ANOVA

You have four groups and want to know if their averages differ. Why not run a t-test on each pair? Because every test carries a false-positive risk, and six tests stack them up. ANOVA does it in one shot.

How It Works

ANOVA compares the variation between group means to the variation within groups. If the between-group spread is large relative to the within-group noise, the means genuinely differ. That ratio is the F-statistic.

• Large F, small p-value → at least one group stands apart
• The chart above shows four group means with their spread
• One-way ANOVA: one grouping factor; two-way: two factors and their interaction

The Catch: Which Groups?

ANOVA tells you that a difference exists, not where. To find which specific groups differ, run a post-hoc test (like Tukey's HSD) that compares pairs while controlling the error rate.

Assumptions

• Roughly normal residuals
• Similar variance across groups (homogeneity)
• Independent observations

If variances differ or data is skewed, use Welch's ANOVA or the nonparametric Kruskal-Wallis test.

ANOVA in the SKARI Statistical Lab

The Statistical Lab runs ANOVA and the post-hoc comparisons together: choose the outcome and the grouping factor, and get the F-test, assumption checks, and pairwise results with a plain-language read.

• One-way and two-way ANOVA
• Built-in assumption checks and Welch's alternative
• Post-hoc pairwise comparisons so you see which groups differ

Frequently Asked Questions

Why not just run t-tests?

Each test has a false-positive chance; running many multiplies it. ANOVA controls the overall error rate.

What does a significant ANOVA tell me?

That at least one group differs — not which. Follow with a post-hoc test to locate the differences.

What if my variances are unequal?

Use Welch's ANOVA, or Kruskal-Wallis if the data is also non-normal.

Conclusion

ANOVA compares many means honestly, and a post-hoc test pinpoints the differences. Together they replace a pile of risky t-tests with one controlled analysis.