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• Null and Alternative Hypotheses | Definitions & Examples

Null and Alternative Hypotheses | Definitions & Examples

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

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

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

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

Table of contents

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

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

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

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

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

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

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

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

Examples of null hypotheses

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

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

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

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

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

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

Examples of alternative hypotheses

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

Null and alternative hypotheses are similar in some ways:

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

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

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

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

Does independent variable affect dependent variable ?

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

Test-specific

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

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

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

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

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

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

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7 Addressing the Null & Alternate Hypotheses

Forming Hypotheses

After coming up with an experimental question, scientists develop hypotheses and predictions.

The null hypothesis H 0 states that there will be no effect of the treatment on the dependent variable, while the alternate hypothesis H A states the opposite, that there will be an effect.

Every hypothesis should include the following information:

• Name of organism (common and Latin name)
• Name of variable being manipulated (independent variable) with units
• Which response will be measured (dependent variable) with units

Example of Null and Alternate Hypotheses

Null hypothesis (H 0 ) : Temperature ( o C) will have no effect on the pulse rate, measured in beats per minute, of mice ( Mus musculus ).

Alternate hypothesis (H A ) : Temperature ( o C) will have an effect on the pulse rate, measured in beats per minute, of mice ( Mus musculus ).

Reject or Fail to Reject the Null Hypothesis

To determine if two groups are different from one another, we look to see whether or not their respective 95% confidence intervals overlap and then relate this conclusion back to our two hypotheses.

If the 95% confidence intervals of two sample means do overlap (e.g., a treatment and the control), we are less than 95% sure (i.e. not sure enough) that these two groups reflect a true difference in the populations. This results in a failure to reject the null hypothesis , as there is insufficient evidence to support our alternative hypothesis that there was an effect.

If the 95% confidence intervals do not overlap, we are 95% sure that these two groups reflect a true difference in the populations. This result allows us to reject our null hypothesis and provide support for our alternative hypothesis. It should be noted that calculating confidence intervals only allows us to compare two groups at one time.

Interpreting Confidence Intervals

For example, the 95% confidence intervals of the 30 o C and 35 o C degrees treatment groups do not overlap with the confidence intervals of the 25 o C (control) (Figure 1). In this case, we reject the null hypothesis and provide support for the alternate hypothesis. We conclude that temperature ( o C) will have an effect on the pulse rate, measured in beats per minute, of mice ( Mus musculus ).

How to Address the Null and Alternate Hypotheses in the Discussion

In the Discussion section of your report you will need to discuss whether or not the 95% confidence intervals of the treatment groups overlap with the control.

When addressing the null and alternate hypothesis in the Discussion:

• State whether the confidence intervals overlap with the control (be specific about which treatment(s) overlap).
• If you reject or fail to reject the null hypothesis (use this language).
• A full restatement of the supported hypothesis.

Click on the hotspots below to learn about how to address the null and alternate hypotheses in the Discussion.

How to Address the Null & Alternate Hypotheses in the Discussion

Results and Discussion Writing Workshop Part 1 Copyright © by Melissa Bodner. All Rights Reserved.

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• Knowledge Base

Methodology

• How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

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 .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, 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 types of variables .

• An independent variable is something the researcher changes or controls.
• A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results.

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 .

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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 ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize 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.

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

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.

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 .

• H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
• H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

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

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

 Statistics

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

Research bias

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

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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).

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.

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.

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How to Write a Null and Alternative Hypothesis: A Guide with Examples

11 December 2023

last updated

When undertaking a qualitative or quantitative research project, researchers must first formulate a research question, from which they develop a hypothesis. By definition, a hypothesis is a prediction that a researcher makes about the research question and can either be affirmative or negative. In this case, a research question has three main components: variables (independent and dependent), a population sample, and the relation between the variables. When the prediction contradicts the research question, it is referred to as a null hypothesis. In short, a null hypothesis is a statement that implies there is no relationship between independent and dependent variables. Hence, researchers need to learn how to write a good null and alternative hypothesis to present quality studies.

General Aspect of Writing a Null and Alternative Hypothesis

Students with qualitative or quantitative research assignments must learn how to formulate and write a good research question and hypothesis. By definition, a hypothesis is an assumption or prediction that a researcher makes before undertaking an experimental investigation. Basically, academic standards require such a prediction to be a precise and testable statement, meaning that researchers must prove or disapprove of it in the course of the assignment. In this case, the main components of a hypothesis are variables (independent and dependent), a population sample, and the relation between the variables. Therefore, a research hypothesis is a prediction that researchers write about the relationship between two or more variables. In turn, the research inquiry is the process that seeks to answer the research question and, in the process, test the hypothesis by confirming or disapproving it.

Types of Hypotheses

There are several types of hypotheses, including an alternative hypothesis, a null hypothesis, a directional hypothesis, and a non-directional hypothesis. Basically, the directional hypothesis is a prediction of how the independent variable affects the dependent variable. In contrast, the non-directional hypothesis predicts that the independent variable influences the dependent variable, but does not specify how. Regardless of the type, all hypotheses are about predicting the relationship between the independent and dependent variables.

What Is a Null and Alternative Hypothesis

A null hypothesis, usually symbolized as “H0,” is a statement that contradicts the research hypothesis. In other words, it is a negative statement, indicating that there is no relationship between the independent and dependent variables. By testing the null hypothesis, a researcher can determine whether the inquiry results are due to the chance or the effect of manipulating the dependent variable. In most instances, a null hypothesis corresponds with an alternative hypothesis, a positive statement that covers a relationship that exists between the independent and dependent variables. Also, it is highly recommendable that a researcher should write the alternative hypothesis first before the null hypothesis.

10 Examples of Research Questions with H0 and H1 Hypotheses

Before developing a hypothesis, a researcher must formulate the research question. Then, the next step is to transform the question into a negative statement that claims the lack of a relationship between the independent and dependent variables. Alternatively, researchers can change the question into a positive statement that includes a relationship that exists between the variables. In turn, this latter statement becomes the alternative hypothesis and is symbolized as H1. Hence, some of the examples of research questions and hull and alternative hypotheses are as follows:

1. Do physical exercises help individuals to age gracefully?

A Null Hypothesis (H0): Physical exercises are not a guarantee for graceful old age.

An Alternative Hypothesis (H1): Engaging in physical exercises enables individuals to remain healthy and active into old age.

2. What are the implications of therapeutic interventions in the fight against substance abuse?

H0: Therapeutic interventions are of no help in the fight against substance abuse.

H1: Exposing individuals with substance abuse disorders to therapeutic interventions help control and even stop their addictions.

3. How do sexual orientation and gender identity affect the experiences of late adolescents in foster care?

H0: Sexual orientation and gender identity have no effects on the experiences of late adolescents in foster care.

