hypothesis formula in research

User Preferences

Content preview.

Arcu felis bibendum ut tristique et egestas quis:

• Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris
• Duis aute irure dolor in reprehenderit in voluptate
• Excepteur sint occaecat cupidatat non proident

Keyboard Shortcuts

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., =).

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, automatically generate references for free.

• Knowledge Base
• Methodology
• How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more variables . An independent variable is something the researcher changes or controls. A dependent variable is something the researcher observes and measures.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

Prevent plagiarism, run a free check.

Step 1: ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2: Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalise more complex constructs.

Step 3: Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

Step 4: Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

Step 5: Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

Step 6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

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.

A hypothesis is not just a guess. It should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

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.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the ‘Cite this Scribbr article’ button to automatically add the citation to our free Reference Generator.

McCombes, S. (2022, May 06). How to Write a Strong Hypothesis | Guide & Examples. Scribbr. Retrieved 21 August 2024, from https://www.scribbr.co.uk/research-methods/hypothesis-writing/

Is this article helpful?

Shona McCombes

Other students also liked, operationalisation | a guide with examples, pros & cons, what is a conceptual framework | tips & examples, a quick guide to experimental design | 5 steps & examples.

• Bipolar Disorder
• Therapy Center
• When To See a Therapist
• Types of Therapy
• Best Online Therapy
• Best Couples Therapy
• Managing Stress
• Sleep and Dreaming
• Understanding Emotions
• Self-Improvement
• Healthy Relationships
• Student Resources
• Personality Types
• Sweepstakes
• Guided Meditations
• Verywell Mind Insights
• 2024 Verywell Mind 25
• Mental Health in the Classroom
• Editorial Process
• Meet Our Review Board
• Crisis Support

How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis.

• Operationalization

Hypothesis Types

Hypotheses examples.

• Collecting Data

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

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

At a Glance

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

The Hypothesis in the Scientific Method

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

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

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

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

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

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

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

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

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

Elements of a Good Hypothesis

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

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

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

How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

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

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

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

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

The Importance of Operational Definitions

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

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

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

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

Replicability

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

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

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

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

Hypothesis Checklist

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

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

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

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

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

A few examples of simple hypotheses:

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

Examples of a complex hypothesis include:

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

Examples of a null hypothesis include:

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

Examples of an alternative hypothesis:

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

Collecting Data on Your Hypothesis

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

Descriptive Research Methods

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

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

Experimental Research Methods

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

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

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

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

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

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

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

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

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

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

Educational resources and simple solutions for your research journey

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

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

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

Table of Contents

What is a hypothesis ?  

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

What is a research hypothesis ?  

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

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

Characteristics of a good hypothesis  

Here are the characteristics of a good hypothesis :  

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

How to create an effective research hypothesis  

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

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

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

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

How to write a research hypothesis  

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

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

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

Population: athletes  

Independent variable: daily cold water showers  

Dependent variable: endurance  

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

Research hypothesis checklist  

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

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

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

Types of research hypothesis  

Different types of research hypothesis are used in scientific research:  

1. Null hypothesis:

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

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

2. Alternative hypothesis:

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

Example: “ The newly identified virus is zoonotic .”  

3. Directional hypothesis :

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

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

4. Non-directional hypothesis:

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

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

5. Simple hypothesis :

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

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

6 . Complex hypothesis :

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

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

7. Associative hypothesis:  

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

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

8 . Causal hypothesis:

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

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

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

Research hypothesis examples  

Here are some good research hypothesis examples :  

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

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

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

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

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

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

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

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

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

Importance of testable hypothesis  

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

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

Frequently Asked Questions (FAQs) on research hypothesis  

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

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

2. When to reject null hypothesis ?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

9. Can research hypotheses be used in qualitative research?

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

Editage All Access is a subscription-based platform that unifies the best AI tools and services designed to speed up, simplify, and streamline every step of a researcher’s journey. The Editage All Access Pack is a one-of-a-kind subscription that unlocks full access to an AI writing assistant, literature recommender, journal finder, scientific illustration tool, and exclusive discounts on professional publication services from Editage.  

Based on 22+ years of experience in academia, Editage All Access empowers researchers to put their best research forward and move closer to success. Explore our top AI Tools pack, AI Tools + Publication Services pack, or Build Your Own Plan. Find everything a researcher needs to succeed, all in one place –  Get All Access now starting at just $14 a month !    

Related Posts

What are the Best Research Funding Sources

Inductive vs. Deductive Research Approach

• How it works

How to Write a Hypothesis – Steps & Tips

Published by Alaxendra Bets at August 14th, 2021 , Revised On October 26, 2023

What is a Research Hypothesis?

You can test a research statement with the help of experimental or theoretical research, known as a hypothesis.

If you want to find out the similarities, differences, and relationships between variables, you must write a testable hypothesis before compiling the data, performing analysis, and generating results to complete.

The data analysis and findings will help you test the hypothesis and see whether it is true or false. Here is all you need to know about how to write a hypothesis for a  dissertation .

Research Hypothesis Definition

Not sure what the meaning of the research hypothesis is?

A research hypothesis predicts an answer to the research question  based on existing theoretical knowledge or experimental data.

Some studies may have multiple hypothesis statements depending on the research question(s).  A research hypothesis must be based on formulas, facts, and theories. It should be testable by data analysis, observations, experiments, or other scientific methodologies that can refute or support the statement.

Variables in Hypothesis

Developing a hypothesis is easy. Most research studies have two or more variables in the hypothesis, particularly studies involving correlational and experimental research. The researcher can control or change the independent variable(s) while measuring and observing the independent variable(s).

“How long a student sleeps affects test scores.”

In the above statement, the dependent variable is the test score, while the independent variable is the length of time spent in sleep. Developing a hypothesis will be easy if you know your research’s dependent and independent variables.

Once you have developed a thesis statement, questions such as how to write a hypothesis for the dissertation and how to test a research hypothesis become pretty straightforward.

Looking for dissertation help?

Researchprospect to the rescue then.

We have expert writers on our team who are skilled at helping students with quantitative dissertations across a variety of STEM disciplines. Guaranteeing 100% satisfaction!

Step-by-Step Guide on How to Write a Hypothesis

Here are the steps involved in how to write a hypothesis for a dissertation.

Step 1: Start with a Research Question

• Begin by asking a specific question about a topic of interest.
• This question should be clear, concise, and researchable.

Example: Does exposure to sunlight affect plant growth?

Step 2: Do Preliminary Research

• Before formulating a hypothesis, conduct background research to understand existing knowledge on the topic.
• Familiarise yourself with prior studies, theories, or observations related to the research question.

Step 3: Define Variables

• Independent Variable (IV): The factor that you change or manipulate in an experiment.
• Dependent Variable (DV): The factor that you measure.

Example: IV: Amount of sunlight exposure (e.g., 2 hours/day, 4 hours/day, 8 hours/day) DV: Plant growth (e.g., height in centimetres)

Step 4: Formulate the Hypothesis

• A hypothesis is a statement that predicts the relationship between variables.
• It is often written as an “if-then” statement.

Example: If plants receive more sunlight, then they will grow taller.

Step 5: Ensure it is Testable

A good hypothesis is empirically testable. This means you should be able to design an experiment or observation to test its validity.

Example: You can set up an experiment where plants are exposed to varying amounts of sunlight and then measure their growth over a period of time.

Step 6: Consider Potential Confounding Variables

• Confounding variables are factors other than the independent variable that might affect the outcome.
• It is important to identify these to ensure that they do not skew your results.

Example: Soil quality, water frequency, or type of plant can all affect growth. Consider keeping these constant in your experiment.

Step 7: Write the Null Hypothesis

• The null hypothesis is a statement that there is no effect or no relationship between the variables.
• It is what you aim to disprove or reject through your research.

Example: There is no difference in plant growth regardless of the amount of sunlight exposure.

Step 8: Test your Hypothesis

Design an experiment or conduct observations to test your hypothesis.

Example: Grow three sets of plants: one set exposed to 2 hours of sunlight daily, another exposed to 4 hours, and a third exposed to 8 hours. Measure and compare their growth after a set period.

Step 9: Analyse the Results

After testing, review your data to determine if it supports your hypothesis.

Step 10: Draw Conclusions

• Based on your findings, determine whether you can accept or reject the hypothesis.
• Remember, even if you reject your hypothesis, it’s a valuable result. It can guide future research and refine questions.

Three Ways to Phrase a Hypothesis

Try to use “if”… and “then”… to identify the variables. The independent variable should be present in the first part of the hypothesis, while the dependent variable will form the second part of the statement. Consider understanding the below research hypothesis example to create a specific, clear, and concise research hypothesis;

If an obese lady starts attending Zomba fitness classes, her health will improve.

In academic research, you can write the predicted variable relationship directly because most research studies correlate terms.

The number of Zomba fitness classes attended by the obese lady has a positive effect on health.

If your research compares two groups, then you can develop a hypothesis statement on their differences.

An obese lady who attended most Zumba fitness classes will have better health than those who attended a few.

How to Write a Null Hypothesis

If a statistical analysis is involved in your research, then you must create a null hypothesis. If you find any relationship between the variables, then the null hypothesis will be the default position that there is no relationship between them. H0 is the symbol for the null hypothesis, while the hypothesis is represented as H1. The null hypothesis will also answer your question, “How to test the research hypothesis in the dissertation.”

H0: The number of Zumba fitness classes attended by the obese lady does not affect her health.

H1: The number of Zumba fitness classes attended by obese lady positively affects health.

Also see:  Your Dissertation in Education

Hypothesis Examples

Research Question: Does the amount of sunlight a plant receives affect its growth? Hypothesis: Plants that receive more sunlight will grow taller than plants that receive less sunlight.

Research Question: Do students who eat breakfast perform better in school exams than those who don’t? Hypothesis: Students who eat a morning breakfast will score higher on school exams compared to students who skip breakfast.

Research Question: Does listening to music while studying impact a student’s ability to retain information? Hypothesis 1 (Directional): Students who listen to music while studying will retain less information than those who study in silence. Hypothesis 2 (Non-directional): There will be a difference in information retention between students who listen to music while studying and those who study in silence.

How can ResearchProspect Help?

If you are unsure about how to rest a research hypothesis in a dissertation or simply unsure about how to develop a hypothesis for your research, then you can take advantage of our dissertation services which cover every tiny aspect of a dissertation project you might need help with including but not limited to setting up a hypothesis and research questions,  help with individual chapters ,  full dissertation writing ,  statistical analysis , and much more.

Frequently Asked Questions

What are the 5 rules for writing a good hypothesis.

• Clear Statement: State a clear relationship between variables.
• Testable: Ensure it can be investigated and measured.
• Specific: Avoid vague terms, be precise in predictions.
• Falsifiable: Design to allow potential disproof.
• Relevant: Address research question and align with existing knowledge.

What is a hypothesis in simple words?

A hypothesis is an educated guess or prediction about something that can be tested. It is a statement that suggests a possible explanation for an event or phenomenon based on prior knowledge or observation. Scientists use hypotheses as a starting point for experiments to discover if they are true or false.

What is the hypothesis and examples?

A hypothesis is a testable prediction or explanation for an observation or phenomenon. For example, if plants are given sunlight, then they will grow. In this case, the hypothesis suggests that sunlight has a positive effect on plant growth. It can be tested by experimenting with plants in varying light conditions.

What is the hypothesis in research definition?

A hypothesis in research is a clear, testable statement predicting the possible outcome of a study based on prior knowledge and observation. It serves as the foundation for conducting experiments or investigations. Researchers test the validity of the hypothesis to draw conclusions and advance knowledge in a particular field.

Why is it called a hypothesis?

The term “hypothesis” originates from the Greek word “hypothesis,” which means “base” or “foundation.” It’s used to describe a foundational statement or proposition that can be tested. In scientific contexts, it denotes a tentative explanation for a phenomenon, serving as a starting point for investigation or experimentation.

You May Also Like

To help students organise their dissertation proposal paper correctly, we have put together detailed guidelines on how to structure a dissertation proposal.

Repository of ten perfect research question examples will provide you a better perspective about how to create research questions.

Penning your dissertation proposal can be a rather daunting task. Here are comprehensive guidelines on how to write a dissertation proposal.

USEFUL LINKS

LEARNING RESOURCES

COMPANY DETAILS

• How It Works

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.

Learn about our Editorial Process

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.

On This Page:

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.

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!

This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...

17 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

Hi” best wishes to you and your very nice blog” 

Trackbacks/Pingbacks

• What Is Research Methodology? Simple Definition (With Examples) - Grad Coach - […] Contrasted to this, a quantitative methodology is typically used when the research aims and objectives are confirmatory in nature. For example,…

Submit a Comment Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

• Print Friendly

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• J Korean Med Sci
• v.36(50); 2021 Dec 27

Formulating Hypotheses for Different Study Designs

Durga prasanna misra.

1 Department of Clinical Immunology and Rheumatology, Sanjay Gandhi Postgraduate Institute of Medical Sciences, Lucknow, India.

Armen Yuri Gasparyan

2 Departments of Rheumatology and Research and Development, Dudley Group NHS Foundation Trust (Teaching Trust of the University of Birmingham, UK), Russells Hall Hospital, Dudley, UK.

Olena Zimba

3 Department of Internal Medicine #2, Danylo Halytsky Lviv National Medical University, Lviv, Ukraine.

Marlen Yessirkepov

4 Department of Biology and Biochemistry, South Kazakhstan Medical Academy, Shymkent, Kazakhstan.

Vikas Agarwal

George d. kitas.

5 Centre for Epidemiology versus Arthritis, University of Manchester, Manchester, UK.

Generating a testable working hypothesis is the first step towards conducting original research. Such research may prove or disprove the proposed hypothesis. Case reports, case series, online surveys and other observational studies, clinical trials, and narrative reviews help to generate hypotheses. Observational and interventional studies help to test hypotheses. A good hypothesis is usually based on previous evidence-based reports. Hypotheses without evidence-based justification and a priori ideas are not received favourably by the scientific community. Original research to test a hypothesis should be carefully planned to ensure appropriate methodology and adequate statistical power. While hypotheses can challenge conventional thinking and may be controversial, they should not be destructive. A hypothesis should be tested by ethically sound experiments with meaningful ethical and clinical implications. The coronavirus disease 2019 pandemic has brought into sharp focus numerous hypotheses, some of which were proven (e.g. effectiveness of corticosteroids in those with hypoxia) while others were disproven (e.g. ineffectiveness of hydroxychloroquine and ivermectin).

Graphical Abstract

DEFINING WORKING AND STANDALONE SCIENTIFIC HYPOTHESES

Science is the systematized description of natural truths and facts. Routine observations of existing life phenomena lead to the creative thinking and generation of ideas about mechanisms of such phenomena and related human interventions. Such ideas presented in a structured format can be viewed as hypotheses. After generating a hypothesis, it is necessary to test it to prove its validity. Thus, hypothesis can be defined as a proposed mechanism of a naturally occurring event or a proposed outcome of an intervention. 1 , 2

Hypothesis testing requires choosing the most appropriate methodology and adequately powering statistically the study to be able to “prove” or “disprove” it within predetermined and widely accepted levels of certainty. This entails sample size calculation that often takes into account previously published observations and pilot studies. 2 , 3 In the era of digitization, hypothesis generation and testing may benefit from the availability of numerous platforms for data dissemination, social networking, and expert validation. Related expert evaluations may reveal strengths and limitations of proposed ideas at early stages of post-publication promotion, preventing the implementation of unsupported controversial points. 4

Thus, hypothesis generation is an important initial step in the research workflow, reflecting accumulating evidence and experts' stance. In this article, we overview the genesis and importance of scientific hypotheses and their relevance in the era of the coronavirus disease 2019 (COVID-19) pandemic.

DO WE NEED HYPOTHESES FOR ALL STUDY DESIGNS?

Broadly, research can be categorized as primary or secondary. In the context of medicine, primary research may include real-life observations of disease presentations and outcomes. Single case descriptions, which often lead to new ideas and hypotheses, serve as important starting points or justifications for case series and cohort studies. The importance of case descriptions is particularly evident in the context of the COVID-19 pandemic when unique, educational case reports have heralded a new era in clinical medicine. 5

Case series serve similar purpose to single case reports, but are based on a slightly larger quantum of information. Observational studies, including online surveys, describe the existing phenomena at a larger scale, often involving various control groups. Observational studies include variable-scale epidemiological investigations at different time points. Interventional studies detail the results of therapeutic interventions.

Secondary research is based on already published literature and does not directly involve human or animal subjects. Review articles are generated by secondary research. These could be systematic reviews which follow methods akin to primary research but with the unit of study being published papers rather than humans or animals. Systematic reviews have a rigid structure with a mandatory search strategy encompassing multiple databases, systematic screening of search results against pre-defined inclusion and exclusion criteria, critical appraisal of study quality and an optional component of collating results across studies quantitatively to derive summary estimates (meta-analysis). 6 Narrative reviews, on the other hand, have a more flexible structure. Systematic literature searches to minimise bias in selection of articles are highly recommended but not mandatory. 7 Narrative reviews are influenced by the authors' viewpoint who may preferentially analyse selected sets of articles. 8

In relation to primary research, case studies and case series are generally not driven by a working hypothesis. Rather, they serve as a basis to generate a hypothesis. Observational or interventional studies should have a hypothesis for choosing research design and sample size. The results of observational and interventional studies further lead to the generation of new hypotheses, testing of which forms the basis of future studies. Review articles, on the other hand, may not be hypothesis-driven, but form fertile ground to generate future hypotheses for evaluation. Fig. 1 summarizes which type of studies are hypothesis-driven and which lead on to hypothesis generation.

STANDARDS OF WORKING AND SCIENTIFIC HYPOTHESES

A review of the published literature did not enable the identification of clearly defined standards for working and scientific hypotheses. It is essential to distinguish influential versus not influential hypotheses, evidence-based hypotheses versus a priori statements and ideas, ethical versus unethical, or potentially harmful ideas. The following points are proposed for consideration while generating working and scientific hypotheses. 1 , 2 Table 1 summarizes these points.

Evidence-based data

A scientific hypothesis should have a sound basis on previously published literature as well as the scientist's observations. Randomly generated (a priori) hypotheses are unlikely to be proven. A thorough literature search should form the basis of a hypothesis based on published evidence. 7

Unless a scientific hypothesis can be tested, it can neither be proven nor be disproven. Therefore, a scientific hypothesis should be amenable to testing with the available technologies and the present understanding of science.

Supported by pilot studies

If a hypothesis is based purely on a novel observation by the scientist in question, it should be grounded on some preliminary studies to support it. For example, if a drug that targets a specific cell population is hypothesized to be useful in a particular disease setting, then there must be some preliminary evidence that the specific cell population plays a role in driving that disease process.

Testable by ethical studies

The hypothesis should be testable by experiments that are ethically acceptable. 9 For example, a hypothesis that parachutes reduce mortality from falls from an airplane cannot be tested using a randomized controlled trial. 10 This is because it is obvious that all those jumping from a flying plane without a parachute would likely die. Similarly, the hypothesis that smoking tobacco causes lung cancer cannot be tested by a clinical trial that makes people take up smoking (since there is considerable evidence for the health hazards associated with smoking). Instead, long-term observational studies comparing outcomes in those who smoke and those who do not, as was performed in the landmark epidemiological case control study by Doll and Hill, 11 are more ethical and practical.

