The chi-square test is a statistical method for testing the association between two categorical variables. It specifically tests the equality of which?

• A. Two frequencies or proportions
• B. Means
• C. Variances
• D. Medians

Answer: (A)

Chi-square is about counts in categorical data. It tests whether the observed frequencies in a contingency table match what would be expected if the two variables were independent, which means comparing frequencies or proportions across the cells. The test looks at how far the observed counts deviate from the expected counts under independence, using a statistic that sums (observed − expected)²/expected across all cells. If the deviations are large, it suggests an association between the variables. This is why the quantity being tested is the equality of frequencies or proportions, not means, variances, or medians, which pertain to continuous data and are addressed by other tests.