Which statistical test is used to compare means across more than two groups?

Which statistical test is used to compare means across more than two groups?

• A. ANOVA (analysis of variance)
• B. t-test
• C. Chi-square
• D. Mann-Whitney U

Answer: (A)

When you want to know if more than two groups differ in their average scores, you need an approach that tests all group means at once rather than doing multiple pairwise comparisons. ANOVA does this by comparing how much the group means vary from each other (between-group variation) to how much individual scores vary within each group (within-group variation). If the between-group variation is large compared with the within-group variation, you get a large F statistic and conclude that at least one group mean differs from the others. This approach controls the overall error rate better than running several separate t-tests, which would inflate the chance of a false positive. If the ANOVA result is significant, it doesn’t specify which groups differ from which; you’d follow up with post hoc tests (like Tukey or Bonferroni) to pinpoint the specific differences. For context, the t-test compares the means of two groups, not more; Chi-square handles categorical data, testing associations or goodness-of-fit; and Mann-Whitney U is a nonparametric alternative to the two-group t-test.

When you want to know if more than two groups differ in their average scores, you need an approach that tests all group means at once rather than doing multiple pairwise comparisons. ANOVA does this by comparing how much the group means vary from each other (between-group variation) to how much individual scores vary within each group (within-group variation). If the between-group variation is large compared with the within-group variation, you get a large F statistic and conclude that at least one group mean differs from the others. This approach controls the overall error rate better than running several separate t-tests, which would inflate the chance of a false positive.

If the ANOVA result is significant, it doesn’t specify which groups differ from which; you’d follow up with post hoc tests (like Tukey or Bonferroni) to pinpoint the specific differences. For context, the t-test compares the means of two groups, not more; Chi-square handles categorical data, testing associations or goodness-of-fit; and Mann-Whitney U is a nonparametric alternative to the two-group t-test.