Balance between scientific temper and controversy

Novel findings, including novel hypotheses, particularly those that challenge established norms, are bound to face resistance for their wider acceptance. Such resistance is inevitable until the time such findings are proven with appropriate scientific rigor. However, hypotheses that generate controversy are generally unwelcome. For example, at the time the pandemic of human immunodeficiency virus (HIV) and AIDS was taking foot, there were numerous deniers that refused to believe that HIV caused AIDS. 12 , 13 Similarly, at a time when climate change is causing catastrophic changes to weather patterns worldwide, denial that climate change is occurring and consequent attempts to block climate change are certainly unwelcome. 14 The denialism and misinformation during the COVID-19 pandemic, including unfortunate examples of vaccine hesitancy, are more recent examples of controversial hypotheses not backed by science. 15 , 16 An example of a controversial hypothesis that was a revolutionary scientific breakthrough was the hypothesis put forth by Warren and Marshall that Helicobacter pylori causes peptic ulcers. Initially, the hypothesis that a microorganism could cause gastritis and gastric ulcers faced immense resistance. When the scientists that proposed the hypothesis themselves ingested H. pylori to induce gastritis in themselves, only then could they convince the wider world about their hypothesis. Such was the impact of the hypothesis was that Barry Marshall and Robin Warren were awarded the Nobel Prize in Physiology or Medicine in 2005 for this discovery. 17 , 18

DISTINGUISHING THE MOST INFLUENTIAL HYPOTHESES

Influential hypotheses are those that have stood the test of time. An archetype of an influential hypothesis is that proposed by Edward Jenner in the eighteenth century that cowpox infection protects against smallpox. While this observation had been reported for nearly a century before this time, it had not been suitably tested and publicised until Jenner conducted his experiments on a young boy by demonstrating protection against smallpox after inoculation with cowpox. 19 These experiments were the basis for widespread smallpox immunization strategies worldwide in the 20th century which resulted in the elimination of smallpox as a human disease today. 20

Other influential hypotheses are those which have been read and cited widely. An example of this is the hygiene hypothesis proposing an inverse relationship between infections in early life and allergies or autoimmunity in adulthood. An analysis reported that this hypothesis had been cited more than 3,000 times on Scopus. 1

LESSONS LEARNED FROM HYPOTHESES AMIDST THE COVID-19 PANDEMIC

The COVID-19 pandemic devastated the world like no other in recent memory. During this period, various hypotheses emerged, understandably so considering the public health emergency situation with innumerable deaths and suffering for humanity. Within weeks of the first reports of COVID-19, aberrant immune system activation was identified as a key driver of organ dysfunction and mortality in this disease. 21 Consequently, numerous drugs that suppress the immune system or abrogate the activation of the immune system were hypothesized to have a role in COVID-19. 22 One of the earliest drugs hypothesized to have a benefit was hydroxychloroquine. Hydroxychloroquine was proposed to interfere with Toll-like receptor activation and consequently ameliorate the aberrant immune system activation leading to pathology in COVID-19. 22 The drug was also hypothesized to have a prophylactic role in preventing infection or disease severity in COVID-19. It was also touted as a wonder drug for the disease by many prominent international figures. However, later studies which were well-designed randomized controlled trials failed to demonstrate any benefit of hydroxychloroquine in COVID-19. 23 , 24 , 25 , 26 Subsequently, azithromycin 27 , 28 and ivermectin 29 were hypothesized as potential therapies for COVID-19, but were not supported by evidence from randomized controlled trials. The role of vitamin D in preventing disease severity was also proposed, but has not been proven definitively until now. 30 , 31 On the other hand, randomized controlled trials identified the evidence supporting dexamethasone 32 and interleukin-6 pathway blockade with tocilizumab as effective therapies for COVID-19 in specific situations such as at the onset of hypoxia. 33 , 34 Clues towards the apparent effectiveness of various drugs against severe acute respiratory syndrome coronavirus 2 in vitro but their ineffectiveness in vivo have recently been identified. Many of these drugs are weak, lipophilic bases and some others induce phospholipidosis which results in apparent in vitro effectiveness due to non-specific off-target effects that are not replicated inside living systems. 35 , 36

Another hypothesis proposed was the association of the routine policy of vaccination with Bacillus Calmette-Guerin (BCG) with lower deaths due to COVID-19. This hypothesis emerged in the middle of 2020 when COVID-19 was still taking foot in many parts of the world. 37 , 38 Subsequently, many countries which had lower deaths at that time point went on to have higher numbers of mortality, comparable to other areas of the world. Furthermore, the hypothesis that BCG vaccination reduced COVID-19 mortality was a classic example of ecological fallacy. Associations between population level events (ecological studies; in this case, BCG vaccination and COVID-19 mortality) cannot be directly extrapolated to the individual level. Furthermore, such associations cannot per se be attributed as causal in nature, and can only serve to generate hypotheses that need to be tested at the individual level. 39

IS TRADITIONAL PEER REVIEW EFFICIENT FOR EVALUATION OF WORKING AND SCIENTIFIC HYPOTHESES?

Traditionally, publication after peer review has been considered the gold standard before any new idea finds acceptability amongst the scientific community. Getting a work (including a working or scientific hypothesis) reviewed by experts in the field before experiments are conducted to prove or disprove it helps to refine the idea further as well as improve the experiments planned to test the hypothesis. 40 A route towards this has been the emergence of journals dedicated to publishing hypotheses such as the Central Asian Journal of Medical Hypotheses and Ethics. 41 Another means of publishing hypotheses is through registered research protocols detailing the background, hypothesis, and methodology of a particular study. If such protocols are published after peer review, then the journal commits to publishing the completed study irrespective of whether the study hypothesis is proven or disproven. 42 In the post-pandemic world, online research methods such as online surveys powered via social media channels such as Twitter and Instagram might serve as critical tools to generate as well as to preliminarily test the appropriateness of hypotheses for further evaluation. 43 , 44

Some radical hypotheses might be difficult to publish after traditional peer review. These hypotheses might only be acceptable by the scientific community after they are tested in research studies. Preprints might be a way to disseminate such controversial and ground-breaking hypotheses. 45 However, scientists might prefer to keep their hypotheses confidential for the fear of plagiarism of ideas, avoiding online posting and publishing until they have tested the hypotheses.

SUGGESTIONS ON GENERATING AND PUBLISHING HYPOTHESES

Publication of hypotheses is important, however, a balance is required between scientific temper and controversy. Journal editors and reviewers might keep in mind these specific points, summarized in Table 2 and detailed hereafter, while judging the merit of hypotheses for publication. Keeping in mind the ethical principle of primum non nocere, a hypothesis should be published only if it is testable in a manner that is ethically appropriate. 46 Such hypotheses should be grounded in reality and lend themselves to further testing to either prove or disprove them. It must be considered that subsequent experiments to prove or disprove a hypothesis have an equal chance of failing or succeeding, akin to tossing a coin. A pre-conceived belief that a hypothesis is unlikely to be proven correct should not form the basis of rejection of such a hypothesis for publication. In this context, hypotheses generated after a thorough literature search to identify knowledge gaps or based on concrete clinical observations on a considerable number of patients (as opposed to random observations on a few patients) are more likely to be acceptable for publication by peer-reviewed journals. Also, hypotheses should be considered for publication or rejection based on their implications for science at large rather than whether the subsequent experiments to test them end up with results in favour of or against the original hypothesis.

Hypotheses form an important part of the scientific literature. The COVID-19 pandemic has reiterated the importance and relevance of hypotheses for dealing with public health emergencies and highlighted the need for evidence-based and ethical hypotheses. A good hypothesis is testable in a relevant study design, backed by preliminary evidence, and has positive ethical and clinical implications. General medical journals might consider publishing hypotheses as a specific article type to enable more rapid advancement of science.

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

Author Contributions:

• Data curation: Gasparyan AY, Misra DP, Zimba O, Yessirkepov M, Agarwal V, Kitas GD.

Tutorial Playlist

Statistics tutorial, everything you need to know about the probability density function in statistics, the best guide to understand central limit theorem, an in-depth guide to measures of central tendency : mean, median and mode, the ultimate guide to understand conditional probability.

A Comprehensive Look at Percentile in Statistics

The Best Guide to Understand Bayes Theorem

Everything you need to know about the normal distribution, an in-depth explanation of cumulative distribution function, a complete guide to chi-square test, what is hypothesis testing in statistics types and examples, understanding the fundamentals of arithmetic and geometric progression, the definitive guide to understand spearman’s rank correlation, mean squared error: overview, examples, concepts and more, all you need to know about the empirical rule in statistics, the complete guide to skewness and kurtosis, a holistic look at bernoulli distribution.

All You Need to Know About Bias in Statistics

A Complete Guide to Get a Grasp of Time Series Analysis

The Key Differences Between Z-Test Vs. T-Test

The Complete Guide to Understand Pearson's Correlation

A complete guide on the types of statistical studies, everything you need to know about poisson distribution, your best guide to understand correlation vs. regression, the most comprehensive guide for beginners on what is correlation, hypothesis testing in statistics - types | examples.

Lesson 10 of 24 By Avijeet Biswal

Table of Contents

In today’s data-driven world, decisions are based on data all the time. Hypothesis plays a crucial role in that process, whether it may be making business decisions, in the health sector, academia, or in quality improvement. Without hypothesis & hypothesis tests, you risk drawing the wrong conclusions and making bad decisions. In this tutorial, you will look at Hypothesis Testing in Statistics.

The Ultimate Ticket to Top Data Science Job Roles

What Is Hypothesis Testing in Statistics?

Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.

Let's discuss few examples of statistical hypothesis from real-life - 

• A teacher assumes that 60% of his college's students come from lower-middle-class families.
• A doctor believes that 3D (Diet, Dose, and Discipline) is 90% effective for diabetic patients.

Now that you know about hypothesis testing, look at the two types of hypothesis testing in statistics.

Hypothesis Testing Formula

Z = ( x̅ – μ0 ) / (σ /√n)

• Here, x̅ is the sample mean,
• μ0 is the population mean,
• σ is the standard deviation,
• n is the sample size.

How Hypothesis Testing Works?

An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.

The null hypothesis is typically an equality hypothesis between population parameters; for example, a null hypothesis may claim that the population means return equals zero. The alternate hypothesis is essentially the inverse of the null hypothesis (e.g., the population means the return is not equal to zero). As a result, they are mutually exclusive, and only one can be correct. One of the two possibilities, however, will always be correct.

Your Dream Career is Just Around The Corner!

Null Hypothesis and Alternative Hypothesis

The Null Hypothesis is the assumption that the event will not occur. A null hypothesis has no bearing on the study's outcome unless it is rejected.

H0 is the symbol for it, and it is pronounced H-naught.

The Alternate Hypothesis is the logical opposite of the null hypothesis. The acceptance of the alternative hypothesis follows the rejection of the null hypothesis. H1 is the symbol for it.

Let's understand this with an example.

A sanitizer manufacturer claims that its product kills 95 percent of germs on average. 

To put this company's claim to the test, create a null and alternate hypothesis.

H0 (Null Hypothesis): Average = 95%.

Alternative Hypothesis (H1): The average is less than 95%.

Another straightforward example to understand this concept is determining whether or not a coin is fair and balanced. The null hypothesis states that the probability of a show of heads is equal to the likelihood of a show of tails. In contrast, the alternate theory states that the probability of a show of heads and tails would be very different.

Become a Data Scientist with Hands-on Training!

Hypothesis Testing Calculation With Examples

Let's consider a hypothesis test for the average height of women in the United States. Suppose our null hypothesis is that the average height is 5'4". We gather a sample of 100 women and determine that their average height is 5'5". The standard deviation of population is 2.

To calculate the z-score, we would use the following formula:

z = ( x̅ – μ0 ) / (σ /√n)

z = (5'5" - 5'4") / (2" / √100)

z = 0.5 / (0.045)

We will reject the null hypothesis as the z-score of 11.11 is very large and conclude that there is evidence to suggest that the average height of women in the US is greater than 5'4".

Steps in Hypothesis Testing

Hypothesis testing is a statistical method to determine if there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. Here’s a breakdown of the typical steps involved in hypothesis testing:

Formulate Hypotheses

• Null Hypothesis (H0): This hypothesis states that there is no effect or difference, and it is the hypothesis you attempt to reject with your test.
• Alternative Hypothesis (H1 or Ha): This hypothesis is what you might believe to be true or hope to prove true. It is usually considered the opposite of the null hypothesis.

Choose the Significance Level (α)

The significance level, often denoted by alpha (α), is the probability of rejecting the null hypothesis when it is true. Common choices for α are 0.05 (5%), 0.01 (1%), and 0.10 (10%).

Select the Appropriate Test

Choose a statistical test based on the type of data and the hypothesis. Common tests include t-tests, chi-square tests, ANOVA, and regression analysis. The selection depends on data type, distribution, sample size, and whether the hypothesis is one-tailed or two-tailed.

Collect Data

Gather the data that will be analyzed in the test. This data should be representative of the population to infer conclusions accurately.

Calculate the Test Statistic

Based on the collected data and the chosen test, calculate a test statistic that reflects how much the observed data deviates from the null hypothesis.

Determine the p-value

The p-value is the probability of observing test results at least as extreme as the results observed, assuming the null hypothesis is correct. It helps determine the strength of the evidence against the null hypothesis.

Make a Decision

Compare the p-value to the chosen significance level:

• If the p-value ≤ α: Reject the null hypothesis, suggesting sufficient evidence in the data supports the alternative hypothesis.
• If the p-value > α: Do not reject the null hypothesis, suggesting insufficient evidence to support the alternative hypothesis.

Report the Results

Present the findings from the hypothesis test, including the test statistic, p-value, and the conclusion about the hypotheses.

Perform Post-hoc Analysis (if necessary)

Depending on the results and the study design, further analysis may be needed to explore the data more deeply or to address multiple comparisons if several hypotheses were tested simultaneously.

Types of Hypothesis Testing

To determine whether a discovery or relationship is statistically significant, hypothesis testing uses a z-test. It usually checks to see if two means are the same (the null hypothesis). Only when the population standard deviation is known and the sample size is 30 data points or more, can a z-test be applied.

A statistical test called a t-test is employed to compare the means of two groups. To determine whether two groups differ or if a procedure or treatment affects the population of interest, it is frequently used in hypothesis testing.

Chi-Square 

You utilize a Chi-square test for hypothesis testing concerning whether your data is as predicted. To determine if the expected and observed results are well-fitted, the Chi-square test analyzes the differences between categorical variables from a random sample. The test's fundamental premise is that the observed values in your data should be compared to the predicted values that would be present if the null hypothesis were true.

Hypothesis Testing and Confidence Intervals

Both confidence intervals and hypothesis tests are inferential techniques that depend on approximating the sample distribution. Data from a sample is used to estimate a population parameter using confidence intervals. Data from a sample is used in hypothesis testing to examine a given hypothesis. We must have a postulated parameter to conduct hypothesis testing.

Bootstrap distributions and randomization distributions are created using comparable simulation techniques. The observed sample statistic is the focal point of a bootstrap distribution, whereas the null hypothesis value is the focal point of a randomization distribution.

A variety of feasible population parameter estimates are included in confidence ranges. In this lesson, we created just two-tailed confidence intervals. There is a direct connection between these two-tail confidence intervals and these two-tail hypothesis tests. The results of a two-tailed hypothesis test and two-tailed confidence intervals typically provide the same results. In other words, a hypothesis test at the 0.05 level will virtually always fail to reject the null hypothesis if the 95% confidence interval contains the predicted value. A hypothesis test at the 0.05 level will nearly certainly reject the null hypothesis if the 95% confidence interval does not include the hypothesized parameter.

Become a Data Scientist through hands-on learning with hackathons, masterclasses, webinars, and Ask-Me-Anything! Start learning now!

Simple and Composite Hypothesis Testing

Depending on the population distribution, you can classify the statistical hypothesis into two types.

Simple Hypothesis: A simple hypothesis specifies an exact value for the parameter.

Composite Hypothesis: A composite hypothesis specifies a range of values.

A company is claiming that their average sales for this quarter are 1000 units. This is an example of a simple hypothesis.

Suppose the company claims that the sales are in the range of 900 to 1000 units. Then this is a case of a composite hypothesis.

One-Tailed and Two-Tailed Hypothesis Testing

The One-Tailed test, also called a directional test, considers a critical region of data that would result in the null hypothesis being rejected if the test sample falls into it, inevitably meaning the acceptance of the alternate hypothesis.

In a one-tailed test, the critical distribution area is one-sided, meaning the test sample is either greater or lesser than a specific value.

In two tails, the test sample is checked to be greater or less than a range of values in a Two-Tailed test, implying that the critical distribution area is two-sided.

If the sample falls within this range, the alternate hypothesis will be accepted, and the null hypothesis will be rejected.

Become a Data Scientist With Real-World Experience

Right Tailed Hypothesis Testing

If the larger than (>) sign appears in your hypothesis statement, you are using a right-tailed test, also known as an upper test. Or, to put it another way, the disparity is to the right. For instance, you can contrast the battery life before and after a change in production. Your hypothesis statements can be the following if you want to know if the battery life is longer than the original (let's say 90 hours):

• The null hypothesis is (H0 <= 90) or less change.
• A possibility is that battery life has risen (H1) > 90.

The crucial point in this situation is that the alternate hypothesis (H1), not the null hypothesis, decides whether you get a right-tailed test.

Left Tailed Hypothesis Testing

Alternative hypotheses that assert the true value of a parameter is lower than the null hypothesis are tested with a left-tailed test; they are indicated by the asterisk "<".

Suppose H0: mean = 50 and H1: mean not equal to 50

According to the H1, the mean can be greater than or less than 50. This is an example of a Two-tailed test.

In a similar manner, if H0: mean >=50, then H1: mean <50

Here the mean is less than 50. It is called a One-tailed test.

Type 1 and Type 2 Error

A hypothesis test can result in two types of errors.

Type 1 Error: A Type-I error occurs when sample results reject the null hypothesis despite being true.

Type 2 Error: A Type-II error occurs when the null hypothesis is not rejected when it is false, unlike a Type-I error.

Suppose a teacher evaluates the examination paper to decide whether a student passes or fails.

H0: Student has passed

H1: Student has failed

Type I error will be the teacher failing the student [rejects H0] although the student scored the passing marks [H0 was true]. 

Type II error will be the case where the teacher passes the student [do not reject H0] although the student did not score the passing marks [H1 is true].

Our Data Scientist Master's Program covers core topics such as R, Python, Machine Learning, Tableau, Hadoop, and Spark. Get started on your journey today!

Limitations of Hypothesis Testing

Hypothesis testing has some limitations that researchers should be aware of:

• It cannot prove or establish the truth: Hypothesis testing provides evidence to support or reject a hypothesis, but it cannot confirm the absolute truth of the research question.
• Results are sample-specific: Hypothesis testing is based on analyzing a sample from a population, and the conclusions drawn are specific to that particular sample.
• Possible errors: During hypothesis testing, there is a chance of committing type I error (rejecting a true null hypothesis) or type II error (failing to reject a false null hypothesis).
• Assumptions and requirements: Different tests have specific assumptions and requirements that must be met to accurately interpret results.

Learn All The Tricks Of The BI Trade

After reading this tutorial, you would have a much better understanding of hypothesis testing, one of the most important concepts in the field of Data Science . The majority of hypotheses are based on speculation about observed behavior, natural phenomena, or established theories.

If you are interested in statistics of data science and skills needed for such a career, you ought to explore the Post Graduate Program in Data Science.

If you have any questions regarding this ‘Hypothesis Testing In Statistics’ tutorial, do share them in the comment section. Our subject matter expert will respond to your queries. Happy learning!

