ANOVA

Definition

Analysis of Variance (ANOVA) is a statistical method used to compare means across three or more groups. It partitions total variance into between-group and within-group components, using the F-statistic to determine whether observed differences are statistically significant.

Why It Matters

When your study includes more than two groups, running multiple t-tests inflates the family-wise error rate and increases the chance of false positives. ANOVA solves this by testing all groups simultaneously under a single hypothesis. It is the foundation of experimental design in psychology, agriculture, medicine, and education research.

Example

Imagine a clinical trial comparing three doses of a new drug against a placebo on blood pressure reduction. Instead of running six separate t-tests, a one-way ANOVA tests whether any dose differs from the others. If the overall F-test is significant, post-hoc comparisons (such as Tukey's HSD) then pinpoint exactly which doses differ.

Related Terms

• T-Test (ANOVA extends the t-test to three or more groups)
• Statistical Significance
• Effect Size (eta-squared or partial eta-squared quantify ANOVA results)
• Normal Distribution

Software Notes

• SPSS: Analyze > Compare Means > One-Way ANOVA (for independent samples) or General Linear Model > Univariate (for factorial designs). Request post-hoc tests under the Post Hoc button.
• R: aov(dv ~ group, data = df) for one-way; summary(aov(dv ~ group * condition, data = df)) for factorial. Post-hoc: TukeyHSD(model).
• Stata: oneway dv group or anova dv group condition for factorial designs. Post-hoc: pwcompare group, mcompare(tukey).