variables and their relationships, the specific group being studied, and the predicted research outcome. 18 Hypotheses construction involves a testable proposition to be deduced from theory, and independent and dependent variables to be separated and measured separately. 3 Therefore, good hypotheses must be based on good research questions constructed at the start of a study or trial. 12

In summary, research questions are constructed after establishing the background of the study. Hypotheses are then developed based on the research questions. Thus, it is crucial to have excellent research questions to generate superior hypotheses. In turn, these would determine the research objectives and the design of the study, and ultimately, the outcome of the research. 12 Algorithms for building research questions and hypotheses are shown in Fig. 2 for quantitative research and in Fig. 3 for qualitative research.

EXAMPLES OF RESEARCH QUESTIONS FROM PUBLISHED ARTICLES

• EXAMPLE 1. Descriptive research question (quantitative research)
• - Presents research variables to be assessed (distinct phenotypes and subphenotypes)
• “BACKGROUND: Since COVID-19 was identified, its clinical and biological heterogeneity has been recognized. Identifying COVID-19 phenotypes might help guide basic, clinical, and translational research efforts.
• RESEARCH QUESTION: Does the clinical spectrum of patients with COVID-19 contain distinct phenotypes and subphenotypes? ” 19
• EXAMPLE 2. Relationship research question (quantitative research)
• - Shows interactions between dependent variable (static postural control) and independent variable (peripheral visual field loss)
• “Background: Integration of visual, vestibular, and proprioceptive sensations contributes to postural control. People with peripheral visual field loss have serious postural instability. However, the directional specificity of postural stability and sensory reweighting caused by gradual peripheral visual field loss remain unclear.
• Research question: What are the effects of peripheral visual field loss on static postural control ?” 20
• EXAMPLE 3. Comparative research question (quantitative research)
• - Clarifies the difference among groups with an outcome variable (patients enrolled in COMPERA with moderate PH or severe PH in COPD) and another group without the outcome variable (patients with idiopathic pulmonary arterial hypertension (IPAH))
• “BACKGROUND: Pulmonary hypertension (PH) in COPD is a poorly investigated clinical condition.
• RESEARCH QUESTION: Which factors determine the outcome of PH in COPD?
• STUDY DESIGN AND METHODS: We analyzed the characteristics and outcome of patients enrolled in the Comparative, Prospective Registry of Newly Initiated Therapies for Pulmonary Hypertension (COMPERA) with moderate or severe PH in COPD as defined during the 6th PH World Symposium who received medical therapy for PH and compared them with patients with idiopathic pulmonary arterial hypertension (IPAH) .” 21
• EXAMPLE 4. Exploratory research question (qualitative research)
• - Explores areas that have not been fully investigated (perspectives of families and children who receive care in clinic-based child obesity treatment) to have a deeper understanding of the research problem
• “Problem: Interventions for children with obesity lead to only modest improvements in BMI and long-term outcomes, and data are limited on the perspectives of families of children with obesity in clinic-based treatment. This scoping review seeks to answer the question: What is known about the perspectives of families and children who receive care in clinic-based child obesity treatment? This review aims to explore the scope of perspectives reported by families of children with obesity who have received individualized outpatient clinic-based obesity treatment.” 22
• EXAMPLE 5. Relationship research question (quantitative research)
• - Defines interactions between dependent variable (use of ankle strategies) and independent variable (changes in muscle tone)
• “Background: To maintain an upright standing posture against external disturbances, the human body mainly employs two types of postural control strategies: “ankle strategy” and “hip strategy.” While it has been reported that the magnitude of the disturbance alters the use of postural control strategies, it has not been elucidated how the level of muscle tone, one of the crucial parameters of bodily function, determines the use of each strategy. We have previously confirmed using forward dynamics simulations of human musculoskeletal models that an increased muscle tone promotes the use of ankle strategies. The objective of the present study was to experimentally evaluate a hypothesis: an increased muscle tone promotes the use of ankle strategies. Research question: Do changes in the muscle tone affect the use of ankle strategies ?” 23

EXAMPLES OF HYPOTHESES IN PUBLISHED ARTICLES

• EXAMPLE 1. Working hypothesis (quantitative research)
• - A hypothesis that is initially accepted for further research to produce a feasible theory
• “As fever may have benefit in shortening the duration of viral illness, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response when taken during the early stages of COVID-19 illness .” 24
• “In conclusion, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response . The difference in perceived safety of these agents in COVID-19 illness could be related to the more potent efficacy to reduce fever with ibuprofen compared to acetaminophen. Compelling data on the benefit of fever warrant further research and review to determine when to treat or withhold ibuprofen for early stage fever for COVID-19 and other related viral illnesses .” 24
• EXAMPLE 2. Exploratory hypothesis (qualitative research)
• - Explores particular areas deeper to clarify subjective experience and develop a formal hypothesis potentially testable in a future quantitative approach
• “We hypothesized that when thinking about a past experience of help-seeking, a self distancing prompt would cause increased help-seeking intentions and more favorable help-seeking outcome expectations .” 25
• “Conclusion
• Although a priori hypotheses were not supported, further research is warranted as results indicate the potential for using self-distancing approaches to increasing help-seeking among some people with depressive symptomatology.” 25
• EXAMPLE 3. Hypothesis-generating research to establish a framework for hypothesis testing (qualitative research)
• “We hypothesize that compassionate care is beneficial for patients (better outcomes), healthcare systems and payers (lower costs), and healthcare providers (lower burnout). ” 26
• Compassionomics is the branch of knowledge and scientific study of the effects of compassionate healthcare. Our main hypotheses are that compassionate healthcare is beneficial for (1) patients, by improving clinical outcomes, (2) healthcare systems and payers, by supporting financial sustainability, and (3) HCPs, by lowering burnout and promoting resilience and well-being. The purpose of this paper is to establish a scientific framework for testing the hypotheses above . If these hypotheses are confirmed through rigorous research, compassionomics will belong in the science of evidence-based medicine, with major implications for all healthcare domains.” 26
• EXAMPLE 4. Statistical hypothesis (quantitative research)
• - An assumption is made about the relationship among several population characteristics ( gender differences in sociodemographic and clinical characteristics of adults with ADHD ). Validity is tested by statistical experiment or analysis ( chi-square test, Students t-test, and logistic regression analysis)
• “Our research investigated gender differences in sociodemographic and clinical characteristics of adults with ADHD in a Japanese clinical sample. Due to unique Japanese cultural ideals and expectations of women's behavior that are in opposition to ADHD symptoms, we hypothesized that women with ADHD experience more difficulties and present more dysfunctions than men . We tested the following hypotheses: first, women with ADHD have more comorbidities than men with ADHD; second, women with ADHD experience more social hardships than men, such as having less full-time employment and being more likely to be divorced.” 27
• “Statistical Analysis
• ( text omitted ) Between-gender comparisons were made using the chi-squared test for categorical variables and Students t-test for continuous variables…( text omitted ). A logistic regression analysis was performed for employment status, marital status, and comorbidity to evaluate the independent effects of gender on these dependent variables.” 27

EXAMPLES OF HYPOTHESIS AS WRITTEN IN PUBLISHED ARTICLES IN RELATION TO OTHER PARTS

• EXAMPLE 1. Background, hypotheses, and aims are provided
• “Pregnant women need skilled care during pregnancy and childbirth, but that skilled care is often delayed in some countries …( text omitted ). The focused antenatal care (FANC) model of WHO recommends that nurses provide information or counseling to all pregnant women …( text omitted ). Job aids are visual support materials that provide the right kind of information using graphics and words in a simple and yet effective manner. When nurses are not highly trained or have many work details to attend to, these job aids can serve as a content reminder for the nurses and can be used for educating their patients (Jennings, Yebadokpo, Affo, & Agbogbe, 2010) ( text omitted ). Importantly, additional evidence is needed to confirm how job aids can further improve the quality of ANC counseling by health workers in maternal care …( text omitted )” 28
• “ This has led us to hypothesize that the quality of ANC counseling would be better if supported by job aids. Consequently, a better quality of ANC counseling is expected to produce higher levels of awareness concerning the danger signs of pregnancy and a more favorable impression of the caring behavior of nurses .” 28
• “This study aimed to examine the differences in the responses of pregnant women to a job aid-supported intervention during ANC visit in terms of 1) their understanding of the danger signs of pregnancy and 2) their impression of the caring behaviors of nurses to pregnant women in rural Tanzania.” 28
• EXAMPLE 2. Background, hypotheses, and aims are provided
• “We conducted a two-arm randomized controlled trial (RCT) to evaluate and compare changes in salivary cortisol and oxytocin levels of first-time pregnant women between experimental and control groups. The women in the experimental group touched and held an infant for 30 min (experimental intervention protocol), whereas those in the control group watched a DVD movie of an infant (control intervention protocol). The primary outcome was salivary cortisol level and the secondary outcome was salivary oxytocin level.” 29
• “ We hypothesize that at 30 min after touching and holding an infant, the salivary cortisol level will significantly decrease and the salivary oxytocin level will increase in the experimental group compared with the control group .” 29
• EXAMPLE 3. Background, aim, and hypothesis are provided
• “In countries where the maternal mortality ratio remains high, antenatal education to increase Birth Preparedness and Complication Readiness (BPCR) is considered one of the top priorities [1]. BPCR includes birth plans during the antenatal period, such as the birthplace, birth attendant, transportation, health facility for complications, expenses, and birth materials, as well as family coordination to achieve such birth plans. In Tanzania, although increasing, only about half of all pregnant women attend an antenatal clinic more than four times [4]. Moreover, the information provided during antenatal care (ANC) is insufficient. In the resource-poor settings, antenatal group education is a potential approach because of the limited time for individual counseling at antenatal clinics.” 30
• “This study aimed to evaluate an antenatal group education program among pregnant women and their families with respect to birth-preparedness and maternal and infant outcomes in rural villages of Tanzania.” 30
• “ The study hypothesis was if Tanzanian pregnant women and their families received a family-oriented antenatal group education, they would (1) have a higher level of BPCR, (2) attend antenatal clinic four or more times, (3) give birth in a health facility, (4) have less complications of women at birth, and (5) have less complications and deaths of infants than those who did not receive the education .” 30

Research questions and hypotheses are crucial components to any type of research, whether quantitative or qualitative. These questions should be developed at the very beginning of the study. Excellent research questions lead to superior hypotheses, which, like a compass, set the direction of research, and can often determine the successful conduct of the study. Many research studies have floundered because the development of research questions and subsequent hypotheses was not given the thought and meticulous attention needed. The development of research questions and hypotheses is an iterative process based on extensive knowledge of the literature and insightful grasp of the knowledge gap. Focused, concise, and specific research questions provide a strong foundation for constructing hypotheses which serve as formal predictions about the research outcomes. Research questions and hypotheses are crucial elements of research that should not be overlooked. They should be carefully thought of and constructed when planning research. This avoids unethical studies and poor outcomes by defining well-founded objectives that determine the design, course, and outcome of the study.

Disclosure: The authors have no potential conflicts of interest to disclose.

Author Contributions:

• Conceptualization: Barroga E, Matanguihan GJ.
• Methodology: Barroga E, Matanguihan GJ.
• Writing - original draft: Barroga E, Matanguihan GJ.
• Writing - review & editing: Barroga E, Matanguihan GJ.

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Home » What is a Hypothesis – Types, Examples and Writing Guide

What is a Hypothesis – Types, Examples and Writing Guide

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Definition:

Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.

Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.

Types of Hypothesis

Types of Hypothesis are as follows:

Research Hypothesis

A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.

Null Hypothesis

The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.

Alternative Hypothesis

An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.

Directional Hypothesis

A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.

Non-directional Hypothesis

A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.

Statistical Hypothesis

A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.

Composite Hypothesis

A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome.

Empirical Hypothesis

An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.

Simple Hypothesis

A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.

Complex Hypothesis

A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.

Applications of Hypothesis

Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:

• Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
• Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
• Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
• Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
• Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
• Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.

How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

Identify the Research Question

The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.

Conduct a Literature Review

Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.

Determine the Variables

The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.

Formulate the Hypothesis

Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.

Write the Null Hypothesis

The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.

Refine the Hypothesis

After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.

Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

• Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
• Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
• Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
• Education : “Implementing a new teaching method will result in higher student achievement scores.”
• Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
• Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
• Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”

Purpose of Hypothesis

The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.

The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.

In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.

When to use Hypothesis

Here are some common situations in which hypotheses are used:

• In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
• In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
• I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.

Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

• Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
• Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
• Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
• Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
• Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed.
• Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
• Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

• Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
• Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
• Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
• Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
• Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
• Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.

Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

• Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
• May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
• May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
• Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
• Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
• May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.

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5.2 - writing hypotheses.

The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis (\(H_0\)) and an alternative hypothesis (\(H_a\)).

When writing hypotheses there are three things that we need to know: (1) the parameter that we are testing (2) the direction of the test (non-directional, right-tailed or left-tailed), and (3) the value of the hypothesized parameter.

• At this point we can write hypotheses for a single mean (\(\mu\)), paired means(\(\mu_d\)), a single proportion (\(p\)), the difference between two independent means (\(\mu_1-\mu_2\)), the difference between two proportions (\(p_1-p_2\)), a simple linear regression slope (\(\beta\)), and a correlation (\(\rho\)). 
• The research question will give us the information necessary to determine if the test is two-tailed (e.g., "different from," "not equal to"), right-tailed (e.g., "greater than," "more than"), or left-tailed (e.g., "less than," "fewer than").
• The research question will also give us the hypothesized parameter value. This is the number that goes in the hypothesis statements (i.e., \(\mu_0\) and \(p_0\)). For the difference between two groups, regression, and correlation, this value is typically 0.

