Which statistical test compares the effects of categorical variables?

The correct choice for comparing the effects of categorical variables is the Chi-squared test. This statistical test is specifically designed to assess whether there is a significant association between two categorical variables in a contingency table. It evaluates how the observed frequencies of occurrences in each category compare to the expected frequencies if there were no association between the variables.

For instance, if you want to examine whether there is a relationship between gender (male, female) and voting preference (yes, no), the Chi-squared test will help determine if the distributions of voting preference differ significantly across the gender categories.

The other statistical tests listed serve different purposes. The T-test is typically used to compare means between two groups, often for continuous data, making it unsuitable for analyzing categorical variables. ANOVA, or Analysis of Variance, is used when comparing means across three or more groups, which again is a focus on numerical data rather than categorical association. Lastly, regression analysis is primarily concerned with predicting a continuous outcome from one or more predictors, which may include categorical variables but is not focused solely on their associations.

In summary, the Chi-squared test stands out as the appropriate choice for evaluating relationships between categorical variables due to its design for analyzing frequency data in various categories.