What does an ANOVA test?

• A. Differences Among Group Means
• B. Normality of Data
• C. Differences in Variances
• D. Correlation Between Variables

Answer: (A)

ANOVA asks whether the average outcomes differ across several groups, beyond what you’d expect from random variation. It works by partitioning the total variability in the data into two pieces: how much of the variation comes from differences between group means, and how much comes from variation within each group. If all group means are the same, the between-group variation should be small relative to the within-group variation, and the test statistic (the F ratio) will be around 1. If there is a real difference in at least one group mean, the between-group variation grows, the F value increases, and you’re more likely to obtain a small p-value that leads to rejecting the idea that all means are equal.

ANOVA, by itself, tells you that at least one group mean differs but not which ones. To pinpoint the specific differences, you’d follow up with post-hoc tests. It also rests on certain assumptions: the residuals should be roughly normally distributed, the observations should be independent, and the variances across groups should be similar. It’s not a test of normality, it doesn’t directly test differences in variances, and it doesn’t assess correlations between variables.