Hypotheses are always written in terms of population parameters (e.g., \(p\) and \(\mu\)).  The tables below display all of the possible hypotheses for the parameters that we have learned thus far. Note that the null hypothesis always includes the equality (i.e., =).

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How to Write a Great Hypothesis

Hypothesis Format, Examples, and Tips

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

Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk,  "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis, operational definitions, types of hypotheses, hypotheses examples.

• Collecting Data

Frequently Asked Questions

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.

One hypothesis example would be a study designed to look at the relationship between sleep deprivation and test performance might have a hypothesis that states: "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."

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. It is only at this point that researchers 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 a number of 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 wisdom 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.

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.

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.

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

In order to measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming other people. In this situation, the researcher might utilize a simulated task to measure aggressiveness.

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 that there is a relationship between one independent variable and one dependent variable.
• Complex hypothesis : This type of hypothesis suggests a relationship between three or more variables, such as two independent variables and a dependent variable.
• 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 sample of the population 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."
• Complex hypothesis: "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."

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:

• "Children who receive a new reading intervention will have scores different than students who do not receive the intervention."
• "There will be no difference in scores on a memory recall task between children and adults."

Examples of an alternative hypothesis:

• "Children who receive a new reading intervention will perform better than students who did not receive the intervention."
• "Adults will perform better on a memory task than children." 

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 it would be impossible or difficult to  conduct an experiment . 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 then be used to look at how the variables are related. This type of 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.

A Word From Verywell

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.

Some examples of how to write a hypothesis include:

• "Staying up late will lead to worse test performance the next day."
• "People who consume one apple each day will visit the doctor fewer times each year."
• "Breaking study sessions up into three 20-minute sessions will lead to better test results than a single 60-minute study session."

The four parts of a hypothesis are:

• The research question
• The independent variable (IV)
• The dependent variable (DV)
• The proposed relationship between the IV and DV

Castillo M. The scientific method: a need for something better? . AJNR Am J Neuroradiol. 2013;34(9):1669-71. doi:10.3174/ajnr.A3401

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."

What Is A Research (Scientific) Hypothesis? A plain-language explainer + examples

By:  Derek Jansen (MBA)  | Reviewed By: Dr Eunice Rautenbach | June 2020

If you’re new to the world of research, or it’s your first time writing a dissertation or thesis, you’re probably noticing that the words “research hypothesis” and “scientific hypothesis” are used quite a bit, and you’re wondering what they mean in a research context .

“Hypothesis” is one of those words that people use loosely, thinking they understand what it means. However, it has a very specific meaning within academic research. So, it’s important to understand the exact meaning before you start hypothesizing. 

Research Hypothesis 101

• What is a hypothesis ?
• What is a research hypothesis (scientific hypothesis)?
• Requirements for a research hypothesis
• Definition of a research hypothesis
• The null hypothesis

What is a hypothesis?

Let’s start with the general definition of a hypothesis (not a research hypothesis or scientific hypothesis), according to the Cambridge Dictionary:

Hypothesis: an idea or explanation for something that is based on known facts but has not yet been proved.

In other words, it’s a statement that provides an explanation for why or how something works, based on facts (or some reasonable assumptions), but that has not yet been specifically tested . For example, a hypothesis might look something like this:

Hypothesis: sleep impacts academic performance.

This statement predicts that academic performance will be influenced by the amount and/or quality of sleep a student engages in – sounds reasonable, right? It’s based on reasonable assumptions , underpinned by what we currently know about sleep and health (from the existing literature). So, loosely speaking, we could call it a hypothesis, at least by the dictionary definition.

But that’s not good enough…

Unfortunately, that’s not quite sophisticated enough to describe a research hypothesis (also sometimes called a scientific hypothesis), and it wouldn’t be acceptable in a dissertation, thesis or research paper . In the world of academic research, a statement needs a few more criteria to constitute a true research hypothesis .

What is a research hypothesis?

A research hypothesis (also called a scientific hypothesis) is a statement about the expected outcome of a study (for example, a dissertation or thesis). To constitute a quality hypothesis, the statement needs to have three attributes – specificity , clarity and testability .

Let’s take a look at these more closely.

Need a helping hand?

Hypothesis Essential #1: Specificity & Clarity

A good research hypothesis needs to be extremely clear and articulate about both what’ s being assessed (who or what variables are involved ) and the expected outcome (for example, a difference between groups, a relationship between variables, etc.).

Let’s stick with our sleepy students example and look at how this statement could be more specific and clear.

Hypothesis: Students who sleep at least 8 hours per night will, on average, achieve higher grades in standardised tests than students who sleep less than 8 hours a night.

As you can see, the statement is very specific as it identifies the variables involved (sleep hours and test grades), the parties involved (two groups of students), as well as the predicted relationship type (a positive relationship). There’s no ambiguity or uncertainty about who or what is involved in the statement, and the expected outcome is clear.

Contrast that to the original hypothesis we looked at – “Sleep impacts academic performance” – and you can see the difference. “Sleep” and “academic performance” are both comparatively vague , and there’s no indication of what the expected relationship direction is (more sleep or less sleep). As you can see, specificity and clarity are key.

Hypothesis Essential #2: Testability (Provability)

A statement must be testable to qualify as a research hypothesis. In other words, there needs to be a way to prove (or disprove) the statement. If it’s not testable, it’s not a hypothesis – simple as that.

For example, consider the hypothesis we mentioned earlier:

Hypothesis: Students who sleep at least 8 hours per night will, on average, achieve higher grades in standardised tests than students who sleep less than 8 hours a night.  

We could test this statement by undertaking a quantitative study involving two groups of students, one that gets 8 or more hours of sleep per night for a fixed period, and one that gets less. We could then compare the standardised test results for both groups to see if there’s a statistically significant difference. 

Again, if you compare this to the original hypothesis we looked at – “Sleep impacts academic performance” – you can see that it would be quite difficult to test that statement, primarily because it isn’t specific enough. How much sleep? By who? What type of academic performance?

So, remember the mantra – if you can’t test it, it’s not a hypothesis 🙂

Defining A Research Hypothesis

You’re still with us? Great! Let’s recap and pin down a clear definition of a hypothesis.

A research hypothesis (or scientific hypothesis) is a statement about an expected relationship between variables, or explanation of an occurrence, that is clear, specific and testable.

So, when you write up hypotheses for your dissertation or thesis, make sure that they meet all these criteria. If you do, you’ll not only have rock-solid hypotheses but you’ll also ensure a clear focus for your entire research project.

What about the null hypothesis?

You may have also heard the terms null hypothesis , alternative hypothesis, or H-zero thrown around. At a simple level, the null hypothesis is the counter-proposal to the original hypothesis.

For example, if the hypothesis predicts that there is a relationship between two variables (for example, sleep and academic performance), the null hypothesis would predict that there is no relationship between those variables.

At a more technical level, the null hypothesis proposes that no statistical significance exists in a set of given observations and that any differences are due to chance alone.

And there you have it – hypotheses in a nutshell. 

If you have any questions, be sure to leave a comment below and we’ll do our best to help you. If you need hands-on help developing and testing your hypotheses, consider our private coaching service , where we hold your hand through the research journey.

Psst… there’s more (for free)

This post is part of our dissertation mini-course, which covers everything you need to get started with your dissertation, thesis or research project. 

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16 Comments

Very useful information. I benefit more from getting more information in this regard.

Very great insight,educative and informative. Please give meet deep critics on many research data of public international Law like human rights, environment, natural resources, law of the sea etc

In a book I read a distinction is made between null, research, and alternative hypothesis. As far as I understand, alternative and research hypotheses are the same. Can you please elaborate? Best Afshin

This is a self explanatory, easy going site. I will recommend this to my friends and colleagues.

Very good definition. How can I cite your definition in my thesis? Thank you. Is nul hypothesis compulsory in a research?

It’s a counter-proposal to be proven as a rejection

Please what is the difference between alternate hypothesis and research hypothesis?

It is a very good explanation. However, it limits hypotheses to statistically tasteable ideas. What about for qualitative researches or other researches that involve quantitative data that don’t need statistical tests?

In qualitative research, one typically uses propositions, not hypotheses.

could you please elaborate it more

I’ve benefited greatly from these notes, thank you.

This is very helpful

well articulated ideas are presented here, thank you for being reliable sources of information

Excellent. Thanks for being clear and sound about the research methodology and hypothesis (quantitative research)

I have only a simple question regarding the null hypothesis. – Is the null hypothesis (Ho) known as the reversible hypothesis of the alternative hypothesis (H1? – How to test it in academic research?

this is very important note help me much more

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8 Different Types of Hypotheses (Plus Essential Facts)

The hypothesis is an idea or a premise used as a jumping off the ground for further investigation. It’s essential to scientific research because it serves as a compass for scientists or researchers in carrying out their experiments or studies.

There are different types of hypotheses but crafting a good hypothesis can be tricky. A sound hypothesis should be logical, affirmative, clear, precise, quantifiable, or can be tested, and has a cause and effect factor.

Types 

Alternative hypothesis.

Also known as a maintained hypothesis or a research hypothesis, an alternative hypothesis is the exact opposite of a null hypothesis, and it is often used in statistical hypothesis testing. There are four main types of alternative hypothesis:

• Point alternative hypothesis . This hypothesis occurs when the population distribution in the hypothesis test is fully defined and has no unknown parameters. It usually has no practical interest, but it is considered important in other statistical activities.
• Non-directional alternative hypothesis. These hypotheses have nothing to do with the either region of rejection (i.e., one-tailed or two-tailed directional hypotheses) but instead, only that the null hypothesis is untrue.
• One-tailed directional hypothesis. This hypothesis is only concerned with the region of direction for one tail of a sampling distribution, not both of them.
• Two-tailed directional hypothesis. This hypothesis is concerned with both regions of rejection of a particular sampling distribution

Known by the symbol H1, this type of hypothesis proclaims the expected relationship between the variables in the theory.

Associative and Causal Hypothesis

Associative hypotheses simply state that there is a relationship between two variables, whereas causal hypotheses state that any difference in the type or amount of one particular variable is going to directly affect the difference in the type or amount of the next variable in the equation.

Note: This post may contain affiliate links which will take you to online retailers that sell products and services. If you click on one and buy something, I may earn from qualifying purchases. See my Affiliate Disclosure for more details.

These hypotheses are often used in the field of psychology. A causal hypothesis looks at how manipulation affects events in the future, while an associative hypothesis looks at how specific events co-occur.

A good example of its practical use occurs when discussing the psychological aspects of eyewitness testimonies, and they generally affect four areas of this phenomenon: emotion and memory, system variables in the line-up, estimation of the duration of the event, and own-race bias.

Complex Hypothesis

In a complex hypothesis, a relationship exists between the variables . In these hypotheses, there are more than two independent and dependent variables, as demonstrated in the following hypotheses:

• Taking drugs and smoking cigarettes leads to respiratory problems, increased tension, and cancer.
• The people who are older and living in rural areas are happier than people who are younger and who live in the city or suburbs.
• If you eat a high-fat diet and a few vegetables, you are more likely to suffer from hypertension and high cholesterol than someone who eats a lot of vegetables and sticks to a low-fat diet.

Directional Hypothesis

A directional hypothesis is one regarding either a positive or negative difference or change in the two variables involved. Typically based on aspects such as accepted theory, literature printed on the topic at hand, past research, and even accepted theory, researchers normally develop this type of hypothesis from research questions, and they use statistical methods to check its validity.

Words you often hear in hypotheses that are directional in nature include more, less, increase, decrease, positive, negative, higher, and lower. Directional hypotheses specify the direction or nature of the relationship between two or more independent variables and two or more dependent variables.

Non-Directional Hypothesis

This hypothesis states that there is a distinct relationship between two variables; however, it does not predict the exact nature or direction of that particular relationship.

Null Hypothesis

Indicated by the symbol Ho, a null hypothesis predicts that the variables in a certain hypothesis have no relationship to one another and that the hypothesis is normally subjected to some type of statistical analysis. It essentially states that the data and variables being investigated do not actually exist.

A perfect example of this comes when looking at scientific medical studies, where you have both an experimental and control group, and you are hypothesizing that there will be no difference in the results of these two groups.

Simple Hypothesis

This hypothesis consists of two variables, an independent variable or cause, and a dependent variable or cause. Simple hypotheses contain a relationship between these two variables. For example, the following are examples of simple hypotheses:

• The more you chew tobacco, the more likely you are to develop mouth cancer.
• The more money you make, the less likely you are to be involved in criminal activity.
• The more educated you are, the more likely you are to have a well-paying job.

Statistical Hypothesis

This is just a hypothesis that is able to be verified through statistics. It can be either logical or illogical, but if you can use statistics to verify it, it is called a statistical hypothesis.

Facts about Hypotheses

Difference Between Simple and Complex Hypotheses

In a simple hypothesis, there is a dependent and an independent variable, as well as a relationship between the two. The independent variable is the cause and comes first when they’re in chronological order, and the dependent variable describes the effect. In a complex hypothesis, the relationship is between two or more independent variables and two or more dependent variables.

Difference Between Non-Directional and Directional Hypotheses

In a directional research hypothesis, the direction of the relationship is predicted. The advantages of this type of hypothesis include one-tailed statistical tests, theoretical propositions that can be tested in a more precise manner, and the fact that the researcher’s expectations are very clear right from the start.

In a non-directional research hypothesis, the relationship between the variables is predicted but not the direction of that relationship. Reasons to use this type of research hypothesis include when your previous research findings contradict one another and when there is no theory on which to base your predictions.

