define null hypothesis and alternative hypothesis with example

Have a language expert improve your writing

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

Knowledge Base
Null and Alternative Hypotheses | Definitions & Examples

Null & Alternative Hypotheses | Definitions, Templates & Examples

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

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

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

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

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

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

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

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

Receive feedback on language, structure, and formatting

Professional editors proofread and edit your paper by focusing on:

Academic style
Vague sentences
Style consistency

See an example

define null hypothesis and alternative hypothesis with example

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

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

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

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

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

Examples of null hypotheses

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

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

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

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

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

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

Examples of alternative hypotheses

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

Null and alternative hypotheses are similar in some ways:

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

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

Prevent plagiarism. Run a free check.

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

General template sentences

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

Does independent variable affect dependent variable ?

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

Test-specific template sentences

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

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

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

Normal distribution
Descriptive statistics
Measures of central tendency
Correlation coefficient

Methodology

Cluster sampling
Stratified sampling
Types of interviews
Cohort study
Thematic analysis

Research bias

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

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

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

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

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

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

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

Cite this Scribbr article

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

Turney, S. (2023, June 22). Null & Alternative Hypotheses | Definitions, Templates & Examples. Scribbr. Retrieved March 20, 2024, from https://www.scribbr.com/statistics/null-and-alternative-hypotheses/

Is this article helpful?

Shaun Turney

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

Have a thesis expert improve your writing

Check your thesis for plagiarism in 10 minutes, generate your apa citations for free.

Knowledge Base
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 .

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

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.

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.

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.

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

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 ≤).

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

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

Cite this Scribbr article

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

Turney, S. (2022, December 06). Null and Alternative Hypotheses | Definitions & Examples. Scribbr. Retrieved 20 March 2024, from https://www.scribbr.co.uk/stats/null-and-alternative-hypothesis/

Is this article helpful?

Shaun Turney

Other students also liked, levels of measurement: nominal, ordinal, interval, ratio, the standard normal distribution | calculator, examples & uses, types of variables in research | definitions & examples.

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 .

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.

OpenStax, Statistics, Null and Alternative Hypotheses. Provided by : OpenStax. Located at : http://cnx.org/contents/[email protected]:58/Introductory_Statistics . License : CC BY: Attribution
Introductory Statistics . Authored by : Barbara Illowski, Susan Dean. Provided by : Open Stax. Located at : http://cnx.org/contents/[email protected] . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]
Simple hypothesis testing | Probability and Statistics | Khan Academy. Authored by : Khan Academy. Located at : https://youtu.be/5D1gV37bKXY . License : All Rights Reserved . License Terms : Standard YouTube License

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 .

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

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

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.

As an Amazon Associate we earn from qualifying purchases.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-statistics . Changes were made to the original material, including updates to art, structure, and other content updates.

Access for free at https://openstax.org/books/statistics/pages/1-introduction

Authors: Barbara Illowsky, Susan Dean
Publisher/website: OpenStax
Book title: Statistics
Publication date: Mar 27, 2020
Location: Houston, Texas
Book URL: https://openstax.org/books/statistics/pages/1-introduction
Section URL: https://openstax.org/books/statistics/pages/9-1-null-and-alternative-hypotheses

© Jan 23, 2024 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

Null Hypothesis and Alternative Hypothesis

Inferential Statistics
Statistics Tutorials
Probability & Games
Descriptive Statistics
Applications Of Statistics
Math Tutorials
Pre Algebra & Algebra
Exponential Decay
Worksheets By Grade
Ph.D., Mathematics, Purdue University
M.S., Mathematics, Purdue University
B.A., Mathematics, Physics, and Chemistry, Anderson University

Hypothesis testing involves the careful construction of two statements: the null hypothesis and the alternative hypothesis. These hypotheses can look very similar but are actually different.

How do we know which hypothesis is the null and which one is the alternative? We will see that there are a few ways to tell the difference.

The Null Hypothesis

The null hypothesis reflects that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign. This hypothesis is denoted by H 0 .

The null hypothesis is what we attempt to find evidence against in our hypothesis test. We hope to obtain a small enough p-value that it is lower than our level of significance alpha and we are justified in rejecting the null hypothesis. If our p-value is greater than alpha, then we fail to reject the null hypothesis.

If the null hypothesis is not rejected, then we must be careful to say what this means. The thinking on this is similar to a legal verdict. Just because a person has been declared "not guilty", it does not mean that he is innocent. In the same way, just because we failed to reject a null hypothesis it does not mean that the statement is true.

For example, we may want to investigate the claim that despite what convention has told us, the mean adult body temperature is not the accepted value of 98.6 degrees Fahrenheit . The null hypothesis for an experiment to investigate this is “The mean adult body temperature for healthy individuals is 98.6 degrees Fahrenheit.” If we fail to reject the null hypothesis, then our working hypothesis remains that the average adult who is healthy has a temperature of 98.6 degrees. We do not prove that this is true.

If we are studying a new treatment, the null hypothesis is that our treatment will not change our subjects in any meaningful way. In other words, the treatment will not produce any effect in our subjects.

The Alternative Hypothesis

The alternative or experimental hypothesis reflects that there will be an observed effect for our experiment. In a mathematical formulation of the alternative hypothesis, there will typically be an inequality, or not equal to symbol. This hypothesis is denoted by either H a or by H 1 .

The alternative hypothesis is what we are attempting to demonstrate in an indirect way by the use of our hypothesis test. If the null hypothesis is rejected, then we accept the alternative hypothesis. If the null hypothesis is not rejected, then we do not accept the alternative hypothesis. Going back to the above example of mean human body temperature, the alternative hypothesis is “The average adult human body temperature is not 98.6 degrees Fahrenheit.”

If we are studying a new treatment, then the alternative hypothesis is that our treatment does, in fact, change our subjects in a meaningful and measurable way.

The following set of negations may help when you are forming your null and alternative hypotheses. Most technical papers rely on just the first formulation, even though you may see some of the others in a statistics textbook.

Null hypothesis: “ x is equal to y .” Alternative hypothesis “ x is not equal to y .”
Null hypothesis: “ x is at least y .” Alternative hypothesis “ x is less than y .”
Null hypothesis: “ x is at most y .” Alternative hypothesis “ x is greater than y .”
An Example of a Hypothesis Test
Hypothesis Test for the Difference of Two Population Proportions
What Is a P-Value?
How to Conduct a Hypothesis Test
Hypothesis Test Example
Chi-Square Goodness of Fit Test
How to Do Hypothesis Tests With the Z.TEST Function in Excel
The Difference Between Type I and Type II Errors in Hypothesis Testing
Type I and Type II Errors in Statistics
The Runs Test for Random Sequences
What 'Fail to Reject' Means in a Hypothesis Test
What Is the Difference Between Alpha and P-Values?
An Example of Chi-Square Test for a Multinomial Experiment
Null Hypothesis Definition and Examples
What Is a Hypothesis? (Science)
Null Hypothesis Examples

Hypothesis Testing: Null Hypothesis and Alternative Hypothesis

Figuring out exactly what the null hypothesis and the alternative hypotheses are is not a walk in the park. Hypothesis testing is based on the knowledge that you can acquire by going over what we have previously covered about statistics in our blog.

So, if you don’t want to have a hard time keeping up, make sure you have read all the tutorials about confidence intervals , distributions , z-tables and t-tables .

We've also made a video on null hypothesis vs alternative hypothesis - you can watch it below or just scroll down if you prefer reading.

Confidence intervals, distributions, z-tables and t-tables

Confidence intervals provide us with an estimation of where the parameters are located. You can obtain them with our confidence interval calculator and learn more about them in the related article.

However, when we are making a decision, we need a yes or no answer. The correct approach, in this case, is to use a test .

Here we will start learning about one of the fundamental tasks in statistics - hypothesis testing !

The Hypothesis Testing Process

First off, let’s talk about data-driven decision-making. It consists of the following steps:

First, we must formulate a hypothesis .
After doing that, we have to find the right test for our hypothesis .
Then, we execute the test.
Finally, we make a decision based on the result.

Steps in data driven decision making, null hypothesis

Let’s start from the beginning.

What is a Hypothesis?

Though there are many ways to define it, the most intuitive must be:

“A hypothesis is an idea that can be tested.”

This is not the formal definition, but it explains the point very well.

So, if we say that apples in New York are expensive, this is an idea or a statement. However, it is not testable, until we have something to compare it with.

Apples in New York are expensive, null hypothesis

For instance, if we define expensive as: any price higher than $1.75 dollars per pound, then it immediately becomes a hypothesis .

What Cannot Be a Hypothesis?

An example may be: would the USA do better or worse under a Clinton administration, compared to a Trump administration? Statistically speaking, this is an idea , but there is no data to test it. Therefore, it cannot be a hypothesis of a statistical test.

No data, cannot be tested = not a hypothesis

Actually, it is more likely to be a topic of another discipline.

Conversely, in statistics, we may compare different US presidencies that have already been completed. For example, the Obama administration and the Bush administration, as we have data on both.

A Two-Sided Test

Alright, let’s get out of politics and get into hypotheses . Here’s a simple topic that CAN be tested.

According to Glassdoor (the popular salary information website), the mean data scientist salary in the US is 113,000 dollars.

So, we want to test if their estimate is correct.

The Null and Alternative Hypotheses

There are two hypotheses that are made: the null hypothesis , denoted H 0 , and the alternative hypothesis , denoted H 1 or H A .

Null hypothesis and alternative hypothesis

The null hypothesis is the one to be tested and the alternative is everything else. In our example:

The null hypothesis would be: The mean data scientist salary is 113,000 dollars.