1. What is hypothesis testing in statistics with example?

Hypothesis testing is a statistical method used to determine if there is enough evidence in a sample data to draw conclusions about a population. It involves formulating two competing hypotheses, the null hypothesis (H0) and the alternative hypothesis (Ha), and then collecting data to assess the evidence. An example: testing if a new drug improves patient recovery (Ha) compared to the standard treatment (H0) based on collected patient data.

2. What is H0 and H1 in statistics?

In statistics, H0​ and H1​ represent the null and alternative hypotheses. The null hypothesis, H0​, is the default assumption that no effect or difference exists between groups or conditions. The alternative hypothesis, H1​, is the competing claim suggesting an effect or a difference. Statistical tests determine whether to reject the null hypothesis in favor of the alternative hypothesis based on the data.

3. What is a simple hypothesis with an example?

A simple hypothesis is a specific statement predicting a single relationship between two variables. It posits a direct and uncomplicated outcome. For example, a simple hypothesis might state, "Increased sunlight exposure increases the growth rate of sunflowers." Here, the hypothesis suggests a direct relationship between the amount of sunlight (independent variable) and the growth rate of sunflowers (dependent variable), with no additional variables considered.

4. What are the 3 major types of hypothesis?

The three major types of hypotheses are:

• Null Hypothesis (H0): Represents the default assumption, stating that there is no significant effect or relationship in the data.
• Alternative Hypothesis (Ha): Contradicts the null hypothesis and proposes a specific effect or relationship that researchers want to investigate.
• Nondirectional Hypothesis: An alternative hypothesis that doesn't specify the direction of the effect, leaving it open for both positive and negative possibilities.

Find our PL-300 Microsoft Power BI Certification Training Online Classroom training classes in top cities:

About the Author

Avijeet is a Senior Research Analyst at Simplilearn. Passionate about Data Analytics, Machine Learning, and Deep Learning, Avijeet is also interested in politics, cricket, and football.

Recommended Resources

Free eBook: Top Programming Languages For A Data Scientist

Normality Test in Minitab: Minitab with Statistics

Machine Learning Career Guide: A Playbook to Becoming a Machine Learning Engineer

• PMP, PMI, PMBOK, CAPM, PgMP, PfMP, ACP, PBA, RMP, SP, and OPM3 are registered marks of the Project Management Institute, Inc.

Hypothesis Testing

Hypothesis testing is a tool for making statistical inferences about the population data. It is an analysis tool that tests assumptions and determines how likely something is within a given standard of accuracy. Hypothesis testing provides a way to verify whether the results of an experiment are valid.

A null hypothesis and an alternative hypothesis are set up before performing the hypothesis testing. This helps to arrive at a conclusion regarding the sample obtained from the population. In this article, we will learn more about hypothesis testing, its types, steps to perform the testing, and associated examples.

What is Hypothesis Testing in Statistics?

Hypothesis testing uses sample data from the population to draw useful conclusions regarding the population probability distribution . It tests an assumption made about the data using different types of hypothesis testing methodologies. The hypothesis testing results in either rejecting or not rejecting the null hypothesis.

Hypothesis Testing Definition

Hypothesis testing can be defined as a statistical tool that is used to identify if the results of an experiment are meaningful or not. It involves setting up a null hypothesis and an alternative hypothesis. These two hypotheses will always be mutually exclusive. This means that if the null hypothesis is true then the alternative hypothesis is false and vice versa. An example of hypothesis testing is setting up a test to check if a new medicine works on a disease in a more efficient manner.

Null Hypothesis

The null hypothesis is a concise mathematical statement that is used to indicate that there is no difference between two possibilities. In other words, there is no difference between certain characteristics of data. This hypothesis assumes that the outcomes of an experiment are based on chance alone. It is denoted as \(H_{0}\). Hypothesis testing is used to conclude if the null hypothesis can be rejected or not. Suppose an experiment is conducted to check if girls are shorter than boys at the age of 5. The null hypothesis will say that they are the same height.

Alternative Hypothesis

The alternative hypothesis is an alternative to the null hypothesis. It is used to show that the observations of an experiment are due to some real effect. It indicates that there is a statistical significance between two possible outcomes and can be denoted as \(H_{1}\) or \(H_{a}\). For the above-mentioned example, the alternative hypothesis would be that girls are shorter than boys at the age of 5.

Hypothesis Testing P Value

In hypothesis testing, the p value is used to indicate whether the results obtained after conducting a test are statistically significant or not. It also indicates the probability of making an error in rejecting or not rejecting the null hypothesis.This value is always a number between 0 and 1. The p value is compared to an alpha level, \(\alpha\) or significance level. The alpha level can be defined as the acceptable risk of incorrectly rejecting the null hypothesis. The alpha level is usually chosen between 1% to 5%.

Hypothesis Testing Critical region

All sets of values that lead to rejecting the null hypothesis lie in the critical region. Furthermore, the value that separates the critical region from the non-critical region is known as the critical value.

Hypothesis Testing Formula

Depending upon the type of data available and the size, different types of hypothesis testing are used to determine whether the null hypothesis can be rejected or not. The hypothesis testing formula for some important test statistics are given below:

• z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\). \(\overline{x}\) is the sample mean, \(\mu\) is the population mean, \(\sigma\) is the population standard deviation and n is the size of the sample.
• t = \(\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}\). s is the sample standard deviation.
• \(\chi ^{2} = \sum \frac{(O_{i}-E_{i})^{2}}{E_{i}}\). \(O_{i}\) is the observed value and \(E_{i}\) is the expected value.

We will learn more about these test statistics in the upcoming section.

Types of Hypothesis Testing

Selecting the correct test for performing hypothesis testing can be confusing. These tests are used to determine a test statistic on the basis of which the null hypothesis can either be rejected or not rejected. Some of the important tests used for hypothesis testing are given below.

Hypothesis Testing Z Test

A z test is a way of hypothesis testing that is used for a large sample size (n ≥ 30). It is used to determine whether there is a difference between the population mean and the sample mean when the population standard deviation is known. It can also be used to compare the mean of two samples. It is used to compute the z test statistic. The formulas are given as follows:

• One sample: z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\).
• Two samples: z = \(\frac{(\overline{x_{1}}-\overline{x_{2}})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}}\).

Hypothesis Testing t Test

The t test is another method of hypothesis testing that is used for a small sample size (n < 30). It is also used to compare the sample mean and population mean. However, the population standard deviation is not known. Instead, the sample standard deviation is known. The mean of two samples can also be compared using the t test.

• One sample: t = \(\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}\).
• Two samples: t = \(\frac{(\overline{x_{1}}-\overline{x_{2}})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}\).

Hypothesis Testing Chi Square

The Chi square test is a hypothesis testing method that is used to check whether the variables in a population are independent or not. It is used when the test statistic is chi-squared distributed.

One Tailed Hypothesis Testing

One tailed hypothesis testing is done when the rejection region is only in one direction. It can also be known as directional hypothesis testing because the effects can be tested in one direction only. This type of testing is further classified into the right tailed test and left tailed test.

Right Tailed Hypothesis Testing

The right tail test is also known as the upper tail test. This test is used to check whether the population parameter is greater than some value. The null and alternative hypotheses for this test are given as follows:

\(H_{0}\): The population parameter is ≤ some value

\(H_{1}\): The population parameter is > some value.

If the test statistic has a greater value than the critical value then the null hypothesis is rejected

Left Tailed Hypothesis Testing

The left tail test is also known as the lower tail test. It is used to check whether the population parameter is less than some value. The hypotheses for this hypothesis testing can be written as follows:

\(H_{0}\): The population parameter is ≥ some value

\(H_{1}\): The population parameter is < some value.

The null hypothesis is rejected if the test statistic has a value lesser than the critical value.

Two Tailed Hypothesis Testing

In this hypothesis testing method, the critical region lies on both sides of the sampling distribution. It is also known as a non - directional hypothesis testing method. The two-tailed test is used when it needs to be determined if the population parameter is assumed to be different than some value. The hypotheses can be set up as follows:

\(H_{0}\): the population parameter = some value

\(H_{1}\): the population parameter ≠ some value

The null hypothesis is rejected if the test statistic has a value that is not equal to the critical value.

Hypothesis Testing Steps

Hypothesis testing can be easily performed in five simple steps. The most important step is to correctly set up the hypotheses and identify the right method for hypothesis testing. The basic steps to perform hypothesis testing are as follows:

• Step 1: Set up the null hypothesis by correctly identifying whether it is the left-tailed, right-tailed, or two-tailed hypothesis testing.
• Step 2: Set up the alternative hypothesis.
• Step 3: Choose the correct significance level, \(\alpha\), and find the critical value.
• Step 4: Calculate the correct test statistic (z, t or \(\chi\)) and p-value.
• Step 5: Compare the test statistic with the critical value or compare the p-value with \(\alpha\) to arrive at a conclusion. In other words, decide if the null hypothesis is to be rejected or not.

Hypothesis Testing Example

The best way to solve a problem on hypothesis testing is by applying the 5 steps mentioned in the previous section. Suppose a researcher claims that the mean average weight of men is greater than 100kgs with a standard deviation of 15kgs. 30 men are chosen with an average weight of 112.5 Kgs. Using hypothesis testing, check if there is enough evidence to support the researcher's claim. The confidence interval is given as 95%.

Step 1: This is an example of a right-tailed test. Set up the null hypothesis as \(H_{0}\): \(\mu\) = 100.

Step 2: The alternative hypothesis is given by \(H_{1}\): \(\mu\) > 100.

Step 3: As this is a one-tailed test, \(\alpha\) = 100% - 95% = 5%. This can be used to determine the critical value.

1 - \(\alpha\) = 1 - 0.05 = 0.95

0.95 gives the required area under the curve. Now using a normal distribution table, the area 0.95 is at z = 1.645. A similar process can be followed for a t-test. The only additional requirement is to calculate the degrees of freedom given by n - 1.

Step 4: Calculate the z test statistic. This is because the sample size is 30. Furthermore, the sample and population means are known along with the standard deviation.

z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\).

\(\mu\) = 100, \(\overline{x}\) = 112.5, n = 30, \(\sigma\) = 15

z = \(\frac{112.5-100}{\frac{15}{\sqrt{30}}}\) = 4.56

Step 5: Conclusion. As 4.56 > 1.645 thus, the null hypothesis can be rejected.

Hypothesis Testing and Confidence Intervals

Confidence intervals form an important part of hypothesis testing. This is because the alpha level can be determined from a given confidence interval. Suppose a confidence interval is given as 95%. Subtract the confidence interval from 100%. This gives 100 - 95 = 5% or 0.05. This is the alpha value of a one-tailed hypothesis testing. To obtain the alpha value for a two-tailed hypothesis testing, divide this value by 2. This gives 0.05 / 2 = 0.025.

Related Articles:

• Probability and Statistics
• Data Handling

Important Notes on Hypothesis Testing

• Hypothesis testing is a technique that is used to verify whether the results of an experiment are statistically significant.
• It involves the setting up of a null hypothesis and an alternate hypothesis.
• There are three types of tests that can be conducted under hypothesis testing - z test, t test, and chi square test.
• Hypothesis testing can be classified as right tail, left tail, and two tail tests.

Examples on Hypothesis Testing

• Example 1: The average weight of a dumbbell in a gym is 90lbs. However, a physical trainer believes that the average weight might be higher. A random sample of 5 dumbbells with an average weight of 110lbs and a standard deviation of 18lbs. Using hypothesis testing check if the physical trainer's claim can be supported for a 95% confidence level. Solution: As the sample size is lesser than 30, the t-test is used. \(H_{0}\): \(\mu\) = 90, \(H_{1}\): \(\mu\) > 90 \(\overline{x}\) = 110, \(\mu\) = 90, n = 5, s = 18. \(\alpha\) = 0.05 Using the t-distribution table, the critical value is 2.132 t = \(\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}\) t = 2.484 As 2.484 > 2.132, the null hypothesis is rejected. Answer: The average weight of the dumbbells may be greater than 90lbs
• Example 2: The average score on a test is 80 with a standard deviation of 10. With a new teaching curriculum introduced it is believed that this score will change. On random testing, the score of 38 students, the mean was found to be 88. With a 0.05 significance level, is there any evidence to support this claim? Solution: This is an example of two-tail hypothesis testing. The z test will be used. \(H_{0}\): \(\mu\) = 80, \(H_{1}\): \(\mu\) ≠ 80 \(\overline{x}\) = 88, \(\mu\) = 80, n = 36, \(\sigma\) = 10. \(\alpha\) = 0.05 / 2 = 0.025 The critical value using the normal distribution table is 1.96 z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\) z = \(\frac{88-80}{\frac{10}{\sqrt{36}}}\) = 4.8 As 4.8 > 1.96, the null hypothesis is rejected. Answer: There is a difference in the scores after the new curriculum was introduced.
• Example 3: The average score of a class is 90. However, a teacher believes that the average score might be lower. The scores of 6 students were randomly measured. The mean was 82 with a standard deviation of 18. With a 0.05 significance level use hypothesis testing to check if this claim is true. Solution: The t test will be used. \(H_{0}\): \(\mu\) = 90, \(H_{1}\): \(\mu\) < 90 \(\overline{x}\) = 110, \(\mu\) = 90, n = 6, s = 18 The critical value from the t table is -2.015 t = \(\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}\) t = \(\frac{82-90}{\frac{18}{\sqrt{6}}}\) t = -1.088 As -1.088 > -2.015, we fail to reject the null hypothesis. Answer: There is not enough evidence to support the claim.

go to slide go to slide go to slide

Book a Free Trial Class

FAQs on Hypothesis Testing

What is hypothesis testing.

Hypothesis testing in statistics is a tool that is used to make inferences about the population data. It is also used to check if the results of an experiment are valid.

What is the z Test in Hypothesis Testing?

The z test in hypothesis testing is used to find the z test statistic for normally distributed data . The z test is used when the standard deviation of the population is known and the sample size is greater than or equal to 30.

What is the t Test in Hypothesis Testing?

The t test in hypothesis testing is used when the data follows a student t distribution . It is used when the sample size is less than 30 and standard deviation of the population is not known.

What is the formula for z test in Hypothesis Testing?

The formula for a one sample z test in hypothesis testing is z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\) and for two samples is z = \(\frac{(\overline{x_{1}}-\overline{x_{2}})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}}\).

What is the p Value in Hypothesis Testing?

The p value helps to determine if the test results are statistically significant or not. In hypothesis testing, the null hypothesis can either be rejected or not rejected based on the comparison between the p value and the alpha level.

What is One Tail Hypothesis Testing?

When the rejection region is only on one side of the distribution curve then it is known as one tail hypothesis testing. The right tail test and the left tail test are two types of directional hypothesis testing.

What is the Alpha Level in Two Tail Hypothesis Testing?

To get the alpha level in a two tail hypothesis testing divide \(\alpha\) by 2. This is done as there are two rejection regions in the curve.

• Skip to secondary menu
• Skip to main content
• Skip to primary sidebar

Statistics By Jim

Making statistics intuitive

Z Test: Uses, Formula & Examples

By Jim Frost Leave a Comment

What is a Z Test?

Use a Z test when you need to compare group means. Use the 1-sample analysis to determine whether a population mean is different from a hypothesized value. Or use the 2-sample version to determine whether two population means differ.

A Z test is a form of inferential statistics . It uses samples to draw conclusions about populations.

For example, use Z tests to assess the following:

• One sample : Do students in an honors program have an average IQ score different than a hypothesized value of 100?
• Two sample : Do two IQ boosting programs have different mean scores?

In this post, learn about when to use a Z test vs T test. Then we’ll review the Z test’s hypotheses, assumptions, interpretation, and formula. Finally, we’ll use the formula in a worked example.

Related post : Difference between Descriptive and Inferential Statistics

Z test vs T test

Z tests and t tests are similar. They both assess the means of one or two groups, have similar assumptions, and allow you to draw the same conclusions about population means.

However, there is one critical difference.

Z tests require you to know the population standard deviation, while t tests use a sample estimate of the standard deviation. Learn more about Population Parameters vs. Sample Statistics .

In practice, analysts rarely use Z tests because it’s rare that they’ll know the population standard deviation. It’s even rarer that they’ll know it and yet need to assess an unknown population mean!

A Z test is often the first hypothesis test students learn because its results are easier to calculate by hand and it builds on the standard normal distribution that they probably already understand. Additionally, students don’t need to know about the degrees of freedom .

Z and T test results converge as the sample size approaches infinity. Indeed, for sample sizes greater than 30, the differences between the two analyses become small.

William Sealy Gosset developed the t test specifically to account for the additional uncertainty associated with smaller samples. Conversely, Z tests are too sensitive to mean differences in smaller samples and can produce statistically significant results incorrectly (i.e., false positives).

When to use a T Test vs Z Test

Let’s put a button on it.

When you know the population standard deviation, use a Z test.

When you have a sample estimate of the standard deviation, which will be the vast majority of the time, the best statistical practice is to use a t test regardless of the sample size.

However, the difference between the two analyses becomes trivial when the sample size exceeds 30.

Learn more about a T-Test Overview: How to Use & Examples and How T-Tests Work .

Z Test Hypotheses

This analysis uses sample data to evaluate hypotheses that refer to population means (µ). The hypotheses depend on whether you’re assessing one or two samples.

One-Sample Z Test Hypotheses

• Null hypothesis (H 0 ): The population mean equals a hypothesized value (µ = µ 0 ).
• Alternative hypothesis (H A ): The population mean DOES NOT equal a hypothesized value (µ ≠ µ 0 ).

When the p-value is less or equal to your significance level (e.g., 0.05), reject the null hypothesis. The difference between your sample mean and the hypothesized value is statistically significant. Your sample data support the notion that the population mean does not equal the hypothesized value.

Related posts : Null Hypothesis: Definition, Rejecting & Examples and Understanding Significance Levels

Two-Sample Z Test Hypotheses

• Null hypothesis (H 0 ): Two population means are equal (µ 1 = µ 2 ).
• Alternative hypothesis (H A ): Two population means are not equal (µ 1 ≠ µ 2 ).

Again, when the p-value is less than or equal to your significance level, reject the null hypothesis. The difference between the two means is statistically significant. Your sample data support the idea that the two population means are different.

These hypotheses are for two-sided analyses. You can use one-sided, directional hypotheses instead. Learn more in my post, One-Tailed and Two-Tailed Hypothesis Tests Explained .

Related posts : How to Interpret P Values and Statistical Significance

Z Test Assumptions

For reliable results, your data should satisfy the following assumptions:

You have a random sample

Drawing a random sample from your target population helps ensure that the sample represents the population. Representative samples are crucial for accurately inferring population properties. The Z test results won’t be valid if your data do not reflect the population.

Related posts : Random Sampling and Representative Samples

Continuous data

Z tests require continuous data . Continuous variables can assume any numeric value, and the scale can be divided meaningfully into smaller increments, such as fractional and decimal values. For example, weight, height, and temperature are continuous.

Other analyses can assess additional data types. For more information, read Comparing Hypothesis Tests for Continuous, Binary, and Count Data .

Your sample data follow a normal distribution, or you have a large sample size

All Z tests assume your data follow a normal distribution . However, due to the central limit theorem, you can ignore this assumption when your sample is large enough.

The following sample size guidelines indicate when normality becomes less of a concern:

• One-Sample : 20 or more observations.
• Two-Sample : At least 15 in each group.

Related posts : Central Limit Theorem and Skewed Distributions

Independent samples

For the two-sample analysis, the groups must contain different sets of items. This analysis compares two distinct samples.