Difference Between a Hypothesis and a Theory

There are many different differences between a theory and a hypothesis, including the following:

• A hypothesis is a suggestion of what might happen when you test out a theory. It is a prediction of a possible correlation between various phenomena. On the other hand, a theory has been tested and is well-substantiated. If a hypothesis succeeds in proving a certain point, it can then be called a theory.
• The data for a hypothesis is most often very limited, whereas the data relating to theory has been tested under numerous circumstances.
• A hypothesis offers a very specific instance; that is, it is limited to just one observation. On the other hand, a theory is more generalized and is put through a multitude of experiments and tests, which can then apply to various specific instances.
• The purposes of these two items are different as well. A hypothesis starts with a possibility that is uncertain but can be studied further via observations and experiments. A theory is used to explain why large sets of observations are continuously made.
• Hypotheses are based on various suggestions and possibilities but have uncertain results, while theories have a steady and reliable consensus among scientists and other professionals.
• Both theories and hypotheses are testable and falsifiable, but unlike theories, hypotheses are neither well-tested nor well-substantiated.

What is the Interaction Effect?

This effect describes the two variables’ relationship to one another.

When Writing the Hypothesis, There is a Certain Format to Follow

This includes three aspects:

• The correlational statement
• The comparative statement
• A statistical analysis

How are Hypotheses Used to Test Theories?

• Do not test the entire theory, just the proposition
• It can never be either proved or disproved

When Formulating a Hypothesis, There are Things to Consider

These include:

• You have to write it in the present tense
• It has to be empirically testable
• You have to write it in a declarative sentence
• It has to contain all of the variables
• It must contain three parts: the purpose statement, the problem statement, and the research question
• It has to contain the population

What is the Best Definition of a Scientific Hypothesis?

It is essentially an educated guess; however, that guess will lose its credibility if it is falsifiable.

How to Use Research Questions

There are two ways to include research questions when testing a theory. The first is in addition to a hypothesis related to the topic’s other areas of interest, and the second is in place of the actual hypothesis, which occurs in some instances.

Tips to Keep in Mind When Developing a Hypothesis

• Use language that is very precise. Your language should be concise, simple, and clean. This is not a time when you want to be vague, because everything needs to be spelled out in great detail.
• Be as logical as possible. If you believe in something, you want to prove it, and remaining logical at all times is a great start.
• Use research and experimentation to determine whether your hypothesis is testable. All hypotheses need to be proven. You have to know that proving your theory is going to work, even if you find out different in the end.

What is the Number-One Purpose of a Scientific Method?

Scientific methods are there to provide a structured way to get the appropriate evidence in order to either refute or prove a scientific hypothesis.

Glossary of Terms Related to Hypotheses

Bivariate Data: This is data that includes two distinct variables, which are random and usually graphed via a scatter plot.

Categorical Data: These data fit into a tiny number of very discrete categories. They are usually either nominal, or non-ordered, which can include things such as age or country; or they can be ordinal, or ordered, which includes aspects such as hot or cold temperature.

Correlation: This is a measure of how closely two variables are to one another. It measures whether a change in one random variable corresponds to a change in the other random variable. For example, the correlation between smoking and getting lung cancer has been widely studied.

Data: These are the results found from conducting a survey or experiment, or even an observation study of some type.

Dependent Event: If the happening of one event affects the probability of another event occurring also, they are said to be dependent events.

Distribution: The way the probability of a random variable taking a certain value is described is called its distribution. Possible distribution functions include the cumulative, probability density, or probability mass function.

Element: This refers to an object in a certain set, and that object is an element of that set.

Empirical Probability: This refers to the likelihood of an outcome happening, and it is determined by the repeat performance of a particular experiment.  You can do this by dividing the number of times that event took place by the number of times you conducted the experiment.

Equality of Sets: If two sets contain the exact same elements, they are considered equal sets. In order to determine if this is so, it can be advantageous to show that each set is contained in the other set.

Equally Likely Outcomes: Refers to outcomes that have the same probability; for example, if you toss a coin there are only two likely outcomes.

Event: This term refers to the subset of a sample space.

Expected Value: This demonstrates the average value of a quantity that is random and which has been observed numerous times in order to duplicate the same results of previous experiments.

Experiment: A scientific process that results in a set of outcomes that is observable. Even selecting a toy from a box of toys can be considered an experiment in this instance.

Experimental Probability: When you estimate how likely something is to occur, this is an experimental probability example. To get this probability, you divide the number of trials that were successful by the total number of trials that were performed.

Finite Sample Space: These sample spaces have a finite number of outcomes that could possibly occur.

Frequency: The frequency is the number of times a certain value occurs when you observe an experiment’s results.

Frequency Distribution: This refers to the data that describes possible groups or values and the frequencies that correspond to those groups or values.

Histogram: A histogram, or frequency histogram, is a bar graph that demonstrates how frequently data points occur.

Independent Event: If two events occur, and one event’s outcome has no effect on the other’s outcome, this is known as an independent event.

Infinite Sample Space: This refers to a sample space that consists of outcomes with an infinite number of possibilities.

Mutually Exclusive: Events are mutually exclusive if their outcomes have absolutely nothing in common.

Notations: Notations are operations or quantities described by symbols instead of numbers.

Observational Study: Like the name implies, these are studies that allow you to collect data through basic observation.

Odds: This is a way to express the likelihood that a certain event will happen. If you see odds of m:n, it means it is expected that a certain event will happen m times for every n times it does not happen.

One-Variable Data: Data that have related behaviors usually associated in some important way.

Outcome: The outcome is simply the result of a particular experiment. If you consider a set of all of the possible outcomes, this is called the sample space.

Probability: A probability is merely the likelihood that a certain event will take place, and it is expressed on a scale of 0 to one, with 0 meaning it is impossible that it will happen and one being a certainty that it will happen. Probability can also be expressed as a percentage, starting with 0 and ending at 100%.

Random Experiment: A random experiment is one whereby the outcome can’t be predicted with any amount of certainty, at least not before the experiment actually takes place.

Random Variable: Random variables take on different numerical values, based on the results of a particular experiment.

Replacement: Replacement is the act of returning or replacing an item back into a sample space, which takes place after an event and allows the item to be chosen more than one time.

Sample Space: This term refers to all of the possible outcomes that could result from a probability experiment.

Set: A collection of objects that is well-defined is called a set.

Simple Event: When an event is a single element of the sample space, it is known as a simple event.

Simulation: A simulation is a type of experiment that mimics a real-life event.

Single-Variable Data: These are data that use only one unknown variable.

Statistics: This is the branch of mathematics that deals with the study of quantitative data. If you analyze certain events that are governed by probability, this is called statistics.

Theoretical Probability: This probability describes the ratio of the number of outcomes in a specific event to the number of outcomes found in the sample space. It is based on the presumption that all outcomes are equally liable.

Union: Usually described by the symbol ∪, or the cup symbol, a union describes the combination of two or more sets and their elements.

Variable: A variable is a quantity that varies and is almost always represented by letters.

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13 Different Types of Hypothesis

There are 13 different types of hypothesis. These include simple, complex, null, alternative, composite, directional, non-directional, logical, empirical, statistical, associative, exact, and inexact.

A hypothesis can be categorized into one or more of these types. However, some are mutually exclusive and opposites. Simple and complex hypotheses are mutually exclusive, as are direction and non-direction, and null and alternative hypotheses.

Below I explain each hypothesis in simple terms for absolute beginners. These definitions may be too simple for some, but they’re designed to be clear introductions to the terms to help people wrap their heads around the concepts early on in their education about research methods .

Types of Hypothesis

Before you Proceed: Dependent vs Independent Variables

A research study and its hypotheses generally examine the relationships between independent and dependent variables – so you need to know these two concepts:

• The independent variable is the variable that is causing a change.
• The dependent variable is the variable the is affected by the change. This is the variable being tested.

Read my full article on dependent vs independent variables for more examples.

Example: Eating carrots (independent variable) improves eyesight (dependent variable).

1. Simple Hypothesis

A simple hypothesis is a hypothesis that predicts a correlation between two test variables: an independent and a dependent variable.

This is the easiest and most straightforward type of hypothesis. You simply need to state an expected correlation between the dependant variable and the independent variable.

You do not need to predict causation (see: directional hypothesis). All you would need to do is prove that the two variables are linked.

Simple Hypothesis Examples

2. complex hypothesis.

A complex hypothesis is a hypothesis that contains multiple variables, making the hypothesis more specific but also harder to prove.

You can have multiple independent and dependant variables in this hypothesis.

Complex Hypothesis Example

In the above example, we have multiple independent and dependent variables:

• Independent variables: Age and weight.
• Dependent variables: diabetes and heart disease.

Because there are multiple variables, this study is a lot more complex than a simple hypothesis. It quickly gets much more difficult to prove these hypotheses. This is why undergraduate and first-time researchers are usually encouraged to use simple hypotheses.

3. Null Hypothesis

A null hypothesis will predict that there will be no significant relationship between the two test variables.

For example, you can say that “The study will show that there is no correlation between marriage and happiness.”

A good way to think about a null hypothesis is to think of it in the same way as “innocent until proven guilty”[1]. Unless you can come up with evidence otherwise, your null hypothesis will stand.

A null hypothesis may also highlight that a correlation will be inconclusive . This means that you can predict that the study will not be able to confirm your results one way or the other. For example, you can say “It is predicted that the study will be unable to confirm a correlation between the two variables due to foreseeable interference by a third variable .”

Beware that an inconclusive null hypothesis may be questioned by your teacher. Why would you conduct a test that you predict will not provide a clear result? Perhaps you should take a closer look at your methodology and re-examine it. Nevertheless, inconclusive null hypotheses can sometimes have merit.

Null Hypothesis Examples

4. alternative hypothesis.

An alternative hypothesis is a hypothesis that is anything other than the null hypothesis. It will disprove the null hypothesis.

We use the symbol H A or H 1 to denote an alternative hypothesis.

The null and alternative hypotheses are usually used together. We will say the null hypothesis is the case where a relationship between two variables is non-existent. The alternative hypothesis is the case where there is a relationship between those two variables.

The following statement is always true: H 0 ≠ H A .

Let’s take the example of the hypothesis: “Does eating oatmeal before an exam impact test scores?”

We can have two hypotheses here:

• Null hypothesis (H 0 ): “Eating oatmeal before an exam does not impact test scores.”
• Alternative hypothesis (H A ): “Eating oatmeal before an exam does impact test scores.”

For the alternative hypothesis to be true, all we have to do is disprove the null hypothesis for the alternative hypothesis to be true. We do not need an exact prediction of how much oatmeal will impact the test scores or even if the impact is positive or negative. So long as the null hypothesis is proven to be false, then the alternative hypothesis is proven to be true.

5. Composite Hypothesis

A composite hypothesis is a hypothesis that does not predict the exact parameters, distribution, or range of the dependent variable.

Often, we would predict an exact outcome. For example: “23 year old men are on average 189cm tall.” Here, we are giving an exact parameter. So, the hypothesis is not composite.

But, often, we cannot exactly hypothesize something. We assume that something will happen, but we’re not exactly sure what. In these cases, we might say: “23 year old men are not on average 189cm tall.”

We haven’t set a distribution range or exact parameters of the average height of 23 year old men. So, we’ve introduced a composite hypothesis as opposed to an exact hypothesis.

Generally, an alternative hypothesis (discussed above) is composite because it is defined as anything except the null hypothesis. This ‘anything except’ does not define parameters or distribution, and therefore it’s an example of a composite hypothesis.

6. Directional Hypothesis

A directional hypothesis makes a prediction about the positivity or negativity of the effect of an intervention prior to the test being conducted.

Instead of being agnostic about whether the effect will be positive or negative, it nominates the effect’s directionality.

We often call this a one-tailed hypothesis (in contrast to a two-tailed or non-directional hypothesis) because, looking at a distribution graph, we’re hypothesizing that the results will lean toward one particular tail on the graph – either the positive or negative.

Directional Hypothesis Examples

7. non-directional hypothesis.

A non-directional hypothesis does not specify the predicted direction (e.g. positivity or negativity) of the effect of the independent variable on the dependent variable.

These hypotheses predict an effect, but stop short of saying what that effect will be.

A non-directional hypothesis is similar to composite and alternative hypotheses. All three types of hypothesis tend to make predictions without defining a direction. In a composite hypothesis, a specific prediction is not made (although a general direction may be indicated, so the overlap is not complete). For an alternative hypothesis, you often predict that the even will be anything but the null hypothesis, which means it could be more or less than H 0 (or in other words, non-directional).

Let’s turn the above directional hypotheses into non-directional hypotheses.

Non-Directional Hypothesis Examples

8. logical hypothesis.

A logical hypothesis is a hypothesis that cannot be tested, but has some logical basis underpinning our assumptions.

These are most commonly used in philosophy because philosophical questions are often untestable and therefore we must rely on our logic to formulate logical theories.

Usually, we would want to turn a logical hypothesis into an empirical one through testing if we got the chance. Unfortunately, we don’t always have this opportunity because the test is too complex, expensive, or simply unrealistic.

Here are some examples:

• Before the 1980s, it was hypothesized that the Titanic came to its resting place at 41° N and 49° W, based on the time the ship sank and the ship’s presumed path across the Atlantic Ocean. However, due to the depth of the ocean, it was impossible to test. Thus, the hypothesis was simply a logical hypothesis.
• Dinosaurs closely related to Aligators probably had green scales because Aligators have green scales. However, as they are all extinct, we can only rely on logic and not empirical data.

9. Empirical Hypothesis

An empirical hypothesis is the opposite of a logical hypothesis. It is a hypothesis that is currently being tested using scientific analysis. We can also call this a ‘working hypothesis’.

We can to separate research into two types: theoretical and empirical. Theoretical research relies on logic and thought experiments. Empirical research relies on tests that can be verified by observation and measurement.

So, an empirical hypothesis is a hypothesis that can and will be tested.

