Which test is used to compare means across three or more groups?

Which test is used to compare means across three or more groups?

• A. T-test
• B. Analysis of Variance
• C. Mann-Whitney U Test
• D. Chi-square

Answer: (B)

When you need to compare means across three or more groups, Analysis of Variance is the appropriate test. It evaluates whether the differences among group means are larger than would be expected by random variation within the groups by partitioning total variance into between-group and within-group components and using an F statistic. This approach tests all group means in one analysis, avoiding the inflated risk of false positives that comes with performing multiple pairwise t-tests. If the ANOVA result is significant, you typically follow with post hoc comparisons to identify exactly which groups differ. Key assumptions include independent observations, normally distributed residuals within groups, and roughly equal variances across groups. If these assumptions aren’t met, or if the data are nonparametric, there are alternatives such as Kruskal-Wallis; for two groups you’d use a t-test or Mann-Whitney U; and Chi-square is for associations between categorical variables rather than comparing means.

When you need to compare means across three or more groups, Analysis of Variance is the appropriate test. It evaluates whether the differences among group means are larger than would be expected by random variation within the groups by partitioning total variance into between-group and within-group components and using an F statistic. This approach tests all group means in one analysis, avoiding the inflated risk of false positives that comes with performing multiple pairwise t-tests. If the ANOVA result is significant, you typically follow with post hoc comparisons to identify exactly which groups differ. Key assumptions include independent observations, normally distributed residuals within groups, and roughly equal variances across groups. If these assumptions aren’t met, or if the data are nonparametric, there are alternatives such as Kruskal-Wallis; for two groups you’d use a t-test or Mann-Whitney U; and Chi-square is for associations between categorical variables rather than comparing means.