While the alternative : The mean data scientist salary is not 113,000 dollars.

Author's note: If you're interested in a data scientist career, check out our articles Data Scientist Career Path , 5 Business Basics for Data Scientists , Data Science Interview Questions , and 15 Data Science Consulting Companies Hiring Now .

An Example of a One-Sided Test

You can also form one-sided or one-tailed tests.

Say your friend, Paul, told you that he thinks data scientists earn more than 125,000 dollars per year. You doubt him, so you design a test to see who’s right.

The null hypothesis of this test would be: The mean data scientist salary is more than 125,000 dollars.

The alternative will cover everything else, thus: The mean data scientist salary is less than or equal to 125,000 dollars.

Important: The outcomes of tests refer to the population parameter rather than the sample statistic! So, the result that we get is for the population.

Important: Another crucial consideration is that, generally, the researcher is trying to reject the null hypothesis . Think about the null hypothesis as the status quo and the alternative as the change or innovation that challenges that status quo. In our example, Paul was representing the status quo, which we were challenging.

Let’s go over it once more. In statistics, the null hypothesis is the statement we are trying to reject. Therefore, the null hypothesis is the present state of affairs, while the alternative is our personal opinion.

The null hypothesis is the present state of affairs, while the alternative is our personal opinion

Why Hypothesis Testing Works

Right now, you may be feeling a little puzzled. This is normal because this whole concept is counter-intuitive at the beginning. However, there is an extremely easy way to continue your journey of exploring it. By diving into the linked tutorial, you will find out why hypothesis testing actually works.

Interested in learning more? You can take your skills from good to great with our statistics course!

Try statistics course for free

Next Tutorial: Hypothesis Testing: Significance Level and Rejection Region

Iliya Valchanov

Co-founder of 365 Data Science

Iliya is a finance graduate with a strong quantitative background who chose the exciting path of a startup entrepreneur. He demonstrated a formidable affinity for numbers during his childhood, winning more than 90 national and international awards and competitions through the years. Iliya started teaching at university, helping other students learn statistics and econometrics. Inspired by his first happy students, he co-founded 365 Data Science to continue spreading knowledge. He authored several of the program’s online courses in mathematics, statistics, machine learning, and deep learning.

We Think you'll also like

Statistics Tutorials

False Positive vs. False Negative: Type I and Type II Errors in Statistical Hypothesis Testing

Hypothesis Testing with Z-Test: Significance Level and Rejection Region

Calculating and Using Covariance and Linear Correlation Coefficient

Getting Familiar with the Central Limit Theorem and the Standard Error

Statistics Resources

Excel - Tutorials
Basic Probability Rules
Single Event Probability
Complement Rule
Levels of Measurement
Independent and Dependent Variables
Entering Data
Central Tendency
Data and Tests
Displaying Data
Discussing Statistics In-text
SEM and Confidence Intervals
Two-Way Frequency Tables
Empirical Rule
Finding Probability
Accessing SPSS
Chart and Graphs
Frequency Table and Distribution
Descriptive Statistics
Converting Raw Scores to Z-Scores
Converting Z-scores to t-scores
Split File/Split Output
Partial Eta Squared
Downloading and Installing G*Power: Windows/PC
Correlation
Testing Parametric Assumptions
One-Way ANOVA
Two-Way ANOVA
Repeated Measures ANOVA
Goodness-of-Fit
Test of Association
Pearson's r
Point Biserial
Mediation and Moderation
Simple Linear Regression
Multiple Linear Regression
Binomial Logistic Regression
Multinomial Logistic Regression
Independent Samples T-test
Dependent Samples T-test
Testing Assumptions
T-tests using SPSS
T-Test Practice
Predictive Analytics This link opens in a new window
Quantitative Research Questions
Null & Alternative Hypotheses
One-Tail vs. Two-Tail
Alpha & Beta
Associated Probability
Decision Rule
Statement of Conclusion
Statistics Group Sessions

ASC Chat Hours

ASC Chat is usually available at the following times ( Pacific Time):

If there is not a coach on duty, submit your question via one of the below methods:

928-440-1325

Ask a Coach

[email protected]

Search our FAQs on the Academic Success Center's Ask a Coach page.

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.

Was this resource helpful?

<< Previous: Hypothesis Testing
Next: One-Tail vs. Two-Tail >>
Last Updated: Jan 16, 2024 12:09 PM
URL: https://resources.nu.edu/statsresources

school Campus Bookshelves
menu_book Bookshelves
perm_media Learning Objects
login Login
how_to_reg Request Instructor Account
hub Instructor Commons
Download Page (PDF)
Download Full Book (PDF)
Periodic Table
Physics Constants
Scientific Calculator
Reference & Cite
Tools expand_more
Readability

selected template will load here

This action is not available.

9.2: Null and Alternative Hypotheses

Last updated
Save as PDF
Page ID 6962

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:

$H_{0}: \mu \geq 5$
$H_{a}: \mu < 5$

Exercise $\PageIndex{3}$

$H_{0}: \mu \ \_ \ 45$
$H_{a}: \mu \ \_ \ 45$
$H_{0}: \mu \geq 45$
$H_{a}: \mu < 45$

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

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 .

Contributors

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] .

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

Published by Zach

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

Want to join the conversation?

Upvote Button navigates to signup page
Downvote Button navigates to signup page
Flag Button navigates to signup page

Video transcript

school Campus Bookshelves
menu_book Bookshelves
perm_media Learning Objects
login Login
how_to_reg Request Instructor Account
hub Instructor Commons
Download Page (PDF)
Download Full Book (PDF)
Periodic Table
Physics Constants
Scientific Calculator
Reference & Cite
Tools expand_more
Readability

selected template will load here

This action is not available.

12.3.1: Null and Alternative Hypotheses

Last updated
Save as PDF
Page ID 109930

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.

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.

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 $\PageIndex{2}$

$H_{0}: \mu \_ 66$
$H_{a}: \mu \_ 66$
$H_{0}: \mu = 66$
$H_{a}: \mu \neq 66$

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 $\PageIndex{3}$

$H_{0}: \mu \_ 45$
$H_{a}: \mu \_ 45$
$H_{0}: \mu \geq 45$
$H_{a}: \mu < 45$

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 $\PageIndex{4}$

$H_{0}: p \_ 0.40$
$H_{a}: p \_ 0.40$
$H_{0}: p = 0.40$
$H_{a}: p > 0.40$

COLLABORATIVE EXERCISE

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 .

Null hypothesis

Null hypothesis n., plural: null hypotheses [nʌl haɪˈpɒθɪsɪs] Definition: a hypothesis that is valid or presumed true until invalidated by a statistical test

Table of Contents

Null Hypothesis Definition

Null hypothesis is defined as “the commonly accepted fact (such as the sky is blue) and researcher aim to reject or nullify this fact”.

More formally, we can define a null hypothesis as “a statistical theory suggesting that no statistical relationship exists between given observed variables” .

In biology , the null hypothesis is used to nullify or reject a common belief. The researcher carries out the research which is aimed at rejecting the commonly accepted belief.

What Is a Null Hypothesis?

A hypothesis is defined as a theory or an assumption that is based on inadequate evidence. It needs and requires more experiments and testing for confirmation. There are two possibilities that by doing more experiments and testing, a hypothesis can be false or true. It means it can either prove wrong or true (Blackwelder, 1982).

For example, Susie assumes that mineral water helps in the better growth and nourishment of plants over distilled water. To prove this hypothesis, she performs this experiment for almost a month. She watered some plants with mineral water and some with distilled water.

In a hypothesis when there are no statistically significant relationships among the two variables, the hypothesis is said to be a null hypothesis. The investigator is trying to disprove such a hypothesis. In the above example of plants, the null hypothesis is:

There are no statistical relationships among the forms of water that are given to plants for growth and nourishment.

Usually, an investigator tries to prove the null hypothesis wrong and tries to explain a relation and association between the two variables.

An opposite and reverse of the null hypothesis are known as the alternate hypothesis . In the example of plants the alternate hypothesis is:

There are statistical relationships among the forms of water that are given to plants for growth and nourishment.

The example below shows the difference between null vs alternative hypotheses:

Alternate Hypothesis: The world is round Null Hypothesis: The world is not round.

Copernicus and many other scientists try to prove the null hypothesis wrong and false. By their experiments and testing, they make people believe that alternate hypotheses are correct and true. If they do not prove the null hypothesis experimentally wrong then people will not believe them and never consider the alternative hypothesis true and correct.

The alternative and null hypothesis for Susie’s assumption is:

Null Hypothesis: If one plant is watered with distilled water and the other with mineral water, then there is no difference in the growth and nourishment of these two plants.
Alternative Hypothesis: If one plant is watered with distilled water and the other with mineral water, then the plant with mineral water shows better growth and nourishment.

The null hypothesis suggests that there is no significant or statistical relationship. The relation can either be in a single set of variables or among two sets of variables.

Most people consider the null hypothesis true and correct. Scientists work and perform different experiments and do a variety of research so that they can prove the null hypothesis wrong or nullify it. For this purpose, they design an alternate hypothesis that they think is correct or true. The null hypothesis symbol is H 0 (it is read as H null or H zero ).

Why is it named the “Null”?

The name null is given to this hypothesis to clarify and explain that the scientists are working to prove it false i.e. to nullify the hypothesis. Sometimes it confuses the readers; they might misunderstand it and think that statement has nothing. It is blank but, actually, it is not. It is more appropriate and suitable to call it a nullifiable hypothesis instead of the null hypothesis.