• Raising the wage of restaurant servers increases staff retention.
• Adding 1 lb of corn per day to cows’ diets decreases their lifespan.
• Mushrooms grow faster at 22 degrees Celsius than 27 degrees Celsius.

Each of the above hypotheses can be tested, making them empirical rather than just logical (aka theoretical).

10. Statistical Hypothesis

A statistical hypothesis utilizes representative statistical models to draw conclusions about broader populations.

It requires the use of datasets or carefully selected representative samples so that statistical inference can be drawn across a larger dataset.

This type of research is necessary when it is impossible to assess every single possible case. Imagine, for example, if you wanted to determine if men are taller than women. You would be unable to measure the height of every man and woman on the planet. But, by conducting sufficient random samples, you would be able to predict with high probability that the results of your study would remain stable across the whole population.

You would be right in guessing that almost all quantitative research studies conducted in academic settings today involve statistical hypotheses.

Statistical Hypothesis Examples

• Human Sex Ratio. The most famous statistical hypothesis example is that of John Arbuthnot’s sex at birth case study in 1710. Arbuthnot used birth data to determine with high statistical probability that there are more male births than female births. He called this divine providence, and to this day, his findings remain true: more men are born than women.
• Lady Testing Tea. A 1935 study by Ronald Fisher involved testing a woman who believed she could tell whether milk was added before or after water to a cup of tea. Fisher gave her 4 cups in which one randomly had milk placed before the tea. He repeated the test 8 times. The lady was correct each time. Fisher found that she had a 1 in 70 chance of getting all 8 test correct, which is a statistically significant result.

11. Associative Hypothesis

An associative hypothesis predicts that two variables are linked but does not explore whether one variable directly impacts upon the other variable.

We commonly refer to this as “ correlation does not mean causation ”. Just because there are a lot of sick people in a hospital, it doesn’t mean that the hospital made the people sick. There is something going on there that’s causing the issue (sick people are flocking to the hospital).

So, in an associative hypothesis, you note correlation between an independent and dependent variable but do not make a prediction about how the two interact. You stop short of saying one thing causes another thing.

Associative Hypothesis Examples

• Sick people in hospital. You could conduct a study hypothesizing that hospitals have more sick people in them than other institutions in society. However, you don’t hypothesize that the hospitals caused the sickness.
• Lice make you healthy. In the Middle Ages, it was observed that sick people didn’t tend to have lice in their hair. The inaccurate conclusion was that lice was not only a sign of health, but that they made people healthy. In reality, there was an association here, but not causation. The fact was that lice were sensitive to body temperature and fled bodies that had fevers.

12. Causal Hypothesis

A causal hypothesis predicts that two variables are not only associated, but that changes in one variable will cause changes in another.

A causal hypothesis is harder to prove than an associative hypothesis because the cause needs to be definitively proven. This will often require repeating tests in controlled environments with the researchers making manipulations to the independent variable, or the use of control groups and placebo effects .

If we were to take the above example of lice in the hair of sick people, researchers would have to put lice in sick people’s hair and see if it made those people healthier. Researchers would likely observe that the lice would flee the hair, but the sickness would remain, leading to a finding of association but not causation.

Causal Hypothesis Examples

13. exact vs. inexact hypothesis.

For brevity’s sake, I have paired these two hypotheses into the one point. The reality is that we’ve already seen both of these types of hypotheses at play already.

An exact hypothesis (also known as a point hypothesis) specifies a specific prediction whereas an inexact hypothesis assumes a range of possible values without giving an exact outcome. As Helwig [2] argues:

“An “exact” hypothesis specifies the exact value(s) of the parameter(s) of interest, whereas an “inexact” hypothesis specifies a range of possible values for the parameter(s) of interest.”

Generally, a null hypothesis is an exact hypothesis whereas alternative, composite, directional, and non-directional hypotheses are all inexact.

See Next: 15 Hypothesis Examples

This is introductory information that is basic and indeed quite simplified for absolute beginners. It’s worth doing further independent research to get deeper knowledge of research methods and how to conduct an effective research study. And if you’re in education studies, don’t miss out on my list of the best education studies dissertation ideas .

[1] https://jnnp.bmj.com/content/91/6/571.abstract

[2] http://users.stat.umn.edu/~helwig/notes/SignificanceTesting.pdf

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]

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 5 Top Tips for Succeeding at University
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 50 Durable Goods Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 100 Consumer Goods Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 30 Globalization Pros and Cons

2 thoughts on “13 Different Types of Hypothesis”

Wow! This introductionary materials are very helpful. I teach the begginers in research for the first time in my career. The given tips and materials are very helpful. Chris, thank you so much! Excellent materials!

You’re more than welcome! If you want a pdf version of this article to provide for your students to use as a weekly reading on in-class discussion prompt for seminars, just drop me an email in the Contact form and I’ll get one sent out to you.

When I’ve taught this seminar, I’ve put my students into groups, cut these definitions into strips, and handed them out to the groups. Then I get them to try to come up with hypotheses that fit into each ‘type’. You can either just rotate hypothesis types so they get a chance at creating a hypothesis of each type, or get them to “teach” their hypothesis type and examples to the class at the end of the seminar.

Cheers, Chris

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• Null and Alternative Hypotheses | Definitions & Examples

Null and Alternative Hypotheses | Definitions & Examples

Published on 5 October 2022 by Shaun Turney . Revised on 6 December 2022.

The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test :

• Null hypothesis (H 0 ): There’s no effect in the population .
• Alternative hypothesis (H A ): There’s an effect in the population.

The effect is usually the effect of the independent variable on the dependent variable .

Table of contents

Answering your research question with hypotheses, what is a null hypothesis, what is an alternative hypothesis, differences between null and alternative hypotheses, how to write null and alternative hypotheses, frequently asked questions about null and alternative hypotheses.

The null and alternative hypotheses offer competing answers to your research question . When the research question asks “Does the independent variable affect the dependent variable?”, the null hypothesis (H 0 ) answers “No, there’s no effect in the population.” On the other hand, the alternative hypothesis (H A ) answers “Yes, there is an effect in the population.”

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample . Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample.

You can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypothesis. However, the hypotheses can also be phrased in a general way that applies to any test.

The null hypothesis is the claim that there’s no effect in the population.

If the sample provides enough evidence against the claim that there’s no effect in the population ( p ≤ α), then we can reject the null hypothesis . Otherwise, we fail to reject the null hypothesis.

Although “fail to reject” may sound awkward, it’s the only wording that statisticians accept. Be careful not to say you “prove” or “accept” the null hypothesis.

Null hypotheses often include phrases such as “no effect”, “no difference”, or “no relationship”. When written in mathematical terms, they always include an equality (usually =, but sometimes ≥ or ≤).

Examples of null hypotheses

The table below gives examples of research questions and null hypotheses. There’s always more than one way to answer a research question, but these null hypotheses can help you get started.

*Note that some researchers prefer to always write the null hypothesis in terms of “no effect” and “=”. It would be fine to say that daily meditation has no effect on the incidence of depression and p 1 = p 2 .

The alternative hypothesis (H A ) is the other answer to your research question . It claims that there’s an effect in the population.

Often, your alternative hypothesis is the same as your research hypothesis. In other words, it’s the claim that you expect or hope will be true.

The alternative hypothesis is the complement to the null hypothesis. Null and alternative hypotheses are exhaustive, meaning that together they cover every possible outcome. They are also mutually exclusive, meaning that only one can be true at a time.

Alternative hypotheses often include phrases such as “an effect”, “a difference”, or “a relationship”. When alternative hypotheses are written in mathematical terms, they always include an inequality (usually ≠, but sometimes > or <). As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis.

Examples of alternative hypotheses

The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own.

Null and alternative hypotheses are similar in some ways:

• They’re both answers to the research question
• They both make claims about the population
• They’re both evaluated by statistical tests.

However, there are important differences between the two types of hypotheses, summarized in the following table.

To help you write your hypotheses, you can use the template sentences below. If you know which statistical test you’re going to use, you can use the test-specific template sentences. Otherwise, you can use the general template sentences.

The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:

Does independent variable affect dependent variable ?

• Null hypothesis (H 0 ): Independent variable does not affect dependent variable .
• Alternative hypothesis (H A ): Independent variable affects dependent variable .

Test-specific

Once you know the statistical test you’ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.

Note: The template sentences above assume that you’re performing one-tailed tests . One-tailed tests are appropriate for most studies.

The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).

The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

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9.1 Null and Alternative Hypotheses

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 , the — null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.

H a —, the alternative hypothesis: a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are reject H 0 if the sample information favors the alternative hypothesis or do not reject H 0 or decline to reject H 0 if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example 9.1

H 0 : No more than 30 percent of the registered voters in Santa Clara County voted in the primary election. p ≤ 30 H a : More than 30 percent of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25 percent. State the null and alternative hypotheses.

Example 9.2

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are the following: H 0 : μ = 2.0 H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 66
• H a : μ __ 66

Example 9.3

We want to test if college students take fewer than five years to graduate from college, on the average. The null and alternative hypotheses are the following: H 0 : μ ≥ 5 H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 45
• H a : μ __ 45

Example 9.4

An article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third of the students pass. The same article stated that 6.6 percent of U.S. students take advanced placement exams and 4.4 percent pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6 percent. State the null and alternative hypotheses. H 0 : p ≤ 0.066 H a : p > 0.066

On a state driver’s test, about 40 percent pass the test on the first try. We want to test if more than 40 percent pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : p __ 0.40
• H a : p __ 0.40

Collaborative Exercise

Bring to class a newspaper, some news magazines, and some internet articles. In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

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10.29: Hypothesis Test for a Difference in Two Population Means (1 of 2)

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Learning Objectives

• Under appropriate conditions, conduct a hypothesis test about a difference between two population means. State a conclusion in context.

Using the Hypothesis Test for a Difference in Two Population Means

The general steps of this hypothesis test are the same as always. As expected, the details of the conditions for use of the test and the test statistic are unique to this test (but similar in many ways to what we have seen before.)

Step 1: Determine the hypotheses.

The hypotheses for a difference in two population means are similar to those for a difference in two population proportions. The null hypothesis, H 0 , is again a statement of “no effect” or “no difference.”

• H 0 : μ 1 – μ 2 = 0, which is the same as H 0 : μ 1 = μ 2

The alternative hypothesis, H a , can be any one of the following.

• H a : μ 1 – μ 2 < 0, which is the same as H a : μ 1 < μ 2
• H a : μ 1 – μ 2 > 0, which is the same as H a : μ 1 > μ 2
• H a : μ 1 – μ 2 ≠ 0, which is the same as H a : μ 1 ≠ μ 2

Step 2: Collect the data.

As usual, how we collect the data determines whether we can use it in the inference procedure. We have our usual two requirements for data collection.

• Samples must be random to remove or minimize bias.
• Samples must be representative of the populations in question.

We use this hypothesis test when the data meets the following conditions.

• The two random samples are independent .
• The variable is normally distributed in both populations . If this variable is not known, samples of more than 30 will have a difference in sample means that can be modeled adequately by the t-distribution. As we discussed in “Hypothesis Test for a Population Mean,” t-procedures are robust even when the variable is not normally distributed in the population. If checking normality in the populations is impossible, then we look at the distribution in the samples. If a histogram or dotplot of the data does not show extreme skew or outliers, we take it as a sign that the variable is not heavily skewed in the populations, and we use the inference procedure. (Note: This is the same condition we used for the one-sample t-test in “Hypothesis Test for a Population Mean.”)

Step 3: Assess the evidence.

If the conditions are met, then we calculate the t-test statistic. The t-test statistic has a familiar form.

Since the null hypothesis assumes there is no difference in the population means, the expression (μ 1 – μ 2 ) is always zero.

As we learned in “Estimating a Population Mean,” the t-distribution depends on the degrees of freedom (df) . In the one-sample and matched-pair cases df = n – 1. For the two-sample t-test, determining the correct df is based on a complicated formula that we do not cover in this course. We will either give the df or use technology to find the df . With the t-test statistic and the degrees of freedom, we can use the appropriate t-model to find the P-value, just as we did in “Hypothesis Test for a Population Mean.” We can even use the same simulation.

Step 4: State a conclusion.

To state a conclusion, we follow what we have done with other hypothesis tests. We compare our P-value to a stated level of significance.

• If the P-value ≤ α, we reject the null hypothesis in favor of the alternative hypothesis.
• If the P-value > α, we fail to reject the null hypothesis. We do not have enough evidence to support the alternative hypothesis.

As always, we state our conclusion in context, usually by referring to the alternative hypothesis.

“Context and Calories”

Does the company you keep impact what you eat? This example comes from an article titled “Impact of Group Settings and Gender on Meals Purchased by College Students” (Allen-O’Donnell, M., T. C. Nowak, K. A. Snyder, and M. D. Cottingham, Journal of Applied Social Psychology 49(9), 2011, onlinelibrary.wiley.com/doi/10.1111/j.1559-1816.2011.00804.x/full) . In this study, researchers examined this issue in the context of gender-related theories in their field. For our purposes, we look at this research more narrowly.

Step 1: Stating the hypotheses.

In the article, the authors make the following hypothesis. “The attempt to appear feminine will be empirically demonstrated by the purchase of fewer calories by women in mixed-gender groups than by women in same-gender groups.” We translate this into a simpler and narrower research question: Do women purchase fewer calories when they eat with men compared to when they eat with women?

Here the two populations are “women eating with women” (population 1) and “women eating with men” (population 2). The variable is the calories in the meal. We test the following hypotheses at the 5% level of significance.

The null hypothesis is always H 0 : μ 1 – μ 2 = 0, which is the same as H 0 : μ 1 = μ 2 .

