Table of Contents
What Is ANOVA?
Analysis of Variance (ANOVA) compares means across three or more groups. It tests the null hypothesis that all group means are equal. Developed by Sir Ronald Fisher, it is one of the most widely used statistical tests in research, biology, psychology, and engineering.
One-way ANOVA examines a single factor's effect on a continuous outcome. It extends the t-test to multiple groups while controlling the Type I error rate that would inflate with multiple pairwise comparisons.
Formulas
ANOVA Table
| Source | SS | df | MS | F |
|---|---|---|---|---|
| Between | SSB | k-1 | SSB/(k-1) | MSB/MSW |
| Within | SSW | N-k | SSW/(N-k) | -- |
| Total | SST | N-1 | -- | -- |
Frequently Asked Questions
What does significant ANOVA mean?
At least one group mean differs, but not which ones. Post-hoc tests (Tukey HSD) identify specific pairwise differences.
Why not multiple t-tests?
Multiple t-tests inflate Type I error. With 3 groups and 3 comparisons, overall error is ~14% instead of 5%. ANOVA controls this.
What if assumptions are violated?
For non-normal data use Kruskal-Wallis test. For unequal variances use Welch's ANOVA. ANOVA is robust to moderate normality violations with large samples.