Overview
ANOVA is the right tool for comparing more than two groups — but only when its assumptions are met, and only when followed by the right post-hoc test. Running multiple t-tests instead of ANOVA inflates the Type I error rate: with 5 groups and α=0.05, the probability of at least one false positive from pairwise t-tests is 40%, not 5%. ANOVA controls that rate — but only if the homogeneity of variance assumption holds, and only if the post-hoc test is chosen to match the comparison structure.
Most ANOVA implementations stop at the F-test: "there is a significant difference somewhere among the groups." That is the least useful result. The useful result is which groups differ, by how much, and whether the difference is practically meaningful. That requires post-hoc tests, effect sizes, and confidence intervals — not just a p-value.
The ANOVA & Variance Analysis Prompt generates a complete analysis framework: assumption checks, one-way and two-way ANOVA specification, post-hoc test selection, effect size calculation, and a results interpretation that identifies the specific group differences that matter.
What you get: - Assumption diagnostic protocol (normality, homogeneity of variance) - One-way and two-way ANOVA specification - Post-hoc test selection by comparison structure - Effect size (eta-squared and omega-squared) - Results interpretation with specific group comparisons
Built for: analysts and researchers comparing performance across multiple groups, segments, or conditions.