ANOVA Summary

Statistics · Axiom Academy

Let's review the key concepts of Analysis of Variance. What It Tests: Compares means across three or more groups to determine if at least one differs significantly from the others Why Not Multiple t-tests: ANOVA controls family-wise error rate, avoiding inflated Type I error from multiple comparisons Null Hypothesis: All group means are equal ( H 0 : μ 1 = μ 2 = ... = μ k ) Alternative Hypothesis: At least one group mean differs from the others Total Variation: ANOVA partitions total variability in the data into explained and unexplained components Between-Group Variance (SSB): Variation due to differences between group means Within-Group Variance (SSW): Variation within each group (error/residual) Key Identity: SST = SSB + SSW, where total variation equals between plus within variation Step 1 - State Hypotheses: Define H 0 (all means equal) and H A (at least one mean differs) Step 2 - Check Assumptions: Verify independence, normality within groups, and equal variances (homogeneity) Step 3 - Calculate Sum of Squares: Compute SST, SSB, and SSW using group means and grand mean Step 4 - Compute F-Statistic: Calculate MSB and MSW, then compute F = MSB / MSW Step 5 - Find p-value: Compare F-statistic to F-distribution with (k-1, N-k) degrees of freedom Step 6 - Make Decision: Reject H 0 if p-value < α, indicating significant group differences Distribution Shape: Right-skewed distribution with two parameters: df numerator and df denominator

This is the written version of the interactive lesson above. See the full Statistics course.