ANOVA is used to determine differences in which scenario?

• A. To compare means of exactly two groups.
• B. To analyze relationships between variables.
• C. To assess central tendency in one group.
• D. To determine differences among three or more groups.

Answer: (D)

ANOVA tests whether means differ across multiple groups. It does this by comparing the variability between the group means to the variability within each group. If all group means are the same, between-group variance is small and the F statistic is not significant. If at least one group mean differs, between-group variance increases, producing a larger F and a significant result. This method is ideal when you have three or more groups to compare and want to avoid inflating the chance of false positives from doing multiple two-group tests. For scenarios with only two groups, a t-test is the standard approach (though ANOVA can yield the same conclusion under certain conditions). ANOVA isn’t used to analyze relationships between variables (that’s correlation or regression) or to describe the central tendency of a single group (that involves measures like the mean).