H1: The reality of stereotypes in society makes sexual orientation and gender identity factors complicate the experiences of late adolescents in foster care.

4. Does income inequality contribute to crime in high-density urban areas?

H0: There is no correlation between income inequality and incidences of crime in high-density urban areas.

H1: The high crime rates in high-density urban areas are due to the incidence of income inequality in those areas.

5. Does placement in foster care impact individuals’ mental health?

H0: There is no correlation between being in foster care and having mental health problems.

H1: Individuals placed in foster care experience anxiety and depression at one point in their life.

6. Do assistive devices and technologies lessen the mobility challenges of older adults with a stroke?

H0: Assistive devices and technologies do not provide any assistance to the mobility of older adults diagnosed with a stroke.

H1: Assistive devices and technologies enhance the mobility of older adults diagnosed with a stroke.

7. Does race identity undermine classroom participation?

H0: There is no correlation between racial identity and the ability to participate in classroom learning.

H1: Students from racial minorities are not as active as white students in classroom participation.

8. Do high school grades determine future success?

H0: There is no correlation between how one performs in high school and their success level in life.

H1: Attaining high grades in high school positions one for greater success in the future personal and professional lives.

9. Does critical thinking predict academic achievement?

H0: There is no correlation between critical thinking and academic achievement.

H1: Being a critical thinker is a pathway to academic success.

10. What benefits does group therapy provide to victims of domestic violence?

H0: Group therapy does not help victims of domestic violence because individuals prefer to hide rather than expose their shame.

H1: Group therapy provides domestic violence victims with a platform to share their hurt and connect with others with similar experiences.

Summing Up on How to Write a Null and Alternative Hypothesis

The formulation of research questions in qualitative and quantitative assignments helps students develop a hypothesis for their experiment. In this case, learning how to write a good hypothesis that helps students and researchers to make their research relevant. Basically, the difference between a null and alternative hypothesis is that the former contradicts the research question, while the latter affirms it. In short, a null hypothesis is a negative statement relative to the research question, and an alternative hypothesis is a positive statement. Moreover, it is important to note that developing the null hypothesis at the beginning of the assignment is for prediction purposes. As such, the research work answers the research question and confirms or disapproves of the hypothesis. Hence, some of the tips that students and researchers need to know when developing a null hypothesis include:

• Formulate a research question that specifies the relationship between an independent variable and a dependent variable.
• Develop an alternative hypothesis that says a relationship that exists between the variables.
• Develop a null hypothesis that says a relationship that does not exist between the variables.
• Conduct the research to answer the research question, which allows the confirmation of a disapproval of a null hypothesis.

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9.1 Null and Alternative Hypotheses

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

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

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

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

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

Mathematical Symbols Used in H 0 and H a :

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

Example 9.1

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

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

Example 9.2

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

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

• H 0 : μ __ 66
• H a : μ __ 66

Example 9.3

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

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

• H 0 : μ __ 45
• H a : μ __ 45

Example 9.4

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

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

• H 0 : p __ 0.40
• H a : p __ 0.40

Collaborative Exercise

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

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Neag School of Education

Educational Research Basics by Del Siegle

Null and alternative hypotheses.

Converting research questions to hypothesis is a simple task. Take the questions and make it a positive statement that says a relationship exists (correlation studies) or a difference exists between the groups (experiment study) and you have the alternative hypothesis. Write the statement such that a relationship does not exist or a difference does not exist and you have the null hypothesis. You can reverse the process if you have a hypothesis and wish to write a research question.

When you are comparing two groups, the groups are the independent variable. When you are testing whether something affects something else, the cause is the independent variable. The independent variable is the one you manipulate.

Teachers given higher pay will have more positive attitudes toward children than teachers given lower pay. The first step is to ask yourself “Are there two or more groups being compared?” The answer is “Yes.” What are the groups? Teachers who are given higher pay and teachers who are given lower pay. The independent variable is teacher pay. The dependent variable (the outcome) is attitude towards school.

You could also approach is another way. “Is something causing something else?” The answer is “Yes.”  What is causing what? Teacher pay is causing attitude towards school. Therefore, teacher pay is the independent variable (cause) and attitude towards school is the dependent variable (outcome).

By tradition, we try to disprove (reject) the null hypothesis. We can never prove a null hypothesis, because it is impossible to prove something does not exist. We can disprove something does not exist by finding an example of it. Therefore, in research we try to disprove the null hypothesis. When we do find that a relationship (or difference) exists then we reject the null and accept the alternative. If we do not find that a relationship (or difference) exists, we fail to reject the null hypothesis (and go with it). We never say we accept the null hypothesis because it is never possible to prove something does not exist. That is why we say that we failed to reject the null hypothesis, rather than we accepted it.

Del Siegle, Ph.D. Neag School of Education – University of Connecticut [email protected] www.delsiegle.com

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11.2: Null and Alternative Hypotheses

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

• The null hypothesis (\(H_{0}\)) is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.
• The alternative hypothesis (\(H_{a}\)) is a claim about the population that is contradictory to \(H_{0}\) and what we conclude when we reject \(H_{0}\).

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data. After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject \(H_{0}\)" if the sample information favors the alternative hypothesis or "do not reject \(H_{0}\)" or "decline to reject \(H_{0}\)" if the sample information is insufficient to reject the null hypothesis.

\(H_{0}\) always has a symbol with an equal in it. \(H_{a}\) never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example \(\PageIndex{1}\)

• \(H_{0}\): No more than 30% of the registered voters in Santa Clara County voted in the primary election. \(p \leq 30\)
• \(H_{a}\): More than 30% of the registered voters in Santa Clara County voted in the primary election. \(p > 30\)

Exercise \(\PageIndex{1}\)

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

• \(H_{0}\): The drug reduces cholesterol by 25%. \(p = 0.25\)
• \(H_{a}\): The drug does not reduce cholesterol by 25%. \(p \neq 0.25\)

Example \(\PageIndex{2}\)

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

• \(H_{0}: \mu = 2.0\)
• \(H_{a}: \mu \neq 2.0\)

Exercise \(\PageIndex{2}\)

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

• \(H_{0}: \mu_ 66\)
• \(H_{a}: \mu_ 66\)
• \(H_{0}: \mu = 66\)
• \(H_{a}: \mu \neq 66\)

Example \(\PageIndex{3}\)

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

• \(H_{0}: \mu \geq 66\)
• \(H_{a}: \mu < 66\)

Exercise \(\PageIndex{3}\)

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

• \(H_{0}: \mu_ 45\)
• \(H_{a}: \mu_ 45\)
• \(H_{0}: \mu \geq 45\)
• \(H_{a}: \mu < 45\)

Example \(\PageIndex{4}\)

In an issue of U. S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

• \(H_{0}: p \leq 0.066\)
• \(H_{a}: p > 0.066\)

Exercise \(\PageIndex{4}\)

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

• \(H_{0}: p_ 0.40\)
• \(H_{a}: p_ 0.40\)
• \(H_{0}: p = 0.40\)
• \(H_{a}: p > 0.40\)

COLLABORATIVE EXERCISE

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

Chapter Review

In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we:

• Evaluate the null hypothesis , typically denoted with \(H_{0}\). The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality \((=, \leq \text{or} \geq)\)
• Always write the alternative hypothesis , typically denoted with \(H_{a}\) or \(H_{1}\), using less than, greater than, or not equals symbols, i.e., \((\neq, >, \text{or} <)\).
• If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.
• Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

Formula Review

\(H_{0}\) and \(H_{a}\) are contradictory.

