When to Use a T-Test, ANOVA, or Chi-Square Test

These three are among the most commonly misapplied tests in graduate research — not because they're complex, but because the choice depends on details (variable type, number of groups) that are easy to overlook under deadline pressure.

T-test

Compares the means of a continuous variable between two groups. An independent-samples t-test compares two separate groups; a paired t-test compares the same group at two time points (e.g., pre/post intervention).

ANOVA

Compares means of a continuous variable across three or more groups. Running multiple t-tests instead inflates your risk of a false positive — this is exactly the problem ANOVA is designed to avoid. A significant ANOVA result tells you groups differ somewhere, but you need post-hoc tests to find out which pairs.

Chi-square test

Used for categorical variables, not continuous ones — testing whether there's an association between two categorical variables (e.g., treatment group and recovery yes/no), based on comparing observed vs. expected frequencies in a contingency table.

Quick decision guide

• Continuous outcome, 2 groups → t-test
• Continuous outcome, 3+ groups → ANOVA
• Categorical outcome, group comparison → chi-square
• Small expected cell counts in your contingency table → Fisher's exact test instead of chi-square

Before you run any of these

Check your test's assumptions first — t-tests and ANOVA assume roughly normal distributions and, for some variants, equal variances between groups. Violating these doesn't always invalidate your test, but it often means a non-parametric alternative (Mann-Whitney U, Kruskal-Wallis) is more appropriate.