ULibraries Research Guides: Introduction to R Programming: Two-Samples Tests with Categorical Variables

Chi-squared Test

Relationship Between Two Categorical Variables:

H_o: Variable 1 is independent of Variable 2.
H_a: Variable 1 is dependent of Variable 2.

Note: This is the test of independence.

H_o: Population 1 and Population 2 have the same chance of success.

H_a: Population 1 and Population 2 do not have the same chance of success.

Note: This is the test of homogeneity of proportions.

Fisher's Exact Test

When the total sample size is less than 1000, suggested by using Fisher's Exact test instead of Chi-squared test. The hypothesis is the same as the test of independence.

Notice:
The 95% confidence interval for odds ratio is (0.64, 1.46), which contains the exact odds ratio values. It is plausible that the true odds ratio could be 1, which means these two variables are independent.