In ANOVA, which statement best describes what the F-statistic tests?

• A. It measures the strength of linear relationship between two variables
• B. It tests whether there are any differences among group means
• C. It estimates the overall mean of the data
• D. It tests homogeneity of variances across groups

Answer: (B)

The F-statistic in ANOVA assesses whether the means of several groups differ. It does this by comparing two sources of variability: how much the group means differ from the overall mean (between-group variability) and how much individual observations differ within each group (within-group variability). If all group means are truly equal, the between-group variability should be about what you’d expect from random sampling, so the F value stays close to 1. If at least one group mean is different, the between-group variability becomes large relative to the within-group variability, yielding a larger F and a small p-value that leads to rejecting the idea that all means are the same. This test does not measure a linear relationship between two variables, nor does it estimate the overall mean. It also isn’t a test of equal variances across groups; homogeneity of variances is an assumption used in this analysis and is typically checked with a separate test.