Which test is used to test independence between two categorical variables in a contingency table?

• A. Chi-Square Test
• B. T-Test
• C. ANOVA
• D. Mann-Whitney U

Answer: (A)

The test is used to determine whether two categorical variables are independent by comparing what we actually observe in a contingency table to what we would expect if the variables did not influence each other. It does this by computing expected counts under the assumption of independence: E = (row total × column total) / grand total. Then it measures how far the observed counts O deviate from those expectations with the chi-square statistic: χ² = Σ (O − E)² / E across all cells. If the variables are independent, χ² follows a chi-square distribution with (r − 1)(c − 1) degrees of freedom, so a large statistic (and thus a small p-value) leads to rejecting independence.

Important practical notes: the approximation is reliable when sample sizes are large and expected cell counts are at least about 5; with small counts, Fisher’s exact test is a preferable alternative. The other tests mentioned are for different purposes—t-test and ANOVA compare means across groups, and the Mann-Whitney U test compares distributions/ranks between two groups—so they’re not appropriate for assessing independence between two categorical variables in a contingency table.