What statistical test involves categorical variables and compares two distributions to check for differences?

The correct answer is the Chi-square test, which is specifically designed for analyzing categorical variables. This statistical test assesses whether there is a significant association between two categorical variables by comparing observed frequencies in each category to the frequencies that would be expected under the null hypothesis of no association.

The Chi-square test is particularly useful in determining if the distribution of sample categorical data deviates from what would be expected if the variables were independent. For example, if researchers wanted to explore whether gender is associated with a particular preference (like favorite sport), the Chi-square test would be the appropriate choice to evaluate the differences in distribution across the categories.

In contrast, the other options serve different purposes: the T-test is used for comparing means between two groups, typically for continuous data; ANOVA can compare means across three or more groups; and regression analysis explores relationships between a dependent variable and one or more independent variables, often used for continuous outcomes rather than categorical distributions. Thus, these tests do not apply when the focus is solely on categorical variables.