The alternative hypothesis H a : μ 1 – μ 2 > 0, which is the same as H a : μ 1 > μ 2 .

Here μ 1 represents the mean number of calories ordered by women when they were eating with other women, and μ 2 represents the mean number of calories ordered by women when they were eating with men.

Note: It does not matter which population we label as 1 or 2, but once we decide, we have to stay consistent throughout the hypothesis test. Since we expect the number of calories to be greater for the women eating with other women, the difference is positive if “women eating with women” is population 1. If you prefer to work with positive numbers, choose the group with the larger expected mean as population 1. This is a good general tip.

Step 2: Collect Data.

As usual, there are two major things to keep in mind when considering the collection of data.

• Samples need to be representative of the population in question.
• Samples need to be random in order to remove or minimize bias.

Representative Samples?

The researchers state their hypothesis in terms of “women.” We did the same. But the researchers gathered data by watching people eat at the HUB Rock Café II on the campus of Indiana University of Pennsylvania during the Spring semester of 2006. Almost all of the women in the data set were white undergraduates between the ages of 18 and 24, so there are some definite limitations on the scope of this study. These limitations will affect our conclusion (and the specific definition of the population means in our hypotheses.)

Random Samples?

The observations were collected on February 13, 2006, through February 22, 2006, between 11 a.m. and 7 p.m. We can see that the researchers included both lunch and dinner. They also made observations on all days of the week to ensure that weekly customer patterns did not confound their findings. The authors state that “since the time period for observations and the place where [they] observed students were limited, the sample was a convenience sample.” Despite these limitations, the researchers conducted inference procedures with the data, and the results were published in a reputable journal. We will also conduct inference with this data, but we also include a discussion of the limitations of the study with our conclusion. The authors did this, also.

Do the data met the conditions for use of a t-test?

The researchers reported the following sample statistics.

• In a sample of 45 women dining with other women, the average number of calories ordered was 850, and the standard deviation was 252.
• In a sample of 27 women dining with men, the average number of calories ordered was 719, and the standard deviation was 322.

One of the samples has fewer than 30 women. We need to make sure the distribution of calories in this sample is not heavily skewed and has no outliers, but we do not have access to a spreadsheet of the actual data. Since the researchers conducted a t-test with this data, we will assume that the conditions are met. This includes the assumption that the samples are independent.

As noted previously, the researchers reported the following sample statistics.

To compute the t-test statistic, make sure sample 1 corresponds to population 1. Here our population 1 is “women eating with other women.” So x 1 = 850, s 1 = 252, n 1 =45, and so on.

Using technology, we determined that the degrees of freedom are about 45 for this data. To find the P-value, we use our familiar simulation of the t-distribution. Since the alternative hypothesis is a “greater than” statement, we look for the area to the right of T = 1.81. The P-value is 0.0385.

Generic Conclusion

The hypotheses for this test are H 0 : μ 1 – μ 2 = 0 and H a : μ 1 – μ 2 > 0. Since the P-value is less than the significance level (0.0385 < 0.05), we reject H 0 and accept H a .

Conclusion in context

At Indiana University of Pennsylvania, the mean number of calories ordered by undergraduate women eating with other women is greater than the mean number of calories ordered by undergraduate women eating with men (P-value = 0.0385).

Comment about Conclusions

In the conclusion above, we did not generalize the findings to all women. Since the samples included only undergraduate women at one university, we included this information in our conclusion. But our conclusion is a cautious statement of the findings. The authors see the results more broadly in the context of theories in the field of social psychology. In the context of these theories, they write, “Our findings support the assertion that meal size is a tool for influencing the impressions of others. For traditional-age, predominantly White college women, diminished meal size appears to be an attempt to assert femininity in groups that include men.” This viewpoint is echoed in the following summary of the study for the general public on National Public Radio (npr.org).

• Both men and women appear to choose larger portions when they eat with women, and both men and women choose smaller portions when they eat in the company of men, according to new research published in the Journal of Applied Social Psychology . The study, conducted among a sample of 127 college students, suggests that both men and women are influenced by unconscious scripts about how to behave in each other’s company. And these scripts change the way men and women eat when they eat together and when they eat apart.

Should we be concerned that the findings of this study are generalized in this way? Perhaps. But the authors of the article address this concern by including the following disclaimer with their findings: “While the results of our research are suggestive, they should be replicated with larger, representative samples. Studies should be done not only with primarily White, middle-class college students, but also with students who differ in terms of race/ethnicity, social class, age, sexual orientation, and so forth.” This is an example of good statistical practice. It is often very difficult to select truly random samples from the populations of interest. Researchers therefore discuss the limitations of their sampling design when they discuss their conclusions.

In the following activities, you will have the opportunity to practice parts of the hypothesis test for a difference in two population means. On the next page, the activities focus on the entire process and also incorporate technology.

National Health and Nutrition Survey

https://assessments.lumenlearning.co...sessments/3705

https://assessments.lumenlearning.co...sessments/3782

https://assessments.lumenlearning.co...sessments/3706

Contributors and Attributions

• Concepts in Statistics. Provided by : Open Learning Initiative. Located at : http://oli.cmu.edu . License : CC BY: Attribution

This is the Difference Between a Hypothesis and a Theory

What to Know A hypothesis is an assumption made before any research has been done. It is formed so that it can be tested to see if it might be true. A theory is a principle formed to explain the things already shown in data. Because of the rigors of experiment and control, it is much more likely that a theory will be true than a hypothesis.

As anyone who has worked in a laboratory or out in the field can tell you, science is about process: that of observing, making inferences about those observations, and then performing tests to see if the truth value of those inferences holds up. The scientific method is designed to be a rigorous procedure for acquiring knowledge about the world around us.

In scientific reasoning, a hypothesis is constructed before any applicable research has been done. A theory, on the other hand, is supported by evidence: it's a principle formed as an attempt to explain things that have already been substantiated by data.

Toward that end, science employs a particular vocabulary for describing how ideas are proposed, tested, and supported or disproven. And that's where we see the difference between a hypothesis and a theory .

A hypothesis is an assumption, something proposed for the sake of argument so that it can be tested to see if it might be true.

In the scientific method, the hypothesis is constructed before any applicable research has been done, apart from a basic background review. You ask a question, read up on what has been studied before, and then form a hypothesis.

What is a Hypothesis?

A hypothesis is usually tentative, an assumption or suggestion made strictly for the objective of being tested.

When a character which has been lost in a breed, reappears after a great number of generations, the most probable hypothesis is, not that the offspring suddenly takes after an ancestor some hundred generations distant, but that in each successive generation there has been a tendency to reproduce the character in question, which at last, under unknown favourable conditions, gains an ascendancy. Charles Darwin, On the Origin of Species , 1859 According to one widely reported hypothesis , cell-phone transmissions were disrupting the bees' navigational abilities. (Few experts took the cell-phone conjecture seriously; as one scientist said to me, "If that were the case, Dave Hackenberg's hives would have been dead a long time ago.") Elizabeth Kolbert, The New Yorker , 6 Aug. 2007

What is a Theory?

A theory , in contrast, is a principle that has been formed as an attempt to explain things that have already been substantiated by data. It is used in the names of a number of principles accepted in the scientific community, such as the Big Bang Theory . Because of the rigors of experimentation and control, its likelihood as truth is much higher than that of a hypothesis.

It is evident, on our theory , that coasts merely fringed by reefs cannot have subsided to any perceptible amount; and therefore they must, since the growth of their corals, either have remained stationary or have been upheaved. Now, it is remarkable how generally it can be shown, by the presence of upraised organic remains, that the fringed islands have been elevated: and so far, this is indirect evidence in favour of our theory . Charles Darwin, The Voyage of the Beagle , 1839 An example of a fundamental principle in physics, first proposed by Galileo in 1632 and extended by Einstein in 1905, is the following: All observers traveling at constant velocity relative to one another, should witness identical laws of nature. From this principle, Einstein derived his theory of special relativity. Alan Lightman, Harper's , December 2011

Non-Scientific Use

In non-scientific use, however, hypothesis and theory are often used interchangeably to mean simply an idea, speculation, or hunch (though theory is more common in this regard):

The theory of the teacher with all these immigrant kids was that if you spoke English loudly enough they would eventually understand. E. L. Doctorow, Loon Lake , 1979 Chicago is famous for asking questions for which there can be no boilerplate answers. Example: given the probability that the federal tax code, nondairy creamer, Dennis Rodman and the art of mime all came from outer space, name something else that has extraterrestrial origins and defend your hypothesis . John McCormick, Newsweek , 5 Apr. 1999 In his mind's eye, Miller saw his case suddenly taking form: Richard Bailey had Helen Brach killed because she was threatening to sue him over the horses she had purchased. It was, he realized, only a theory , but it was one he felt certain he could, in time, prove. Full of urgency, a man with a mission now that he had a hypothesis to guide him, he issued new orders to his troops: Find out everything you can about Richard Bailey and his crowd. Howard Blum, Vanity Fair , January 1995

And sometimes one term is used as a genus, or a means for defining the other:

Laplace's popular version of his astronomy, the Système du monde , was famous for introducing what came to be known as the nebular hypothesis , the theory that the solar system was formed by the condensation, through gradual cooling, of the gaseous atmosphere (the nebulae) surrounding the sun. Louis Menand, The Metaphysical Club , 2001 Researchers use this information to support the gateway drug theory — the hypothesis that using one intoxicating substance leads to future use of another. Jordy Byrd, The Pacific Northwest Inlander , 6 May 2015 Fox, the business and economics columnist for Time magazine, tells the story of the professors who enabled those abuses under the banner of the financial theory known as the efficient market hypothesis . Paul Krugman, The New York Times Book Review , 9 Aug. 2009

Incorrect Interpretations of "Theory"

Since this casual use does away with the distinctions upheld by the scientific community, hypothesis and theory are prone to being wrongly interpreted even when they are encountered in scientific contexts—or at least, contexts that allude to scientific study without making the critical distinction that scientists employ when weighing hypotheses and theories.

The most common occurrence is when theory is interpreted—and sometimes even gleefully seized upon—to mean something having less truth value than other scientific principles. (The word law applies to principles so firmly established that they are almost never questioned, such as the law of gravity.)

This mistake is one of projection: since we use theory in general use to mean something lightly speculated, then it's implied that scientists must be talking about the same level of uncertainty when they use theory to refer to their well-tested and reasoned principles.

The distinction has come to the forefront particularly on occasions when the content of science curricula in schools has been challenged—notably, when a school board in Georgia put stickers on textbooks stating that evolution was "a theory, not a fact, regarding the origin of living things." As Kenneth R. Miller, a cell biologist at Brown University, has said , a theory "doesn’t mean a hunch or a guess. A theory is a system of explanations that ties together a whole bunch of facts. It not only explains those facts, but predicts what you ought to find from other observations and experiments.”

While theories are never completely infallible, they form the basis of scientific reasoning because, as Miller said "to the best of our ability, we’ve tested them, and they’ve held up."

More Differences Explained

• Epidemic vs. Pandemic
• Diagnosis vs. Prognosis
• Treatment vs. Cure

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• Null and Alternative Hypotheses | Definitions & Examples

Null & Alternative Hypotheses | Definitions, Templates & Examples

Published on May 6, 2022 by Shaun Turney . Revised on June 22, 2023.

The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test :

• Null hypothesis ( H 0 ): There’s no effect in the population .
• Alternative hypothesis ( H a or H 1 ) : There’s an effect in the population.

Table of contents

Answering your research question with hypotheses, what is a null hypothesis, what is an alternative hypothesis, similarities and differences between null and alternative hypotheses, how to write null and alternative hypotheses, other interesting articles, frequently asked questions.

The null and alternative hypotheses offer competing answers to your research question . When the research question asks “Does the independent variable affect the dependent variable?”:

• The null hypothesis ( H 0 ) answers “No, there’s no effect in the population.”
• The alternative hypothesis ( H a ) answers “Yes, there is an effect in the population.”

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample . Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses .

You can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypothesis. However, the hypotheses can also be phrased in a general way that applies to any test.

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The null hypothesis is the claim that there’s no effect in the population.

If the sample provides enough evidence against the claim that there’s no effect in the population ( p ≤ α), then we can reject the null hypothesis . Otherwise, we fail to reject the null hypothesis.

Although “fail to reject” may sound awkward, it’s the only wording that statisticians accept . Be careful not to say you “prove” or “accept” the null hypothesis.

Null hypotheses often include phrases such as “no effect,” “no difference,” or “no relationship.” When written in mathematical terms, they always include an equality (usually =, but sometimes ≥ or ≤).

You can never know with complete certainty whether there is an effect in the population. Some percentage of the time, your inference about the population will be incorrect. When you incorrectly reject the null hypothesis, it’s called a type I error . When you incorrectly fail to reject it, it’s a type II error.

Examples of null hypotheses

The table below gives examples of research questions and null hypotheses. There’s always more than one way to answer a research question, but these null hypotheses can help you get started.

*Note that some researchers prefer to always write the null hypothesis in terms of “no effect” and “=”. It would be fine to say that daily meditation has no effect on the incidence of depression and p 1 = p 2 .

The alternative hypothesis ( H a ) is the other answer to your research question . It claims that there’s an effect in the population.

Often, your alternative hypothesis is the same as your research hypothesis. In other words, it’s the claim that you expect or hope will be true.

The alternative hypothesis is the complement to the null hypothesis. Null and alternative hypotheses are exhaustive, meaning that together they cover every possible outcome. They are also mutually exclusive, meaning that only one can be true at a time.

Alternative hypotheses often include phrases such as “an effect,” “a difference,” or “a relationship.” When alternative hypotheses are written in mathematical terms, they always include an inequality (usually ≠, but sometimes < or >). As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis.