• If \(\alpha \leq p\)-value, then do not reject \(H_{0}\).
• If\(\alpha > p\)-value, then reject \(H_{0}\).

\(\alpha\) is preconceived. Its value is set before the hypothesis test starts. The \(p\)-value is calculated from the data.References

Data from the National Institute of Mental Health. Available online at http://www.nimh.nih.gov/publicat/depression.cfm .

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Once you have developed a clear and focused research question or set of research questions, you’ll be ready to conduct further research, a literature review, on the topic to help you make an educated guess about the answer to your question(s). This educated guess is called a hypothesis.

In research, there are two types of hypotheses: null and alternative. They work as a complementary pair, each stating that the other is wrong.

• Null Hypothesis (H 0 ) – This can be thought of as the implied hypothesis. “Null” meaning “nothing.”  This hypothesis states that there is no difference between groups or no relationship between variables. The null hypothesis is a presumption of status quo or no change.
• Alternative Hypothesis (H a ) – This is also known as the claim. This hypothesis should state what you expect the data to show, based on your research on the topic. This is your answer to your research question.

Null Hypothesis:   H 0 : There is no difference in the salary of factory workers based on gender. Alternative Hypothesis :  H a : Male factory workers have a higher salary than female factory workers.

Null Hypothesis :  H 0 : There is no relationship between height and shoe size. Alternative Hypothesis :  H a : There is a positive relationship between height and shoe size.

Null Hypothesis :  H 0 : Experience on the job has no impact on the quality of a brick mason’s work. Alternative Hypothesis :  H a : The quality of a brick mason’s work is influenced by on-the-job experience.

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The Craft of Writing a Strong Hypothesis

Table of Contents

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

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

What is a Hypothesis?

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

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

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

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

Different Types of Hypotheses‌

Types of hypotheses

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

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

1. Null hypothesis

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

2. Alternative hypothesis

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

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

3. Simple hypothesis

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

4. Complex hypothesis

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

5. Associative and casual hypothesis

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

6. Empirical hypothesis

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

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

7. Statistical hypothesis

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

Characteristics of a Good Hypothesis

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

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

Separating a Hypothesis from a Prediction

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

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

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

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

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

Finally, How to Write a Hypothesis

Quick tips on writing a hypothesis

1.  Be clear about your research question

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

2. Carry out a recce

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

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

3. Create a 3-dimensional hypothesis

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

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

4. Write the first draft

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

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

5. Proof your hypothesis

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

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

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

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

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

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

Frequently Asked Questions (FAQs)

1. what is the definition of hypothesis.

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

2. What is an example of hypothesis?

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

3. What is an example of null hypothesis?

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

4. What are the types of research?

• Fundamental research

• Applied research

• Qualitative research

• Quantitative research

• Mixed research

• Exploratory research

• Longitudinal research

• Cross-sectional research

• Field research

• Laboratory research

• Fixed research

• Flexible research

• Action research

• Policy research

• Classification research

• Comparative research

• Causal research

• Inductive research

• Deductive research

5. How to write a hypothesis?

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

• Avoid wordiness by keeping it simple and brief.

• Your hypothesis should contain observable and testable outcomes.

• Your hypothesis should be relevant to the research question.

6. What are the 2 types of hypothesis?

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

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

7. Difference between research question and research hypothesis?

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

8. What is plural for hypothesis?

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

9. What is the red queen hypothesis?

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

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

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

11. When to reject null hypothesis?

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

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AP®︎/College Statistics

Course: ap®︎/college statistics   >   unit 10.

• Idea behind hypothesis testing

Examples of null and alternative hypotheses

• Writing null and alternative hypotheses
• P-values and significance tests
• Comparing P-values to different significance levels
• Estimating a P-value from a simulation
• Estimating P-values from simulations
• Using P-values to make conclusions

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Video transcript

Statistics Made Easy

How to Write a Null Hypothesis (5 Examples)

A hypothesis test uses sample data to determine whether or not some claim about a population parameter is true.

Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:

H 0 (Null Hypothesis): Population parameter =,  ≤, ≥ some value

H A  (Alternative Hypothesis): Population parameter <, >, ≠ some value

Note that the null hypothesis always contains the equal sign .

We interpret the hypotheses as follows:

Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.

Alternative hypothesis: The sample data  does provide sufficient evidence to support the claim being made by an individual.

For example, suppose it’s assumed that the average height of a certain species of plant is 20 inches tall. However, one botanist claims the true average height is greater than 20 inches.

To test this claim, she may go out and collect a random sample of plants. She can then use this sample data to perform a hypothesis test using the following two hypotheses:

H 0 : μ ≤ 20 (the true mean height of plants is equal to or even less than 20 inches)

H A : μ > 20 (the true mean height of plants is greater than 20 inches)

If the sample data gathered by the botanist shows that the mean height of this species of plants is significantly greater than 20 inches, she can reject the null hypothesis and conclude that the mean height is greater than 20 inches.

Read through the following examples to gain a better understanding of how to write a null hypothesis in different situations.

Example 1: Weight of Turtles

A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles.

Here is how to write the null and alternative hypotheses for this scenario:

H 0 : μ = 300 (the true mean weight is equal to 300 pounds)

H A : μ ≠ 300 (the true mean weight is not equal to 300 pounds)

Example 2: Height of Males

It’s assumed that the mean height of males in a certain city is 68 inches. However, an independent researcher believes the true mean height is greater than 68 inches. To test this, he goes out and collects the height of 50 males in the city.

H 0 : μ ≤ 68 (the true mean height is equal to or even less than 68 inches)

H A : μ > 68 (the true mean height is greater than 68 inches)

Example 3: Graduation Rates

A university states that 80% of all students graduate on time. However, an independent researcher believes that less than 80% of all students graduate on time. To test this, she collects data on the proportion of students who graduated on time last year at the university.