Why do we need to assess it? Why not just verify an alternate one?

In science, the scientific method is used. It involves a series of different steps. Scientists perform these steps so that a hypothesis can be proved false or true. Scientists do this to confirm that there will be any limitation or inadequacy in the new hypothesis. Experiments are done by considering both alternative and null hypotheses, which makes the research safe. It gives a negative as well as a bad impact on research if a null hypothesis is not included or a part of the study. It seems like you are not taking your research seriously and not concerned about it and just want to impose your results as correct and true if the null hypothesis is not a part of the study.

Development of the Null

In statistics, firstly it is necessary to design alternate and null hypotheses from the given problem. Splitting the problem into small steps makes the pathway towards the solution easier and less challenging. how to write a null hypothesis?

Writing a null hypothesis consists of two steps:

Firstly, initiate by asking a question.
Secondly, restate the question in such a way that it seems there are no relationships among the variables.

In other words, assume in such a way that the treatment does not have any effect.

The usual recovery duration after knee surgery is considered almost 8 weeks.

A researcher thinks that the recovery period may get elongated if patients go to a physiotherapist for rehabilitation twice per week, instead of thrice per week, i.e. recovery duration reduces if the patient goes three times for rehabilitation instead of two times.

Step 1: Look for the problem in the hypothesis. The hypothesis either be a word or can be a statement. In the above example the hypothesis is:

“The expected recovery period in knee rehabilitation is more than 8 weeks”

Step 2: Make a mathematical statement from the hypothesis. Averages can also be represented as μ, thus the null hypothesis formula will be.

In the above equation, the hypothesis is equivalent to H1, the average is denoted by μ and > that the average is greater than eight.

Step 3: Explain what will come up if the hypothesis does not come right i.e., the rehabilitation period may not proceed more than 08 weeks.

There are two options: either the recovery will be less than or equal to 8 weeks.

H 0 : μ ≤ 8

In the above equation, the null hypothesis is equivalent to H 0 , the average is denoted by μ and ≤ represents that the average is less than or equal to eight.

What will happen if the scientist does not have any knowledge about the outcome?

Problem: An investigator investigates the post-operative impact and influence of radical exercise on patients who have operative procedures of the knee. The chances are either the exercise will improve the recovery or will make it worse. The usual time for recovery is 8 weeks.

Step 1: Make a null hypothesis i.e. the exercise does not show any effect and the recovery time remains almost 8 weeks.

H 0 : μ = 8

In the above equation, the null hypothesis is equivalent to H 0 , the average is denoted by μ, and the equal sign (=) shows that the average is equal to eight.

Step 2: Make the alternate hypothesis which is the reverse of the null hypothesis. Particularly what will happen if treatment (exercise) makes an impact?

In the above equation, the alternate hypothesis is equivalent to H1, the average is denoted by μ and not equal sign (≠) represents that the average is not equal to eight.

Significance Tests

To get a reasonable and probable clarification of statistics (data), a significance test is performed. The null hypothesis does not have data. It is a piece of information or statement which contains numerical figures about the population. The data can be in different forms like in means or proportions. It can either be the difference of proportions and means or any odd ratio.

The following table will explain the symbols:

P-value is the chief statistical final result of the significance test of the null hypothesis.

P-value = Pr(data or data more extreme | H 0 true)
| = “given”
Pr = probability
H 0 = the null hypothesis

The first stage of Null Hypothesis Significance Testing (NHST) is to form an alternate and null hypothesis. By this, the research question can be briefly explained.

Null Hypothesis = no effect of treatment, no difference, no association Alternative Hypothesis = effective treatment, difference, association

When to reject the null hypothesis?

Researchers will reject the null hypothesis if it is proven wrong after experimentation. Researchers accept null hypothesis to be true and correct until it is proven wrong or false. On the other hand, the researchers try to strengthen the alternate hypothesis. The binomial test is performed on a sample and after that, a series of tests were performed (Frick, 1995).

Step 1: Evaluate and read the research question carefully and consciously and make a null hypothesis. Verify the sample that supports the binomial proportion. If there is no difference then find out the value of the binomial parameter.

Show the null hypothesis as:

H 0 :p= the value of p if H 0 is true

To find out how much it varies from the proposed data and the value of the null hypothesis, calculate the sample proportion.

Step 2: In test statistics, find the binomial test that comes under the null hypothesis. The test must be based on precise and thorough probabilities. Also make a list of pmf that apply, when the null hypothesis proves true and correct.

When H 0 is true, X~b(n, p)

N = size of the sample

P = assume value if H 0 proves true.

Step 3: Find out the value of P. P-value is the probability of data that is under observation.

Rise or increase in the P value = Pr(X ≥ x)

X = observed number of successes

P value = Pr(X ≤ x).

Step 4: Demonstrate the findings or outcomes in a descriptive detailed way.

Sample proportion
The direction of difference (either increases or decreases)

Perceived Problems With the Null Hypothesis

Variable or model selection and less information in some cases are the chief important issues that affect the testing of the null hypothesis. Statistical tests of the null hypothesis are reasonably not strong. There is randomization about significance. (Gill, 1999) The main issue with the testing of the null hypothesis is that they all are wrong or false on a ground basis.

There is another problem with the a-level . This is an ignored but also a well-known problem. The value of a-level is without a theoretical basis and thus there is randomization in conventional values, most commonly 0.q, 0.5, or 0.01. If a fixed value of a is used, it will result in the formation of two categories (significant and non-significant) The issue of a randomized rejection or non-rejection is also present when there is a practical matter which is the strong point of the evidence related to a scientific matter.

The P-value has the foremost importance in the testing of null hypothesis but as an inferential tool and for interpretation, it has a problem. The P-value is the probability of getting a test statistic at least as extreme as the observed one.

The main point about the definition is: Observed results are not based on a-value

Moreover, the evidence against the null hypothesis was overstated due to unobserved results. A-value has importance more than just being a statement. It is a precise statement about the evidence from the observed results or data. Similarly, researchers found that P-values are objectionable. They do not prefer null hypotheses in testing. It is also clear that the P-value is strictly dependent on the null hypothesis. It is computer-based statistics. In some precise experiments, the null hypothesis statistics and actual sampling distribution are closely related but this does not become possible in observational studies.

Some researchers pointed out that the P-value is depending on the sample size. If the true and exact difference is small, a null hypothesis even of a large sample may get rejected. This shows the difference between biological importance and statistical significance. (Killeen, 2005)

Another issue is the fix a-level, i.e., 0.1. On the basis, if a-level a null hypothesis of a large sample may get accepted or rejected. If the size of simple is infinity and the null hypothesis is proved true there are still chances of Type I error. That is the reason this approach or method is not considered consistent and reliable. There is also another problem that the exact information about the precision and size of the estimated effect cannot be known. The only solution is to state the size of the effect and its precision.

Null Hypothesis Examples

Here are some examples:

Example 1: Hypotheses with One Sample of One Categorical Variable

Among all the population of humans, almost 10% of people prefer to do their task with their left hand i.e. left-handed. Let suppose, a researcher in the Penn States says that the population of students at the College of Arts and Architecture is mostly left-handed as compared to the general population of humans in general public society. In this case, there is only a sample and there is a comparison among the known population values to the population proportion of sample value.

Research Question: Do artists more expected to be left-handed as compared to the common population persons in society?
Response Variable: Sorting the student into two categories. One category has left-handed persons and the other category have right-handed persons.
Form Null Hypothesis: Arts and Architecture college students are no more predicted to be lefty as compared to the common population persons in society (Lefty students of Arts and Architecture college population is 10% or p= 0.10)

Example 2: Hypotheses with One Sample of One Measurement Variable

A generic brand of antihistamine Diphenhydramine making medicine in the form of a capsule, having a 50mg dose. The maker of the medicines is concerned that the machine has come out of calibration and is not making more capsules with the suitable and appropriate dose.

Research Question: Does the statistical data recommended about the mean and average dosage of the population differ from 50mg?
Response Variable: Chemical assay used to find the appropriate dosage of the active ingredient.
Null Hypothesis: Usually, the 50mg dosage of capsules of this trade name (population average and means dosage =50 mg).

Example 3: Hypotheses with Two Samples of One Categorical Variable

Several people choose vegetarian meals on a daily basis. Typically, the researcher thought that females like vegetarian meals more than males.

Research Question: Does the data recommend that females (women) prefer vegetarian meals more than males (men) regularly?
Response Variable: Cataloguing the persons into vegetarian and non-vegetarian categories. Grouping Variable: Gender
Null Hypothesis: Gender is not linked to those who like vegetarian meals. (Population percent of women who eat vegetarian meals regularly = population percent of men who eat vegetarian meals regularly or p women = p men).

Example 4: Hypotheses with Two Samples of One Measurement Variable

Nowadays obesity and being overweight is one of the major and dangerous health issues. Research is performed to confirm that a low carbohydrates diet leads to faster weight loss than a low-fat diet.

Research Question: Does the given data recommend that usually, a low-carbohydrate diet helps in losing weight faster as compared to a low-fat diet?
Response Variable: Weight loss (pounds)
Explanatory Variable: Form of diet either low carbohydrate or low fat
Null Hypothesis: There is no significant difference when comparing the mean loss of weight of people using a low carbohydrate diet to people using a diet having low fat. (population means loss of weight on a low carbohydrate diet = population means loss of weight on a diet containing low fat).

Example 5: Hypotheses about the relationship between Two Categorical Variables

A case-control study was performed. The study contains nonsmokers, stroke patients, and controls. The subjects are of the same occupation and age and the question was asked if someone at their home or close surrounding smokes?

