Welch's ANOVA calculator

Compare three or more group means without assuming equal variances. Run Welch's ANOVA online with Games-Howell post-hoc tests.

What it does

Compares means across 3+ independent groups without assuming equal variances or equal group sizes — the engine default for one-factor comparisons.

Cautions

• Assumes approximate normality within each group (robust once n ≥ 30/group); does not assume equal variances or equal group sizes.
• Post-hoc pairwise comparisons use Games–Howell, not Tukey HSD (which assumes equal variances) — the card will show it automatically if the omnibus is significant.

Alternatives

• One-way ANOVA — only if equal variances are confirmed and groups are balanced
• Kruskal-Wallis — non-normal outcome or small samples

How to read the output

F-statistic and fractional df

Welch's F with adjusted, non-integer degrees of freedom — the price of not assuming equal variances, and the sign that the correction was applied.

p-value

How surprising a difference at least this large would be IF the groups really were identical on this measure. A small p means the data would be surprising under that assumption. It is not the probability that the result is due to chance, and not the probability that the groups are the same — those read the conditional backwards. It also answers 'would this be surprising?', never 'is this big enough to matter?': with a large sample a trivial difference returns a small p, and the result looks identical to an important one.

Games–Howell (post-hoc)

The pairwise follow-up matched to this test: like Tukey, but each pair uses its own variance and its own df rather than a pooled one. Do not follow a Welch ANOVA with Tukey HSD — Tukey pools the variances the Welch test was chosen to avoid pooling.

How this calculator is validated · Which statistical test should I use?