Which statement best describes the purpose of ANOVA?

Which statement best describes the purpose of ANOVA?

• A. It tests whether variances are equal across groups
• B. It tests whether the means across three or more groups differ
• C. It tests independence between two categorical variables
• D. It estimates a regression coefficient

Answer: (B)

ANOVA is used to determine whether the means across three or more groups differ. It tests the null hypothesis that all group means are equal, versus the alternative that at least one group mean is different. It does this by comparing two sources of variability: the differences between group means (between-group variability) and the variability within each group (within-group variability). If the groups truly have different means, the between-group variability will be large relative to the within-group variability, yielding a large F-statistic and a small p-value, which leads to rejecting the null. This approach generalizes the idea of a two-sample t-test to more than two groups. It does not assess whether variances are equal (that would be a separate test), nor does it test independence between categorical variables (that’s a chi-square test), nor does it estimate a regression coefficient (that’s regression analysis). Note that if ANOVA shows a difference, post hoc tests are typically needed to identify exactly which groups differ.

ANOVA is used to determine whether the means across three or more groups differ. It tests the null hypothesis that all group means are equal, versus the alternative that at least one group mean is different. It does this by comparing two sources of variability: the differences between group means (between-group variability) and the variability within each group (within-group variability). If the groups truly have different means, the between-group variability will be large relative to the within-group variability, yielding a large F-statistic and a small p-value, which leads to rejecting the null. This approach generalizes the idea of a two-sample t-test to more than two groups. It does not assess whether variances are equal (that would be a separate test), nor does it test independence between categorical variables (that’s a chi-square test), nor does it estimate a regression coefficient (that’s regression analysis). Note that if ANOVA shows a difference, post hoc tests are typically needed to identify exactly which groups differ.