Examples of alternative hypotheses

The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own.

Null and alternative hypotheses are similar in some ways:

• They’re both answers to the research question.
• They both make claims about the population.
• They’re both evaluated by statistical tests.

However, there are important differences between the two types of hypotheses, summarized in the following table.

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To help you write your hypotheses, you can use the template sentences below. If you know which statistical test you’re going to use, you can use the test-specific template sentences. Otherwise, you can use the general template sentences.

General template sentences

The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:

Does independent variable affect dependent variable ?

• Null hypothesis ( H 0 ): Independent variable does not affect dependent variable.
• Alternative hypothesis ( H a ): Independent variable affects dependent variable.

Test-specific template sentences

Once you know the statistical test you’ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.

Note: The template sentences above assume that you’re performing one-tailed tests . One-tailed tests are appropriate for most studies.

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

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).

The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (“ x affects y because …”).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses . In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

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Open Access

Peer-reviewed

Research Article

Mind to move: Differences in running biomechanics between sensing and intuition shod runners

Contributed equally to this work with: Cyrille Gindre, Aurélien Patoz, Bastiaan Breine, Thibault Lussiana

Roles Conceptualization, Writing – review & editing

Affiliations Research and Development Department, Volodalen, Chavéria, France, Research and Development Department, Volodalen SwissSportLab, Aigle, Switzerland, MPFRPV, Université de Franche-Comté, Besançon, France, Exercise Performance Health Innovation (EPHI) Platform, Besançon, France

Roles Data curation, Formal analysis, Writing – original draft, Writing – review & editing

* E-mail: [email protected]

Affiliations Research and Development Department, Volodalen SwissSportLab, Aigle, Switzerland, Institute of Sport Sciences, University of Lausanne, Lausanne, Switzerland

Roles Data curation, Formal analysis, Writing – review & editing

Affiliations Research and Development Department, Volodalen SwissSportLab, Aigle, Switzerland, Department of Movement and Sports Sciences, Ghent University, Ghent, Belgium

Roles Conceptualization, Data curation, Formal analysis, Writing – original draft, Writing – review & editing

• Cyrille Gindre, 
• Aurélien Patoz, 
• Bastiaan Breine, 
• Thibault Lussiana

• Published: April 3, 2024
• https://doi.org/10.1371/journal.pone.0300108
• Peer Review
• Reader Comments

Delving into the complexities of embodied cognition unveils the intertwined influence of mind, body, and environment. The connection of physical activity with cognition sparks a hypothesis linking motion and personality traits. Hence, this study explored whether personality traits could be linked to biomechanical variables characterizing running forms. To do so, 80 runners completed three randomized 50-m running-trials at 3.3, 4.2, and 5m/s during which their running biomechanics [ground contact time ( t c ), flight time ( t f ), duty factor (DF), step frequency (SF), leg stiffness ( k leg ), maximal vertical ground reaction force ( F max ), and maximal leg compression of the spring during stance (Δ L )] was evaluated. In addition, participants’ personality traits were assessed through the Myers-Briggs Type Indicator (MBTI) test. The MBTI classifies personality traits into one of two possible categories along four axes: extraversion-introversion; sensing-intuition; thinking-feeling; and judging-perceiving. This exploratory study offers compelling evidence that personality traits, specifically sensing and intuition, are associated with distinct running biomechanics. Individuals classified as sensing demonstrated a more grounded running style characterized by prolonged t c , shorter t f , higher DF, and greater Δ L compared to intuition individuals ( p ≤0.02). Conversely, intuition runners exhibited a more dynamic and elastic running style with a shorter t c and higher k leg than their sensing counterparts ( p ≤0.02). Post-hoc tests revealed a significant difference in t c between intuition and sensing runners at all speeds ( p ≤0.02). According to the definition of each category provided by the MBTI, sensing individuals tend to focus on concrete facts and physical realities while intuition individuals emphasize abstract concepts and patterns of information. These results suggest that runners with sensing and intuition personality traits differ in their ability to use their lower limb structures as springs. Intuition runners appeared to rely more in the stretch-shortening cycle to energetically optimize their running style while sensing runners seemed to optimize running economy by promoting more forward progression than vertical oscillations. This study underscores the intriguing interplay between personality traits of individuals and their preferred movement patterns.

Citation: Gindre C, Patoz A, Breine B, Lussiana T (2024) Mind to move: Differences in running biomechanics between sensing and intuition shod runners. PLoS ONE 19(4): e0300108. https://doi.org/10.1371/journal.pone.0300108

Editor: Yaodong Gu, Ningbo University, CHINA

Received: November 7, 2023; Accepted: February 21, 2024; Published: April 3, 2024

Copyright: © 2024 Gindre et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: The datasets for this study are freely available using the access link https://github.com/aurelienPatoz/we-run-the-way-we-are .

Funding: The author(s) received no specific funding for this work.

Competing interests: No authors have competing interests.

Introduction

Embodied cognition, a compelling theoretical framework in cognitive science, challenges conventional notions that divorce the mind from the body [ 1 ]. This paradigm asserts a symbiotic relationship between cognitive processes and the physical body, underscoring the significance of sensory and motor experiences in shaping mental functions [ 2 ]. Unlike traditional views that confine cognition to the brain, embodied cognition recognizes the profound impact of the body’s interactions with the environment on cognitive phenomena [ 3 ]. This approach emphasizes both bottom-up processes, where sensory information informs cognitive processes, and top-down influences, where higher-order cognitive functions shape our perception and interaction with the world.

Exploring the intricate dynamics of embodied cognition sheds light on the reciprocal influence between the mind, body, and the vibrant world they jointly navigate. For example, an investigation revealed that the extraverted-introverted continuum influences upright posture, with 96% of extraverted individuals maintaining an “ideally aligned” posture, while 83% of introverted individuals exhibit a kyphosis-lordosis posture [ 4 ]. Furthermore, higher levels of extraversion and conscientiousness have been linked to increased physical activity levels [ 5 ] and to faster walking speeds [ 6 , 7 ], suggesting that the way individuals move may reflect their underlying personality traits. Conscientiousness, notably, has shown the capacity to mitigate the age-related decline in walking speed [ 6 , 8 ]. Research has also uncovered that personality traits manifest in an individual’s walking gait [ 9 ]. For instance, it was observed that greater pelvis motion in the horizontal plane during walking is associated with greater agreeableness in females, while, for males, greater thorax motion in the horizontal plane is linked with extraversion [ 9 ]. Since there were no significant distinctions in the horizontal motion of the thorax and pelvis between females and males, these correlations might be influenced by individual personalities, thus removing the influence of gender [ 9 ]. In a recent development, machine learning techniques were employed with notable accuracy to assess personality traits through the analysis of gait recorded using videos [ 10 ] or smartphone sensors [ 11 ].

Extending this line of inquiry into the realm of running, research on middle-aged male runners has identified common personality profiles and associated positive self-perception with long-term involvement in running and training [ 12 ]. Runners demonstrated heightened intelligence, creativity, self-sufficiency, sobriety, and forthrightness compared to the general population, embodying traits of introversion, shyness, and a propensity for imaginative pursuits in their personality composition [ 13 ]. Besides, a prospective study found that runners with high scores on the type A behaviour (characterized by agitation, hostility, rapid speech, and an extremely competitive nature) screening questionnaire experienced significantly more injuries, especially multiple injuries [ 14 ]. Nonetheless, limited information on the personality of recreational runners is available, primarily derived from older studies, and to the best of the author’s knowledge, with no recent research on this topic. This underscores the imperative for contemporary, original research specifically addressing the personality traits of recreational runners [ 15 ].

Personality traits could be effectively classified into one of two possible categories along various axes using the Myers-Briggs Type Indicator (MBTI) test, a tool rooted in Jungʼs psychology [ 16 ]. Notably, there is no superior category in each MBTI axis. Additionally, recent research suggested that the duty factor (DF) plays a pivotal role in illustrating two distinct spontaneous running forms in recreational runners, i.e., runners with either low or high DF [ 17 , 18 ]. DF represents the proportion of time spent in contact with the ground during a running stride and could be considered as a global variable to describe the running pattern. Both running forms (low or high DF runners) could be efficiently employed at endurance running speeds, leading to similar running economy measures [ 17 ]. Low DF runners were shown to exhibit a shorter contact time ( t c ), larger vertical oscillation of the center of mass during flight time ( t f ), and more anterior (midfoot and forefoot) strike pattern, favoring elastic energy reuse. Conversely, high DF runners demonstrated a longer t c , more rearfoot strike pattern, and reduced work against gravity to promote forward progression. Similarly, decreasing and increasing t c could represent two opposing yet efficient strategies for enhancing running economy [ 19 , 20 ]. The first strategy involves an increase in vertical stiffness to improve running economic [ 19 ] while the second strategy posits that generating force over a longer period might be more economical [ 20 ]. Consequently, one may contemplate whether each of these running strategies could be associated with a specific personality trait category.

In the present study, we delve into the intriguing realm of embodied cognition by exploring whether an intricate connection could exist between personality traits and the spontaneous running patterns of shod runners. Indeed, the aim of this study was to explore whether the two categories of personality traits within the various MBTI axes could be linked to biomechanical variables that characterize two distinct running forms naturally embraced by individuals. This exploration should shed light on the complex relationship between the mind and motion. We hypothesized that personality traits would demonstrate association with spontaneous running patterns.

Materials and methods

Participants.

Eighty recreational endurance runners with regular running training, 67 males (age: 29.3 ± 11.1 years, height: 178.2 ± 6.4 cm, body mass: 72.0 ± 8.5 kg, and weekly running hours: 6.4 ± 3.8 h/week) and 13 females (age: 29.8 ± 11.6 years, height: 167.2 ± 6.9 cm, body mass: 60.8 ± 9.1 kg, and weekly running hours: 8.5 ± 7.8 h/week), participated in this study. All runners identified as Caucasians. To ensure diverse participation in the study, we sought a heterogeneous panel of runners with varying training backgrounds. Consequently, participants were only mandated to run a minimum of one hour per week and maintain good self-reported general health, without any current or recent (<6 months) musculoskeletal injuries. However, nothing specific about their spontaneous running pattern such as their foot-strike pattern was required because the running pattern is assumed to be a global system with several interconnected variables [ 17 , 18 , 21 , 22 ]. All participants completed the study on a voluntary basis. The university’s institutional review board (Comité de Protection des Personnes Est 1 (CPP EST 1) approved the protocol prior to participant recruitment (ID RCB 2014-A00336-41), and the study was conducted in accordance with the latest amendments of the Declaration of Helsinki. Participants were recruited between the September 1 st and November 30 th of 2014. Each participant underwent two experimental sessions within one week: a running biomechanical analysis during the first session, and a personality traits assessment during the second one. All participants wore their habitual running shoes during the biomechanical analysis.

Assessment of biomechanical variables

After providing written informed consent, participants performed a 10-min warm-up run at a self-selected speed (range: 2.5–3.5 m/s) on an indoor athletic track. Subsequently, participants completed three randomized 50-m running-trials at speeds of 3.3, 4.2, and 5 m/s starting from a standing-still position (2-min rest period between trials). These running speeds were chosen because they represent the 10-km race pace of most of endurance runners [ 23 ]. Speed was monitored using photoelectric cells (Racetime2, MicroGate, Timing and Sport, Bolzano, Italy) placed at the 20 and 40-m marks. No participants showed difficulty in running at the requested paces. A running trial was accepted if the monitored speed was within ± 5% of the requested speed and repeated otherwise after a 2-min rest period. Less than 15% of the trials were discarded. The Optojump ® photoelectric cells (MicroGate Timing and Sport, Bolzano, Italy) were used to measure t c (in ms) and t f (in ms) between the 20 and 40-m marks. The cells consist of two parallel bars which were set 1 m apart and were connected to a personal computer. One bar acts as a transmitter unit containing light emitting diodes positioned 3 mm above the ground, whereas the other bar acts as the receiver unit. When the light is interrupted by an individual’s foot during running, a timer within the Optojump system records time with a precision of 1 ms (sampling frequency of 1000 Hz). This allows measuring t c as the time that the light is interrupted and t f as the time between interruptions. As for each participant, the average value over the 20-m distance was computed for t c and t f and used in what follows. The test-retest reliability of the Optojump system was demonstrated to be excellent, with low coefficients of variation (2.7%) and high intraclass correlation coefficients (range: 0.982 to 0.989) [ 24 ].

Assessment of personality traits

Based on the answers to 93 questions, the MBTI classifies personality traits into one of two possible categories along four axes: extraversion-introversion (favorite world); sensing-intuition (information processing preference); thinking-feeling (decision making); and judging-perceiving (structure). Together, these axes influence how an individual perceives a situation and decides on a course of action. The MBTI has demonstrated excellent stability with test-retest correlations between 0.83 and 0.97 over a 4-week interval, exceeding the stability of many established trait measures, and between 0.77 and 0.84 over a 9-month interval [ 29 ]. Moreover, each dichotomy showed an agreement of 84 to 96% over 4 weeks, with a median agreement of 90% [ 16 ]. Given potential context-dependent results of the MBTI [ 29 ], the personality traits of participants were reassessed through a face-to-face meeting lasting approximately one hour, conducted by an MBTI-certified practitioner, to ensure data quality.