H 0 : p ≥ 0.80 (the true proportion of students who graduate on time is 80% or higher)

H A : μ < 0.80 (the true proportion of students who graduate on time is less than 80%)

Example 4: Burger Weights

A food researcher wants to test whether or not the true mean weight of a burger at a certain restaurant is 7 ounces. To test this, he goes out and measures the weight of a random sample of 20 burgers from this restaurant.

H 0 : μ = 7 (the true mean weight is equal to 7 ounces)

H A : μ ≠ 7 (the true mean weight is not equal to 7 ounces)

Example 5: Citizen Support

A politician claims that less than 30% of citizens in a certain town support a certain law. To test this, he goes out and surveys 200 citizens on whether or not they support the law.

H 0 : p ≥ .30 (the true proportion of citizens who support the law is greater than or equal to 30%)

H A : μ < 0.30 (the true proportion of citizens who support the law is less than 30%)

Additional Resources

Introduction to Hypothesis Testing Introduction to Confidence Intervals An Explanation of P-Values and Statistical Significance

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Module 9: Hypothesis Testing With One Sample

Null and alternative hypotheses, learning outcomes.

• Describe hypothesis testing in general and in practice

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

H 0 : The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.

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

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

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

Mathematical Symbols Used in  H 0 and H a :

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

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

H a : More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30

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

H 0 : The drug reduces cholesterol by 25%. p = 0.25

H a : The drug does not reduce cholesterol by 25%. p ≠ 0.25

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

H 0 : μ = 2.0

H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 66 H a : μ __ 66

• H 0 : μ = 66
• H a : μ ≠ 66

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

H 0 : μ ≥ 5

H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 45 H a : μ __ 45

• H 0 : μ ≥ 45
• H a : μ < 45

In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

H 0 : p ≤ 0.066

H a : p > 0.066

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : p __ 0.40 H a : p __ 0.40

• H 0 : p = 0.40
• H a : p > 0.40

Concept Review

In a  hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis , typically denoted with H 0 . The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis , typically denoted with H a or H 1 , using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

Formula Review

H 0 and H a are contradictory.

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Problems and alternatives of testing significance using null hypothesis and P -value in food research

Won-seok choi.

Department of Food Science and Technology, Korea National University of Transportation, Jeungpyeong-gun, 27909 Chungbuk Republic of Korea

A testing method to identify statistically significant differences by comparing the significance level and the probability value based on the Null Hypothesis Significance Test (NHST) has been used in food research. However, problems with this testing method have been discussed. Several alternatives to the NHST and the P -value test methods have been proposed including lowering the P -value threshold and using confidence interval (CI), effect size, and Bayesian statistics. The CI estimates the extent of the effect or difference and determines the presence or absence of statistical significance. The effect size index determines the degree of effect difference and allows for the comparison of various statistical results. Bayesian statistics enable predictions to be made even when only a small amount of data is available. In conclusion, CI, effect size, and Bayesian statistics can complement or replace traditional statistical tests in food research by replacing the use of NHST and P -value.

Introduction

In food of animal or plant resources research, quantitative methods such as experimental research are mainly used. After food research became a separate field of applied science, the use of statistical methods that use the null hypothesis and the P -value increased. This was due in part to Fisher, a pioneer in the field of statistics, who mentioned these methods in a tea- tasting sensory test (Fisher, 1935 , 1936 ). In food research, statistical significance at a P -value of 0.05 (5%) first appeared in the early 1940s (Eheart and Sholes, 1945 ; Griswold and Wharton, 1941 ). Only in the early 1970s, the statistical test procedure was described in the materials and methods of papers (Bouton et al., 1975 ; Froning et al., 1971 ; Reddy et al., 1970 ). In Korea, it was not until the 1990s that statistical tests began to be used in food research papers using animal or plant materials on a variety of topics beyond just sensory tests (Chung et al., 1991 ; Kim and Lee, 1998 ; Shin et al., 1991 ).

The expression “showed a significant difference (at a significance level of 0.05 (5%))” was used to determine whether difference between the control and the experimental groups was statistically significant by comparing the significance level (α) and probability ( P ) based on the Null Hypothesis Significance Test (NHST) (Goodman, 1999 ; Wasserstein et al., 2019 ). As previously mentioned, this statistical verification method was started in the early 20th century by Fisher (Bandit and Boen, 1972 ).

In food research, the significance of the differences is determined using the P -value based on the NHST theory when comparing the experimental group of a new method or material to the control group. This statistical reasoning method is a common practice in food research, especially in Korean food research. However, the problems with NHST were actually raised 50 years ago in 1972 (Edwards, 1972 ). While there has been more recent attention drawn to these problems. In 1988, the International Medical Journal Editors' Committee recognized the problem of using NHST and P -value and requested that statistics be reported using confidence interval (CI) instead (Bailar and Mosteller, 1988 ). Some social science journals even banned using the NHST method in 2015 (Trafimow and Marks, 2015 ). In addition, the American Statistical Association (ASA) has published a statement on statistical significance and P- value, arguing that passing a certain threshold (significance level) the P -value should not be the basis for making scientific conclusions, business, or policy decisions (Ronald and Nicole, 2016 ).

Although there are many reasons for the continued use of NHST and P -values in food research despite these controversies, one of the key reasons is that using NHST and P -value in statistical testing has become universal and commonplace as a mathematical formula for the solution. In addition, it may be because of the denying the results of numerous published papers or acknowledging that there may be errors by judging whether there is a difference from the control group only with the P -value based on the NHST theory. The author is no exception to this conventional behavior and burden. Nevertheless, it is clear that there is a problem in blindly using NHST and P values, and there is a need for gradual improvement.

Several methods have been proposed as alternatives to using NHST and P -value. However, the most prominent ones include lowering the P -value threshold and using confidence interval (CI), effect size, and Bayesian statistics (Benjamin et al., 2018 ; Joo et al., 1994 ; Lee, 2013 , 2016 ; Sullivan and Feinn, 2012 ; Yeo, 2021 ).

In this paper, I will discuss the problems of using NHST and P -value. I will also provide an introduction to basic knowledge and related details on complementary or alternative methods for food researchers who may not have a strong background in statistics. These methods include lowering the P -value threshold, and using CI, effect size, and Bayesian statistics. I will argue that using dichotomous statistical tests based solely on NHST and P -value should be avoided in food research, and that researchers should gradually incorporate supplementary or alternative statistical testing methods such as CI, effect size, and Bayesian statistics, which can provide more diverse information from the same data.

Meaning of NHST and P -value

The NHST used in statistics is a part of the verification method for inferring the characteristics of the entire population. NHST is used to estimate the characteristics of the population from samples collected from the entire population when it is not possible to obtain information (data) from the entire population, and testing is conducted based on hypotheses such as “no difference” or “no effect” (null hypothesis). The null hypothesis is generally the opposite of the hypothesis the researcher intends to infer (alternative hypothesis), which the researcher wants to reject (Joo et al., 1994 ; Verdam et al., 2014 ; Yeo, 2021 ).