Related post : Independent and Dependent Samples

Population standard deviation is known

As I mention in the Z test vs T test section, use a Z test when you know the population standard deviation. However, when n > 30, the difference between the analyses becomes trivial.

Related post : Standard Deviations

Z Test Formula

These Z test formulas allow you to calculate the test statistic. Use the Z statistic to determine statistical significance by comparing it to the appropriate critical values and use it to find p-values.

The correct formula depends on whether you’re performing a one- or two-sample analysis. Both formulas require sample means (x̅) and sample sizes (n) from your sample. Additionally, you specify the population standard deviation (σ) or variance (σ 2 ), which does not come from your sample.

I present a worked example using the Z test formula at the end of this post.

Learn more about Z-Scores and Test Statistics .

One Sample Z Test Formula

The one sample Z test formula is a ratio.

The numerator is the difference between your sample mean and a hypothesized value for the population mean (µ 0 ). This value is often a strawman argument that you hope to disprove.

The denominator is the standard error of the mean. It represents the uncertainty in how well the sample mean estimates the population mean.

Learn more about the Standard Error of the Mean .

Two Sample Z Test Formula

The two sample Z test formula is also a ratio.

The numerator is the difference between your two sample means.

The denominator calculates the pooled standard error of the mean by combining both samples. In this Z test formula, enter the population variances (σ 2 ) for each sample.

Z Test Critical Values

As I mentioned in the Z vs T test section, a Z test does not use degrees of freedom. It evaluates Z-scores in the context of the standard normal distribution. Unlike the t-distribution , the standard normal distribution doesn’t change shape as the sample size changes. Consequently, the critical values don’t change with the sample size.

To find the critical value for a Z test, you need to know the significance level and whether it is one- or two-tailed.

Learn more about Critical Values: Definition, Finding & Calculator .

Z Test Worked Example

Let’s close this post by calculating the results for a Z test by hand!

Suppose we randomly sampled subjects from an honors program. We want to determine whether their mean IQ score differs from the general population. The general population’s IQ scores are defined as having a mean of 100 and a standard deviation of 15.

We’ll determine whether the difference between our sample mean and the hypothesized population mean of 100 is statistically significant.

Specifically, we’ll use a two-tailed analysis with a significance level of 0.05. Looking at the table above, you’ll see that this Z test has critical values of ± 1.960. Our results are statistically significant if our Z statistic is below –1.960 or above +1.960.

The hypotheses are the following:

• Null (H 0 ): µ = 100
• Alternative (H A ): µ ≠ 100

Entering Our Results into the Formula

Here are the values from our study that we need to enter into the Z test formula:

• IQ score sample mean (x̅): 107
• Sample size (n): 25
• Hypothesized population mean (µ 0 ): 100
• Population standard deviation (σ): 15

The Z-score is 2.333. This value is greater than the critical value of 1.960, making the results statistically significant. Below is a graphical representation of our Z test results showing how the Z statistic falls within the critical region.

We can reject the null and conclude that the mean IQ score for the population of honors students does not equal 100. Based on the sample mean of 107, we know their mean IQ score is higher.

Now let’s find the p-value. We could use technology to do that, such as an online calculator. However, let’s go old school and use a Z table.

To find the p-value that corresponds to a Z-score from a two-tailed analysis, we need to find the negative value of our Z-score (even when it’s positive) and double it.

In the truncated Z-table below, I highlight the cell corresponding to a Z-score of -2.33.

The cell value of 0.00990 represents the area or probability to the left of the Z-score -2.33. We need to double it to include the area > +2.33 to obtain the p-value for a two-tailed analysis.

P-value = 0.00990 * 2 = 0.0198

That p-value is an approximation because it uses a Z-score of 2.33 rather than 2.333. Using an online calculator, the p-value for our Z test is a more precise 0.0196. This p-value is less than our significance level of 0.05, which reconfirms the statistically significant results.

See my full Z-table , which explains how to use it to solve other types of problems.

Share this:

Reader Interactions

Comments and questions cancel reply.

How to Write a Hypothesis

If I [do something], then [this] will happen.

This basic statement/formula should be pretty familiar to all of you as it is the starting point of almost every scientific project or paper. It is a hypothesis – a statement that showcases what you “think” will happen during an experiment. This assumption is made based on the knowledge, facts, and data you already have.

How do you write a hypothesis? If you have a clear understanding of the proper structure of a hypothesis, you should not find it too hard to create one. However, if you have never written a hypothesis before, you might find it a bit frustrating. In this article from EssayPro - custom essay writing services , we are going to tell you everything you need to know about hypotheses, their types, and practical tips for writing them.

Hypothesis Definition

According to the definition, a hypothesis is an assumption one makes based on existing knowledge. To elaborate, it is a statement that translates the initial research question into a logical prediction shaped on the basis of available facts and evidence. To solve a specific problem, one first needs to identify the research problem (research question), conduct initial research, and set out to answer the given question by performing experiments and observing their outcomes. However, before one can move to the experimental part of the research, they should first identify what they expect to see for results. At this stage, a scientist makes an educated guess and writes a hypothesis that he or she is going to prove or refute in the course of their study.

Get Help With Writing a Hypothesis Now!

Head on over to EssayPro. We can help you with editing and polishing up any of the work you speedwrite.

A hypothesis can also be seen as a form of development of knowledge. It is a well-grounded assumption put forward to clarify the properties and causes of the phenomena being studied.

As a rule, a hypothesis is formed based on a number of observations and examples that confirm it. This way, it looks plausible as it is backed up with some known information. The hypothesis is subsequently proved by turning it into an established fact or refuted (for example, by pointing out a counterexample), which allows it to attribute it to the category of false statements.

As a student, you may be asked to create a hypothesis statement as a part of your academic papers. Hypothesis-based approaches are commonly used among scientific academic works, including but not limited to research papers, theses, and dissertations.

Note that in some disciplines, a hypothesis statement is called a thesis statement. However, its essence and purpose remain unchanged – this statement aims to make an assumption regarding the outcomes of the investigation that will either be proved or refuted.

Characteristics and Sources of a Hypothesis

Now, as you know what a hypothesis is in a nutshell, let’s look at the key characteristics that define it:

• It has to be clear and accurate in order to look reliable.
• It has to be specific.
• There should be scope for further investigation and experiments.
• A hypothesis should be explained in simple language—while retaining its significance.
• If you are making a relational hypothesis, two essential elements you have to include are variables and the relationship between them.

The main sources of a hypothesis are:

• Scientific theories.
• Observations from previous studies and current experiences.
• The resemblance among different phenomena.
• General patterns that affect people’s thinking process.

Types of Hypothesis

Basically, there are two major types of scientific hypothesis: alternative and null.

• Alternative Hypothesis

This type of hypothesis is generally denoted as H1. This statement is used to identify the expected outcome of your research. According to the alternative hypothesis definition, this type of hypothesis can be further divided into two subcategories:

• Directional — a statement that explains the direction of the expected outcomes. Sometimes this type of hypothesis is used to study the relationship between variables rather than comparing between the groups.
• Non-directional — unlike the directional alternative hypothesis, a non-directional one does not imply a specific direction of the expected outcomes.

Now, let’s see an alternative hypothesis example for each type:

Directional: Attending more lectures will result in improved test scores among students. Non-directional: Lecture attendance will influence test scores among students.

Notice how in the directional hypothesis we specified that the attendance of more lectures will boost student’s performance on tests, whereas in the non-directional hypothesis we only stated that there is a relationship between the two variables (i.e. lecture attendance and students’ test scores) but did not specify whether the performance will improve or decrease.

• Null Hypothesis

This type of hypothesis is generally denoted as H0. This statement is the complete opposite of what you expect or predict will happen throughout the course of your study—meaning it is the opposite of your alternative hypothesis. Simply put, a null hypothesis claims that there is no exact or actual correlation between the variables defined in the hypothesis.

To give you a better idea of how to write a null hypothesis, here is a clear example: Lecture attendance has no effect on student’s test scores.

Both of these types of hypotheses provide specific clarifications and restatements of the research problem. The main difference between these hypotheses and a research problem is that the latter is just a question that can’t be tested, whereas hypotheses can.

Based on the alternative and null hypothesis examples provided earlier, we can conclude that the importance and main purpose of these hypotheses are that they deliver a rough description of the subject matter. The main purpose of these statements is to give an investigator a specific guess that can be directly tested in a study. Simply put, a hypothesis outlines the framework, scope, and direction for the study. Although null and alternative hypotheses are the major types, there are also a few more to keep in mind:

Research Hypothesis — a statement that is used to test the correlation between two or more variables.

For example: Eating vitamin-rich foods affects human health.

Simple Hypothesis — a statement used to indicate the correlation between one independent and one dependent variable.

For example: Eating more vegetables leads to better immunity.

Complex Hypothesis — a statement used to indicate the correlation between two or more independent variables and two or more dependent variables.

For example: Eating more fruits and vegetables leads to better immunity, weight loss, and lower risk of diseases.

Associative and Causal Hypothesis — an associative hypothesis is a statement used to indicate the correlation between variables under the scenario when a change in one variable inevitably changes the other variable. A causal hypothesis is a statement that highlights the cause and effect relationship between variables.

Be sure to read how to write a DBQ - this article will expand your understanding.

Add a secret ingredient to your hypothesis

Help of a professional writer.

Hypothesis vs Prediction

When speaking of hypotheses, another term that comes to mind is prediction. These two terms are often used interchangeably, which can be rather confusing. Although both a hypothesis and prediction can generally be defined as “guesses” and can be easy to confuse, these terms are different. The main difference between a hypothesis and a prediction is that the first is predominantly used in science, while the latter is most often used outside of science.

Simply put, a hypothesis is an intelligent assumption. It is a guess made regarding the nature of the unknown (or less known) phenomena based on existing knowledge, studies, and/or series of experiments, and is otherwise grounded by valid facts. The main purpose of a hypothesis is to use available facts to create a logical relationship between variables in order to provide a more precise scientific explanation. Additionally, hypotheses are statements that can be tested with further experiments. It is an assumption you make regarding the flow and outcome(s) of your research study.

A prediction, on the contrary, is a guess that often lacks grounding. Although, in theory, a prediction can be scientific, in most cases it is rather fictional—i.e. a pure guess that is not based on current knowledge and/or facts. As a rule, predictions are linked to foretelling events that may or may not occur in the future. Often, a person who makes predictions has little or no actual knowledge of the subject matter he or she makes the assumption about.

Another big difference between these terms is in the methodology used to prove each of them. A prediction can only be proven once. You can determine whether it is right or wrong only upon the occurrence or non-occurrence of the predicted event. A hypothesis, on the other hand, offers scope for further testing and experiments. Additionally, a hypothesis can be proven in multiple stages. This basically means that a single hypothesis can be proven or refuted numerous times by different scientists who use different scientific tools and methods.

To give you a better idea of how a hypothesis is different from a prediction, let’s look at the following examples:

Hypothesis: If I eat more vegetables and fruits, then I will lose weight faster.

This is a hypothesis because it is based on generally available knowledge (i.e. fruits and vegetables include fewer calories compared to other foods) and past experiences (i.e. people who give preference to healthier foods like fruits and vegetables are losing weight easier). It is still a guess, but it is based on facts and can be tested with an experiment.

Prediction: The end of the world will occur in 2023.

This is a prediction because it foretells future events. However, this assumption is fictional as it doesn’t have any actual grounded evidence supported by facts.

Based on everything that was said earlier and our examples, we can highlight the following key takeaways:

• A hypothesis, unlike a prediction, is a more intelligent assumption based on facts.
• Hypotheses define existing variables and analyze the relationship(s) between them.
• Predictions are most often fictional and lack grounding.
• A prediction is most often used to foretell events in the future.
• A prediction can only be proven once – when the predicted event occurs or doesn’t occur. 
• A hypothesis can remain a hypothesis even if one scientist has already proven or disproven it. Other scientists in the future can obtain a different result using other methods and tools.

We also recommend that you read about some informative essay topics .

Now, as you know what a hypothesis is, what types of it exist, and how it differs from a prediction, you are probably wondering how to state a hypothesis. In this section, we will guide you through the main stages of writing a good hypothesis and provide handy tips and examples to help you overcome this challenge:

1. Define Your Research Question

Here is one thing to keep in mind – regardless of the paper or project you are working on, the process should always start with asking the right research question. A perfect research question should be specific, clear, focused (meaning not too broad), and manageable.

Example: How does eating fruits and vegetables affect human health?

2. Conduct Your Basic Initial Research

As you already know, a hypothesis is an educated guess of the expected results and outcomes of an investigation. Thus, it is vital to collect some information before you can make this assumption.

At this stage, you should find an answer to your research question based on what has already been discovered. Search for facts, past studies, theories, etc. Based on the collected information, you should be able to make a logical and intelligent guess.

3. Formulate a Hypothesis

Based on the initial research, you should have a certain idea of what you may find throughout the course of your research. Use this knowledge to shape a clear and concise hypothesis.

Based on the type of project you are working on, and the type of hypothesis you are planning to use, you can restate your hypothesis in several different ways:

Non-directional: Eating fruits and vegetables will affect one’s human physical health. Directional: Eating fruits and vegetables will positively affect one’s human physical health. Null: Eating fruits and vegetables will have no effect on one’s human physical health.

4. Refine Your Hypothesis

Finally, the last stage of creating a good hypothesis is refining what you’ve got. During this step, you need to define whether your hypothesis:

• Has clear and relevant variables;
• Identifies the relationship between its variables;
• Is specific and testable;
• Suggests a predicted result of the investigation or experiment.

In case you need some help with your essay, leave us a notice ' pay someone to write my essay ' and we'll help asap. We also provide nursing writing services .

Hypothesis Examples

Following a step-by-step guide and tips from our essay writers for hire , you should be able to create good hypotheses with ease. To give you a starting point, we have also compiled a list of different research questions with one hypothesis and one null hypothesis example for each:

Ask Pros to Make a Perfect Hypothesis for You!

Sometimes, coping with a large academic load is just too much for a student to handle. Papers like research papers and dissertations can take too much time and effort to write, and, often, a hypothesis is a necessary starting point to get the task on track. Writing or editing a hypothesis is not as easy as it may seem. However, if you need help with forming it, the team at EssayPro is always ready to come to your rescue! If you’re feeling stuck, or don’t have enough time to cope with other tasks, don’t hesitate to send us you rewrite my essay for me or any other request.

is an expert in nursing and healthcare, with a strong background in history, law, and literature. Holding advanced degrees in nursing and public health, his analytical approach and comprehensive knowledge help students navigate complex topics. On EssayPro blog, Adam provides insightful articles on everything from historical analysis to the intricacies of healthcare policies. In his downtime, he enjoys historical documentaries and volunteering at local clinics.

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

• Knowledge Base
• 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.

Receive feedback on language, structure, and formatting

Professional editors proofread and edit your paper by focusing on:

• Academic style
• Vague sentences
• Style consistency

See an example

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.

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.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

Turney, S. (2023, June 22). Null & Alternative Hypotheses | Definitions, Templates & Examples. Scribbr. Retrieved August 21, 2024, from https://www.scribbr.com/statistics/null-and-alternative-hypotheses/

Is this article helpful?

Shaun Turney

Other students also liked, inferential statistics | an easy introduction & examples, hypothesis testing | a step-by-step guide with easy examples, type i & type ii errors | differences, examples, visualizations, what is your plagiarism score.

Definition of a Hypothesis

What it is and how it's used in sociology

• Key Concepts
• Major Sociologists
• News & Issues
• Research, Samples, and Statistics
• Recommended Reading
• Archaeology

A hypothesis is a prediction of what will be found at the outcome of a research project and is typically focused on the relationship between two different variables studied in the research. It is usually based on both theoretical expectations about how things work and already existing scientific evidence.

Within social science, a hypothesis can take two forms. It can predict that there is no relationship between two variables, in which case it is a null hypothesis . Or, it can predict the existence of a relationship between variables, which is known as an alternative hypothesis.

In either case, the variable that is thought to either affect or not affect the outcome is known as the independent variable, and the variable that is thought to either be affected or not is the dependent variable.

Researchers seek to determine whether or not their hypothesis, or hypotheses if they have more than one, will prove true. Sometimes they do, and sometimes they do not. Either way, the research is considered successful if one can conclude whether or not a hypothesis is true. 

Null Hypothesis

A researcher has a null hypothesis when she or he believes, based on theory and existing scientific evidence, that there will not be a relationship between two variables. For example, when examining what factors influence a person's highest level of education within the U.S., a researcher might expect that place of birth, number of siblings, and religion would not have an impact on the level of education. This would mean the researcher has stated three null hypotheses.

Alternative Hypothesis

Taking the same example, a researcher might expect that the economic class and educational attainment of one's parents, and the race of the person in question are likely to have an effect on one's educational attainment. Existing evidence and social theories that recognize the connections between wealth and cultural resources , and how race affects access to rights and resources in the U.S. , would suggest that both economic class and educational attainment of the one's parents would have a positive effect on educational attainment. In this case, economic class and educational attainment of one's parents are independent variables, and one's educational attainment is the dependent variable—it is hypothesized to be dependent on the other two.

Conversely, an informed researcher would expect that being a race other than white in the U.S. is likely to have a negative impact on a person's educational attainment. This would be characterized as a negative relationship, wherein being a person of color has a negative effect on one's educational attainment. In reality, this hypothesis proves true, with the exception of Asian Americans , who go to college at a higher rate than whites do. However, Blacks and Hispanics and Latinos are far less likely than whites and Asian Americans to go to college.

Formulating a Hypothesis

Formulating a hypothesis can take place at the very beginning of a research project , or after a bit of research has already been done. Sometimes a researcher knows right from the start which variables she is interested in studying, and she may already have a hunch about their relationships. Other times, a researcher may have an interest in ​a particular topic, trend, or phenomenon, but he may not know enough about it to identify variables or formulate a hypothesis.

Whenever a hypothesis is formulated, the most important thing is to be precise about what one's variables are, what the nature of the relationship between them might be, and how one can go about conducting a study of them.

Updated by Nicki Lisa Cole, Ph.D

• What It Means When a Variable Is Spurious
• Understanding Path Analysis
• Pilot Study in Research
• Simple Random Sampling
• Exploitation
• What Is Multiculturalism? Definition, Theories, and Examples
• Convenience Samples for Research
• What Is Cultural Capital? Do I Have It?
• What Does Consumerism Mean?
• Visualizing Social Stratification in the U.S.
• What Is Symbolic Interactionism?
• What Is Cultural Hegemony?
• Understanding Stratified Samples and How to Make Them
• What Is Groupthink? Definition and Examples
• What Is a Reference Group?
• What Is Ethnography?

• Search Menu
• Sign in through your institution
• Advance Articles
• Virtual Issues
• High-Impact Research Collection
• Celebrate 40 years of MBE
• Perspectives
• Discoveries
• Cover Archive
• Brief Communications
• Submission site
• Author guidelines
• Open access
• Self-archiving policy
• Reasons to submit
• About Molecular Biology and Evolution
• About the Society for Molecular Biology and Evolution
• Editorial Board
• Advertising and Corporate Services
• Journals Career Network
• Journals on Oxford Academic
• Books on Oxford Academic

Article Contents

Introduction, conclusions, materials and methods, supplementary material, acknowledgments, data availability.