Sample size calculations determined that 80 participants were required for this study, assuming moderate effect sizes (~0.5) for biomechanical differences between MBTI axes, an α error of 0.05, and a power of 0.8 [ 30 ] and was obtained using G*Power (v3.1, available at https://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower ) [ 31 ]. Descriptive statistics are presented as mean ± standard deviation. Data normality and homogeneity of variance were evaluated using Kolmogorov-Smirnov and Levene’s tests, respectively. Participant characteristics were compared along each MBTI axis using ANOVA and non-parametric ANOVA when data normality was not verified. Repeated-measures ANOVA (speed x MBTI axes) with Mauchly’s correction for sphericity and employing Holm corrections for pair-wise post-hoc comparisons were used to investigate the effect of each MBTI axis on the biomechanical variables ( t c , t f , DF, SF, k leg , F max , and Δ L ) while accounting for the effect of running speed. 95% confidence intervals [lower, upper] of mean differences (Δs) were calculated for each significant post-hoc comparison along the MBTI axes. Cohen’s d effect sizes were calculated for participant characteristics along the four MBTI axes and for each significant post-hoc comparison. Effect sizes were classified as small , moderate , or large based on the magnitude of d values (0.2, 0.5, and 0.8, respectively) [ 32 ]. Statistical analysis was conducted using Jamovi (v1.6.23, available at https://www.jamovi.org ), with significance set at α ≤ 0.05.

Classifications of participants along the four MBTI axes are reported in Table 1 . Normality and homogeneity of variance were verified for age, height, body mass, and weekly running hours ( p ≥ 0.07; Table 1 ) except for age and weekly running hours which were not normally distributed ( p ≤ 0.04; Table 1 ). ANOVA and non-parametric ANOVA results indicated no main effect of the MBTI axes on age, height, body mass, and weekly running hours ( p ≥ 0.07; Table 1 ), suggesting that these characteristics were similar across each MBTI axis. Effect sizes were small for age, height, body mass, and weekly running hours between the categories of each MBTI axis (| d | ≤ 0.27; Table 1 ), except for weekly running hours of the extraversion-introversion axis, and height and body mass of the thinking-feeling axis which were moderate (0.40 ≤ | d | ≤ 0.66; Table 1 ).

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Significant differences ( p ≤ 0.05) are indicated in bold. Participant characteristics along each MBTI axis were compared using ANOVA and non-parametric ANOVA when data normality was not verified. Data normality and homogeneity of variance were evaluated using Kolmogorov-Smirnov and Levene’s tests, respectively.

https://doi.org/10.1371/journal.pone.0300108.t001

Data normality and homogeneity of variance of the biomechanical variables were all verified ( p ≥ 0.07; Table 2 ).

No significant difference was reported ( p > 0.05).

https://doi.org/10.1371/journal.pone.0300108.t002

A speed x sensing-intuition axis interaction effect was observed for t c ( p = 0.02), with no other significant interaction effects reported (other interactions: p ≥ 0.06). Pair-wise post-hoc comparisons revealed significantly shorter t c for intuition runners compared to sensing runners at all running speeds examined ( p ≤ 0.02; Fig 1a ) with moderate to large effect sizes (0.73 ≤ d ≤ 1.02).

a , contact time ( t c ); b , flight time ( t f ); c , duty factor (DF). Intuition runners (blue symbols; left side) exhibited shorter t c ( p = 0.002), longer t f ( p < 0.001), and lower DF ( p < 0.001) than sensing runners (red symbols; right side). A significant speed x sensing-intuition axis interaction effect was observed for t c ( p = 0.02). * Significantly shorter t c for intuition than sensing runners, as reported by the pair-wise post-hoc comparisons ( p ≤ 0.02). Empty circles denote the data of each participant.

https://doi.org/10.1371/journal.pone.0300108.g001

The sensing-intuition axis reported significant differences among the biomechanical variables, leading to sensing runners showing a longer t c (Δ = 13 ms [5 ms, 21 ms]; p = 0.002; small effect size; d = 0.44), shorter t f (Δ = -16 ms [-22 ms, -10 ms]; p < 0.001; moderate effect size; d = -0.73), higher DF (Δ = 2.1% [1.3%, 2.9%]; p < 0.001; moderate effect size; d = 0.66), smaller k leg (Δ = -1.1 kN [-1.5 kN, -0.7 kN]; p = 0.01; moderate effect size; d = -0.68), and larger Δ L (Δ = 1.4 cm [0.7 cm, 2.1 cm]; p = 0.02; moderate effect size; d = 0.55) than intuition runners ( Fig 1 and Table 3 ). The other three axes did not report any significant differences among the biomechanical variables ( p ≥ 0.09).

Significant sensing-intuition axis effects ( p ≤ 0.05) identified by the two-way repeated measures ANOVA are indicated in bold.

https://doi.org/10.1371/journal.pone.0300108.t003

All the biomechanical variables investigated herein ( t c , t f , DF, SF, k leg , F max , and Δ L ) reported a significant running speed effect ( p ≤ 0.02), where t c and DF decreased with increasing speed while t f , SF, k leg , F max , and Δ L increased with increasing running speed.

In this exploratory study, we delved into the relationship between personality traits, as determined by the MBTI and the biomechanical characteristics of runners. On the one hand, our findings revealed distinct differences in running biomechanics between "sensing" and "intuition" runners, supporting our initial hypothesis. Sensing runners adopted a grounded running form characterized by several key biomechanical attributes. They exhibited longer t c , shorter t f , higher DF, and larger Δ L compared to intuition runners. In essence, sensing runners seemed to favor a more earthbound running style. Conversely, intuition runners demonstrated a more dynamic and elastic running form. They displayed shorter t c and larger k leg than their sensing counterparts, indicating a propensity to harness the stretch-shortening cycle and utilize their lower limb structures as efficient springs during each stride. On the other hand, no association was found between running biomechanics and the remaining three MBTI axes, contradicting our initial hypothesis.

Based on the biomechanical variables observed herein (main effect for t c , t f , DF, Δ L , and k leg : p ≤ 0.02, Fig 1 and Table 1 ), sensing runners preferentially adopt a running form that favors a larger forward displacement during t c and smaller vertical displacement of the center of mass during t f compared to intuition runners. In terms of energetics, sensing runners would optimize running economy by promoting forward progression rather than vertical oscillations of the center of mass [ 17 ]. This forward progression strategy characterizes terrestrial runners [ 33 ] as well as high DF runners [ 17 , 18 ]. The linearity of the force-length relationship was shown to significantly decrease with increasing DF, suggesting a lower utilization of the spring-mass model with increasing DF [ 34 ]. These terrestrial and high DF runners were also characterized by an accentuated lower limb flexion during t c and a rearfoot strike pattern [ 17 , 18 , 33 ]. Sensing runners might describe their running form as: “I run very close to the ground to save as much energy as possible”. These individuals, according to the definition provided by the MBTI, should pay attention to physical realities and prefer practical and specific facts, preferably something they could perceive with their physical senses [ 16 , 35 ]. Hence, individuals with a more grounded running form should focus on practical facts (sensing individuals). The "physical contact" down-to-earth aspect of this personality trait seems to be reflected in both the mind and running form of sensing runners.

In contrast, intuition runners preferentially run with a larger vertical displacement of their center of mass during t f than sensing runners. The more elastic running form of intuition than sensing runners, along with their larger k leg , suggested that the re-use of elastic energy was an inherent feature of intuition runners. These individuals were better able to use their lower limb structures as springs, representing one of the multiple functional roles of the musculoskeletal system [ 36 ]. In other words, intuition runners promote the re-use of elastic energy (spring-mass model) and rely on the stretch-shortening cycle to optimize their running economy [ 17 ]. The greater reliance on the spring-mass model was a characteristic of the aerial running form [ 33 ] as well as of low DF runners [ 17 , 18 ]. These aerial and low DF runners were also characterized by an extended lower limb during t c and a forefoot/midfoot strike pattern [ 17 , 18 , 33 ]. Intuition runners might describe their running form as: “I spend energy to fight against gravity because I can use my leg springs to recover energy from each step”. These individuals, according to the definition provided by the MBTI, should pay attention to the meaning and patterns of information, prefer abstract concepts and theories, and make unconscious connections across their disciplines of knowledge [ 16 , 35 ]. Hence, individuals with a more dynamic and elastic running form should focus on abstract things (intuition individuals). While this specific study did not permit drawing causal or predictive conclusions, it highlights the fascinating interaction between an individual’s personality traits and their preferred movement patterns.

Importantly, our study noted that age, height, mass, and weekly running hours did not significantly differ between sensing and intuition runners ( p ≥ 0.07), removing potential confounding variables in our analysis [ 37 , 38 ]. However, it is worth noting that further investigations could explore whether differences in lower limb anatomy, such as tendon length or heel structure, might contribute to these observed biomechanical distinctions. Indeed, tendons and smaller moment arms of the Achilles tendon better support the elastic strategy than muscles and longer moment arms [ 39 ]. In addition, larger thickness and cross-sectional area of both the Achilles tendon and plantar fascia resulted in lower DF in barefoot running [ 40 ]. Hence, such investigations might reveal thicker and slenderer lower limbs, as well as shorter heels in intuition than sensing runners. This preliminary study has raised further questions about potential interactions between body morphology, movement preferences, and personality traits. Besides, given that DF is associated with foot-strike pattern, the degree of lower limb flexion during stance, and external forces [ 17 , 18 , 34 , 41 ], it would be valuable for future studies to investigate the connection between personality traits and these additional biomechanical variables.

It was previously demonstrated that the biomechanical characteristics of aerial and terrestrial running forms relate to feelings of pleasure-displeasure [ 42 ]. Ratings of pleasure-displeasure in runners change according to external variables, e.g., running speed. Feelings of pleasure are positively impacted in runners in situations where they are more biomechanically efficient, i.e., individuals with shorter t c and longer t f prefer running at faster speeds. As locomotion performance reflects trade-offs between different aspects of an individual’s biomechanics and environmental conditions [ 43 ], and that these aspects are linked with feelings of pleasure-displeasure, we could expect that intuition and sensing runners would take more pleasure at faster and slower running speeds, respectively. This assumption aligns with the MBTI description of both personality traits, where intuitive individuals are described as people living in the fast world of future possibilities, and sensing individuals as people living in the slow world of concrete things [ 16 ]. With such an integrative perspective that considers an individual’s movement patterns and environmental conditions, we can speculate that sensing and intuition runners would prefer different environments, supporting the theoretical framework of embodied cognition [ 2 , 3 ]. For instance, intuition runners may lean towards shorter and faster running events, opt for harder running surfaces, and favor more minimalist running shoes, whereas sensing runners may gravitate towards longer and slower running events, softer surfaces, and opt for more cushioned running shoes, reflecting their potential connection to DF and, consequently, the intuition-sensing personality. The assumption about the choice of running shoes is in line with previous observations that runners who have attempted barefoot running tend to be more open and less conscientious than shod runners [ 44 ]. Future work may further explore the interaction between personality traits, running biomechanics, and several environmental variables, including ground surface, running speed, and running footwear.

Notwithstanding, understanding the connections between personality traits and movement holds potential public health implications. Indeed, tailoring physical interventions through suitable exercises and instructions could mitigate non-adherence [ 45 ] and variability in responses [ 46 ] to a running training program in the context of a modern sedentary lifestyle. The disparities in running biomechanics associated with sensing and intuition personality traits might result in distinct injury locations or different underlying causes for a given injury. This suggests the need for tailored rehabilitation treatments, as previously advocated [ 47 ]. These observations partially align with findings from a prospective study, indicating that runners characterized by agitation, hostility, rapid speech, and an extremely competitive nature (Type A behavior) encountered significantly more injuries, particularly multiple injuries [ 14 ].

A few limitations to the present study exist. First, no causal or predictive conclusions could be drawn using this specific study’s design, but this study provides valuable information about personality traits and running forms. Then, even though runners were shown to demonstrate their most valid biomechanical running characteristics at their preferred running speed [ 48 ], biomechanical variables were evaluated at fixed running speeds to allow us comparing these variables between individuals. Besides, the MBTI validity has been questioned [ 49 ] and is regarded as a controversial approach [ 50 ], with psychometric limitations [ 51 , 52 ]. Nevertheless, this tool is still the most widely used personality assessment in the world [ 29 , 35 ]. Moreover, MBTI correlates well with the Neuroticism, Extraversion, Openness (NEO) Personality Inventory, another widely used personality assessment tool that examines the Big Five personality traits [ 53 , 54 ] and MBTI has been utilized, though several decades ago, to assess personality traits in middle-age male runners [ 12 ]. The MBTI was preferred over the Big Five in the present study due to its nuanced nature. The MBTI assigns a personality trait among two distinct categories for each axis, as opposed to the Big Five, which merely indicates the absence or presence of a given personality trait. As researchers, we assert that the Big Five tends to involve value judgments, whereas the MBTI assigns one of two possible personality traits to each axis without implying superiority for either. Next, several factors, such as emotion, mood, or facial expression, which were not measured herein, might have partly confounded the results of the present study. For instance, Williams, Exell [ 55 ] reported that sadness might increase running asymmetry while anger might facilitate symmetry and Brick, McElhinney [ 56 ] showed that oxygen consumption was lower when smiling than frowning during running and perceived effort was higher when frowning than smiling. However, to the best of authors knowledge, there was no direct scientific evidence that these factors could influence the biomechanical variables measured herein. Moreover, the present study did not account for sex distinctions. Despite utilizing a relatively large sample size ( n = 80), the decision was made not to differentiate between males ( n = 67) and females ( n = 13) to maintain simplicity and ensure an easily comprehensible manuscript, additionally given that separating the genders would have compromised statistical power. Nevertheless, future investigations should prioritize exploring the influence of sex when analyzing the connection between personality traits and running patterns, considering the demonstrated but subtle differences in personality types between males and females [ 57 ]. Furthermore, participants wore their own running shoes during testing, which could be confounding our results. Given that differences in footwear characteristics can underpin differences in running biomechanics [ 58 – 62 ], using a standardized shoe might have led to different study outcomes in terms of running biomechanics. Nonetheless, recreational runners are more comfortable wearing their own shoes [ 63 ], and show individual responses to novel footwear [ 63 , 64 ] and cushioning properties [ 65 ]. Finally, this study did not measure the foot-strike pattern of participants, despite existing biomechanical variations reported among different patterns [ 66 , 67 ]. Notably, forefoot and midfoot strikers exhibited significantly shorter contact times t c compared to heel strikers [ 68 ]. However, it’s crucial to recognize that the foot-strike pattern is just one element within the broader running pattern, encompassing various interconnected variables [ 17 , 18 , 21 , 22 ]. Considering this, runners with a more grounded running form, and associated with sensing personality trait, should exhibit a more rearfoot strike pattern because of the longer t c , while those with a more dynamic and elastic form, often associated with intuition personality trait, should demonstrate a more forefoot/midfoot strike pattern due to the shorter t c . Nevertheless, this statement requires validation through future research.