In general, rejection of the null hypothesis in NHST is determined by comparing the significance level and the P value. Here, the P value refers to the probability value at which the data value of the sample can be obtained under the condition that the null hypothesis is true (Cohen, 2011 ; Goodman, 1999 ; Trafimow and Rice, 2009 ). That is, a P value of 0.01 means that the probability of obtaining a sample data value (with a difference or effect greater than or equal to the usual level) from the population for which the null hypothesis is true is a very rare (based on significance level of 0.05) with a probability of 1% (0.01), and a P -value of 0.10 is interpreted as the probability of obtaining a sample statistic (sample data value) from the population for which the null hypothesis is true is a relatively high probability (based on significance level of 0.05) with a probability of 10% (0.1). Very high or very rare is a relative concept that requires a criterion and the criterion is called the significance level (generally 0.05 (5%)). If the P -value is smaller than the significance level, it is considered that an unlikely event has occurred. As a result, the null hypothesis is rejected and deemed to have statistical significance.

In fact, NHST is a test method that combines Fisher's significance test and Neyman and Pearson's hypothesis test (Lee, 2013 ). These masters of statistics belonged to different schools, and Fisher, the founder of the concept of the null hypothesis, used the P -value only to reject the null hypothesis, and set the rejection criterion (significance level) at a “convenient and flexible” value of 0.05. On the other hand, Neyman and Pearson supplemented Fisher’s theory and formulated the concept of alternative hypotheses in order to draw mathematical and scientific conclusions, providing a “fixed” criterion for the selection (adoption of the null hypothesis) and rejection (adoption of the alternative hypothesis) of the hypothesis with the use of Type I error (false rejection) probability as α. In other words, if Fisher’s test recommended flexible conclusions, Neyman and Pearson insisted on making strict conclusions. The problem arose when a new theory emerged amid the confrontation and debate between the two schools of thought. Fisher’s P value began to be used with Neyman and Pearson's α, which corresponded to Fisher’s significance level to draw a mathematically rigorous conclusion (Perezgonzalez, 2015 ). Many current problems are the result of blindly using this testing method, which is a simple blend of different schools of thought in an attempt to unify theories.

Problems with using NHST and P -values

As mentioned in the introduction, the problems of making statistical inference using NHST and P -value are as follows (Lee, 2013 ; Sullivan and Feinn, 2012 ; Yeo, 2021 ).

First of all, the most problematic of misunderstandings about the P -value is that it misinterprets “the probability of observing the data value of the sample under the condition that the null hypothesis is correct (true)” as “the probability of the null hypothesis being true based on the observed sample statistic” (Carver, 1978 ; Nickerson, 2000 ). Since the value of P is calculated on the premise that the null hypothesis is true, it cannot be a value of the probability that the null hypothesis is true. A P -value of 0.01 means that the probability of obtaining a sample data value is 1% (0.01) from the population for which the null hypothesis is true, which is a very rare (based on significance level of 0.05) probability and does not mean that there is only a 1% chance that the null hypothesis is true. In other words, when the null hypothesis is rejected, the interpretation that the probability of this being an error is 1% (a very rare probability based on the significance level of 0.05) is an incorrect interpretation. In general, it is wrong to think of the P -value as the probability of making an error, i.e., the error rate, and Sellke et al. ( 2001 ) reported that for a P value of 0.05, the error rate is estimated as “at least 29% (typically around 50%).”

Second, the NHST lacks an explanation of the results, and may sometimes provide no meaning at all. When establishing a null hypothesis such as “there is no (performance) effect of the program” or “there is no difference between the two groups” in a study, the researcher might be interested in the extent of the effect, i.e., effect size along with the presence or absence of an effect, if indeed there was one. When the null hypothesis is rejected, the effect is “statistically” significant, but it is not known whether this effect is “actually” meaningful or meaningless. The same is true for the analysis of differences between the two groups. In the natural sciences, especially in physics, theoretically, the effect can have a value of 0 (zero), but in reality, the case where the effect of a program is 0 is extremely rare; particularly, in the field of social science, it is almost impossible for an effect to have a value of zero. Between the two groups, it is highly probable that there will be a difference of 0 or more mostly due to the surrounding conditions other than the essence, such as the difference in the test method and the number of samples in the groups (McShane and Gal, 2017 ; Yeo, 2021 ).

Third, the P -value is inevitably affected by the number of samples (cases). The larger the number of samples, the smaller the P -value, and conversely, the smaller the number of samples, the higher the P -value. Therefore, if the researcher intends to show a significant effect or difference by lowering the P -value, the researcher has a higher probability of probabilistic success if the number of samples is increased, which leads to the misunderstanding that the smaller the P -value, the greater the effect. That is, the usefulness of the P -value decreases as the number of samples increases (Sullivan and Feinn, 2012 ).

Fourth, papers that performed statistical inference using NHST and P -value have no choice but to interpret the results dichotomously. Determining significance by the size of the P -value at a specific statistical significance level (generally 0.05) has the advantage of being simple and clear to judge the result, but can it be said that the effect is 0 or there is no difference if the P -value is 0.051 at the significance level of 0.05? In other words, can we say that the 0.002 difference between the P -values 0.051 and 0.049 is the absolute difference that will decide the fate? Also, the significance level of 0.05 was an arbitrary and reference only value suggested by Fisher, but now many researchers regard it as an almost absolute reference point (McShane and Gal, 2017 ).

Fifth, it leads to publication bias. Publication bias refers to the selection and publication of only papers with favorable results by an academic organization (Gerber and Malhotra, 2008 ). The use of NHST and P -value is likely to categorize various studies dichotomously into successful and failed studies, leading to the publication of only the studies with so-called statistical significance showing a P -value that is lower than the significance level (Bruns and Ioannidis, 2016 ; Fanelli, 2012 ). This could further lead to side effects such as over-interpretation of study results or preventing various results from being published (Simonsohn et al., 2014 ).

Sixth, NHST and P -value are not correlated with the reproducibility of results, which refers to the ability to obtain the same or similar results when published studies are repeatedly performed in the same way (Plucker and Makel, 2021 ). The majority of readers believe that papers that use NHST and P -value to publish statistically significant results have reproducibility. However, unfortunately, according to the study by Ioannidis (Ioannidis, 2005 ), although there are differences between studies, a significant number of papers published in the medical field did not reproduce the statistical significance. This paper is currently cited more than 7000 times (PLOS MEDICINE, 2023 ). Even when the P value of the research results is 0.001, the reproducibility of the research results cannot be guaranteed (Yeo, 2021 ).

Meanwhile, the American Statistical Association (ASA) mentioned the following principles regarding P -values (Ronald and Nicole, 2016 ).

