What Is The Null Hypothesis and How Does It Work?

By Indeed Editorial Team

Published 7 May 2022

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

When conducting a statistical test, the null hypothesis is the default assumption. In data analysis, it's what you may expect to happen if there's no treatment or intervention because it means that there exists no statistical differences or relationships in the two phenomena you want to measure. If you work in data analysis or are interested in a career involving data, understanding this topic in deeper, broader terms can help you excel in your career by supporting your professional development. In this article, we define the term, provide examples, describe how it works and compare it to the alternative hypothesis.

What is the null hypothesis?

The null hypothesis, or the conjecture, is a statement in inferential statistics declaring that no existing relationship or association exists between two measured phenomena. Contrarily, there's usually also an alternative hypothesis suggesting that some sort of relationship exists between the variables. Null hypotheses can be important because they allow researchers to make predictions about how data might behave and test their theories. They're particularly important in data analysis because they can determine the statistical significance of results. Essentially, you test the hypothesis to find out if there exists evidence against it.

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How does the conjecture work?

Researchers use statistical tests to prove or disprove their hypothesis and determining if there exists any evidence against it. This is the case when there's no real or clear difference between the two groups. Therefore, its test can determine if there's a statistically significant difference between two variables and whether there's any relation between them. Hypothesis testing has the purpose of testing the assumptions researchers make about a population or phenomenon parameter.

To make this verdict, researchers compare the experiment's results with the predictions of their hypothesis. The two typical scenarios are that either the data supports the hypothesis or it rejects it. If the data supports the prediction, then that usually means no significant relationship exists between the two measured variables. If the data rejects the hypothesis, then researchers may conclude that there indeed does exist a significant relationship between the two groups.

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What is significance testing?

Researchers conduct significance testing to disprove the conjecture. This test determines the likelihood of the differences between the two variables being simply by chance. If there's a low probability of the difference happening by chance, then researchers reject the conjecture and accept the alternative hypothesis. There are two types of errors that can happen during a significance test, namely type I and type II.

A type I error is a false positive, meaning researchers wrongfully rejected the conjecture instead of accepting it. A type II error is a false negative, meaning the researchers made the mistake of accepting the hypothesis instead of rejecting it. To avoid these two errors, researchers can set the level of significance, namely a threshold for what they can consider a statistically significant result. The lower the level of significance, the higher the likelihood that they wrongfully reject it.

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How do researchers disprove the conjecture?

Researchers can never prove this hypothesis, they can only disprove it. They may reject the hypothesis for two reasons. Firstly, they can reject it if the difference between the two variables is statistically significant. This means that the chances of the hypothesis being true is very unlikely. Secondly, they can reject the hypothesis if there's no statistical significance in the difference between the two variables. This means that the conjecture may still be true and that the small difference might exist simply by chance.

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Null hypothesis vs. alternative hypothesis

In data analysis, the conjecture is the statement that researchers try to disprove. It states that the difference between two groups is random and by chance, instead of due to some other factor. Researchers always assume it's true until they can disprove it. The contrast is the alternative hypothesis, namely the statement that researchers attempt to prove. The alternative hypothesis is always false until it's proved true.

Essentially, the main difference is that the conjecture states that two measured phenomena, groups or variables are equal while the alternative hypothesis states that they aren't. Other differences include:

  • The conjecture always assumes no difference, while the alternative can assume a difference.

  • Researchers cannot prove the conjecture, only the alternative hypothesis.

  • The type I and type II errors only relate to the conjecture.

  • The level of significance is the only universal thing between these two hypotheses.

  • When completing a significance test, researchers assume the conjecture is true and that the alternative hypothesis is false. This is because it's easier to disprove something than to prove it.

  • Researchers denote the conjecture as H0 and the alternative hypothesis as H1.

Examples of the null and alternative hypotheses

Understanding how these hypotheses can look in real-world situations might help you expand your own knowledge and comprehension of the topic. Here are eight examples:

Example 1

Here's an example from the educational sector:

A school's principal makes the claim that their students receive an average of nine out of 10 on their science tests. This means that the conjecture is that the school's science students receive average test scores of nine out of 10. The alternative hypothesis is that the school's science students receive average test scores that are not equal to nine out of 10.

Example 2

Here's an example from the medical field:

In this scenario, a new medication enters the market. Now, researchers want to know if it affects a patient's heart health. In this case, the conjecture is that the new medication has no effect on a patient's heart health. The alternative hypothesis is that the new medication does have an effect on a patient's heart.

Example 3

This example shows how a data analyst in the human resources (HR) or business sector might use this concept:

A company introduces a new work schedule. Researchers now want to know if this new work schedule has an effect on the productivity of the company's employees. In this situation, the conjecture is that the new work schedule has zero effect on the company's employee productivity. The alternative hypothesis is that the new work schedule does have an effect on employee productivity.

Example 4

This example shows how analysts who work on behalf of the city might use this concept:

In this situation, a city wants to know if there's a difference in the number of traffic accidents, depending on what day of the week it is. In this case, the conjecture states that there is no difference in the number of traffic accidents on certain days of the week. The alternative hypothesis states that there is a difference in the number of traffic accidents, depending on the day.

Example 5

This example shows how analysts studying crime might use this hypothesis:

In this scenario, a city wants to know if there's a difference in crime rates between different neighbourhoods. This means that the conjecture states that there's no difference in crime rates between the different neighbourhoods. Meanwhile, the alternative hypothesis states that there does exist differences in crime rates between the different neighbourhoods.

Important terminology to know

Here's some important terminology you can use when broadening your understanding of this topic:

P-value

The first important term to know is the p-value. In significance testing, this signifies the probability of obtaining results that are at least as extreme as the results observed. It assumes that the conjecture is correct. The value is usually between zero and one.

Alpha

Alpha is an important term because it's the level of significance that you set for your test. This means that it's the probability of rejecting the conjecture when it's actually true. This is also the type I error rate.

Beta

Beta is the opposite of alpha. This means that it's the probability of failing to reject the conjecture when it's actually false. This is the type II error rate. It's important to know because it can affect the power of your significance testing.

Standard of deviation

In significance testing, the standard of deviation can calculate the p-value. Its purpose is to measure the spread of data points around the mean. This is important to know because the larger the standard of deviation, the less confident you can be in your results.

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