Conclusions

This exploratory study offers compelling evidence that personality traits, specifically sensing and intuition, are associated with distinct running biomechanics. Sensing runners, who pay attention to physical realities and prefer practical and specific facts, tend to adopt a more grounded running form associated with longer t c , shorter t f , higher DF, and larger Δ L than intuition runners. On the contrary, intuition runners, who prefer abstract concepts and theories, and make unconscious connections across their disciplines of knowledge, tend to opt for a more dynamic and elastic running form with shorter t c and larger k leg than sensing runners.

Supporting information

S1 file. personal protection committee est i..

https://doi.org/10.1371/journal.pone.0300108.s001

Acknowledgments

We thank Dr. Jean-Denis Rouillon and Prof. Laurent Mourot (University of Franche-Comté) for initiating this study. We also thank Dr. Kim Hébert-Losier (University of Waikato, New Zealand) for useful discussions and comments on the manuscript. We thank Stephanie Giordano Assante (MBTI certified practitioner) for the assessment of the personality traits of participants. We are grateful to the many volunteer runners who participated in this experiment.

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Hypothesis Testing for Difference Between Groups - Mar. 30 @ 1009 am.edited

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A difference-based method for testing no effect in nonparametric regression

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• Published: 27 March 2024

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• Zhijian Li   ORCID: orcid.org/0009-0007-0674-0738 1 ,
• Tiejun Tong 2 &
• Yuedong Wang 3  

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The paper proposes a novel difference-based method for testing the hypothesis of no relationship between the dependent and independent variables. We construct three test statistics for nonparametric regression with Gaussian and non-Gaussian random errors. These test statistics have the standard normal as the asymptotic null distribution. Furthermore, we show that these tests can detect local alternatives that converge to the null hypothesis at a rate close to \(n^{-1/2}\) previously achieved only by the residual-based tests. We also propose a permutation test as a flexible alternative. Our difference-based method does not require estimating the mean function or its first derivative, making it easy to implement and computationally efficient. Simulation results demonstrate that our new tests are more powerful than existing methods, especially when the sample size is small. The usefulness of the proposed tests is also illustrated using two real data examples.

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Acknowledgements

Zhijian Li was supported in part by the Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, project code 2022B1212010006 and UIC research grant R0400001-22, and UIC Start-up Research Fund/Grant UICR0700024-22. Tiejun Tong was supported in part by the General Research Fund of Hong Kong (HKBU12300123, HKBU12303421) and the National Natural Science Foundation of China (12071305). The authors thank the editor, the associate editor and two reviewers for their constructive comments and suggestions that have led to a substantial improvement in the paper and thank the authors of Zhang et al ( 2021 ) and Liu et al ( 2020 ) for providing the real data sets.

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Appendix 1: Some lemmas and their proofs

Assume that \(m \rightarrow \infty\) and \(m = o(n)\) . We have

\(\sum _{k=1}^{m}h_k= \frac{15}{16}n+o(n)\) ;

\(\sum _{k=1}^{m} k^2 h_k = n^2m +o(n^2m)\) ;

\(\sum _{k=1}^{i-1}h_k= \frac{15n^2}{4\,m^4}(i^3 - m^2i) + O\big (\frac{n^2}{m^2}\big ) + o\big (\frac{n^2i}{m^2}\big )\) ;

\(\sum _{k=i}^{m}k h_k= O(n^2)\) ;

\(\sum _{k=1}^{i-1} k^2 h_k = O(\frac{n^2i^3}{m^2})\) ;

\(\sum _{k=1}^{m}h_k^2 = \frac{45n^4}{4m^3} +o(\frac{n^4}{m^3})\) ;

\(\sum _{k=1}^{m}k h_k^2 = \frac{225n^4}{32m^2} +o(\frac{n^4}{m^2})\) .

Following the Appendix in Tong and Wang ( 2005 ), we have

By ( A1 ) and ( A2 ), we have

By ( A2 ) and ( A3 ), we have

For \(1 \le i \le m\) , by ( A2 ) and ( A3 ) we have

For \(1\le i \le m\) , by ( A2 ) we have

By ( A2 ), we have

\(\square\)

Assume that \(m \rightarrow \infty\) and \(m=o(n)\) , and let \(\textbf{g} = (g(x_1), \dots , g(x_n))^T\) . We have

\(\textbf{g}^T \varvec{B} \textbf{g} = 2\beta mn+O(m^2)\) ;

\(\textbf{g}^T \varvec{B}^2\textbf{g} = O(n^2m)\) .

Let \(\varvec{A}= (a_{ij})_{n\times n}\) be a symmetric matrix with \(a_{ij}\) having the same form as \(b_{ij}\) in ( 7 ) but \(h_0 = 0\) and \(h_k = 1\) for \(k = 1, \dots , m\) . Let \(\varvec{D} = (d_{ij})_{n\times n}\) is the matrix defined in Theorem 1 of Tong and Wang ( 2005 ). Then,

To simplify the notation, we let \(g_i=g(x_i)\) . We can show that

where \(\beta = \int _{0}^{1} (g'(x))^2 \, dx/2\) . Note also that \({\textbf {g}}^T \varvec{D} {\textbf {g}} = O(m^4/n^2)\) by Lemma 2 in Tong et al ( 2013 ). Then by ( A3 ), we have

Noting that \(\varvec{B}\) is a symmetric matrix, we let \({\textbf {g}}^T \varvec{B}^2 {\textbf {g}} = (\varvec{B}{} {\textbf {g}})^T (\varvec{B}{} {\textbf {g}}) = \varvec{q}^T \varvec{q}\) , where \(\varvec{q} = \varvec{B}{} {\textbf {g}} = (q_1, \dots , q_n)^T\) . For \(i \in [1,m]\) , by parts (b), (d) and (e) of Lemma 1 , we have

Similary, we can show that \(q_i=O(n)\) for \(i \in [n-m+1,n]\) . While for \(i \in [m+1,n-m]\) , by Lemma 1 (b) we have

Taken together the above results, it yields that

\(\sum _{i=1}^{n}b_{ii}^2= \frac{15n^4}{14m}+ o(\frac{n^4}{m})\) ;

\(\sum _{i=1}^{n}\sum _{j=1,j\ne i}^{n} b_{ij}^2=\frac{45n^5}{2\,m^3} + o(\frac{n^5}{m^3})\) .

By parts (a) and (c) of Lemma 1 , we have

By parts (f) and (g) of Lemma 1 , we have

Appendix 2: Proof of Theorem  1

Let \({\textbf {g}} = (g(x_1), \dots , g(x_n))^T\) and \(\varvec{\epsilon } = (\epsilon _1, \dots , \epsilon _n)^T\) . By ( 1 ) and ( 6 ), we have

From Lemma 2 (a) we have

Using Lemma 2 (b), we have \({{E}}({\textbf {g}}^T \varvec{B} \varvec{\epsilon } /N)^2 = \sigma ^2 {\textbf {g}}^T \varvec{B}^2{\textbf {g}}/N^2 = O(1/m)\) . This leads to

Let \(\varvec{\epsilon }^T \varvec{B} \varvec{\epsilon }/(2N) = \varvec{\epsilon }^T \varvec{C} \varvec{\epsilon } - \varvec{\epsilon }^T \varvec{U} \varvec{\epsilon }\) , where the elements of matrix \(\varvec{C}\) are

and \(\varvec{U}=\textrm{diag}(u_1, \cdots , u_n)\) with \(u_i = \sum _{k=min\{i,n+1-i,m+1\} }^{m+1} h_k/(2N)\) , for \(i = 1, \dots , n\) and \(h_{m+1} = 0\) . Let \(c_0 = \sum _{k=1}^{m}h_k/N\) , \(c_{i-j} = c_{j-i} = -h_{|i-j|}/(2N)\) for \(1 \le |i-j| \le m\) , and \(c_{i-j} = c_{j-i} = 0\) for \(|i-j| >m\) . Then \(\varvec{\epsilon }^T \varvec{C} \varvec{\epsilon } = \sum _{i=1}^{n}\sum _{j=1}^{n} c_{i-j} \epsilon _i \epsilon _j\) , where \(\epsilon _i\) are i.i.d. with mean zero. Thus by parts (a) and (f) of Lemma 1 ,

as \(m = \lceil n^r\rceil\) with \(2/5 \le r<1\) . Assuming \(E(\epsilon ^6) < \infty\) , by Theorem 2 in Whittle ( 1962 ), \(\varvec{\epsilon }^T \varvec{C} \varvec{\epsilon }\) is asymptotically normally distributed.

We have \(\varvec{\epsilon }^T \varvec{U} \varvec{\epsilon } = \sum _{i=1}^{n} u_i \epsilon _i^2\) . Let \(X_i = u_i \epsilon _i^2\) , then \(X_1, X_2, \dots , X_n\) are independent random variables, where \(X_i = \sum _{k=i}^{m} h_k \epsilon _i^2/(2N)\) for \(1 \le i \le m\) , \(X_i = \sum _{k=n-i+1}^{m} h_k \epsilon _i^2/(2N)\) for \(n-m+1 \le i \le n\) , and \(X_i = 0\) for \(m+1 \le i \le n-m\) . For \(1 \le i \le m\) , using parts (a) and (c) of Lemma 1 we have

as \(m = \lceil n^r\rceil\) with \(1/2< r<1\) . For \(n-m+1 \le i \le n\) , the results are similar. It is intuitive to show that for \(1 \le i \le m\) , the variance of \(X_i\) is

as \(n \rightarrow \infty\) and \(m = \lceil n^r\rceil\) with \(1/2< r<1\) . We have similar results for \(n-m+1 \le i \le n\) , and \(\text {Var}(X_i) = 0\) for \(m+1 \le i \le n-m\) . Noting also that \(\sum _{i=1}^{m} \text {Var}(X_i) = \sum _{i=n-m+1}^{n} \text {Var}(X_i)\) , we can derive the sum of variance as

Thus \(s_n^2\) is finite as \(m = \lceil n^r\rceil\) with \(2/3 \le r<1\) . Moreover, we have

where \(\tau _0\) and \(\tau _1\) are some constants and \(m \rightarrow \infty\) with \(n \rightarrow \infty\) . Thus

By the Lyapunov CLT, \(\varvec{\epsilon }^T \varvec{U} \varvec{\epsilon }\) is asymptotically normally distributed. Therefore, \(\varvec{\epsilon }^T \varvec{B} \varvec{\epsilon }/(2N)\) is asymptotically normally distributed. The mean of \(\varvec{\epsilon }^T \varvec{B} \varvec{\epsilon }/(2N)\) can be shown to be

and the variance is

Using parts (a) and (b) of Lemma 3 and combining the above results, we have

where \(m = \lceil n^r\rceil\) with \(2/3< r<1\) . This then leads to

as \(n \rightarrow \infty\) , where \(\sigma _{b}=\sqrt{15(\gamma _4-1)\sigma ^4/56}\) . \(\square\)

Appendix 3: Proofs of Theorem  2 and Theorem  3

Proof of theorem 2.

The estimated error variance of \(\hat{\beta }\) given in ( 9 ) can be written as \(\tilde{\sigma }_{\beta }^2 = \tau _n \hat{\sigma }^4\) . As \(n \rightarrow \infty\) , \(\tau _n \rightarrow (15/28)n^{2-3r}\) with \(m = \lceil n^r\rceil\) in ( 9 ). Let \(\hat{\sigma }^2\) be a consistent estimator of \(\sigma ^2\) , and \(\sigma _\beta ^2=(15/28)n^{2-3r}\sigma ^4\) . Under Theorem 1 and the null hypothesis \(H_0\) in ( 4 ), we have \(\hat{\beta }/\sigma _{\beta } \xrightarrow []{D} N(0,1)\) when the random errors are normally distributed. In addition, we have \(\sigma _{\beta }/\tilde{\sigma }_{\beta } \rightarrow 1\) as \(n\rightarrow \infty\) . Thus by Slutsky’s theorem,

Proof of Theorem 3

Given that \(\hat{\kappa }\) and \(\hat{\sigma }^2\) are consistent estimators of \(\kappa\) and \(\sigma ^2\) respectively, we note that \(\check{\sigma }_{\beta g}^2\) in ( 12 ) is also a consistent estimator of \(\sigma _{\beta }^2= (15/56)n^{2-3r}(\kappa -(\sigma ^2)^2)\) . Therefore under Theorem 1 and the null hypothesis \(H_0\) in ( 4 ), by Slutsky’s theorem we have

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Li, Z., Tong, T. & Wang, Y. A difference-based method for testing no effect in nonparametric regression. Comput Stat (2024). https://doi.org/10.1007/s00180-024-01479-0

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Received : 11 June 2023

Accepted : 21 February 2024

Published : 27 March 2024

DOI : https://doi.org/10.1007/s00180-024-01479-0

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