ANOVA

Compare means across three or more groups.

Definition

Analysis of Variance (ANOVA) tests whether at least one group differs significantly from the others in terms of mean. StatsLab offers classic one-way ANOVA, Welch's ANOVA (robust to unequal variances), and Bonferroni post-hoc tests to identify differing group pairs.

When to use it

• Compare 3 or more groups on a continuous variable
• Test the effect of a factor with multiple levels
• Analyze groups of unequal size

Requirements

• At least 3 independent groups
• Continuous dependent variable
• Approximate normality within each group
• Homogeneity of variances (or use Welch)

What StatsLab computes

• ANOVA table (SS, df, MS, F, p)
• η² (eta-squared) — effect size
• Bonferroni post-hoc test (pairwise comparisons)
• Levene / Brown-Forsythe test
• Means and 95% CI per group
• Means plot with error bars

Worked example

Context : Comparing reaction time (ms) across 3 age groups: young, adult, senior.

Result : F(2, 87) = 12.4, p < 0.001, η² = 0.22

Interpretation : Highly significant difference between groups. Large effect size (η² = 0.22). Bonferroni post-hoc reveals that seniors differ significantly from young (p < 0.001) and adults (p = 0.012).

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