• < Previous

Diversity and Molecular Evolution of Nonvisual Opsin Genes across Environmental, Developmental, and Morphological Adaptations in Frogs

• Article contents
• Figures & tables
• Supplementary Data

John L Boyette, Rayna C Bell, Matthew K Fujita, Kate N Thomas, Jeffrey W Streicher, David J Gower, Ryan K Schott, Diversity and Molecular Evolution of Nonvisual Opsin Genes across Environmental, Developmental, and Morphological Adaptations in Frogs, Molecular Biology and Evolution , Volume 41, Issue 6, June 2024, msae090, https://doi.org/10.1093/molbev/msae090

• Permissions Icon Permissions

Nonvisual opsins are transmembrane proteins expressed in the eyes and other tissues of many animals. When paired with a light-sensitive chromophore, nonvisual opsins form photopigments involved in various nonvisual, light-detection functions including circadian rhythm regulation, light-seeking behaviors, and seasonal responses. Here, we investigate the molecular evolution of nonvisual opsin genes in anuran amphibians (frogs and toads). We test several evolutionary hypotheses including the predicted loss of nonvisual opsins due to nocturnal ancestry and potential functional differences in nonvisual opsins resulting from environmental light variation across diverse anuran ecologies. Using whole-eye transcriptomes of 81 species, combined with genomes, multitissue transcriptomes, and independently annotated genes from an additional 21 species, we identify which nonvisual opsins are present in anuran genomes and those that are also expressed in the eyes, compare selective constraint among genes, and test for potential adaptive evolution by comparing selection between discrete ecological classes. At the genomic level, we recovered all 18 ancestral vertebrate nonvisual opsins, indicating that anurans demonstrate the lowest documented amount of opsin gene loss among ancestrally nocturnal tetrapods. We consistently found expression of 14 nonvisual opsins in anuran eyes and detected positive selection in a subset of these genes. We also found shifts in selective constraint acting on nonvisual opsins in frogs with differing activity periods, habitats, distributions, life histories, and pupil shapes, which may reflect functional adaptation. Although many nonvisual opsins remain poorly understood, these findings provide insight into the diversity and evolution of these genes across anurans, filling an important gap in our understanding of vertebrate opsins and setting the stage for future research on their functional evolution across taxa.

Animals rely on light detection to accomplish many biologically critical functions. Visual photosensitivity allows animals to acquire food, locate mates, and avoid predators. In recent years, the role of nonvisual photosensitivity has received increasing attention, revealing a diverse suite of physiologically important nonvisual functions including calibration of circadian rhythms, regulation of light-seeking behaviors, and initiation of seasonal reproductive changes ( Nakane et al. 2010 , 2014 ; Fernandes et al. 2012 ; Andrabi et al. 2023 ). The basis of animal photosensitivity lies in the conversion of light stimuli into neural stimuli—a process known as phototransduction—which is initiated by photopigments embedded in the membranes of light-sensitive cells. Each photopigment is composed of a transmembrane opsin protein encapsulating a light-sensitive chromophore. Different opsins confer distinct ranges of spectral sensitivity to their respective photopigments by maximally absorbing a specific wavelength of light. Upon absorption of light, the chromophore photoisomerizes, undergoing a conformational change that initiates phototransduction, generating a neural signal that can be interpreted for either visual or nonvisual functions ( Terakita 2005 ; Hunt and Collin 2014 ). The function of opsins in initiating phototransduction and light detection is illustrated in Fig. 1 .

General overview of opsin function in vertebrates exemplified using the eye of a frog ( Boana albomarginata , pictured here). 1) Light enters the eye and is focused on the retina. 2) Light reaches a photopigment (composed of an opsin and chromophore) embedded in the membrane of a light-sensitive retinal cell. The photopigment maximally absorbs a specific wavelength of light. In this example, the photopigment maximally absorbs blue light. 3) Absorption of light stimulates photoisomerization of the chromophore encapsulated within the opsin. 4) A neural signal is generated, processed in the retina and sent to the brain to be further processed and interpreted for visual or nonvisual purposes.

Opsins are divided broadly into eight groups based on amino-acid sequence similarity, molecular function, and signaling properties. The vertebrate visual opsin group contains opsins involved in initiating the formation of visual images, including rod opsin (RH1) and the cone opsins (LWS, RH2, SWS1, and SWS2). These opsins are associated with “bleaching” photopigments, meaning that following light exposure and photoisomerization, the chromophore dissociates from the opsin and renders the photopigment unreactive until the visual pigment can be regenerated with a new chromophore ( Tsukamoto 2014 ). Opsins in the retinal photoisomerase group (RGR) and the peropsin group (RRH) function to regenerate chromophores used by bleaching photopigments ( Terakita 2005 ; Radu et al. 2008 ; Zhang 2015 ). The other opsin groups include the encephalopsin/tmt-opsin group (OPN3 and TMT1 to 3), the Gq-coupled opsin/melanopsin group (OPN4m and OPN4x), the Go-coupled opsin group, the neuropsin group (NEUR1 to 6), and the paraphyletic vertebrate nonvisual opsin group (parietopsin [PAR], parapinopsin [PARA], vertebrate ancient opsin [VAOP], and pinopsin [PIN]), which forms a clade with the visual opsins. These opsin groups are generally found in photoreceptor cells in various major organs including the eyes, brain, and skin of many vertebrates (e.g. Foster and Bellingham 2004 ; Nakane et al. 2010 ; Davies et al. 2015 ; Kelley and Davies 2016 ). These opsins function in either bleaching or “nonbleaching” photopigments. Nonbleaching photopigments, also referred to as bistable photopigments, retain their chromophore following light exposure and photoisomerization. This is relevant to nonvisual photopigments because many are expressed in extraocular tissues that lack the specialized chromophore-regeneration mechanisms of the retina ( Tsukamoto 2014 ; Steindal and Whitmore 2020 ). For the purposes of this study, we broadly refer to all opsins outside the vertebrate visual opsin group as nonvisual opsins. A summary of vertebrate opsin diversity and known spectral sensitivities, tissue expression, and functions is presented in Fig. 2 .

Summarized diversity of exemplar spectral sensitivities, tissue expression, and functions across visual and nonvisual opsins. Phylogenetic hypothesis based on Beaudry et al. (2017) and Davies et al. (2015) . Peak absorbance measurements and corresponding color are displayed beside the taxa in which each measurement was observed. Note that these values may vary across lineages. Tissue expression based on transcriptomic profiles in zebrafish ( Davies et al. 2015 ). Citations for peak absorbance and functional overview notes can be found in supplementary table S1, Supplementary Material online.

The scope of opsin diversity coupled with the breadth of tissues and taxa expressing these genes suggests that the biological relevance of light detection extends far beyond the visual system. Among vertebrates, teleost fishes demonstrate the greatest opsin diversity, with 10 visual and 32 nonvisual opsins reported in zebrafish ( Davies et al. 2015 ). This diversity likely arose through whole-genome duplication events, and the retention of these opsin genes in zebrafish is hypothesized to confer an adaptive advantage in dynamic freshwater light environments. Mammals, on the other hand, have lost multiple opsins, with 11 opsins (two visual) inferred to have been lost ancestrally, and an additional three opsins (one visual) lost in placentals ( Gemmell et al. 2020 ). This disparity of opsin diversity across vertebrates emphasizes the importance of ecology in the evolution of opsin systems. For example, the loss of opsin diversity in mammals is hypothesized to result from a “nocturnal bottleneck” in which ancestral mammals transitioned to nocturnal lifestyles and encountered a reduced need for broad spectral sensitivity ( Gerkema et al. 2013 ; Borges et al. 2018 ). Ecological transitions to low-light environments are also thought to explain the loss of opsin diversity in other tetrapod taxa, including geckos ( Pinto et al. 2019 ), crocodilians ( Emerling 2017 ), snakes ( Davies et al. 2009 ; Schott et al. 2018 ; Gower et al. 2022 ), whales ( Meredith et al. 2013 ), burrowing rodents ( Emerling and Springer 2014 ), and nocturnal primates ( Kawamura and Kubotera 2004 ). These examples highlight the impact of low-light ecological transitions on opsin diversity and evolution; however, the influence of other environmental, developmental, and morphological adaptations remains poorly studied.

Frogs and toads (Anura, hereafter collectively “frogs”) provide an opportune system in which to investigate opsin diversity and evolution because they demonstrate remarkable variation in activity period, habitat, distribution, life history, and pupil shape (e.g. Wiens et al. 2006 ; Moen et al. 2013 ; Thomas et al. 2022a ). This variation exposes frogs to diverse light environments and sensory constraints, which in turn introduce unique evolutionary challenges to the nonvisual system that we hypothesize have driven functional adaptation, and loss, of nonvisual opsins. Specifically, the nocturnal bottleneck hypothesis exemplifies a connection between the evolution of nonvisual opsins and adaptation to new activity periods and habitats in several tetrapod groups but has not yet been investigated in anurans. We also hypothesize that species distribution has influenced nonvisual opsin functional evolution, because species distributed outside tropical zones experience more predictable seasonal variation in photoperiod ( Canavero and Arim 2009 ; Borah et al. 2019 ). Variation in both seasonality and photoperiod has implications for nonvisual opsin function because these proteins are involved in responses to seasonality ( Nakane et al. 2010 ) and regulation of circadian rhythm ( Göz et al. 2008 ). Many frog species also experience a dramatic shift in light environment across development as they metamorphose from aquatic larvae to terrestrial adults. We hypothesize that this biphasic life history subjects nonvisual opsins to disparate environmental constraints and selective pressures across metamorphosis, resulting in adaptive decoupling in biphasic frog species ( Schott et al. 2022 ). Furthermore, a subset of frog species, known as direct developers, lack a free-living aquatic larval stage, which provides an opportunity to test whether species with different life history strategies exhibit differences in selection across nonvisual opsins. Finally, frogs demonstrate a strikingly diverse suite of pupil shapes that regulate the amount of light reaching the retina through pupillary constriction ( Malmström and Kröger 2006 ; Thomas et al. 2022a ). We hypothesize that this morphological diversity is associated with nonvisual opsin evolution because these proteins have been implicated in the regulation of pupillary light responses ( Keenan et al. 2016 ). Taken together, the environmental, developmental, and morphological diversity of frogs makes them an attractive study system in which to investigate nonvisual opsin diversity and evolution.

Here, we extract nonvisual opsin genes from de novo whole-eye transcriptome assemblies of 81 frog species. Sampling only eye transcriptomes may provide an incomplete picture of nonvisual opsin diversity because these genes are expressed in many extraocular tissues; therefore, we supplement our whole-eye transcriptome sampling with publicly available genomes, multitissue transcriptomes, and independently annotated genes from an additional 21 species. Together, these 102 frog species represent 34 of 56 currently recognized frog families, including a broad sampling of environmental, developmental, and morphological adaptations. We predict that this variation has influenced the diversity and molecular evolution of the nonvisual opsins ( Fig. 3 ). We aim to (i) identify which nonvisual opsin genes are expressed in the eyes of frogs and test whether a nocturnal ancestry has driven opsin gene loss in frog genomes; (ii) compare selection among nonvisual opsin genes; and (iii) test hypotheses of adaptive evolution by comparing selection among frogs with differing ecologies.

Variation in adult activity period, adult habitat, distribution, life history, and pupil shape across our species sampling. Each column represents one of seven trait partitions used to analyze shifts in selective constraint across discrete environmental, developmental, and morphological transitions in frogs. Filled (colored) bubbles in trait columns indicate the foreground partition for selection analyses (e.g. diurnal). Unfilled (gray) bubbles indicate the background partition for selection analyses (e.g. nondiurnal). Phylogenetic hypothesis based on several large-scale phylogenetic studies ( Pyron and Wiens 2011 ; Feng et al. 2017 ; Jetz and Pyron 2018 ; Streicher et al. 2018 ). Trait coding citations are available in supplementary table S4, Supplementary Materials online. Photographs by M.K.F. ( Rhinophrynus dorsalis and Xenopus tropicalis ), J.W.S. and D.J.G. ( Lepidobatrachus laevis and Cornufer guentheri ), J.L.B. ( Brachycephalus pitanga , Haddadus binotatus , Vitreorana uranoscopa , Rhinella icterica , Gastrophryne olivacea , and L. catesbeianus ), Christian Irian ( Hyperolius tuberculatus ), and John Clare ( P. adspersus ).

Fourteen Nonvisual Opsins Consistently Expressed in Frog Eyes

Our total sampling included 92 whole-eye transcriptomes from 81 species, 19 genomes from 15 additional species, and multitissue transcriptomes or independently annotated genes from six additional species. Across the frog genomes, we recovered all 18 nonvisual opsins inferred to be present in the ancestral vertebrate ( Beaudry et al. 2017 ; Gemmell et al. 2020 ), although recovery success varied across genes. OPN3 was recovered from the fewest genomes (10), while NEUR4 and PIN were recovered in all 19 genomes ( supplementary table S5, Supplementary Material online). Most cases where a gene was not recovered are likely due to incomplete genome coverage and assembly. However, there is evidence for the loss of NEUR2 in some frog lineages because we were unable to recover this gene from the multiple hylid and bufonid genomes that are presently available (five species). Furthermore, this gene was not recovered from any of the eye transcriptomes with the exception of a single partial transcript in Spea bombifrons .

In terms of expression in the eye, we found that four genes ( NEUR2 , OPN3 , PAR , and PARA ) were expressed in very few samples (0 to 11). For the four species in which our sampling included both an eye transcriptome and a genome ( Lithobates catesbeianus , Pyxicephalus adspersus , Scaphiopus couchii , and S. bombifrons ), NEUR2 , OPN3 , PAR , and PARA were mostly absent from the eye transcriptome and present in the genome (with a few exceptions noted in supplementary table S5, Supplementary Material online). These four genes were dropped from downstream analyses because their low rates of recovery success limited our ability to generate reliable phylogenies and perform selection analyses. We recovered the remaining 14 nonvisual opsins with some degree of consistency (ranging from 34.2% to 94.7% recovery of whole or partial coding sequences, detailed in supplementary table S5, Supplementary Materials online) across our total sampling.

Evidence for Positive Selection in a Subset of Frog Nonvisual Opsins

To determine the overall selective constraint acting on each nonvisual opsin, we used the PAML M0 model to estimate the average rate ratio of nonsynonymous to synonymous substitutions ( d N / d S or ω ) across all codon sites in each gene alignment. These tests revealed fairly consistent selective constraint acting on frog nonvisual opsins, with most genes demonstrating mean ω values between 0.09 and 0.18 as illustrated in Fig. 4a . Only NEUR6 fell outside of this range, with an elevated mean ω value of 0.25. Taken together, all 14 nonvisual opsins have a mean ω < 1, indicating negative purifying selection. This is expected in most functional protein-coding genes, whose proteins are made up of a high proportion of invariable amino acids (with ω near 0) due to strong functional constraints ( Yang et al. 2000 ). However, genes demonstrating overall negative selection may still contain positively selected codon sites. We tested for this using the PAML M8 model, which unlike the M0 model, allows ω to vary between sites in a gene. The M8 model is compared with the null models M7 and M8a (which allow ω to vary but constrain ω ≤ 1) to test for the presence of positively selected sites using a likelihood ratio test (LRT). Using this approach, we found statistically significant positive selection at a proportion of sites in PIN , TMT1 , TMT2 , and VAOP as illustrated in Fig. 4b . The most extreme signature of positive selection was detected in PIN , which had an ω value of 3.17 (M8 vs. M8a: LRT = 13.2, P < 0.001). For comparison, the second most elevated signature of positive selection was observed in VAOP , with an ω value of 1.90 (M8 vs. M8a: LRT = 4.91, P = 0.027). Because the PAML M8 model estimates ω as a single parameter, it is possible for ω to be overestimated in instances of synonymous rate variation across a phylogeny. We tested for this using BUSTED with synonymous rate variation and identified statistically significant evidence of episodic diversifying selection in NEUR4 , NEUR5 , OPN4m , and OPN4x , which do not overlap with the genes identified by our PAML M8 results supplementary fig. S1, Supplementary Material online. Analyses with BUSTED that instead do not allow synonymous rate variation do not have evidence for positive selection in three of the four genes identified by M8 ( TMT1 , TMT2 , and VAOP ). PIN was significant with M8 and BUSTED without synonymous rate variation, but not BUSTED with synonymous rate variation; although the estimated rates were similar, the test was not significant (LRT = 3, P = 0.107). An opposite pattern is seen in two of the four genes identified with BUSTED where not allowing synonymous rate variation results in statistical nonsignificance ( NEUR4 and NEUR5 ), whereas no difference was found for the other two genes ( OPN4m and OPN4x ). These results suggest that not accounting for synonymous rate variation is not a cause of false inferences of positive selection but does result in statistical differences. Differences between BUSTED and M8 appear primarily due to differences in model formulation (including the use of a discretized beta distribution to determine site classes in M8 vs. three site classes in BUSTED). Overall, these results provide evidence for positive selection on frog nonvisual opsins and suggest that adaptive evolution may be occurring within a subset of these genes. Complete PAML random sites models and BUSTED results are presented in supplementary tables S6 and S7, Supplementary Material online, while the number and position of positively selected sites estimated with the PAML M8 model are detailed in supplementary table S8, Supplementary Material online.

Patterns of selective constraint across nonvisual opsin genes. a) The PAML M0 analysis averages ω values across all codon sites in a gene alignment. Among nonvisual opsins, NEUR6 had the most elevated ω while RGR had the least elevated ω , suggesting variation in selective constraint among nonvisual opsin genes. b) The PAML M8 analysis tests for the presence of positively selected codon sites in a gene alignment. The ω of the positively selected site class is shown. Four nonvisual opsins demonstrated statistically significant ( P < 0.05) evidence for positively selected sites (indicated with an asterisk). Note that graphs a) and b) use different scales along the x axes.

Shifts in Selective Constraint among Nonvisual Opsins Are Associated with Variation in Adult Activity Period, Adult Habitat, Distribution, Life History, and Pupil Shape

Because analyses of gene and species phylogenetic topologies sometimes yielded different significant results, we gave greater weight to results where the same partition was significant across analyses of both topologies and reported only those results here unless otherwise noted. Full results are available in supplementary tables S9 to S11, Supplementary Material online. Significant differences in selective constraint were detected for many of our trait partitions ( Fig. 5 ). The adult activity partition was significant in four genes and was the best-fit partition for OPN4x ( ω diu = 0.35/ ω nondiu = 0.28, P = 0.006), PIN ( ω diu = 0.35/ ω nondiu = 0.28, P = 0.051), and VAOP ( ω diu = 0.26/ ω nondiu = 0.21, P = 0.056), indicating that within each gene, the difference in selective constraint between foreground (diurnal) and background (nondiurnal) groups was greater than the difference in any other partition. The adult activity partitions for PIN and VAOP were significant for analyses of the gene topologies ( P = 0.016 and 0.039, respectively) and were marginally nonsignificant ( P = 0.051 and 0.056, respectively) for analyses of the species topologies, yet the adult activity partitions were the best fits for PIN and VAOP across both sets of topologies. Among the three adult habitat partitions, the aquatic partition was significant in three genes and was the best fit for NEUR3 ( ω aqu = 0.34/ ω nonaqu = 0.26, P = 0.003) and NEUR4 ( ω aqu = 0.30/ ω nonaqu = 0.21, P = 0.001). The scansorial partition was significant in two genes and was the best fit for NEUR6 ( ω sca = 0.48/ ω nonsca = 0.32, P < 0.001). The secretive partition was significant in one gene, with no best fits. The distribution partition was significant and a best fit for TMT3 ( ω trp = 0.26/ ω nontrp = 0.33, P = 0.019). Interestingly, the life history partition was the most frequent significant partition among nonvisual opsins, with eight genes having a significant difference in selective constraint between direct-developing and biphasic species. The life history partition was also the best-fit partition for five of these genes, including NEUR1 ( ω drd = 0.38/ ω bip = 0.28, P = 0.016), OPN4m ( ω drd = 0.48/ ω bip = 0.27, P < 0.001), RRH ( ω drd = 0.35/ ω bip = 0.24, P = 0.028), TMT1 ( ω drd = 0.44/ ω bip = 0.26, P < 0.001), and TMT2 ( ω drd = 0.44/ ω bip = 0.25, P < 0.001). Finally, because OPN4m has been implicated in regulating the pupillary light response, we tested the elongated pupil partition to explore how constricted pupil shape might relate more generally to nonvisual opsin evolution. The elongated pupil partition was not significant in OPN4m across topologies, but was otherwise significant in two genes, and was the best fit for RGR ( ω elp = 0.21/ ω nonelp = 0.33, P = 0.002).