Research Question: Did second-hand smoke enhance the chances of stroke?
Variables: There are 02 diverse categories of variables. (Controls and stroke patients) (whether the smoker lives in the same house). The chances of having a stroke will be increased if a person is living with a smoker.
Null Hypothesis: There is no significant relationship between a passive smoker and stroke or brain attack. (odds ratio between stroke and the passive smoker is equal to 1).

Example 6: Hypotheses about the relationship between Two Measurement Variables

A financial expert observes that there is somehow a positive and effective relationship between the variation in stock rate price and the quantity of stock bought by non-management employees

Response variable- Regular alteration in price
Explanatory Variable- Stock bought by non-management employees
Null Hypothesis: The association and relationship between the regular stock price alteration ($) and the daily stock-buying by non-management employees ($) = 0.

Example 7: Hypotheses about comparing the relationship between Two Measurement Variables in Two Samples

Research Question: Is the relation between the bill paid in a restaurant and the tip given to the waiter, is linear? Is this relation different for dining and family restaurants?
Explanatory Variable- total bill amount
Response Variable- the amount of tip
Null Hypothesis: The relationship and association between the total bill quantity at a family or dining restaurant and the tip, is the same.

Try to answer the quiz below to check what you have learned so far about the null hypothesis.

Choose the best answer.

Send Your Results (Optional)

Time is Up!

Blackwelder, W. C. (1982). “Proving the null hypothesis” in clinical trials. Controlled Clinical Trials , 3(4), 345–353.
Frick, R. W. (1995). Accepting the null hypothesis. Memory & Cognition, 23(1), 132–138.
Gill, J. (1999). The insignificance of null hypothesis significance testing. Political Research Quarterly , 52(3), 647–674.
Killeen, P. R. (2005). An alternative to null-hypothesis significance tests. Psychological Science, 16(5), 345–353.

©BiologyOnline.com. Content provided and moderated by Biology Online Editors.

Last updated on June 16th, 2022

You will also like...

Geological Periods

Geological periods is a study guide that cites the different geological periods on Earth's timeline. Each has a brief ov..

Evolution of Life – Ancient Earth

Autotrophs flourished, absorbing carbon and light. Soon after, primitive life forms that could assimilate oxygen thrived..

Kidneys and Regulation of Water and Inorganic Ions

The kidneys are responsible for the regulation of water and inorganic ions. Read this tutorial to learn about the differ..

Plant Cell Defense

Plants protect themselves by releasing hydrogen peroxide to fight against fungal invasion. Another way is by secreting c..

Nutrients in the soil are essential to the proper growth of a land plant. This tutorial deals with the properties of soi..

Adaptive Radiation

The diversification of several new species from a recent ancestral source, each adapted to utilize or occupy a vacant ad..

Null Hypothesis

Null Hypothesis , often denoted as H 0, is a foundational concept in statistical hypothesis testing. It represents an assumption that no significant difference, effect, or relationship exists between variables within a population. It serves as a baseline assumption, positing no observed change or effect occurring. The null is t he truth or falsity of an idea in analysis.

In this article, we will discuss the null hypothesis in detail, along with some solved examples and questions on the null hypothesis.

Table of Content

What Is a Null Hypothesis?

Symbol of Null Hypothesis

Formula of null hypothesis, types of null hypothesis, principle of null hypothesis, how do you find null hypothesis, what is a null hypothesis.

Null Hypothesis in statistical analysis suggests the absence of statistical significance within a specific set of observed data. Hypothesis testing, using sample data, evaluates the validity of this hypothesis. Commonly denoted as H 0 or simply “null,” it plays an important role in quantitative analysis, examining theories related to markets, investment strategies, or economies to determine their validity.

Definition of Null Hypothesis

Null Hypothesis represent a default position, often suggesting no effect or difference, against which researchers compare their experimental results. The Null Hypothesis, often denoted as H 0 , asserts a default assumption in statistical analysis. It posits no significant difference or effect, serving as a baseline for comparison in hypothesis testing.

Null Hypothesis is represented as H 0 , the Null Hypothesis symbolizes the absence of a measurable effect or difference in the variables under examination.

Certainly, a simple example would be asserting that the mean score of a group is equal to a specified value like stating that the average IQ of a population is 100.

The Null Hypothesis is typically formulated as a statement of equality or absence of a specific parameter in the population being studied. It provides a clear and testable prediction for comparison with the alternative hypothesis. The formulation of the Null Hypothesis typically follows a concise structure, stating the equality or absence of a specific parameter in the population.

Mean Comparison (Two-sample t-test)

H 0 : μ 1 = μ 2

This asserts that there is no significant difference between the means of two populations or groups.

Proportion Comparison

H 0 : p 1 − p 2 = 0

This suggests no significant difference in proportions between two populations or conditions.

Equality in Variance (F-test in ANOVA)

H 0 : σ 1 = σ 2

This states that there’s no significant difference in variances between groups or populations.

Independence (Chi-square Test of Independence):

H 0 : Variables are independent

This asserts that there’s no association or relationship between categorical variables.

Null Hypotheses vary including simple and composite forms, each tailored to the complexity of the research question. Understanding these types is pivotal for effective hypothesis testing.

Equality Null Hypothesis (Simple Null Hypothesis)

The Equality Null Hypothesis, also known as the Simple Null Hypothesis, is a fundamental concept in statistical hypothesis testing that assumes no difference, effect or relationship between groups, conditions or populations being compared.

Non-Inferiority Null Hypothesis

In some studies, the focus might be on demonstrating that a new treatment or method is not significantly worse than the standard or existing one.

Superiority Null Hypothesis

The concept of a superiority null hypothesis comes into play when a study aims to demonstrate that a new treatment, method, or intervention is significantly better than an existing or standard one.

Independence Null Hypothesis

In certain statistical tests, such as chi-square tests for independence, the null hypothesis assumes no association or independence between categorical variables.

Homogeneity Null Hypothesis

In tests like ANOVA (Analysis of Variance), the null hypothesis suggests that there’s no difference in population means across different groups.

Examples of Null Hypothesis

Medicine: Null Hypothesis: “No significant difference exists in blood pressure levels between patients given the experimental drug versus those given a placebo.”
Education: Null Hypothesis: “There’s no significant variation in test scores between students using a new teaching method and those using traditional teaching.”
Economics: Null Hypothesis: “There’s no significant change in consumer spending pre- and post-implementation of a new taxation policy.”
Environmental Science: Null Hypothesis: “There’s no substantial difference in pollution levels before and after a water treatment plant’s establishment.”

The principle of the null hypothesis is a fundamental concept in statistical hypothesis testing. It involves making an assumption about the population parameter or the absence of an effect or relationship between variables.

In essence, the null hypothesis (H 0 ) proposes that there is no significant difference, effect, or relationship between variables. It serves as a starting point or a default assumption that there is no real change, no effect or no difference between groups or conditions.

$\alpha$

Null Hypothesis Rejection

Rejecting the Null Hypothesis occurs when statistical evidence suggests a significant departure from the assumed baseline. It implies that there is enough evidence to support the alternative hypothesis, indicating a meaningful effect or difference. Null Hypothesis rejection occurs when statistical evidence suggests a deviation from the assumed baseline, prompting a reconsideration of the initial hypothesis.

Identifying the Null Hypothesis involves defining the status quotient, asserting no effect and formulating a statement suitable for statistical analysis.

When is Null Hypothesis Rejected?

The Null Hypothesis is rejected when statistical tests indicate a significant departure from the expected outcome, leading to the consideration of alternative hypotheses. It occurs when statistical evidence suggests a deviation from the assumed baseline, prompting a reconsideration of the initial hypothesis.

Null Hypothesis and Alternative Hypothesis

In the realm of hypothesis testing, the null hypothesis (H 0 ) and alternative hypothesis (H₁ or Ha) play critical roles. The null hypothesis generally assumes no difference, effect, or relationship between variables, suggesting that any observed change or effect is due to random chance. Its counterpart, the alternative hypothesis, asserts the presence of a significant difference, effect, or relationship between variables, challenging the null hypothesis. These hypotheses are formulated based on the research question and guide statistical analyses.

Null Hypothesis vs Alternative Hypothesis

The null hypothesis (H 0 ) serves as the baseline assumption in statistical testing, suggesting no significant effect, relationship, or difference within the data. It often proposes that any observed change or correlation is merely due to chance or random variation. Conversely, the alternative hypothesis (H 1 or Ha) contradicts the null hypothesis, positing the existence of a genuine effect, relationship or difference in the data. It represents the researcher’s intended focus, seeking to provide evidence against the null hypothesis and support for a specific outcome or theory. These hypotheses form the crux of hypothesis testing, guiding the assessment of data to draw conclusions about the population being studied.

Example of Alternative and Null Hypothesis

Let’s envision a scenario where a researcher aims to examine the impact of a new medication on reducing blood pressure among patients. In this context:

Null Hypothesis (H 0 ): “The new medication does not produce a significant effect in reducing blood pressure levels among patients.”

Alternative Hypothesis (H 1 or Ha): “The new medication yields a significant effect in reducing blood pressure levels among patients.”

The null hypothesis implies that any observed alterations in blood pressure subsequent to the medication’s administration are a result of random fluctuations rather than a consequence of the medication itself. Conversely, the alternative hypothesis contends that the medication does indeed generate a meaningful alteration in blood pressure levels, distinct from what might naturally occur or by random chance.