• The P -value indicates how much the data is inconsistent with a specific statistical model (hypothesis) rather than interpreting it as a probability that a given hypothesis is true based on the sample dataset. In other words, if the basic assumption used to calculate the P -value is maintained, the smaller the P -value, the greater the statistical discrepancy between the null hypothesis and the data;
• The P -value does not measure the probability that the research hypothesis is true or the probability that the data were created by chance;
• One should not make any scientific conclusion, business or policy decisions based only on the passing of a specific threshold (significance level) of the P -value;
• For proper inference, it is necessary to report all statistics transparently and completely in addition to the P -value;
• The P -value or statistical significance does not measure the size of the effect or the importance of the outcome;
• The P -value by itself is not a good evidence for a statistical model or hypothesis (e.g., whether the null hypothesis is true or false).

As an alternative to the problem of using NHST and P -value, several researchers have proposed lowering the P -value threshold, and using CIs, effect sizes, and Bayesian statistics (Benjamin et al., 2018 ; Joo et al., 1994 ; Lee, 2013 , 2016 ; Lin et al., 2013 ).

Lowering the P -value threshold

Benjamin et al. ( 2018 ) numerically analyzed the problems that occur when using a P -value of 0.05. As a result, when the two-sided P -value is 0.05, the minimum probability that the alternative (research) hypothesis is true is 75%, which means that the maximum probability that the null hypothesis is also true is also 25%. In order to solve this problem, they argued that the significance level should be lowered and the P -value should be 0.005. According to the simulation results of these researchers, when the P -value is 0.005, the probability that the alternative (research) hypothesis is true increased about 6.8 times compared to when the P -value was 0.05, and the percentage of false positives decreased by about 6.6 times (33% → 5%). In addition, it was argued that the study results with a P -value of 0.05 to 0.005 are suggestive results, which are inadequate and should be treated as a study that requires further research. Opposition to this argument has also been published. Ioannidis ( 2018 ) argued that lowering the threshold of P -value to 0.005 is a temporary measure, a lower threshold may be preferred, and the magnitude of the effect may be more exaggerated than in the previous case. The power (1-β) corresponding to a P -value of 0.0001 was reported to be about 0.85 (sample size 100) (Norman, 2019 ).

Confidence interval

When estimating population parameters from study data (sample), the best estimate is a single value, which is called point estimation. This is one of the infinitely possible numbers, and the probability of being able to estimate the single value is very low. Therefore, it is more preferable to present the estimate as a value of a range (interval), and when the expected values of an unknown parameter, consistent with the observed data (within a limited range), are expressed as a series of ranges, it is called a CI and this estimation is called interval estimation (Langman, 1986 ). The range of the CI is affected by the number of variables and the confidence level, which is an arbitrary number (Lee, 2016 ; So, 2016 ). Confidence level of 95% is mainly used, and it is directly related to the significance level, so it corresponds to a value of (1–significance level) × 100. That is, the 95% CI corresponds to a significance level of 0.05. In interpreting this, if the 95% confidence level interval for the population mean difference or population ratio between the two groups does not include the null value (0 or 1, respectively) of the parameter and is included in the 99% CI, the P -value of this parameter can be said to be greater than 0.01 and less than 0.05. That is, it is not statistically significant at the significance level of 0.01, but is at the significance level of 0.05. However, the interpretation of this requires attention as in the interpretation of the P value. In calculating the 95% CI of the mean value from the sample, it should be interpreted as meaning that the population mean value is included in 95 CI s (that is, 95% CI) among the CIs calculated from 100 samples obtained by the same method from the same population; it would be erroneous to interpret this as a 95% probability (or the population mean is included with 95% probability) that the 95% CI of the mean value calculated from a “single sample” contains the population mean value.

If two groups with a small sample size satisfy the assumption of normal distribution and equal variance, the CI for the difference in mean values between the two groups can be obtained from the following equation using t-statistics (Lee, 2016 ).

( s pooled , n i ; pooled sample variance at equal variance assumption, sample size of group i)

Confidence interval;

( Xi ¯ , n i , t α df ; mean of group i, sample size of group i, critical value of the t-distribution for the probability α and degrees of freedom)

I would like to explain the difference between using NHST and P -value and using CIs. When comparing the effects of the existing treatment A and the new treatment B, if the NHST-based P value is 0.06, it is generally concluded that “there is no significant difference between the two treatments”. In this case, when the P -value is expressed as P  = 0.06 rather than P  > 0.05, a more diverse meaning can be provided. Nevertheless, the P -value only judges the significance of the difference in the treatment effect between the two treatments, but does not explain the extent of the difference in the treatment effect (Joo et al., 1994 ).

In Fig.  1 . the individual 95% CIs for the study results of A and B and the 95% CI for the difference between the population means of the two studies was shown (Choi and Han, 2017 ). It can be thought that there is no significant difference between A and B at the 0.05 (5%) significance level because the individual CIs of A and B partially overlap, but this would be an incorrect interpretation; given the 95% CI (far right, B-A) for the population mean value difference between A and B, the correct interpretation would be that there is a statistically significant difference at the significance level of 0.05 because 0 (null value for the mean value difference) is not included. Also, since each CI represents the expected size of the effect, which means that it can have an effect within the range, it can be estimated that B is more effective than A (Choi and Han, 2017 ; Joo et al., 1994 ; Lee, 2016 ). In other words, the CI provides information on the extent (size) as well as the statistical significance of the effect or difference. It is possible to compare more than 3 groups by this method.

95% confidence intervals.

Adapted from Choi and Han ( 2017 )

Usually, the distribution of numerical values in the CI is not uniformly distributed but roughly follows a normal distribution, so it can be estimated that the data are mainly located in the center rather than at the boundary, which is both ends of the CI. That is, the boundary values of the CI mean that the frequency of the data is small and does not significantly affect the interpretation. Different interpretations may occur depending on the location of the boundary value, but this is not a big problem because such cases are rare. That is, comparing the P value with the significance level (e.g., 0.05) is equivalent to focusing all on the boundary value of the CI while ignoring information on the extent (size) of the effect or difference (Joo et al., 1994 ).

As a result of using CIs to re-interpret 71 clinical trial papers published with the conclusion that there was no effect based on the NHST and P value, Freiman et al. ( 1978 ) reported that the results of many studies were misinterpreted and that there were actually effects.

Effect size

CIs provide some information about the magnitude of effects that NHST and P value do not, but they only provide a range of possibilities.

