How to Write a Null and Alternative Hypothesis with Examples

What is Null and Alternative hypothesis in statistics and how to write them, explained with simple and easy examples.

Hypothesis testing is the fundamental and the most important concept of statistics used in Six Sigma and data analysis. And the first step of hypothesis testing is forming Null and Alternative hypothesis.

Before we move to write our null hypothesis, let us first understand the need of doing hypothesis testing.

Why do Hypothesis Testing

In the Measure Phase of a DMAIC project, we conduct brain storming exercises with subject matter experts and prepare a list of probable causes.

Similarly, basis initial data analysis we identify certain trends and form assumptions. All these probable causes and assumptions are nothing but our hypothesis in simple language.

Below are the specific reasons why we perform hypothesis testing.

• To improve processes, there is a need to identify Xs which impact the mean or standard deviation.
• Once these Xs are identified and adjustments are made for improvement, actual improvement needs to be validated
• Sometimes it cannot be decided graphically or by using calculated statistics (sample mean and standard deviation) if there is a statistically significant difference between processes (Pre & Post)
• In such cases, the decision will be subjective.
• Hence the need to perform a formal statistical hypothesis test to decide objectively if there is a difference.

Definition of Null and Alternative Hypothesis

With the help of sample data we form assumptions about the population, then we have to test our assumptions statistically. This is called Hypothesis testing.

A null hypothesis is a statement of the status quo, one of no difference or no effect. For example, if you make a change in the process then the null hypothesis could be that the output is similar from both the previous and changed process.

An alternative hypothesis is one in which some difference or effect is expected. Thus the alternative hypothesis is the opposite of null hypothesis.

The null hypothesis is always the hypothesis that is tested. The null hypothesis may be rejected but never be accepted based on a single test.

A statistical test can have one of two outcomes. One is that the null hypothesis is rejected and the alternative hypothesis is accepted. The other outcome is that the null hypothesis is not rejected based on the evidence.

Ho = Null Hypothesis

Statement of ‘no effect’ or ‘no difference’ or the “status quo”. Nothing new is happening.

Ha = Alternative Hypothesis

Statement/claim assumed to be true and we are trying to prove it to be true. Something new is happening

The burden of proof rests with Ha.

Assume that Ho = “true”, unless proven otherwise

Testing a hypothesis is similar to a court trial. The hypothesis is that the defendant is presumed not guilty until proven guilty. A null hypothesis can only be rejected or fail to be rejected, it cannot be accepted because of lack of evidence to reject it.

If the means of two populations are different, the null hypothesis of equality can be rejected if enough data is collected. When rejecting the null hypothesis, the alternate hypothesis must be accepted.

Difference between Null and Alternate hypothesis

It is summarized here because it is very important to understand the difference:

Writing Null and Alternative Hypothesis Example 1

As step 1, let us take an example and learn how to form the null and alternate hypothesis statements.

• The histograms below show the weight of people of countries A and B.
• Both samples are of size 250, the scale is the same, and the unit of measurement is Kilograms.

Question : Is the people of country B, heavier than that of country A?

In the previous section, we have read that Null hypothesis is about the status quo or no difference. So here also the Null hypothesis will be µA = µB (mean of country A=mean of country B), this means in simple words that there is no significant difference between the average weight of country A and B.

The hypotheses are always statements about the population parameters

Formulate Null Hypothesis (Ho)

• Ho:The Weight of citizens in country A is equal to the weight of citizens in country B (µA = µB)

Formulate an Alternative Hypothesis (Ha)

• Ha:The weight of citizens in country A is not equal to the weight of citizens in country B (µA = µB)

This test of hypothesis is a two-tailed test because alternative hypothesis is not directional as it doesn’t say that mean of A is more or lesser than mean of B.

Writing Null and Alternative Hypothesis Example 2

Let us assume that there is a department store, which is considering the introduction of an internet shopping service. The new service will be introduced if more than 60% of its customers use internet to shop.

In this scenario the null hypothesis would be that % of customers using internet is less or equal to 60%. As we know, the alternative hypothesis will be opposite of null hypothesis.

Ho: %(proportion) of customers using internet for shopping <= 60%

Ha: %(proportion) of customers using internet for shopping > 60%

If the null hypothesis is rejected, then the alternative hypothesis Ha will be accepted and the new internet shopping service will be introduced.

This test of hypothesis is a one-tailed test, because the alternative hypothesis is one sided as it says customers using internet for shopping is >60%.

Writing Null and Alternative Hypothesis Example 3

In the development of new drugs for the treatment on anxiety, it is important to check the drugs effect on various motor functions, one of which is driving.

A pharmacy company is testing four different tranquilizing drugs for their effect on driving skills. Subjects take a simulated driving test, and their scores reflect their errors. More severe errors lead to higher scores. The results of the teats are as per following table:

Ho: Average of Drug 1 = Average of Drug 2 = Average of Drug 3 = Average of Drug 4

Ha: At least effect of one Drug is different

This test of hypothesis is a two-tailed test.