Also, Check

Solved Examples on Null Hypothesis

Example 1: A researcher claims that the average time students spend on homework is 2 hours per night.

Null Hypothesis (H 0 ): The average time students spend on homework is equal to 2 hours per night. Data: A random sample of 30 students has an average homework time of 1.8 hours with a standard deviation of 0.5 hours. Test Statistic and Decision: Using a t-test, if the calculated t-statistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis. Conclusion: Based on the statistical analysis, we fail to reject the null hypothesis, suggesting that there is not enough evidence to dispute the claim of the average homework time being 2 hours per night.

Example 2: A company asserts that the error rate in its production process is less than 1%.

Null Hypothesis (H 0 ): The error rate in the production process is 1% or higher. Data: A sample of 500 products shows an error rate of 0.8%. Test Statistic and Decision: Using a z-test, if the calculated z-statistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis. Conclusion: The statistical analysis supports rejecting the null hypothesis, indicating that there is enough evidence to dispute the company’s claim of an error rate of 1% or higher.

Null Hypothesis – Practice Problems

Q1. A researcher claims that the average time spent by students on homework is less than 2 hours per day. Formulate the null hypothesis for this claim?

Q2. A manufacturing company states that their new machine produces widgets with a defect rate of less than 5%. Write the null hypothesis to test this claim?

Q3. An educational institute believes that their online course completion rate is at least 60%. Develop the null hypothesis to validate this assertion?

Q4. A restaurant claims that the waiting time for customers during peak hours is not more than 15 minutes. Formulate the null hypothesis for this claim?

Q5. A study suggests that the mean weight loss after following a specific diet plan for a month is more than 8 pounds. Construct the null hypothesis to evaluate this statement?

Null Hypothesis – Frequently Asked Questions

How to form a null hypothesis.

A null hypothesis is formed based on the assumption that there is no significant difference or effect between the groups being compared or no association between variables being tested. It often involves stating that there is no relationship, no change, or no effect in the population being studied.

When Do we reject the Null Hypothesis?

In statistical hypothesis testing, if the p-value (the probability of obtaining the observed results) is lower than the chosen significance level (commonly 0.05), we reject the null hypothesis. This suggests that the data provides enough evidence to refute the assumption made in the null hypothesis.

What is a Null Hypothesis in Research?

In research, the null hypothesis represents the default assumption or position that there is no significant difference or effect. Researchers often try to test this hypothesis by collecting data and performing statistical analyses to see if the observed results contradict the assumption.

What Are Alternative and Null Hypotheses?

The null hypothesis (H0) is the default assumption that there is no significant difference or effect. The alternative hypothesis (H1 or Ha) is the opposite, suggesting there is a significant difference, effect or relationship.

What Does it Mean to Reject the Null Hypothesis?

Rejecting the null hypothesis implies that there is enough evidence in the data to support the alternative hypothesis. In simpler terms, it suggests that there might be a significant difference, effect or relationship between the groups or variables being studied.

How to Find Null Hypothesis?

Formulating a null hypothesis often involves considering the research question and assuming that no difference or effect exists. It should be a statement that can be tested through data collection and statistical analysis, typically stating no relationship or no change between variables or groups.

How is Null Hypothesis denoted?

The null hypothesis is commonly symbolized as H 0 in statistical notation.

What is the Purpose of the Null hypothesis in Statistical Analysis?

The null hypothesis serves as a starting point for hypothesis testing, enabling researchers to assess if there’s enough evidence to reject it in favor of an alternative hypothesis.

What happens if we Reject the Null hypothesis?

Rejecting the null hypothesis implies that there is sufficient evidence to support an alternative hypothesis, suggesting a significant effect or relationship between variables.

Is it Possible to Prove the Null Hypothesis?

No, statistical testing aims to either reject or fail to reject the null hypothesis based on evidence from sample data. It does not prove the null hypothesis to be true.

What are Test for Null Hypothesis?

Various statistical tests, such as t-tests or chi-square tests, are employed to evaluate the validity of the Null Hypothesis in different scenarios.

Please Login to comment...

Geeks Premier League 2023
Math-Concepts
Geeks Premier League
School Learning
School Mathematics
10 Best Chegg Alternatives in 2024
Devin AI: World’s First AI Software Engineer
12 Best FlexClip Alternatives & Competitors in 2024 [Free + Paid]
What Is Trunk-Or-Treat?
30 OOPs Interview Questions and Answers (2024)

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

Key Differences

Know the Differences & Comparisons

Difference Between Null and Alternative Hypothesis

Null hypothesis implies a statement that expects no difference or effect. On the contrary, an alternative hypothesis is one that expects some difference or effect. Null hypothesis This article excerpt shed light on the fundamental differences between null and alternative hypothesis.

Content: Null Hypothesis Vs Alternative Hypothesis

Comparison chart, definition of null hypothesis.

A null hypothesis is a statistical hypothesis in which there is no significant difference exist between the set of variables. It is the original or default statement, with no effect, often represented by H 0 (H-zero). It is always the hypothesis that is tested. It denotes the certain value of population parameter such as µ, s, p. A null hypothesis can be rejected, but it cannot be accepted just on the basis of a single test.

Definition of Alternative Hypothesis

A statistical hypothesis used in hypothesis testing, which states that there is a significant difference between the set of variables. It is often referred to as the hypothesis other than the null hypothesis, often denoted by H 1 (H-one). It is what the researcher seeks to prove in an indirect way, by using the test. It refers to a certain value of sample statistic, e.g., x¯, s, p

The acceptance of alternative hypothesis depends on the rejection of the null hypothesis i.e. until and unless null hypothesis is rejected, an alternative hypothesis cannot be accepted.

Key Differences Between Null and Alternative Hypothesis

The important points of differences between null and alternative hypothesis are explained as under:

A null hypothesis is a statement, in which there is no relationship between two variables. An alternative hypothesis is a statement; that is simply the inverse of the null hypothesis, i.e. there is some statistical significance between two measured phenomenon.
A null hypothesis is what, the researcher tries to disprove whereas an alternative hypothesis is what the researcher wants to prove.
A null hypothesis represents, no observed effect whereas an alternative hypothesis reflects, some observed effect.
If the null hypothesis is accepted, no changes will be made in the opinions or actions. Conversely, if the alternative hypothesis is accepted, it will result in the changes in the opinions or actions.
As null hypothesis refers to population parameter, the testing is indirect and implicit. On the other hand, the alternative hypothesis indicates sample statistic, wherein, the testing is direct and explicit.
A null hypothesis is labelled as H 0 (H-zero) while an alternative hypothesis is represented by H 1 (H-one).
The mathematical formulation of a null hypothesis is an equal sign but for an alternative hypothesis is not equal to sign.
In null hypothesis, the observations are the outcome of chance whereas, in the case of the alternative hypothesis, the observations are an outcome of real effect.

There are two outcomes of a statistical test, i.e. first, a null hypothesis is rejected and alternative hypothesis is accepted, second, null hypothesis is accepted, on the basis of the evidence. In simple terms, a null hypothesis is just opposite of alternative hypothesis.

You Might Also Like:

Zipporah Thuo says

February 22, 2018 at 6:06 pm

The comparisons between the two hypothesis i.e Null hypothesis and the Alternative hypothesis are the best.Thank you.

Getu Gamo says

March 4, 2019 at 3:42 am

Thank you so much for the detail explanation on two hypotheses. Now I understood both very well, including their differences.

Jyoti Bhardwaj says

May 28, 2019 at 6:26 am

Thanks, Surbhi! Appreciate the clarity and precision of this content.

January 9, 2020 at 6:16 am

John Jenstad says

July 20, 2020 at 2:52 am

Thanks very much, Surbhi, for your clear explanation!!

Navita says

July 2, 2021 at 11:48 am

Thanks for the Comparison chart! it clears much of my doubt.

GURU UPPALA says

July 21, 2022 at 8:36 pm

Thanks for the Comparison chart!

Enock kipkoech says

September 22, 2022 at 1:57 pm

What are the examples of null hypothesis and substantive hypothesis

Alternative Hypothesis

Alternative hypothesis defines there is a statistically important relationship between two variables. Whereas null hypothesis states there is no statistical relationship between the two variables. In statistics, we usually come across various kinds of hypotheses. A statistical hypothesis is supposed to be a working statement which is assumed to be logical with given data. It should be noticed that a hypothesis is neither considered true nor false.

The alternative hypothesis is a statement used in statistical inference experiment. It is contradictory to the null hypothesis and denoted by H a or H 1 . We can also say that it is simply an alternative to the null. In hypothesis testing, an alternative theory is a statement which a researcher is testing. This statement is true from the researcher’s point of view and ultimately proves to reject the null to replace it with an alternative assumption. In this hypothesis, the difference between two or more variables is predicted by the researchers, such that the pattern of data observed in the test is not due to chance.

To check the water quality of a river for one year, the researchers are doing the observation. As per the null hypothesis, there is no change in water quality in the first half of the year as compared to the second half. But in the alternative hypothesis, the quality of water is poor in the second half when observed.

Difference Between Null and Alternative Hypothesis

Basically, there are three types of the alternative hypothesis, they are;

Left-Tailed : Here, it is expected that the sample proportion (π) is less than a specified value which is denoted by π 0 , such that;

H 1 : π < π 0

Right-Tailed: It represents that the sample proportion (π) is greater than some value, denoted by π 0 .

H 1 : π > π 0

Two-Tailed: According to this hypothesis, the sample proportion (denoted by π) is not equal to a specific value which is represented by π 0 .