Effect size refers to the difference in standardized scores between groups, i.e., the size of the difference when testing for differences between groups. For example, if the test scores in each subject increased by an average of 30 points (based on 100 points) through a series of programs, the absolute effect size would be 30 points or 30%. Absolute effect sizes are useful when variables are numerical values that have intrinsic meaning (such as sleep time) while the calculated effect size, such as Cohen's d, is used for numerical values that have no intrinsic meaning, such as the Likert scale (Sullivan and Feinn, 2012 ). The calculated effect size is commonly used in meta-analysis as it enables the comparison of statistical results by solving the difficulty of comparison due to inconsistency in measurement units or using other measurement methods (Kim, 2011 ; Lee, 2016 ).

The process of obtaining the effect size index calculated to confirm the difference in the effect between two independent groups (control group and experimental group, etc.) is simple and has the advantage of leading to a more direct interpretation of results. Several types of effect size indices exist, and are mentioned in Table ​ Table1 1 (Lee, 2016 ; Sullivan and Feinn, 2012 ).

Effect size indices

Adapted from Sullivan and Feinn ( 2012 )

The formula for calculating the d value, which is a representative effect size index, is as follows.

( X i ¯ , s pooled ; mean of group I, pooled sample variance at equal variance assumption)

According to the criteria proposed by Cohen ( 1988 ), a d value of 0.2 is considered a small effect size, a value of 0.5 is considered a medium effect size, and a value of 0.8 is considered a large effect size; however, just as significance level criterion P value of 0.05 is a value proposed by Fisher for reference, this value should not be interpreted as an absolute value. Cohen's d = 0.5 means that the mean score of the experimental group is 0.5 SD (standard deviation) higher than the mean score of the control group, which means that about 69% of the control group (standard normal cumulative distribution function value 0.5) is lower than the mean score of the experimental group (Kim, 2015 ).

A typical example of using an effect size is the following. When aspirin was administered to prevent myocardial infarction to 22,000 subjects for 5 years, a statistically significant result of P  < 0.00001 was found. Based on this, aspirin was recommended for the prevention of myocardial infarction. However, the effect size of this study was very small, and further studies showed much smaller effects, so the recommendation for aspirin use was revised (Bartolucci et al., 2011 ). In addition, using the effect size can save us from the dichotomous conclusion resulting from the use of NHST and P value; it is also independent of the sample size (Sullivan and Feinn, 2012 ).

In the paper titled Concept and application of effect size, Kim ( 2011 ) asserted that attention should be paid not only to statistical significance but also to practical effect (usefulness), as the calculated effect size, Cohen’s d, ranged between 0.40 and 0.72 for the studies that did not have statistically significant results because the P value slightly deviated from 0.05 (0.055 to 0.066).

Despite these various advantages, there are criticisms that another effect not related to the effect size can be ignored by oversimplifying the interpretation of Cohen's d. For example, if there is a drug that is inexpensive and safe, although the effect size is small for curing the patient's disease, the effect size for the patient may be small in the medical aspect, but the effect in terms of economic and social aspect is not so small (McGough and Faraone, 2009 ).

Bayesian statistics

Whereas the aforementioned frequentist statistics of Fisher and Neyman–Pearson are a method of estimating fixed-value parameters based on the statistical distribution of a repeated sample, Bayesian statistics is a method of estimating parameters based on the posterior probability that combines the priori probability of parameters with new data (sample) after assuming that the parameter has a probability distribution (prior probability). Therefore, sequential inference is possible, and it is similar to the human thought-judgment process. In other words, the strength of Bayesian statistics is that the previous research data (prior probability) and new research data are placed on a continuous flow line without distinction, therefore are updated (posterior probability) in response to new data in real time; as the data accumulates, the estimation becomes more accurate. In addition, Bayesian statistics have the advantage of being able to make estimates in various environments as there is no null or alternative hypotheses; they provide reliable results even when the sample size is small, do not require a significance level, and do not depend on the limits of assumption of multivariate normality and assumption of equal variance. On the other hand, since prior probabilities are used, the subjectivity of the researcher may be involved and there is the disadvantage of using very complex mathematics; however, these shortcomings can be overcome by using uninformative prior probability or by the development of computer calculation functions (Kim et al., 2016 ; Lee, 2013 ; Noh et al., 2014 ).

By overcoming these limitations, Bayesian statistics are being used in various fields such as IT business for estimating the behavior or search form of Internet consumers, imaging for noise removal, diagnosis through prediction in the medical field, analysis and prediction of surveys and agricultural production, and climate factor analysis. In addition, as the basic study of deep learning model, it is gaining popularity (Kim et al., 2016 ; Nurminen and Mutanen, 1987 ; Wang and Campbell, 2013 ).

Nevertheless, Bayesian statistics is a completely different concept from the existing frequentist statistics, and it is not easy to understand and utilize it for researchers in the food field who do not have a deep academic depth in the statistics.

A typical example of using Bayesian statistics is a case related to COVID-19. It involves calculating the probability of a person who tested positive on a diagnostic kit actually being infected with the disease. The core of the kit is sensitivity and specificity, where sensitivity is “the probability that the diagnostic kit will determine that an infected person has the infection (positive)”, and specificity is “the probability that a person who is not infected will be determined as not infected (negative)”.

Assuming a prevalence rate of (the number of patients with a specific disease/total population) 50% for COVID-19, and sensitivity of 99% and specificity of 90% for the test kit, the probability of actually having the disease when the test result is positive is calculated as follows (Lee, 2013 ).

Here, P(disease│positive) is the probability of having the disease, given a positive test, (corresponds to the “posterior probability” of the disease), P(positive│disease) is sensitivity (“referred to as likelihood”), P(disease) is the probability of having the disease (corresponds to the “prior probability” of the disease, referred to as prevalence), P(positive) is the probability of testing positive, (“marginal probability”). This expression is Bayes’ theorem in Bayesian statistics.

P(positive) can be expressed as the sum of P(positive│D) × P(D), i.e., the probability of true positive and P(positive│not D) × P(not D), i.e., the probability of false positive.

Here, P(positive│not D) is the probability that a healthy person may test positive, referred to as false positive, and is calculated as ‘1- specificity’; P(not D) is the probability of being healthy and is calculated as ‘1-prevalence’.

If the test result came out to be positive using this formula, P(D│positive) = 0.99 × 0.5/((0.99 × 0.5) + (0.1 × 0.5)) = 0.908, i.e., 90.8% is the probability of actually having COVID-19.

Unlike the calculated value of 90.8%, many may think that the probability of actually having the disease to be 99%, but this is the result of confusing the sensitivity of the kit (P(positive│D)) with the probability of actually having the disease (P(D│positive)) when test result is positive. The posterior probability, P(D│positive) is directly and decisively influenced by the prior probability, P(D), so if it is assumed that the prevalence is low (P(disease) = 10%), the probability of actually having the disease may drop significantly (52.4%) even when the positive result is obtained using the diagnostic kit having the same sensitivity (99%) and specificity (90%).