Shifts in selective pressure on nonvisual opsin genes across frog trait partitions as illustrated in Fig. 3 . The ω ( d N / d S ) values of the divergent site class using CmC analysis of nonvisual opsin species topologies are shown, highlighting the difference between the foreground (filled circle) and the background (unfilled circle) partitions for each gene. Under each trait partition, genes with statistically significant ( P < 0.05) shifts in selection across analyses of both gene and species topologies are shown. Best-fit partitions are indicated with a star. Complete PAML results are available in supplementary tables S9 to S11, Supplementary Material online.

We used RELAX to test specific hypotheses regarding nonvisual opsin evolution in genes with known functions that demonstrated a significant shift in selective constraint across a partition. These analyses revealed significant evidence for relaxed selection acting on PIN , OPN4m , OPN4x , and VAOP in diurnal species ( K = 0.81, 0.11, 0.89, and 0.77, P ≤ 0.029). Furthermore, these analyses revealed evidence for relaxed selection in six of the eight significant direct-developing partitions, including NEUR1 ( K = 0.66, P = 0.004), NEUR3 ( K = 0.47, P = 0.002), NEUR6 ( K = 0.68, P = 0.007), OPN4m ( K = 0.11, P < 0.001), RRH ( K = 0.58, P = 0.006), and TMT2 ( K = 0.52, P < 0.001). A full summary of our RELAX results is available in supplementary table S12, Supplementary Material online.

Using a combination of de novo assembled whole-eye transcriptomes and previously published genomic and transcriptomic resources, we obtained nonvisual opsin sequences from 102 frog species spanning 34 families. We consistently recovered 14 nonvisual opsin genes from frog eye transcriptomes, and positive selection was detected in a subset of these genes, most notably PIN . We also found variation in selective constraint between frog lineages partitioned by adult activity period, adult habitat, distribution, life history, and pupil shape, which may reflect functional adaptation in frog nonvisual opsin genes. Below, we discuss these findings with respect to our current understanding of nonvisual opsin diversity, expression, function, and evolution.

Unexpected Nonvisual Opsin Diversity across Frogs

The common ancestor of all vertebrates is estimated to have had a genomic complement of 18 nonvisual opsins ( Beaudry et al. 2017 ; Gemmell et al. 2020 ). However, over the course of vertebrate evolution, nonvisual opsin diversity has shifted across groups. Nonvisual opsin gene losses have been most apparent in groups with primarily nocturnal evolutionary histories, including between nine and 11 losses in mammals, nine losses in snakes, five losses in geckos, and four losses in crocodilians ( Gemmell et al. 2020 ). These losses have all been attributed to a “nocturnal bottleneck” in which ancestors of each group transitioned to nocturnal lifestyles and encountered a reduced need for broad spectral sensitivity ( Emerling and Springer 2014 ; Borges et al. 2018 ; Pinto et al. 2019 ). Adults of most frog species are primarily nocturnal, and this activity period is thought to be the ancestral condition for anurans ( Anderson and Wiens 2017 ). Given this evolutionary history, we expected frogs to have reduced nonvisual opsin diversity compared to the common ancestor of vertebrates. Instead, we recovered remarkable nonvisual opsin diversity across frogs, with 14 of 18 nonvisual opsins consistently recovered from eye tissues. Of the four genes we failed to consistently recover, two genes, PAR and PARA , are thought to be expressed exclusively in the pineal region of the brain, and thus, it is not surprising that we had limited success recovering these nonvisual opsins from our eye transcriptome data set. The inconsistent recovery of the other two genes, NEUR2 and OPN3 , is less straightforward to understand. To our knowledge, there is no published expression profile or functional study of NEUR2 in any taxa, which limits our ability to speculate on why we failed to consistently recover this gene. On the other hand, OPN3 studies in other vertebrates report expression in many tissues, including the retina, brain, and liver ( Halford et al. 2001 ). Thus, the absence of OPN3 in all of our 92 frog eye transcriptomes is surprising given reports of its expression in eye or retinal tissue across diverse taxa, including human retinas ( Halford et al. 2001 ), chicken retinas ( Rios et al. 2019 ), and zebrafish eyes ( Davies et al. 2015 ). Although the retina is reported to have the greatest opsin diversity of any tissue ( Davies et al. 2015 ), some nonvisual opsins may be expressed at very low levels ( Do 2019 ), and there remains a possibility that both NEUR2 and OPN3 are expressed at levels below our threshold of detection, especially considering that we sequenced whole-eye tissue and not isolated retinal tissue.

Comparatively, across our whole-genome data set, we had much greater success recovering PAR and PARA , with whole or partial sequences recovered from 18 of 19 genomes for both genes ( supplementary table S5, Supplementary Materials online). This suggests that both PAR and PARA are retained in frogs; however, these genes appear to be expressed primarily in extraocular tissues. We also recovered NEUR2 and OPN3 with greater consistency across the whole-genome data set, with whole or partial sequences recovered in 11 and 10 genomes, respectively ( supplementary table S5, Supplementary Materials online). Additionally, for both NEUR2 and OPN3 , we found no evidence of nonfunctionalization among our recovered sequences, although we found preliminary support for the loss of NEUR2 in hylids and bufonids, based on consistent absence in the five genomes from those taxa. Consequently, we conclude that none of the ancestral vertebrate nonvisual opsins has been lost across frogs and, instead, frogs appear to have maintained a remarkably diverse repertoire of these genes.

Adaptive Decoupling, the Nocturnal Bottleneck, and an Alternative Hypothesis of Opsin Evolution

Frogs have maintained an unexpectedly diverse complement of nonvisual opsins, especially for a group demonstrating primarily nocturnal activity patterns. This may be due, at least in part, to the biphasic life history of most frogs. Although many fully metamorphosed frogs are nocturnal, this is not necessarily true of their aquatic larvae. Instead, many species that are nocturnal as adults are active and forage in daylight as larvae ( Beiswenger 1977 ; Griffiths and Mylotte 1988 ; Ding et al. 2014 ). This biphasic life history may subject nonvisual opsins to disparate environmental constraints and selective pressures across metamorphosis, resulting in adaptive decoupling between larvae active in bright light and adults active in low light ( Ebenman 1992 ; Schott et al. 2022 ). Adaptive decoupling may complicate our ability to test expectations of the nocturnal bottleneck hypothesis, which posits low-light adaptation as the most proximate driver of opsin evolution and diversity in many taxa ( Emerling 2017 ; Borges et al. 2018 ; Pinto et al. 2019 ), because it obscures the distinction between light-adapted and dark-adapted species.

In this study, we partitioned frogs based on adult activity period. This was necessary because larval activity period is poorly characterized across frogs. Despite this potential lack of nuance, a significant difference in ω between diurnal and nondiurnal frog species was detected in four genes with clade model C (CmC), and in each case, the diurnal species demonstrated elevated ω . This elevated rate of nonsynonymous nucleotide substitution among diurnal frogs may be the product of either relaxed or adaptive selection. Considering the nocturnal bottleneck hypothesis, we predicted that the elevated ω values observed in diurnal lineages are driven by intensified (i.e. adaptive) selection on nonvisual opsins because broad spectral sensitivity is likely adaptive in diurnal species. Our RELAX analyses did not support this prediction, instead revealing significant evidence for relaxed selection in all four genes ( OPN4m , OPN4x , PIN , and VAOP ; supplementary table S12, Supplementary Material online). Considering the unexpected diversity of frog nonvisual opsins alongside these selection signatures, it appears that expectations of the nocturnal bottleneck hypothesis do not hold true for frogs, and we suggest this may be due to widespread adaptive decoupling across frogs.

Through the lens of adaptive decoupling, our findings may offer support for an alternative hypothesis of opsin evolution. Beaudry et al. (2017) critiqued the nocturnal bottleneck hypothesis’ focus on evolutionary transitions to low-light ecologies and instead focused on developmental transitions as driving opsin evolution and diversity. They pointed to opsin losses in Mammalia, Aves, and Squamata, emphasizing that these groups undergo much of their development within the dark confines of a womb or shelled egg. By contrast, most amphibians and fishes undergo free-living larval development in relatively bright environments and appear to have retained large opsin repertoires ( Davies et al. 2015 ; this paper). Opsin diversity imparts sensitivity to a broad range of light wavelengths, which is likely beneficial to larval amphibians and fishes, whose translucent or transparent bodies make them particularly susceptible to photo-oxidative stress and DNA damage caused by exposure to light ( Beaudry et al. 2017 ). However, Beaudry et al. (2017) only considered opsin losses in Squamata at a coarse taxonomic scale and it should be noted that losses in squamates are restricted to ancestrally nocturnal groups (i.e. snakes and geckos; Gemmell et al. 2020 ). While this should cast doubt on the relevance of egg-based development in driving opsin diversity and evolution, the emphasis on development is still worthwhile. For example, recent annotation of the tuatara genome revealed only one opsin loss despite nocturnal ancestry ( Gemmell et al. 2020 ). This maintenance of opsin diversity was hypothesized to result from the tuatara's unusual life history, in which juvenile tuatara often adopt diurnal and arboreal lifestyles to avoid predation by cannibalistic adults, which hunt primarily at night. Thus, tuataras and many frogs experience disparate light environments across life stages, which may explain why these groups demonstrate the lowest documented levels of opsin gene loss among ancestrally nocturnal tetrapod groups.

The importance of adaptive decoupling in driving opsin evolution may further explain why the life history partition was the most frequently significant partition among nonvisual opsins, with eight genes demonstrating a significant difference in ω between direct-developing and biphasic frog species with CmC. The life history partition was also the best fit for five of these genes, and in each case, the direct-developing species demonstrated elevated ω . Considering the adaptive decoupling hypothesis, we predicted that elevated ω values in direct-developing lineages are driven by relaxed selection on nonvisual opsins because these genes are less adaptive in species without larvae. Our RELAX analyses supported this prediction, revealing significant evidence for relaxed selection in six of the genes with significant direct-development CmC partitions ( NEUR1 , NEUR3 , NEUR6 , OPN4m , RRH , and TMT2 ; supplementary table S12, Supplementary Material online). In parallel analyses of frog visual opsins, we did not observe the same pattern of repeated significance across direct-development partitions ( Schott et al. 2024a ), suggesting that the pattern observed in nonvisual opsins is specific to these genes and not necessarily reflective of broadly elevated ω in photosensitivity genes across the genomes of direct-developing species. Collectively, these results support the hypothesis that many nonvisual opsins are especially relevant in species whose complex life histories expose them to disparate light environments across development.

OPN4, Behavioral Light Responses, and Life History

In zebrafish larvae, OPN4 plays a role in triggering nondirectional, stochastic hyperactivity in darkness, resulting in the aggregation of larvae into illuminated areas where they remain due to reduced activity ( Fernandes et al. 2012 ). This behavior, known as dark photokinesis, is understood to drive zebrafish larvae out of dark areas, allowing them to maintain a homeostatic distribution in illuminated waters. Similar behavioral light responses have been observed in frog larvae (e.g. Muntz 1963 ; Jaeger and Hailman 1976 ; Beiswenger 1977 ; Roberts 1978 ; Branch 1983 ; Fraker 2008 ; Ding et al. 2014 ). Given these observations, we hypothesized that OPN4 may play a role in regulating the behavioral light responses of frog larvae. We tested this hypothesis using the direct-development partition from our PAML clade-model analyses with the two OPN4 genes found in frogs. We found a significant difference in selective constraint acting on OPN4m between direct-developing and biphasic frog species, with the former demonstrating elevated ω . Our RELAX analysis indicated that this elevated ω is the result of relaxed selection in direct-developing species. Considering our understanding of OPN4's function in larval zebrafish, the relaxed selection observed in direct-developing frogs may be evidence of reduced functional relevance in species without aquatic larvae. Furthermore, OPN4m is differentially expressed in leopard frog eyes across metamorphosis, with significantly reduced expression in fully metamorphosed juveniles compared to larvae ( Schott et al. 2022 ). Taken together, these findings suggest that the function of OPN4m is especially relevant in larval frogs, potentially contributing to behavioral light responses. However, further functional study in a broad diversity of frogs is needed to support this hypothesis.

PIN and Low-Light Photoreception

PIN was first discovered in the chicken pineal gland in 1994, making it the first opsin to be characterized in an extraocular organ ( Okano et al. 1994 ). Because expression of PIN was initially observed only in the pineal gland, the opsin was thought to function strictly in regulating the production and secretion of melatonin ( Csernus et al. 1999 ). However, low levels of PIN expression were later reported in the outer retina of a gecko ( Taniguchi et al. 2001 ) and more recently in rod cells in the outer retina of a fish and frog ( Sato et al. 2018 ). In addition to being expressed in rod cells, PIN also exhibits a thermal isomerization rate strikingly similar to that of RH1, the rod visual opsin responsible for high-sensitivity dim-light vision. This observation suggests that, at least in the eyes of fishes and frogs, PIN may function as an RH1-like visual pigment contributing to low-light photoreception ( Sato et al. 2018 ). We found a significant difference in selective constraint acting on PIN between diurnal and nondiurnal frogs, with diurnal species having an elevated ω value. Considering PIN's hypothesized role in low-light photoreception, we predicted that this elevated ω value is the result of relaxed selective constraint in diurnal species, which are likely less dependent on low-light photoreception to sense their environments. The RELAX analysis supports this hypothesis, revealing significant evidence for relaxed selection in diurnal species and supporting PIN's hypothesized role in low-light photoreception.

Nonvisual Opsins and Seasonality

Tropically distributed species are typically exposed to less seasonal variation in photoperiod, often causing them to rely on humidity cues to synchronize physiological and behavioral changes with seasonality ( Canavero and Arim 2009 ; Borah et al. 2019 ). In amphibians, seasonal precipitation has historically received the most attention as a potential cue stimulating physiological and behavioral changes related to reproduction ( Feder and Burggren 1992 ; Duellman and Trueb 1994 ; Stebbins and Cohen 1997 ). However, growing evidence indicates that photoperiod sensitivity may be the most proximal factor determining seasonal changes in physiology and activity in amphibians ( Canavero and Arim 2009 ). Nonvisual opsins have been implicated in the seasonal sensitivity of birds (specifically NEUR1; Nakane et al. 2010 ) and may serve a similar function in frogs. To test if selection signatures support this hypothesis, the distribution partition was designed to approximate exposure to seasonal variation in tropical versus nontropical taxa. We found a significant difference in selective constraint of a single gene ( TMT3 ) between tropical and nontropical frogs, with nontropical species demonstrating elevated ω values.

As far as we are aware, nothing is known about TMT3 function in frogs, and more broadly, little is known about its function in vertebrates. We had predicted the distribution partition would be significant for NEUR1, which is reported to regulate seasonal reproductive changes in quail, including thyroid-stimulating hormone secretion and subsequent testicular growth ( Nakane et al. 2014 ). However, NEUR1 showed differences in selective constraint only for the direct-developing partition. Like birds, frogs demonstrate many conspicuous seasonal changes associated with breeding. These changes include hormone secretion and testicular growth ( Delgado et al. 1989 ), as well as nuptial pad development ( Willaert et al. 2013 ) and dynamic sexual dichromatism ( Bell et al. 2017 ). One particularly well-studied example of seasonal reproductive changes is found in subtropical Leishan mustache toads ( Leptobrachium leishanense ). During the breeding season, males of this species develop mustache-like nuptial spines on their maxillary skin. The development of these spines has been linked to seasonal steroid biosynthesis and thyroid hormone secretion ( Li et al. 2019 ), implicating similar hormonal pathways to those activated by NEUR1 in quail. It is possible that TMT3, rather than NEUR1, is contributing to seasonal sensitivity and reproductive changes in frogs. TMT2, a very closely related opsin, has been implicated in behavioral adjustment of medaka fish in response to the onset of cold temperatures ( Zekoll et al. 2021 ), creating a precedent for seasonally linked function within the tmt-opsin group. If TMT3 is playing a role in the seasonal response, we would expect that this elevated ω is the product of adaptive selection in nontropical species due to the greater seasonal variation in the photoperiod they experience. However, our RELAX analysis revealed no signature of relaxed or adaptive selection in nontropical species. This may be because partitioning species as tropical or nontropical fails to capture exactly which species rely on photoperiod to cue seasonal reproduction. A better test of TMT3's relevance to seasonal reproduction might be to partition frogs that are observed to reproduce continuously throughout the year, such as the tropical toad Duttaphrynus melanostictus ( Jørgensen et al. 1986 ) and frogs that reproduce on a strictly seasonal basis. This test would require a more extensive understanding of seasonal reproduction in frogs than is available in current literature, as well as denser taxonomic sampling of nonvisual opsins. Given our findings, TMT3 warrants further study to clarify its role in frogs, including the possibility of regulating seasonal reproductive changes and as a candidate for the basis of seasonal sensitivity in frogs.

Frogs offer a compelling system in which to study the evolution of light sensitivity across diverse ecologies, morphologies, and life history strategies. We found that frogs have retained a diverse repertoire of nonvisual opsins, with 14 genes consistently recovered from frog eye transcriptomes. At the genomic level, frogs appear to have broadly maintained all 18 ancestral vertebrate nonvisual opsins and thus demonstrate the lowest documented rate of opsin gene loss among ancestrally nocturnal tetrapod groups. Signatures of positive selection were detected in a subset of these genes. We also found variation in selective constraint between discrete ecological, life history, and morphological classes, which may reflect functional adaptation in frog nonvisual opsin genes. Our findings provide genomic support for emerging hypotheses of nonvisual opsin evolution, including the role of PIN in low-light photoreception and the adaptive importance of many nonvisual opsins in species with complex life histories.

Species Sampling

Our sampling included a total of 92 whole-eye transcriptomes from 81 species, 19 genomes from 15 additional species, and multitissue transcriptomes or independently annotated genes from 6 additional species. Of the 92 whole-eye transcriptomes, 83 of these samples were collected from adult frogs, and the remaining nine were collected from larval frogs ( supplementary table S2, Supplementary Materials online). Frogs were sampled from wild populations in Australia, Brazil, Cameroon, Ecuador, Equatorial Guinea, French Guiana, Gabon, the Seychelles, the United Kingdom, and the United States ( supplementary table S2, Supplementary Materials online). Additional species were obtained from commercial dealers or captive colonies. Most individuals were kept in complete darkness (i.e. were dark adapted) for 3+ h prior to euthanasia (via immersion in a solution of MS222) because one eye was removed for microspectrophotometry measurements as part of another study ( Schott et al. 2024a ). Whole eyes were extracted, punctured, and placed in RNAlater (Ambion) for at least 24 h at 4 °C to allow the RNAlater to saturate the cells prior to freezing and storage at −80 °C until use. Some samples were collected at remote field sites and were kept as cool as possible in RNAlater prior to freezing at −80 °C at the earliest opportunity. Voucher specimens and tissues for further genetic analysis were accessioned in natural history museums ( supplementary table S2, Supplementary Materials online). To supplement the phylogenetic and ecological diversity of species we collected, we searched GenBank for publicly available frog genomes and multitissue transcriptomes to include in our analyses. These included 19 genomes and 6 multitissue transcriptomes or independently annotated genes from adult, larval, or mixed adult/larval frog samples ( supplementary table S3, Supplementary Materials online). Our combined sampling includes 102 species, representing 34 of 56 currently recognized frog families ( Frost 2024 ; Fig. 3 ).

