What is the chi-square test used for?

• A. Testing association between two categorical variables.
• B. Estimating the population mean.
• C. Comparing means of two groups on a continuous outcome.
• D. Measuring the strength of a relationship between two continuous variables.

Answer: (A)

The chi-square test is used to examine whether two categorical variables are associated. You lay out the data in a contingency table, count how often each combination occurs, and compare those observed counts to what would be expected if the variables were independent. The test statistic sums (O − E)² / E across all cells, where O is the observed count and E is the expected count under independence. A large statistic indicates the observed pattern differs from independence, and the p-value from the chi-square distribution (with (rows − 1) × (columns − 1) degrees of freedom) tells you if that difference is unlikely by chance.

This fits because it focuses on relationships between categories rather than on estimating a mean or comparing means of continuous outcomes, which would involve t-tests, ANOVA, or correlation instead.