If we want to compare three or more groups of discrete data in categories, which test should we use?

The most appropriate test for comparing three or more groups of discrete data in categories is ANOVA. This statistical method is specifically designed for analyzing differences among group means when the dependent variable is continuous, and the independent variable is categorical with two or more levels. In your case, since the data is discrete and organized into categories, using ANOVA allows for an efficient comparison across those groups to determine whether significant differences exist.

The Chi-Square test is indeed useful for categorical data, primarily for examining the association between two categorical variables rather than for comparing means across multiple groups. The proposed answer emphasizes comparisons among groups of categorical data, but ANOVA is more fitting for the specific context of comparing group means.

For the other tests mentioned, the 2-Sample t-test is limited to comparing the means of exactly two groups, and the 2-Proportion test is designed for comparing proportions between two groups. Thus, they do not fulfill the requirement for comparing three or more groups, further solidifying ANOVA's role as the most suitable choice for such an analysis.