Transcriptome Sequencing and Assembly

Total RNA was extracted from whole eyes using the Promega Total SV RNA Extraction Kit (Promega). Tissue was homogenized in lysis buffer using the Qiagen Tissuelyzer (10 min at 20 Hz). Messenger RNA library construction was performed using the Kapa HyperPrep mRNA Stranded with Riboerase Kit (Roche). Each indexed sample was pooled in equimolar amounts and sequenced with paired-end 150-bp reads on a HiSeq4000 at the QB3 Genomics Core at the University of California, Berkeley or a NovaSeq6000 at the UT Arlington North Texas Genome Center. Prior to assembly, adapters and low-quality bases ( q < 5) were removed with TrimGalore! ( https://www.bioinformatics.babraham.ac.uk/projects/trim_galore/ ), which implements Cutadapt ( Martin 2011 ). Read pairs shorter than 36 bp after trimming were discarded, as were unpaired reads. The quality of processed reads was assessed with FastQC ( http://www.bioinformatics.babraham.ac.uk/projects/fastqc/ ). Transcriptome assembly of each sample was performed de novo using Trinity ( Grabherr et al. 2011 ) incorporating all paired reads following the standard protocol.

Nonvisual Opsin Sequence Recovery

Eighteen nonvisual opsin coding sequences were extracted from frog genomes, consisting of six neuropsins ( NEUR1 to 6 ), encephalopsin ( OPN3 ), two melanopsins ( OPN4m and OPN4x ), PAR , PARA , PIN , retinal g-protein coupled receptor ( RGR ), RRH , three teleost multiple tissue opsins ( TMT1 to 3 ), and VAOP , using query sequences from tetrapods ( Gemmell et al. 2020 ) and nucleotide BLAST searches ( Altschul et al. 1990 ). We used the discontiguous megablast approach with an e -value cutoff of 1 × 10 −10 to identify transcript hits, which were imported into MEGA, aligned with the reference, and manually trimmed to the coding sequence ensuring the longest open-reading frame was recovered. Gene identifications were confirmed by BLAST searches against the NCBI nucleotide database and later by phylogenetic analysis. Partial transcripts of the same gene (e.g. due to incomplete transcript assembly or sequence coverage) were combined to produce as complete a coding sequence as possible. We found that fully automated approaches often produced incomplete or incorrect transcripts. Complete sequences were compiled and in turn used as queries for additional BLAST extraction from the frog eye transcriptomes and genomes and for searches against the NCBI nucleotide database. BLAST results from whole genomes were extracted using a custom parser. Recovered coding sequences for each gene were assembled and aligned using codon alignment with MACSE ( Ranwez et al. 2011 ). Alignments were manually edited to remove terminal stop codons, remove unique insertions, and trim nonhomologous regions that were due to annotation errors or transcript variants. When present, premature stop codons were converted to sequence gaps to enable their inclusion in downstream analyses ( Yohe et al. 2017 ; Janiak et al. 2018 ). Several genes showed considerable variation at the beginning or ends and these were aligned using PRANK codon alignment, which can better resolve insertions, but at the cost of increased computation time ( Löytynoja and Goldman 2005 ). A coding sequence was considered whole if it was recovered in entirety from start to stop codon, and partial if the sequence was incomplete but more than 50% of codons were recovered relative to the reference sequence. Coding sequences were excluded from analyses if less than 50% of codons were recovered.

Species Trait Classification

Frog species were partitioned into seven binary trait categories that we predicted to influence the evolution of nonvisual light detection. The adult activity period partition separated diurnal (including strictly diurnal and mixed diurnal/nocturnal species) vs. nondiurnal species. Our three adult habitat partitions separated aquatic (including semiaquatic) vs. nonaquatic, scansorial vs. nonscansorial, and secretive (defined as species with lifestyles generally dominated by low-intensity light, including fossorial, burrowing, and leaf-litter species) vs. nonsecretive. We used a distribution partition as a proxy for seasonality, separating tropical vs. nontropical species. Our life history partition separated direct developing vs. biphasic species. Finally, our pupil shape partition separated species with elongated (horizontal or vertical pupils) vs. nonelongated pupils (other symmetrical shapes), because this distinction appears to be ecologically meaningful in frogs ( Thomas et al. 2022a ). Partitions for all traits are illustrated in Fig. 3 . We used peer-reviewed literature, online natural history resources, field guides, and field observations to partition species into these trait categories ( supplementary table S4, Supplementary Materials online). These partitions largely conform to trait scoring in previous studies of frog visual biology ( Thomas et al. 2020 , 2022a , 2022b ; Mitra et al. 2022 ; Schott et al. 2024a ).

Selection Analyses

To estimate the strength and form of selection acting on anuran nonvisual opsins, each data set was analyzed using codon-based likelihood models from the codeml program of the PAML 4 software package ( Yang 2007 ). Maximum likelihood (ML) gene trees were inferred using PhyML 3 ( Guindon and Gascuel 2003 ) under the GTR + G + I nucleotide model with a BioNJ starting tree, the best of NNI and SPR tree improvement, and approximate Bayes-like branch supports (aByes; Anisimova et al. 2011 ). Because individual gene trees do not always reflect species’ evolutionary histories, it is a common approach in selection analyses to compare results from gene-tree topologies to those that reflect the current understanding of evolutionary relationships among species (species-tree topology) to ensure that results are robust to minor topological differences (e.g. Schott et al. 2018 ; Van Nynatten et al. 2021 ). To produce species-tree topologies for each gene, we generated a topology that matched expected species relationships based on several large-scale phylogenies ( Pyron and Wiens 2011 ; Feng et al. 2017 ; Jetz and Pyron 2018 ; Streicher et al. 2018 ) and trimmed these to match the taxon sampling of the individual genes ( Boyette et al 2024 ).

All analyses were performed twice; once using the ML gene-tree topology, and again using the species-tree topology. All topologies were rooted on Ascaphus truei and modified to contain the basal trichotomy required by PAML 4. PAML analyses were carried out for each alignment with the two tree topologies using the BLASTPHYME interface ( Schott et al. 2019 ). Random site models (M0, M1a, M2a, M2a_rel, M3, M7, M8a, and M8) were used to estimate the rates of nonsynonymous to synonymous nucleotide substitutions ( ω or d N / d S ), infer alignment-wide selection patterns, and test for positive selection acting on nonvisual opsin genes. For genes with evidence of positively selected sites, we used BUSTED ( Murrell et al. 2015 ), implemented on the Datamonkey webserver ( Delport et al. 2010 ), to test for evidence of synonymous rate variation that could influence our estimates of positive selection. To test if shifts in selection among nonvisual opsins corresponded to variation in adult activity period, adult habitat, distribution, life history, and pupil shape, we used PAML CmC ( Bielawski and Yang 2004 ). These clade models test for evidence of a codon site class demonstrating a shift in selection between prepartitioned “foreground” and “background” groups (e.g. diurnal frogs and nondiurnal frogs), which can be any combination of branches and clades within a phylogeny. CmC is compared to the null model M2a_rel and assumes that some sites evolve conservatively across the phylogeny (two classes of sites where 0 < ω 0 < 1 and ω 1 = 1), whereas a class of sites is free to evolve differently among two or more partitions (e.g. ω D1 > 0 and ω D1 ≠ ω D2 > 0; Weadick and Chang 2012 ). The partition schemes were tested in each nonvisual opsin, with each partition corresponding to one of the seven binary trait categories illustrated in Fig. 3 . PAML analyses were run using varying ω starting values (1, 2, and 3) to increase the likelihood of finding global optima. If models failed to converge (worse likelihood score than the null model), we increased the range and frequency of starting values (e.g. 0.5 intervals from 0.5 to 3.5). Significance and best fit among model pairs were determined using a LRT with a χ 2 distribution and a significance threshold of 5% ( α = 0.05).

In cases where PAML analyses found significantly elevated ω in a particular group of interest (e.g. elevated ω in diurnal frogs compared to nondiurnal frogs), we used RELAX ( Wertheim et al. 2015 ), implemented on the Datamonkey web server ( Delport et al. 2010 ), to determine if the elevated ω was the product of relaxed selective constraint (i.e. lack of selection against a change) or adaptive selection (i.e. selection for a change). Such a distinction is useful when attempting to interpret the biological significance of an elevated ω value. RELAX produces a selection intensity parameter, or K value, which modulates the degree to which different ω site classes diverge from neutrality ( ω = 1) in prepartitioned background and foreground groups. When K < 1, this indicates relaxed selection on foreground group branches compared to background group branches. Alternatively, when K > 1, this indicates adaptive selection on foreground group branches compared to background group branches.

Supplementary material is available at Molecular Biology and Evolution online.

We thank the following field companions who helped obtain specimens for this work: Hannah Augustijnen, Abraham G. Bamba Kaya, C. Guillherme Becker, Gabriela Bittencourt-Silva, Itzue Calviedes Solis, Patrick Campbell, Diego Cisneros-Heredia, Simon Clulow, Christian L. Cox, Mateo Davila, Paul Doughty, Juvencio Eko Mengue, TJ Firneno, Carl Franklin, Philippe Gaucher, Ivan Gomez- Mestre, Shakuntala Devi Gopal, Jon and Krittee Gower, Célio F. B. Haddad, Anthony Herrel, Sunita Janssenswillen, Jim Labisko, H. Christoph Liedtke, Simon Loader, Simon Maddock, Michael Mahony, Renato A. Martins, Matthew McElroy, Christopher Michaels, Nicki Mitchell, Justino Nguema Mituy, Diego Moura, Martin Nsue, Daniel M. Portik, Ivan Prates, Kim Roelants, Corey Roelke, Lauren Scheinberg, Bruno Simões, Ben Tapley, Elie Tobi, Rose Upton, Mark Wilkinson, and Molly Womack. We thank the Gabon Biodiversity Program and Bioko Biodiversity Protection Program for logistical support in the field; Grant Webster, Scott Keogh, and Jared Grummer for advice on where to find key species; Carolina Reyes-Puig for help with specimen numbers; and Jodi Rowley and Stephen Mahony for assistance exporting tissues for analysis. Sampling was conducted following IACUC protocols (NHMUK, NMNH 2016-012, UNESP Rio Claro CEUA-23/2017, UTA A17.005, ANU A2017/47) and with scientific research authorizations (the United States: Texas Parks and Wildlife Division SR-0814-159, North Cascades National Parks NCCO-2018-SCI-0009; Brazil: ICMBio MMA 22511-4, ICMBio SISBIO 30309-12; the United Kingdom: NE Licence WML-OR04; French Guiana: RAA: R03-2018-06-12-006; Gabon: CENAREST AR0020/17; Australia: New South Wales National Parks & Wildlife Service SL102014, Queensland Department of National Parks WITK18705517; Equatorial Guinea: INDEFOR-AP 0130/020-2019). This research was supported by grants from the Natural Environment Research Council, UK (NE/R002150/1), the National Science Foundation (DEB-1655751), and an NSERC Discovery Grant (to R.K.S.). J.L.B. was supported by the NMNH Natural History Research Experience REU program (NSF-OCE:1560088). The authors thank two anonymous reviewers and the Associate Editor for constructive feedback that substantially improved the manuscript.

The data underlying this article are available on NCBI under Bioproject PRJNA1073881 and on Zenodo ( Boyette et al. 2024 ; Schott, Fujita, Streicher, Gower, Thomas, and Bell 2024 ), as well as in the Supplementary Materials online. See supplementary table S2, Supplementary Materials online for individual BioSample and SRA accession numbers.

Altschul   SF , Gish   W , Miller   W , Myers   EW , Lipman   DJ . 1990 . Basic local alignment search tool . J Mol Biol   215 ( 3 ): 403 – 410 . https://doi.org/10.1016/S0022-2836(05)80360-2 .

Google Scholar

Anderson   SR , Wiens   JJ . 2017 . Out of the dark: 350 million years of conservatism and evolution in diel activity patterns in vertebrates . Evolution   71 ( 8 ): 1944 – 1959 . https://doi.org/10.1111/evo.13284 .

Andrabi   M , Upton   BA , Lang   RA , Vemaraju   S . 2023 . An expanding role for nonvisual opsins in extraocular light sensing physiology . Annu Rev Vis Sci   9 ( 1 ): 245 – 267 . https://doi.org/10.1146/annurev-vision-100820-094018 .

Anisimova   M , Gil   M , Dufayard   J-F , Dessimoz   C , Gascuel   O . 2011 . Survey of branch support methods demonstrates accuracy, power, and robustness of fast likelihood-based approximation schemes . Syst Biol   60 ( 5 ): 685 – 699 . https://doi.org/10.1093/sysbio/syr041 .

Beaudry   FEG , Iwanicki   TW , Mariluz   BRZ , Darnet   S , Brinkmann   H , Schneider   P , Taylor   JS . 2017 . The non-visual opsins: eighteen in the ancestor of vertebrates, astonishing increase in ray-finned fish, and loss in amniotes . J Exp Zool B: Mol Dev Evol   328 ( 7 ): 685 – 696 . https://doi.org/10.1002/jez.b.22773 .

Beiswenger   RE . 1977 . Diel patterns of aggregative behavior in tadpoles of bufo americanus, in relation to light and temperature . Ecology   58 ( 1 ): 98 – 108 . https://doi.org/10.2307/1935111 .

Bell   RC , Webster   GN , Whiting   MJ . Breeding biology and the evolution of dynamic sexual dichromatism in frogs . J Evol Biol . 2017 : 30 ( 12 ): 2104 – 2115 . https://doi.org/10.1111/jeb.13170 .

Bielawski   JP , Yang   Z . 2004 . A maximum likelihood method for detecting functional divergence at individual codon sites, with application to gene family evolution . J Mol Evol   59 ( 1 ): 121 – 132 . https://doi.org/10.1007/s00239-004-2597-8 .

Borah   BK , Renthlei   Z , Trivedi   AK . 2019 . Seasonality in terai tree frog ( Polypedates teraiensis ): role of light and temperature in regulation of seasonal breeding . J Photochem Photobiol B: Biol   191 : 44 – 51 . https://doi.org/10.1016/j.jphotobiol.2018.12.005 .

Borges   R , Johnson   WE , O’Brien   SJ , Gomes   C , Heesy   CP , Antunes   A . 2018 . Adaptive genomic evolution of opsins reveals that early mammals flourished in nocturnal environments . BMC Genomics   19 ( 1 ): 121 . https://doi.org/10.1186/s12864-017-4417-8 .

Boyette   JL , Bell   RC , Fujita   MK , Thomas   KN , Streicher   JW , Gower   DJ , Schott   RK . 2024 . Data from: diversity and molecular evolution of non-visual opsin genes across environmental, developmental, and morphological adaptations in frogs. [Data set] . Zenodo . https://doi.org/10.5281/zenodo.10573191 .

Branch   L . 1983 . Social behavior of the tadpoles of phyllomedusa vaillanti . Copeia   1983 ( 2 ): 420 . https://doi.org/10.2307/1444385 .

Canavero   A , Arim   M . 2009 . Clues supporting photoperiod as the main determinant of seasonal variation in amphibian activity . J Nat History   43 ( 47-48 ): 2975 – 2984 . https://doi.org/10.1080/00222930903377539 .

Csernus   V , Becher   P , Mess   B . 1999 . Wavelength dependency of light-induced changes in rhythmic melatonin secretion from chicken pineal gland in vitro . Neuro Endocrinol Lett   20 : 299 – 304 .

Davies   WIL , Cowing   JA , Bowmaker   JK , Carvalho   LS , Gower   DJ , Hunt   DM . 2009 . Shedding light on serpent sight: the visual pigments of henophidian snakes . J Neurosci.   29 ( 23 ): 7519 – 7525 . https://doi.org/10.1523/JNEUROSCI.0517-09.2009 .

Davies   WIL , Tamai   TK , Zheng   L , Fu   JK , Rihel   J , Foster   RG , Whitmore   D , Hankins   MW . 2015 . An extended family of novel vertebrate photopigments is widely expressed and displays a diversity of function . Genome Res   25 ( 11 ): 1666 – 1679 . https://doi.org/10.1101/gr.189886.115 .

Delgado   MJ , Gutirrez   P , Alonso-Bedate   M . Seasonal cycles in testicular activity in the frog, Rana perezi . Gen Comp Endocrinol . 1989 : 73 ( 1 ): 1 – 11 . https://doi.org/10.1016/0016-64808990049-X .

Delport   W , Poon   AFY , Frost   SDW , Kosakovsky Pond   SL . 2010 . Datamonkey 2010: a suite of phylogenetic analysis tools for evolutionary biology . Bioinformatics   26 ( 19 ): 2455 – 2457 . https://doi.org/10.1093/bioinformatics/btq429 .

Ding   G-H , Lin   Z-H , Zhao   L-H , Fan   X-L , Wei   L . Effects of light intensity on activity in four sympatric anuran tadpoles . Zool Res . 2014 : 35 : 332 . https://doi.org/10.13918/j.issn.2095-8137.2014.4.332 .

Do   MTH . 2019 . Melanopsin and the intrinsically photosensitive retinal ganglion cells: biophysics to behavior . Neuron   104 ( 2 ): 205 – 226 . https://doi.org/10.1016/j.neuron.2019.07.016 .

Duellman   WE , Trueb   L . Biology of amphibians . Baltimore (MD) : Johns Hopkins University Press ; 1994 .

Google Preview

Ebenman   B . 1992 . Evolution in organisms that change their niches during the life cycle . Am Nat   139 ( 5 ): 990 – 1021 . https://doi.org/10.1086/285370 .

Emerling   CA . 2017 . Archelosaurian color vision, parietal eye loss, and the crocodylian nocturnal bottleneck . Mol Biol Evol   34 ( 3 ): 666 – 676 . https://doi.org/10.1093/molbev/msw265 .

Emerling   CA , Springer   MS . 2014 . Eyes underground: regression of visual protein networks in subterranean mammals . Mol Phylogenet Evol   78 : 260 – 270 . https://doi.org/10.1016/j.ympev.2014.05.016 .

Feder   ME , Burggren   WW . Environmental physiology of the amphibians . Chicago (IL) : University of Chicago Press ; 1992 . https://press.uchicago.edu/ucp/books/book/chicago/E/bo3636401.html .

Feng   Y-J , Blackburn   DC , Liang   D , Hillis   DM , Wake   DB , Cannatella   DC , Zhang   P . Phylogenomics reveals rapid, simultaneous diversification of three major clades of Gondwanan frogs at the Cretaceous–Paleogene boundary . Proc Natl Acad Sci . 2017 : 114 : E5864 . https://doi.org/10.1073/pnas.1704632114 .

