Question

Describe the null hypothesis for the test of independence. List the assumptions for the χ² test of independence. What is the major difference between the assumptions for this test and the assumptions for the previous tests we have studied?

Answer 1

We use the Chi square test for independence between two categorical variables for checking the independence or relationship between the given two categorical variables.

The null and alternative hypothesis for the test of independence is given as below:

Null hypothesis: H₀: The two categorical variables are independent of each other.

Alternative hypothesis: H_a: The two categorical variables are not independent of each other.

The assumptions for this test are given as below:

For this test, given two variables should be categorical in nature.

Data for this test should be frequencies or counts and it would not be simple observations.

The sample data should be displayed in contingency table and the expected frequency for each cell should be at least 5.

This test is different than the previous tests. Most of the previous tests have an assumption of normality, that is, data should come from normal or approximately normal distribution. But this test do not require normality. For the previous tests, we need discrete or continuous data, while here we need categorical data.