Which statistical test is used to determine whether the means of more than two groups are equal?

Which statistical test is used to determine whether the means of more than two groups are equal?

• A. t-test
• B. ANOVA
• C. Bar chart
• D. Correlation

Answer: (B)

When you want to know if more than two group means differ, you use analysis of variance. It tests the idea that all group means are equal versus the possibility that at least one group differs. ANOVA works by comparing variability between the group means to variability within the groups, producing an F statistic. If every group truly has the same mean, the between-group variability is small and the F value is close to 1, so you don’t reject the null. If at least one group mean differs, the between-group variability rises, the F value gets larger, and you may reject the null. This single test avoids the inflation of false positives that would come from doing multiple t-tests on all pairs of groups. The other options don’t fit the question: a t-test compares two means, a bar chart is just a graph, and a correlation looks at the association between two variables rather than differences among multiple group means. Also, remember the usual assumptions for ANOVA (independence, normality within groups, and equal variances across groups) and that there are follow-up post hoc tests if you find a significant result and want to know which specific means differ.

When you want to know if more than two group means differ, you use analysis of variance. It tests the idea that all group means are equal versus the possibility that at least one group differs. ANOVA works by comparing variability between the group means to variability within the groups, producing an F statistic. If every group truly has the same mean, the between-group variability is small and the F value is close to 1, so you don’t reject the null. If at least one group mean differs, the between-group variability rises, the F value gets larger, and you may reject the null. This single test avoids the inflation of false positives that would come from doing multiple t-tests on all pairs of groups.

The other options don’t fit the question: a t-test compares two means, a bar chart is just a graph, and a correlation looks at the association between two variables rather than differences among multiple group means. Also, remember the usual assumptions for ANOVA (independence, normality within groups, and equal variances across groups) and that there are follow-up post hoc tests if you find a significant result and want to know which specific means differ.