Fernandes   AM , Fero   K , Arrenberg   AB , Bergeron   SA , Driever   W , Burgess   HA . 2012 . Deep brain photoreceptors control light-seeking behavior in zebrafish larvae . Curr Biol   22 ( 21 ): 2042 – 2047 . https://doi.org/10.1016/j.cub.2012.08.016 .

Foster   RG , Bellingham   J . 2004 . Inner retinal photoreceptors (IRPs) in mammals and teleost fish . Photochem Photobiol Sci.   3 ( 6 ): 617 – 627 . https://doi.org/10.1039/b400092g .

Fraker   ME . 2008 . The influence of the circadian rhythm of green frog ( Rana clamitans ) tadpoles on their antipredator behavior and the strength of the nonlethal effects of predators . Am Nat   171 ( 4 ): 545 – 552 . https://doi.org/10.1086/528961 .

Frost   DR.   2024 . Amphibian species of the world: an online reference. Version 6.2 (January 26, 2024). Electronic Database accessible at https://amphibiansoftheworld.amnh.org . American Museum of Natural History, New York, USA [Internet]. https://amphibiansoftheworld.amnh.org/index.php

Gemmell   NJ , Rutherford   K , Prost   S , Tollis   M , Winter   D , Macey   JR , Adelson   DL , Suh   A , Bertozzi   T , Grau   JH , et al.    2020 . The tuatara genome reveals ancient features of amniote evolution . Nature   584 ( 7821 ): 403 – 409 . https://doi.org/10.1038/s41586-020-2561-9 .

Gerkema   MP , Davies   WIL , Foster   RG , Menaker   M , Hut   RA . The nocturnal bottleneck and the evolution of activity patterns in mammals . Proc R Soc B Biol Sci . 2013 : 280 ( 1765 ): 20130508 . https://doi.org/10.1098/rspb.2013.0508 .

Gower   DJ , Hauzman   E , Simões   BF , Schott   RK . Eyes, vision and the origins and early evolution of snakes. In: Gower   DJ , Zaher   H , editors. The origin and early evolutionary history of snakes . Cambridge : Cambridge University Press ; 2022 . p. 316 – 348 .

Göz   D , Studholme   K , Lappi   DA , Rollag   MD , Provencio   I , Morin   LP . 2008 . Targeted destruction of photosensitive retinal ganglion cells with a saporin conjugate alters the effects of light on mouse circadian rhythms . PLoS One   3 ( 9 ): e3153 . https://doi.org/10.1371/journal.pone.0003153 .

Grabherr   MG , Haas   BJ , Yassour   M , Levin   JZ , Thompson   DA , Amit   I , Adiconis   X , Fan   L , Raychowdhury   R , Zeng   Q , et al.    2011 . Trinity: reconstructing a full-length transcriptome without a genome from RNA-Seq data . Nat Biotechnol   29 ( 7 ): 644 – 652 . https://doi.org/10.1038/nbt.1883 .

Griffiths   RA , Mylotte   JMGAVJ . Diel patterns of activity and vertical migration in tadpoles of the common toad, Bufo bufo . Herpetol J . 1988 : 1 : 223 – 226 .

Guindon   S , Gascuel   O . 2003 . A simple, fast, and accurate algorithm to estimate large phylogenies by maximum likelihood . Syst Biol   52 ( 5 ): 696 – 704 . https://doi.org/10.1080/10635150390235520 .

Halford   S , Freedman Melanie   S , Bellingham   J , Inglis   SL , Poopalasundaram   S , Soni   BG , Foster   RG , Hunt   DM . 2001 . Characterization of a novel human opsin gene with wide tissue expression and identification of embedded and flanking genes on chromosome 1q43 . Genomics   72 ( 2 ): 203 – 208 . https://doi.org/10.1006/geno.2001.6469 .

Hunt   DM , Collin   SP . The evolution of photoreceptors and visual photopigments in vertebrates. In: Hunt   DM , Hankins   MW , Collin   SP , Marshall   NJ , editors. Evolution of visual and non-visual pigments. Springer Series in Vision Research . Boston, MA : Springer US ; 2014 . p. 163 – 217 . https://doi.org/10.1007/978-1-4614-4355-1_6

Jaeger   RG , Hailman   JP . 1976 . Ontogenetic shift of spectral phototactic preferences in anuran tadpoles . J Comp Physiol Psychol   90 ( 10 ): 930 – 945 . https://doi.org/10.1037/h0077275 .

Janiak   MC , Chaney   ME , Tosi   AJ . 2018 . Evolution of acidic mammalian chitinase genes (CHIA) is related to body mass and insectivory in primates . Mol Biol Evol   35 ( 3 ): 607 – 622 . https://doi.org/10.1093/molbev/msx312 .

Jetz   W , Pyron   RA . 2018 . The interplay of past diversification and evolutionary isolation with present imperilment across the amphibian tree of life . Nat Ecol Evol   2 ( 5 ): 850 – 858 . https://doi.org/10.1038/s41559-018-0515-5 .

Jørgensen   CB , Shakuntala   K , Vijayakumar   S . Body size, reproduction and growth in a tropical toad, bufo melanostictus, with a comparison of ovarian cycles in tropical and temperate zone anurans . Oikos . 1986 : 46 ( 3 ): 379 . https://doi.org/10.2307/3565838 .

Kawamura   S , Kubotera   N . 2004 . Ancestral loss of short wave-sensitive cone visual pigment in lorisiform prosimians, contrasting with its strict conservation in other prosimians . J Mol Evol   58 ( 3 ): 314 – 321 . https://doi.org/10.1007/s00239-003-2553-z .

Keenan   WT , Rupp   AC , Ross   RA , Somasundaram   P , Hiriyanna   S , Wu   Z , Badea   TC , Robinson   PR , Lowell   BB , Hattar   SS . 2016 . A visual circuit uses complementary mechanisms to support transient and sustained pupil constriction . eLife   5 : e15392 . https://doi.org/10.7554/eLife.15392 .

Kelley   JL , Davies   WIL . The biological mechanisms and behavioral functions of opsin-based light detection by the skin . Front Ecol Evol . 2016 : 4 . https://doi.org/10.3389/fevo.2016.00106 .

Li   J , Yu   H , Wang   W , Fu   C , Zhang   W , Han   F , Wu   H . Genomic and transcriptomic insights into molecular basis of sexually dimorphic nuptial spines in Leptobrachium leishanense . Nat Commun . 2019 : 10 ( 1 ). https://doi.org/10.1038/s41467-019-13531-5 .

Löytynoja   A , Goldman   N.   2005 . An algorithm for progressive multiple alignment of sequences with insertions . Proc Natl Acad Sci . 102 ( 30 ): 10557 – 10562 . https://doi.org/10.1073/pnas.0409137102 .

Malmström   T , Kröger   RHH . 2006 . Pupil shapes and lens optics in the eyes of terrestrial vertebrates . J Exp Biol   209 ( 1 ): 18 – 25 . https://doi.org/10.1242/jeb.01959 .

Martin   M . 2011 . Cutadapt removes adapter sequences from high-throughput sequencing reads . EMBnet J   17 ( 1 ): 10 – 12 . https://doi.org/10.14806/ej.17.1.200 .

Meredith   RW , Gatesy   J , Emerling   CA , York   VM , Springer   MS . 2013 . Rod monochromacy and the coevolution of cetacean retinal opsins . PLoS Genet   9 ( 4 ): e1003432 . https://doi.org/10.1371/journal.pgen.1003432 .

Mitra   AT , Womack   MC , Gower   DJ , Streicher   JW , Clark   B , Bell   RC , Schott   RK , Fujita   MK , Thomas   KN.   2022 . Ocular lens morphology is influenced by ecology and metamorphosis in frogs and toads . Proc R Soc B: Biol Sci   289 ( 1987 ): 20220767 . https://doi.org/10.1098/rspb.2022.0767 .

Moen   DS , Irschick   DJ , Wiens   JJ.   2013 . Evolutionary conservatism and convergence both lead to striking similarity in ecology, morphology and performance across continents in frogs . Proc R Soc B: Biol Sci   280 ( 1773 ): 20132156 . https://doi.org/10.1098/rspb.2013.2156 .

Muntz   WRA . 1963 . The development of phototaxis in the frog ( Rana temporaria ) . J Exp Biol   40 ( 2 ): 371 – 379 . https://doi.org/10.1242/jeb.40.2.371 .

Murrell   B , Weaver   S , Smith   MD , Wertheim   JO , Murrell   S , Aylward   A , Eren   K , Pollner   T , Martin   DP , Smith   DM , et al.    2015 . Gene-wide identification of episodic selection . Mol Biol Evol   32 ( 5 ): 1365 – 1371 . https://doi.org/10.1093/molbev/msv035 .

Nakane   Y , Ikegami   K , Ono   H , Yamamoto   N , Yoshida   S , Hirunagi   K , Ebihara   S , Kubo   Y , Yoshimura   T . 2010 . A mammalian neural tissue opsin (Opsin 5) is a deep brain photoreceptor in birds . PNAS   107 ( 34 ): 15264 – 15268 . https://doi.org/10.1073/pnas.1006393107 .

Nakane   Y , Shimmura   T , Abe   H , Yoshimura   T . 2014 . Intrinsic photosensitivity of a deep brain photoreceptor . Curr Biol   24 ( 13 ): R596 – R597 . https://doi.org/10.1016/j.cub.2014.05.038 .

Okano   T , Yoshizawa   T , Fukada   Y . 1994 . Pinopsin is a chicken pineal photoreceptive molecule . Nature   372 ( 6501 ): 94 – 97 . https://doi.org/10.1038/372094a0 .

Pinto   BJ , Nielsen   SV , Gamble   T . 2019 . Transcriptomic data support a nocturnal bottleneck in the ancestor of gecko lizards . Mol Phylogenet Evol   141 : 106639 . https://doi.org/10.1016/j.ympev.2019.106639 .

Pyron   AR , Wiens   JJ . 2011 . A large-scale phylogeny of Amphibia including over 2800 species, and a revised classification of extant frogs, salamanders, and caecilians . Mol Phylogenet Evol   61 ( 2 ): 543 – 583 . https://doi.org/10.1016/j.ympev.2011.06.012 .

Radu   RA , Hu   J , Peng   J , Bok   D , Mata   NL , Travis   GH . 2008 . Retinal pigment epithelium-retinal g protein receptor-opsin mediates light-dependent translocation of all-trans-retinyl esters for synthesis of visual chromophore in retinal pigment epithelial cells . J Biol Chem   283 ( 28 ): 19730 – 19738 . https://doi.org/10.1074/jbc.M801288200 .

Ranwez   V , Harispe   S , Delsuc   F , Douzery   EJP . 2011 . MACSE: multiple alignment of coding sequences accounting for frameshifts and stop codons . PLoS One   6 ( 9 ): e22594 . https://doi.org/10.1371/journal.pone.0022594 .

Rios   MN , Marchese   NA , Guido   ME . Expression of non-visual opsins opn3 and opn5 in the developing inner retinal cells of birds. Light-responses in müller glial cells . Front Cell Neurosci . 2019 : 13 . https://doi.org/10.3389/fncel.2019.00376 .

Roberts   A . 1978 . Pineal eye and behaviour in Xenopus tadpoles . Nature   273 ( 5665 ): 774 – 775 . https://doi.org/10.1038/273774a0 .

Sato   K , Yamashita   T , Kojima   K , Sakai   K , Matsutani   Y , Yanagawa   M , Yamano   Y , Wada   A , Iwabe   N , Ohuchi   H , et al.    2018 . Pinopsin evolved as the ancestral dim-light visual opsin in vertebrates . Commun Biol   1 ( 1 ): 1 – 10 . https://doi.org/10.1038/s42003-018-0164-x .

Schott   RK , Bell   RC , Loew   ER , Thomas   KN , Gower   DJ , Streicher   JW , Fujita   MK . 2022 . Transcriptomic evidence for visual adaptation during the aquatic to terrestrial metamorphosis in leopard frogs . BMC Biol   20 ( 1 ): 138 . https://doi.org/10.1186/s12915-022-01341-z .

Schott   RK , Fujita   MK , Streicher   JW , Gower   DJ , Thomas   KN , Bell   RC . Frog eye transcriptome assemblies [data set] . Zenodo . 2024b . https://doi.org/10.5281/zenodo.10620583 .

Schott   RK , Fujita   MK , Streicher   JW , Gower   DJ , Thomas   KN , Loew   ER , Bamba Kaya   AG , Bittencourt-Silva   GB , Guillherme Becker   C , Cisneros-Heredia   D , et al. Diversity and evolution of frog visual opsins: spectral tuning and adaptation to distinct light environments . Mol Biol Evol.   2024a : 41 ( 4 ): msae049 . https://doi.org/10.1093/molbev/msae049 .

Schott   RK , Gow   D , Chang   BS.   2019 . BlastPhyMe: a toolkit for rapid generation and analysis of protein-coding sequence datasets. bioRxiv 059881. https://doi.org/10.1101/059881 , preprint: not peer reviewed.

Schott   RK , Van Nynatten   A , Card   DC , Castoe   TA , Chang   BSW . 2018 . Shifts in selective pressures on snake phototransduction genes associated with photoreceptor transmutation and dim-light ancestry . Mol Biol Evol   35 ( 6 ): 1376 – 1389 . https://doi.org/10.1093/molbev/msy025 .

Stebbins   RC , Cohen   NW . A natural history of amphibians . Princeton (NJ) : Princeton University Press ; 1997 . https://press.princeton.edu/books/paperback/9780691102511/a-natural-history-of-amphibians .

Steindal   IAF , Whitmore   D . Zebrafish circadian clock entrainment and the importance of broad spectral light sensitivity . Front Physiol . 2020 : 11 . https://doi.org/10.3389/fphys.2020.01002/full .

Streicher   JW , Miller   EC , Guerrero   PC , Correa   C , Ortiz   JC , Crawford   AJ , Pie   MR , Wiens   JJ . 2018 . Evaluating methods for phylogenomic analyses, and a new phylogeny for a major frog clade (Hyloidea) based on 2214 loci . Mol Phylogenet Evol   119 : 128 – 143 . https://doi.org/10.1016/j.ympev.2017.10.013 .

Taniguchi   Y , Hisatomi   O , Yoshida   M , Tokunaga   F . 2001 . Pinopsin expressed in the retinal photoreceptors of a diurnal gecko . FEBS Lett   496 ( 2–3 ): 69 – 74 . https://doi.org/10.1016/S0014-5793(01)02395-X .

Terakita   A . 2005 . The opsins . Genome Biol   6 ( 3 ): 213 . https://doi.org/10.1186/gb-2005-6-3-213 .

Thomas   KN , Gower   DJ , Bell   RC , Fujita   MK , Schott   RK , Streicher   JW.   2020 . Eye size and investment in frogs and toads correlate with adult habitat, activity pattern and breeding ecology . Proc R Soc B: Biol Sci   287 ( 1935 ): 20201393 . https://doi.org/10.1098/rspb.2020.1393 .

Thomas KN, Gower DJ, Streicher JW, Bell RC, Fujita MK, Schott RK, Liedtke HC, Haddad CFB, Becker CG, Cox CL, et al.   Ecology drives patterns of spectral transmission in the ocular lenses of frogs and salamanders. Funct Ecol. 2022b: 36 :850–864.

Thomas   KN , Rich   C , Quock   RC , Streicher   JW , Gower   DJ , Schott   RK , Fujita   MK , Douglas   RH , Bell   RC . Diversity and evolution of amphibian pupil shapes . Biol J Linn Soc . 2022a : 137 ( 3 ): 434 – 449 . https://doi.org/10.1093/biolinnean/blac095 .

Tsukamoto   H . Diversity and functional properties of bistable photopigments. In: Hunt   DM , Hankins   MW , Collin   SP , Marshall   NJ , editors. Evolution of visual and non-visual pigments. Springer Series in Vision Research . Boston (MA) : Springer US ; 2014 . p. 219 – 239 . https://doi.org/10.1007/978-1-4614-4355-1_7

Van Nynatten   A , Castiglione   GM , Gutierrez   EdeA , Lovejoy   NR , Chang   BSW . 2021 . Recreated ancestral opsin associated with marine to freshwater croaker invasion reveals kinetic and spectral adaptation . Mol Biol Evol   38 ( 5 ): 2076 – 2087 . doi: 10.1093/molbev/msab008 .

Weadick   CJ , Chang   BSW . 2012 . An improved likelihood ratio test for detecting site-specific functional divergence among clades of protein-coding genes . Mol Biol Evol   29 ( 5 ): 1297 – 1300 . https://doi.org/10.1093/molbev/msr311 .

Wertheim   JO , Murrell   B , Smith   MD , Kosakovsky Pond   SL , Scheffler   K . 2015 . RELAX: detecting relaxed selection in a phylogenetic framework . Mol Biol Evol   32 ( 3 ): 820 – 832 . https://doi.org/10.1093/molbev/msu400 .

Wiens   JJ , Graham   CH , Moen   DS , Smith   SA , Reeder   TW . 2006 . Evolutionary and ecological causes of the latitudinal diversity gradient in hylid frogs: treefrog trees unearth the roots of high tropical diversity . Am Nat   168 ( 5 ): 579 – 596 . https://doi.org/10.1086/507882 .

Willaert   B , Bossuyt   F , Janssenswillen   S , Adriaens   D , Baggerman   G , Matthijs   S , Pauwels   E , Proost   P , Raepsaet   A , Schoofs   L . Frog nuptial pads secrete mating season-specific proteins related to salamander pheromones . J Exp Biol . 2013 . https://doi.org/10.1242/jeb.086363 .

Yang   Z . 2007 . PAML 4: phylogenetic analysis by maximum likelihood . Mol Biol Evol   24 ( 8 ): 1586 – 1591 . https://doi.org/10.1093/molbev/msm088 .

Yang   Z , Nielsen   R , Goldman   N , Pedersen   A-MK . 2000 . Codon-substitution models for heterogeneous selection pressure at amino acid sites . Genetics   155 ( 1 ): 431 – 449 . https://doi.org/10.1093/genetics/155.1.431 .

Yohe   LR , Abubakar   R , Giordano   C , Dumont   E , Sears   KE , Rossiter   SJ , Dávalos   LM . 2017 . Trpc2 pseudogenization dynamics in bats reveal ancestral vomeronasal signaling, then pervasive loss . Evolution   71 ( 4 ): 923 – 935 . https://doi.org/10.1111/evo.13187 .

Zekoll   T , Waldherr   M , Tessmar-Raible   K . Characterization of tmt-opsin2 in medaka fish provides insight into the interplay of light and temperature for behavioral regulation . Front Physiol . 2021 : 12 . https://doi.org/10.3389/fphys.2021.726941 .

Zhang   Y . Why do we study animal toxins?   Zool Res . 2015 : 36 : 183 – 222 . https://doi.org/10.13918/j.issn.2095-8137.2015.4.183 .

Supplementary data

Email alerts

Citing articles via.

• Author Guidelines

Affiliations

• Online ISSN 1537-1719
• Copyright © 2024 Society for Molecular Biology and Evolution
• About Oxford Academic
• Publish journals with us
• University press partners
• What we publish
• New features  
• Institutional account management
• Rights and permissions
• Get help with access
• Accessibility
• Advertising
• Media enquiries
• Oxford University Press
• Oxford Languages
• University of Oxford

Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide

• Copyright © 2024 Oxford University Press
• Cookie settings
• Cookie policy
• Privacy policy
• Legal notice

This Feature Is Available To Subscribers Only

Sign In or Create an Account

This PDF is available to Subscribers Only

For full access to this pdf, sign in to an existing account, or purchase an annual subscription.