What is an Analysis of Variance (ANOVA) used for?

• A. It tests whether at least one group means differs among three or more groups.
• B. It compares variances across groups.
• C. It measures correlation between variables.
• D. It estimates population percentiles.

Answer: (A)

ANOVA is used to compare means across three or more groups to determine if they come from populations with the same average. The idea is to test whether the group means are all equal (the null) or if at least one group has a different mean (the alternative). It does this by looking at how much of the total variation in the data is due to differences between the group means versus variation within each group. If the between-group differences are large relative to the within-group differences, the F statistic is large and the result is unlikely under the null, leading to the conclusion that at least one mean differs. When you find a significant overall result, you can then use follow-up tests to identify exactly which groups differ.

Choosing other options would miss the focus on means: comparing variances across groups looks at spread rather than central tendency; measuring correlation examines relationships between variables; estimating population percentiles concerns distribution and ordering rather than mean differences.