H 1 : π ≠ π 0

Note: The null hypothesis for all the three alternative hypotheses, would be H 1 : π = π 0 .

Share Share

Register with BYJU'S & Download Free PDFs

CRO Platform

Test your insights. Run experiments. Win. Or learn. And then win.

eCommerce Customer Analytics Platform

Fully Automated CRO Platform

Hundreds of interactive, simultaneous experiments on your eCommerce website. On autopilot.

Customer Survey Platform

Managed Services
How we Help

Acquisition matters. But retention matters more. Understand, monitor & nurture the best customers.

Certified Partners
Case Studies
Ebooks, Tools, Templates
Digital Marketing Glossary
eCommerce Growth Stories
eCommerce Growth Show
Help & Technical Documentation

Home > Uncategorized > Null and Alternative Hypothesis in A/B Testing

Null and Alternative Hypothesis in A/B Testing

Article last updated: March 18, 2024
Article first published: March 18, 2024

In digital marketing, A/B testing involves comparing two versions of a webpage to determine which one delivers a higher conversion rate . This conversion could mean making a purchase, signing up for a newsletter, completing a form, or whichever is the desired action for that specific experiment.

Its purpose is to systematically improve website performance by identifying elements that influence visitor behavior .

However, before designing your A/B test, you must first establish both the null hypothesis and the alternative hypothesis .

The null hypothesis states that sample observations appear solely due to random chance.

In the context of A/B testing, the null hypothesis suggests that no difference exists between the control and variant groups .

In terms of A/B testing, the alternative hypothesis suggests that there is a difference between the control and variant groups .

For example, during an experiment, your null hypothesis might state that changing the color of the website’s CTA button from green to blue will not lead to any notable difference in conversion rates between the control and variant groups.

On the other hand, the alternative hypothesis states that the same action will deliver a noticeable difference in conversion rates.

Why use an alternative hypothesis?

While the null hypothesis says there’s no difference, the alternative hypothesis keeps you open to the possibility that changes could have a meaningful impact on metrics like user behavior and conversion rates.

Paying attention to the alternative hypothesis involves actively looking for ways to improve your website and overall marketing strategies.

It encourages you to stay curious and explore your data for different ideas to make our websites better – it’s a way to overcome organizational inertia and change the status quo to better meet the needs of your visitors.

Understanding the Alternative Hypothesis

To recap: the alternative hypothesis presents a contrasting idea to the null hypothesis .

While the null hypothesis suggests a certain outcome is true, the alternative hypothesis proposes that the opposite is true.

It’s often the hypothesis you investigate when aiming to challenge the null hypothesis.

If you collect sufficient evidence to support the alternative hypothesis, it replaces the null hypothesis as the explanation for the observed results.

Different types of alternative hypotheses can play a role in your CRO experiments, including:

One-tailed directional

In a one-tailed directional test for CRO, the alternative hypothesis focuses on changes happening in one direction only .

For instance, it might evaluate whether a particular change leads to an increase or decrease in conversion rates, but not both at the same time .

If the CRO specialist suspects the change will lead to a decrease in bounce rates, they might describe the test as left-tailed.

Conversely, if they predict the change will increase the click-through rates, they might describe the test as right-tailed.

Two-tailed or nondirectional

In a two-tailed or nondirectional test for CRO, the alternative hypothesis suggests that changes are happening, but it doesn’t specify whether those changes are positive or negative .

This means the test acknowledges that variations exist, but it doesn’t assume a particular direction of change.

In the context of CRO, a two-tailed test might suggest that changes to a website’s layout affect user behavior, without indicating whether the changes will increase or decrease conversion rates .

Formulating an Effective Alternative Hypothesis

To run the best experiments, make sure you base your hypotheses on psychology, data from web analytics, customer research, and what you’ve found out from previous experiments.

A good hypothesis follows a simple structure:

“If [we do this], then [this will happen].”

Here are a few examples to help you understand:

If we put a customer testimonial on the product page, then more people will feel confident and buy.
If we mention our fast delivery in the product description, then more people will notice it and fewer people will leave the website without doing anything.
If we change the text on the button to ‘Add to cart’, then people will feel less worried and add more things to their cart.

Besides the basic structure, you must also pay attention to the contents of your hypothesis. Ensure your hypothesis is:

Relevant : the hypothesis must align with the KPIs you’re using to evaluate the experiment.
Unambiguous: be very clear in specifying which change will be tested.
Measurable : ensure your results can be measured with the available tools in your suite.
Specific: include all crucial information about the variables tested in the hypothesis.

The Role of the Alternative Hypothesis in A/B Testing

Finding meaningful patterns in your data can be challenging, especially when your data is susceptible to random fluctuations.

Random noise can create apparent patterns purely by chance, adding unneeded complexity to your interpretation process.

One widely used method to avoid random occurrences directing your strategies is through hypothesis testing.

This approach is much more structured, allowing you to evaluate the likelihood of observed patterns that have appeared merely by random chance.

Now, let’s see how the alternative hypothesis shapes the very core of your experimentation process.

Guiding Experimental Design

At the heart of every A/B test lies a hypothesis waiting to be explored.

The alternative hypothesis provides the framework for our experiments, guiding you in crafting specific changes and variations to test against the control group.

It’s the “the voice of reason” that ensures your tests remain purposeful and focused, driving you towards meaningful discoveries.

Determining the Metrics for Measurement

Remember when we discussed how your hypothesis must be measurable in order to deliver effective insights?

Well, metrics are the pulse of A/B testing; it’s through them that you’re evaluating the efficiency of your experiments.

With that in mind, the alternative hypothesis outlines expected differences between the control and variant groups , revealing the metrics you need to track to evaluate these differences.

These metrics then become our benchmarks, helping you validate your hypotheses.

Evaluating Test Outcomes

At its end, A/B testing is all about discovering alternative ways to design your website – both from a UI and a UX perspective.

The alternative hypothesis guides your interpretation of test results and informs decision-making processes.

When the data aligns with the alternative hypothesis, it signals a breakthrough – your proposed changes have made a tangible impact .

This validation empowers you to move forward with confidence, armed with insights derived from experimentation.

Conversely, if the data disproves your hypothesis, it forces you to recalibrate your approach and explore new variations in your experiments.

Setting Up A/B Tests with the Alternative Hypothesis in Mind

So – how do you test your alternative hypothesis during an A/B test?

The process is pretty straightforward:

you identify the variable you want to test,
choose the metrics that will evaluate your hypothesis,
and finally, ensure your sample size delivers statistically significant results.

Now, let’s dive into the process and discuss each step in detail.

Define the Goals

Begin by aligning the objectives of your A/B testing with the core business goals of your company.

For example, imagine you’re a product manager at “Company X” in its startup phase. The company aims to boost user numbers , particularly active users measured by the Daily Active Users (DAU) metric.

Assuming this can be achieved by improving retention rates or increasing new registrations, you’ll focus your efforts accordingly.

Define the Metric

Determine the metric that will serve as the yardstick for evaluating the success of your A/B test.

While conversion rates are commonly used, you might opt for an intermediate metric like the Click-Through Rate (CTR).

In our example, the registration rate —calculated by the number of new users who register divided by total new site visitors— serves as the metric .

KPI tracking in Omniconvert Explore.

Develop a Hypothesis

Craft a hypothesis outlining the expected changes and the rationale behind them.

For instance, suppose you want to test whether changing the main page image increases registration rates.

The hypothesis could state: “If the main registration page image is changed, more new users will register due to the image better conveying product values.”

Identify both the null and alternative hypotheses to guide your testing approach.

Prepare an Experiment

To make sure your experiment is set up for success, follow these steps:

Create a new variation (B) reflecting the changes to be tested.
Define control and experimental groups, specifying user selection criteria and group size.
Randomly assign users to version A or B to ensure unbiased results.
Determine the statistical significance level (α) and minimum sample size required for each version.
Establish a time frame for the experiment based on daily traffic and sample size.

Experiment setup in Omniconvert’s complete A/B testing tool – Explore .

Conduct the Experiment

To execute the experiment diligently, it is crucial to coordinate with team members for smooth execution.

The next step is requesting access to a closed test site, if available, for data verification purposes.

Finally, you have to validate the experiment setup and avoid premature result analysis – this way your experiment will be both accurate and reliable.

Analyze the Results

To analyze the results, delve into the data to assess the performance of each version and determine statistical significance. Start by calculating success metric values for versions A and B.

Segment the data by relevant parameters, such as platforms or geographical regions, to gain deeper insights.

Evaluate statistical significance using p-values and significance levels to ascertain the validity of your findings. Interpret the results: if version B outperforms version A, your hypothesis is validated.

It’s important to note that A/B testing outcomes can vary; version B may win, lose, or show no significant difference. Understanding these results informs future testing and optimization efforts, driving continuous improvement in achieving business objectives.

Need more? Here’s how you can interpret experiment results using Omniconvert Explore. Check out the entire process and see for yourself how intuitive and straightforward it is!

Statistical Significance and the Alternative Hypothesis

In order to either accept or reject your hypothesis, your experiments must reach a certain significance level – which becomes the criteria you’re using to assess the results.

The significance level, often referred to as the alpha level or critical value, is commonly denoted by the Greek letter alpha (α) and represents a probability value.

Moreover, to determine the strength of evidence supporting either hypothesis (null or alternative), you’ll measure it against the p-value.

The p-value quantifies how likely it is to observe the data or something more extreme if the null hypothesis were true. Essentially, it indicates the probability of obtaining the observed results or more extreme results when the null hypothesis is true. A lower p-value suggests stronger evidence against the null hypothesis.

