When is the Chi-square test of independence appropriate and what are the key requirements?

• A. It compares means of two continuous variables assuming normal distribution
• B. Categorical data to test association between two variables; expected cell counts should be sufficiently large (commonly ≥5)
• C. It tests whether a single categorical variable fits a theoretical distribution
• D. It measures the strength of a linear relationship between two variables

Answer: (B)

This question is about using the chi-square test of independence to determine whether two categorical variables are related. The test looks at a contingency table of observed counts and asks whether these counts differ from what would be expected if the variables were independent.

Key requirements to use this test: the data must be counts from independent observations arranged in a contingency table with two categorical variables (each variable having two or more categories). The expected frequency in every cell should be large enough to rely on the chi-square approximation, commonly at least 5. If many cells have small expected counts, the chi-square approximation may be unreliable, and an exact test (like Fisher’s exact test) is preferred. The test statistic is based on the squared differences between observed and expected counts, summarized across all cells, with degrees of freedom equal to (rows − 1) × (columns − 1). The null hypothesis is that the variables are independent; a small p-value suggests an association between the variables.