In Bayesian statistics, various statistical analysis programs such as SPSS and JAMOVI can still be used to perform common statistical analyses like correlation, regression, and ANOVA.

Bayesian statistics can express both subjective concepts, such as “approximately,” and objective concepts, such as “numerical values,” which can be advantageous for statistical estimation in fields related to food, such as sensory science, that encompass many social scientific aspects.

In recent years, food research has increasingly utilized large datasets. Bayesian statistics, as a fusion of artificial intelligence and statistics, is one of the techniques that can solve the problem of time-consuming and difficult to manage classical (frequentist) statistical analysis. Due to its advantages, Bayesian statistics is widely used in a variety of fields. However, it has only recently made its presence felt in the food industry (Van Boekel, 2004 ).

Initially, modeling with Bayesian statistics was primarily focused on microbial risk assessment in food production, using structured and simple models that added new information in an organized manner (Barker et al., 2002 ). Bayesian statistics is also used in kinetics to understand food reactions and influence product and process design. Bayesian statistics has the benefit of being easy to interpret and can be applied to a wide variety of complex models with varying degrees of complexity (Van Boekel, 2020 ).

Bayesian statistics can be applied in various ways to the food industry. It can estimate the shelf life of food products by analyzing data on degradation and considering factors such as temperature, humidity, and pH (Calle et al., 2006 ; Luong et al., 2022 ). In sensory analysis, Bayesian statistics can evaluate food samples and estimate the distribution of sensory attributes in the population, helping food companies make informed decisions about product development (Calle et al., 2006 ). Bayesian statistics is also useful for assessing the risk of foodborne illness from microbial contamination (Oishi et al., 2021 ). By incorporating uncertainty, Bayesian statistics can provide more accurate estimates and predictions in all these applications. Overall, Bayesian statistics is a powerful tool for food scientists to draw more reliable conclusions and make more accurate predictions in their studies.

To summarize, the contents are as follows. Although the statistical testing method of determining statistically significant differences by comparing significance level (α) and probability (P) based on the NHST has been commonly used in food research, problems with this testing method have been identified, and some social science journals even banned the use of the NHST method in 2015. Given the limitations of NHST and P -value, several alternative methods have been proposed, including lowering the P -value threshold and utilizing measures such as CI, effect size, and Bayesian statistics. Lowering the threshold for P -value to 0.005, increases the probability that the alternative hypothesis is true by about 6.8 times compared to when the P -value is 0.05, while reducing the ratio of false positives by approximately 6.6 times (33% → 5%). The CI is another alternative, that provides information about the extent of effect or difference and the presence or absence of statistical significance unlike the P -value, which only determines the statistical significance of an effect or difference. The third alternative is the use of effect size. Using an effect size index such as Cohen's d can distinguish the extent of effect difference and enables the comparison of various statistical results by solving the difficulty in comparison due to the inconsistency of measurement units and the use of different measurement methods. Lastly, Bayesian statistics can be used. Bayesian statistics can express the subjective concept of “approximately” as an objective concept of “numerical value”, which can be useful for statistical estimation in the food field, such as sensory science, which involves many social scientific aspects. Additionally, Bayesian statistics can be updated in real time by incorporating new data into the previous research data (prior probability), resulting in increasingly accurate as more data is accumulated.

In conclusion, dichotomous statistical analysis using NHST and P -values in food research is problematic. As a complement or alternative, it is worth considering a gradual transition to using relatively simple statistical concepts such as CI and effect size, which can provide more information about your results compared to dichotomous statistical analysis using NHST and P -values. Additionally, although Bayesian statistics are more complex, it can also be a valuable alternative to consider.

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number NRF-2018R1D1A1B07048619).

Declarations

The author declare no conflict of interest.

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9.1: Null and Alternative Hypotheses

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

\(H_0\): The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.

\(H_a\): The alternative hypothesis: It is a claim about the population that is contradictory to \(H_0\) and what we conclude when we reject \(H_0\). This is usually what the researcher is trying to prove.

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

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject \(H_0\)" if the sample information favors the alternative hypothesis or "do not reject \(H_0\)" or "decline to reject \(H_0\)" if the sample information is insufficient to reject the null hypothesis.

\(H_{0}\) always has a symbol with an equal in it. \(H_{a}\) never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example \(\PageIndex{1}\)

• \(H_{0}\): No more than 30% of the registered voters in Santa Clara County voted in the primary election. \(p \leq 30\)
• \(H_{a}\): More than 30% of the registered voters in Santa Clara County voted in the primary election. \(p > 30\)

Exercise \(\PageIndex{1}\)

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

• \(H_{0}\): The drug reduces cholesterol by 25%. \(p = 0.25\)
• \(H_{a}\): The drug does not reduce cholesterol by 25%. \(p \neq 0.25\)

Example \(\PageIndex{2}\)

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

• \(H_{0}: \mu = 2.0\)
• \(H_{a}: \mu \neq 2.0\)

Exercise \(\PageIndex{2}\)

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

• \(H_{0}: \mu \_ 66\)
• \(H_{a}: \mu \_ 66\)
• \(H_{0}: \mu = 66\)
• \(H_{a}: \mu \neq 66\)

Example \(\PageIndex{3}\)

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

• \(H_{0}: \mu \geq 5\)
• \(H_{a}: \mu < 5\)

Exercise \(\PageIndex{3}\)

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

• \(H_{0}: \mu \_ 45\)
• \(H_{a}: \mu \_ 45\)
• \(H_{0}: \mu \geq 45\)
• \(H_{a}: \mu < 45\)

Example \(\PageIndex{4}\)

In an issue of U. S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

• \(H_{0}: p \leq 0.066\)
• \(H_{a}: p > 0.066\)

Exercise \(\PageIndex{4}\)

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

• \(H_{0}: p \_ 0.40\)
• \(H_{a}: p \_ 0.40\)
• \(H_{0}: p = 0.40\)
• \(H_{a}: p > 0.40\)

COLLABORATIVE EXERCISE

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

In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we:

• Evaluate the null hypothesis , typically denoted with \(H_{0}\). The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality \((=, \leq \text{or} \geq)\)
• Always write the alternative hypothesis , typically denoted with \(H_{a}\) or \(H_{1}\), using less than, greater than, or not equals symbols, i.e., \((\neq, >, \text{or} <)\).
• If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.
• Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

Formula Review

\(H_{0}\) and \(H_{a}\) are contradictory.

• If \(\alpha \leq p\)-value, then do not reject \(H_{0}\).
• If\(\alpha > p\)-value, then reject \(H_{0}\).

\(\alpha\) is preconceived. Its value is set before the hypothesis test starts. The \(p\)-value is calculated from the data.References

Data from the National Institute of Mental Health. Available online at http://www.nimh.nih.gov/publicat/depression.cfm .