When conducting hypothesis testing, researchers compare the calculated p-value to a pre-determined significance level, often denoted as α.

The significance level represents the threshold for determining statistical significance. Commonly used significance levels include 0.05, 0.01, or 0.1.

If the calculated p-value is lower than the significance level (e.g., p < 0.05), it indicates that the observed difference is statistically significant. In this case, the evidence favors the alternative hypothesis over the null hypothesis.

Thus, researchers reject the null hypothesis in favor of the alternative hypothesis.

>> click here to read more about Statistical Significance in A/B testing.

Type I and Type II Errors

Balancing risks in hypothesis testing involves understanding Type I and Type II errors.

A Type I error occurs when the null hypothesis is incorrectly rejected, indicating significance when there is none. This is basically a false positive.

Conversely, a Type II error appears when the null hypothesis is erroneously accepted, failing to detect a true effect or difference. This is essentially a false negative.

Lowering the significance level decreases the risk of Type I errors but increases the likelihood of Type II errors, and vice versa.

To balance these risks, carefully consider the consequences and the context of the hypothesis test.

>> here’s a full article on Type I and Type II errors.

Power Analysis in the Context of the Alternative Hypothesis

Before undertaking power analysis, we must first understand the idea of “a statistical test power.”

The statistical power of a test refers to its likelihood of achieving statistical significance , thus delivering meaningful conclusions.

Unfortunately, power analysis is frequently overlooked in CRO.

There are various forms of power analyses, each serving distinct purposes.

Typically, power analysis is conducted during the initial design phase of a test to determine the required sample size.

Alternatively, post hoc analysis, another type of power analysis, occurs after the study concludes.

Post hoc analysis addresses questions such as:

determining the necessary sample size to detect a particular effect size
identifying the minimum effect size detectable with the given sample size,
and evaluating the power of the test procedure.

These questions, among others, can be addressed through power analysis.

Should you ever need to increase the power of an A/B test, try these ideas:

increase sample size
reduce variability within groups
select appropriate statistical methods
minimize experimental noise
focus on relevant variables

Interpreting Results in Light of the Alternative Hypothesis

As you review your A/B test outcomes, begin by conducting statistical tests to determine if your A/B test attained a sufficiently large sample size .

Fortunately, most A/B testing tools automate this process, allowing you to review results on your dashboard effortlessly.

Subsequently, identify the variant that outperformed others in terms of your primary metric. This early identification provides a frontrunner for the version you may eventually roll out to all your site visitors.

A good practice is examining your test results across multiple dimensions of customer behavior beyond just conversion rates, which typically serve as the primary metric for A/B testing.

Consider metrics like click-through rate, time spent on page, and revenue generated to gain a comprehensive understanding of your web pages and marketing campaigns.

For example, you might find that a targeted approach resulted in fewer conversions than expected- however, people who converted are higher-valued customers, with increased AOVs and more chances to return for future purchases.

Finally, besides analyzing the A/B test data, it’s crucial to consider external variables that might influence your results.

For instance, conducting an A/B test during peak holiday seasons or after significant industry events might skew your results. While controlling all variables is impractical, strive to ensure that your test generates generalizable results.

If you suspect external factors significantly impacted your A/B test results, consider repeating the test to validate your findings.

As for accepting or rejecting the alternative hypothesis, the rule is pretty straightforward:

When the p-value falls below the alpha threshold, the null hypothesis is rejected , and the alternative hypothesis is accepted.

Conversely, if the p-value exceeds the alpha threshold, we do not reject the null hypothesis .

Making Decisions Based on the Outcome of the Hypothesis Test

By the end of this process, you’ll have a clear idea of whether the new variations you tested in your A/B test have achieved the desired results.

If you find that there isn’t a significant difference between the variations you tested, that’s perfectly okay because testing is all about exploring different hypotheses. In such cases, you might decide to stick with your original design or continue experimenting to find improvements.

On the flip side, if you discover a new variation that outperforms your previous efforts, it’s time to celebrate and consider rolling it out to your entire audience.

There are various possible outcomes at this stage, and they can’t all be covered here. For example, if you have a variant with a high conversion rate but mediocre revenue generation, deciding whether to keep testing can be challenging.

The key advice is to view A/B testing as part of an ongoing process of optimizing conversion rates and continuously refining your website.

A Practical Case Study

Here’s how the A/B test with the alternative hypothesis looks in action, based on a real experiment we conducted for AliveCor.

AliveCor is a leading brand in the digital health technology sector, specializing in innovative solutions for heart health monitoring.

Their portable electrocardiogram (ECG) devices, integrated with user-friendly mobile applications, empower individuals to monitor their cardiovascular well-being proactively.

AliveCor faced the challenge of promoting its newly launched single lead device, KardiaMobile Card, without negatively impacting the sales of its existing devices.

KardiaMobile Card aimed to serve as an upgraded alternative to the widely acclaimed KardiaMobile, which had garnered attention across the healthcare industry.

Previous experiments revealed that users tended to interact more frequently with highlighted elements and products on AliveCor’s website.

Based on this insight, we hypothesized that adding a “New” badge to the KardiaMobile Card product detail page and the product tile on the listing page would increase the conversion rate across all devices.

Following the implementation of the “New” badge:

Conversion Rate increased by 25.17%
Revenue per user increased by 29.58%
Confidence level of success was 99.4%

Lessons Learned

The experiment demonstrated that a simple highlighting badge on new products significantly boosted the conversion rate without diminishing the sales of other products.

This finding underscores the effectiveness of strategic product highlighting in driving user engagement and sales.

Moving forward, AliveCor can leverage these findings to inform its marketing strategies and product promotions.

By continuing to emphasize new product offerings through strategic highlighting and promotion, AliveCor can effectively engage users and drive sales while maintaining a positive user experience.

This experiment highlights the importance of data-driven decision-making and iterative optimization in achieving business objectives in the digital health technology sector.

>> check out the full Case Study here .

Challenges and Considerations

As powerful a practice as it can be, the A/B test isn’t without its pitfalls. Here are some common challenges to be aware of:

1. Vague Hypotheses

Formulating a clear and specific alternative hypothesis is crucial for meaningful A/B testing.

Vague hypotheses can lead to ambiguous results and misinterpretation of data.

Without a precise hypothesis, it becomes challenging to draw actionable insights from the test outcomes.

Remember that your hypothesis must be relevant, unambiguous, measurable, and specific .

2. Overfitting

Overfitting occurs when a hypothesis is tailored too closely to the observed data, leading to inflated results that may not generalize well to other scenarios.

In A/B testing, overfitting can occur when the hypothesis is overly complex or when the test is run on a small sample size.

It’s important to strike a balance between complexity and generalizability to avoid overfitting.

3. Ignoring External Factors

As you saw earlier, external factors can, and will, influence your test results; failing to consider them can lead to biased conclusions .

Variables like seasonality, marketing campaigns, and user behavior trends can all impact the outcome of an A/B test.

Make sure you take them into consideration, so you don’t end up with inaccurate interpretations of the data and ineffective optimization efforts.

Ethical Considerations in A/B Testing

Finally, there are a few additional considerations, this time on the ethics’ side. These include:

Informed Consent

Users should be informed about their participation in A/B tests and any potential changes to their experience.

Transparency about the testing process and its implications is essential for maintaining trust.

Providing clear and accessible information about the purpose of the test, how data will be used, and any potential impact on the user experience helps ensure that users can make informed decisions about their participation.

Fair Treatment

It’s essential you ensure that all users are treated fairly throughout the A/B testing process.

This means that variations tested should not disproportionately impact certain groups negatively.

Careful consideration should be given to factors such as demographics, behavior patterns, and accessibility requirements to avoid inadvertently discriminating against specific segments of the user population.

Data Privacy

Respecting user privacy is paramount in A/B testing.

This involves anonymizing data and adhering to relevant data protection regulations to safeguard user information.

Avoid collecting unnecessary personal information during testing and ensure that data is handled securely and responsibly.

Prioritizing data privacy will build trust with your users and mitigate the risk of privacy breaches.

Embracing Continuous Learning

It’s important to note that A/B testing isn’t just a one-time activity; it’s an ongoing journey of learning and optimization .

Through continuous testing, you will refine your digital experiences over time, leading to improved user engagement and conversion rates .

Moreover, digital landscapes are dynamic, with user preferences, technology, and market trends constantly evolving.

Continuous testing ensures that websites and applications remain relevant and effective in meeting user needs.

By staying proactive and responsive to changes, you can adapt their digital strategies to align with shifting consumer behaviors and industry trends.

Lastly, when you embrace a culture of continuous testing and optimization, you gain a significant advantage.

You’re continually refining your digital offerings, thus staying ahead of the curve and responding to market changes better.

Continuous testing enables you to identify emerging opportunities, address user pain points, and maintain your position as an industry leader.

Whether you’re launching a new landing page or fine-tuning the subject line of an email marketing campaign, A/B testing stands as a vital tool for creating user experiences that drive conversions and boost sales.

Testing is the backbone of making informed decisions based on solid data.

However, it’s important to note that the efficacy of your A/B testing depends on the thoroughness of your results analysis.

You must understand the significance level of your tests, examine various KPIs, and formulate a hypothesis that is relevant, unambiguous, measurable, and specific.

While it sounds like a lot of work, it’s also necessary work.

Once you’re on top of the nuances of this critical stage of A/B testing, you’ll unlock the potential to achieve results beyond your expectations.

Sign up to our bi-monthly newsletter!

Actionable eCommerce insights only.

By clicking the button, you confirm that you agree with our Terms and Conditions .

Master what matters most in eCommerce

✅ Get more loyal customers

✅ Improve Customer Lifetime Value

✅ Maximize profits

30-day free trial, no credit card necessary.

Blog Categories

Oana Predoiu

If you liked this article, make it shine on your page :)

Latest Articles in the Category

See more related articles on these topics:

Uncategorized

What is a Good LTV to CAC Ratio?

How monitoring the LTV: CAC reveals true insights about your business health and why you can’t ignore it in 2024.

Understanding Customer Feedback: NPS vs CSAT vs CES

Why the NPS, CSAT, and CES are crucial metrics in measuring customer loyalty. How to track and apply these metrics in 2024.

How to Do Conversion Funnel Analysis Like a Pro

How to analyse and improve your conversion funnels to help you convert better, faster, and more effectively.

What topic do you want to explore?

We’ve got everything you need to broaden your eCommerce knowledge.

From concepts to hands-on materials on eCommerce optimizations, software and automation, data analysis and reporting. You name it!

We’re a team of people that want to empower marketers around the world to create marketing campaigns that matter to consumers in a smart way. Meet us at the intersection of creativity, integrity, and development, and let us show you how to optimize your marketing.

Our Software

> Book a Demo
> Partner Program
Blog Sitemap
Terms and Conditions
Privacy & Security
Cookies Policy
REVEAL Terms and Conditions

IMAGES

Null Hypothesis and Alternative Hypothesis
Difference between Null and Alternative Hypothesis
13 Different Types of Hypothesis (2024)
Null and Alternative Hypothesis Examples
Difference between Null and Alternative Hypothesis
Null Hypothesis and Alternative Hypothesis

VIDEO

What is Hypothesis #hypothesis
Hypothesis (complete)
Research Methods
Statistics Two tailed Hypothesis example
null hypothesis vs alternative hypothesis#statistics #youtube #yt #fbise_exams
What is Hypothesis? Example of Hypothesis [#shorts] [#statistics

COMMENTS

Null & Alternative Hypotheses
The null hypothesis (H 0) answers "No, there's no effect in the population." The alternative hypothesis (H a) answers "Yes, there is an effect in the population." The null and alternative are always claims about the population. That's because the goal of hypothesis testing is to make inferences about a population based on a sample.
Null and Alternative Hypotheses
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There's no effect in the population. Alternative hypothesis (HA): There's an effect in the population. The effect is usually the effect of the independent variable on the dependent ...
Null Hypothesis: Definition, Rejecting & Examples
Alternative Hypothesis H A: The correlation in the population is not zero: ρ ≠ 0. For all these cases, the analysts define the hypotheses before the study. After collecting the data, they perform a hypothesis test to determine whether they can reject the null hypothesis. The preceding examples are all for two-tailed hypothesis tests.
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: 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.
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.
Null Hypothesis and Alternative Hypothesis
Most technical papers rely on just the first formulation, even though you may see some of the others in a statistics textbook. Null hypothesis: " x is equal to y .". Alternative hypothesis " x is not equal to y .". Null hypothesis: " x is at least y .". Alternative hypothesis " x is less than y .". Null hypothesis: " x is at ...
Null Hypothesis and Alternative Hypothesis
The Null and Alternative Hypotheses. There are two hypotheses that are made: the null hypothesis, denoted H 0, and the alternative hypothesis, denoted H 1 or H A. The null hypothesis is the one to be tested and the alternative is everything else. In our example: The null hypothesis would be: The mean data scientist salary is 113,000 dollars.
Null & Alternative Hypotheses
Null Hypothesis (H0) - 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 (Ha) - This is also known as the claim.
10.2: Null and Alternative 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.
9.2: Null and Alternative Hypotheses
The null hypothesis ( H0. 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 ( Ha. H a. ) is a claim about the population that is contradictory to H0. H 0.
How to Write a Null Hypothesis (5 Examples)
Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms: H0 (Null Hypothesis): Population parameter =, ≤, ≥ some value. HA (Alternative Hypothesis): Population parameter <, >, ≠ some value. Note that the null hypothesis always contains the equal sign.
Examples of null and alternative hypotheses
It is the opposite of your research hypothesis. The alternative hypothesis--that is, the research hypothesis--is the idea, phenomenon, observation that you want to prove. If you suspect that girls take longer to get ready for school than boys, then: Alternative: girls time > boys time. Null: girls time <= boys time.
Null hypothesis and alternative hypothesis with 9 differences
The null hypothesis is a general statement that states that there is no relationship between two phenomenons under consideration or that there is no association between two groups. An alternative hypothesis is a statement that describes that there is a relationship between two selected variables in a study. Symbol. It is denoted by H 0.
Null Hypothesis Definition and Examples, How to State
Step 1: Figure out the hypothesis from the problem. The hypothesis is usually hidden in a word problem, and is sometimes a statement of what you expect to happen in the experiment. The hypothesis in the above question is "I expect the average recovery period to be greater than 8.2 weeks.". Step 2: Convert the hypothesis to math.
Null vs. Alternative Hypothesis
Null Hypothesis. The null hypothesis is a predictive statement that describes the statistical relationship between two or more variables or study groups. A variable refers to any trait or response ...
12.3.1: 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: 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.
Null Hypothesis
Null Hypothesis: Alternative Hypothesis. 1. The null hypothesis is a statement. There exists no relation between two variables: Alternative hypothesis a statement, there exists some relationship between two measured phenomenon. 2. Denoted by H 0: Denoted by H 1. 3. The observations of this hypothesis are the result of chance
Null hypothesis
Biology definition: A null hypothesis is an assumption or proposition where an observed difference between two samples of a statistical population is purely accidental and not due to systematic causes. It is the hypothesis to be investigated through statistical hypothesis testing so that when refuted indicates that the alternative hypothesis is true. . Thus, a null hypothesis is a hypothesis ...
Null Hypothesis
Null hypothesis, often denoted as H0, is a foundational concept in statistical hypothesis testing. It represents an assumption that no significant difference, effect, or relationship exists between variables within a population. Learn more about Null Hypothesis, its formula, symbol and example in this article
Difference Between Null and Alternative Hypothesis
A null hypothesis is what, the researcher tries to disprove whereas an alternative hypothesis is what the researcher wants to prove. A null hypothesis represents, no observed effect whereas an alternative hypothesis reflects, some observed effect. If the null hypothesis is accepted, no changes will be made in the opinions or actions.
Alternative Hypothesis-Definition, Types and Examples
Definition. The alternative hypothesis is a statement used in statistical inference experiment. It is contradictory to the null hypothesis and denoted by H a or H 1. We can also say that it is simply an alternative to the null. In hypothesis testing, an alternative theory is a statement which a researcher is testing.
Null and Alternative Hypothesis in A/B Testing
However, before designing your A/B test, you must first establish both the null hypothesis and the alternative hypothesis. The null hypothesis states that sample observations appear solely due to random chance. In the context of A/B testing, the null hypothesis suggests that no difference exists between the control and variant groups. In terms ...

Have a language expert improve your writing

Null & Alternative Hypotheses | Definitions, Templates & Examples

Table of contents

Receive feedback on language, structure, and formatting

Examples of null hypotheses

Examples of alternative hypotheses

Prevent plagiarism. Run a free check.

General template sentences

Test-specific template sentences

Cite this Scribbr article

Is this article helpful?

Shaun Turney

Have a thesis expert improve your writing

Null and Alternative Hypotheses | Definitions & Examples

Table of contents

Examples of null hypotheses

Examples of alternative hypotheses

Test-specific

Cite this Scribbr article

Is this article helpful?

Shaun Turney

Module 9: Hypothesis Testing With One Sample

Concept Review

Formula Review

9.1 Null and Alternative Hypotheses

Example 9.1

Example 9.2

Example 9.3

Example 9.4

Collaborative Exercise

Null Hypothesis and Alternative Hypothesis

The Null Hypothesis

The Alternative Hypothesis

Hypothesis Testing: Null Hypothesis and Alternative Hypothesis

The Hypothesis Testing Process

What is a Hypothesis?

What Cannot Be a Hypothesis?

A Two-Sided Test

The Null and Alternative Hypotheses

An Example of a One-Sided Test

Why Hypothesis Testing Works

Statistics Resources

ASC Chat Hours

Was this resource helpful?

9.2: Null and Alternative Hypotheses

Chapter Review

Formula Review

Contributors

How to Write a Null Hypothesis (5 Examples)

Example 1: Weight of Turtles

Example 2: Height of Males

Example 3: Graduation Rates

Example 4: Burger Weights

Example 5: Citizen Support

Additional Resources

Published by Zach

AP®︎/College Statistics

Examples of null and alternative hypotheses

Want to join the conversation?

Video transcript

12.3.1: Null and Alternative Hypotheses

Example \(\PageIndex{1}\)

Exercise \(\PageIndex{1}\)

Example \(\PageIndex{2}\)

Exercise \(\PageIndex{2}\)

Example \(\PageIndex{3}\)

Exercise \(\PageIndex{3}\)

Example \(\PageIndex{4}\)

Exercise \(\PageIndex{4}\)

COLLABORATIVE EXERCISE

Formula Review

Null Hypothesis Definition

What Is a Null Hypothesis?

Development of the Null

Significance Tests

Perceived Problems With the Null Hypothesis

Null Hypothesis Examples

Example 1: Hypotheses with One Sample of One Categorical Variable

Example 2: Hypotheses with One Sample of One Measurement Variable

Example 3: Hypotheses with Two Samples of One Categorical Variable