Welch's ANOVA compares three or more group means when the groups have unequal variances, which the classic one-way ANOVA assumes they do not. Its write-up looks like a one-way ANOVA with two differences: the second degrees of freedom is a decimal, and the post hoc tests are Games-Howell rather than Tukey. This guide gives you the exact APA 7 format and a worked example.
What you need before you write a single word
- Each group's mean (M), standard deviation (SD) and n.
- Welch's F with its two degrees of freedom (the second is fractional).
- The exact p value.
- An effect size: η² (or ω²) from the ordinary ANOVA table is the usual choice.
- Games-Howell post hoc comparisons, which also do not assume equal variances.
- The Levene's test result, if it is why you chose Welch's test.
The APA 7 format template
Because Levene's test indicated unequal variances, F(df1, df2) = X.XX, p = .XXX, Welch's ANOVA was used. [Outcome] differed significantly across [groups], F(df1, XX.XX) = X.XX, p = .XXX, η² = .XX. Games-Howell comparisons showed that [group A] (M = X.XX, SD = X.XX) [scored lower] than [group B] (M = X.XX, SD = X.XX), p = .XXX.
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Formatting rules reviewers actually check:
- Report Welch's error df to two decimals: F(2, 48.57).
- Name the test ("Welch's ANOVA" or "Welch's F") so the reader knows the variances were not pooled.
- Use Games-Howell post hoc tests, not Tukey's HSD, which assumes equal variances.
- No leading zero on p or η²; italicize F, p, M and SD.
A worked example
Suppose you compared patient waiting times (minutes) at three clinics.
- Clinic A (n = 30): M = 21.88, SD = 3.86
- Clinic B (n = 30): M = 29.65, SD = 7.11
- Clinic C (n = 30): M = 31.49, SD = 15.54
- Levene's test: F(2, 87) = 20.34, p < .001
- Welch's ANOVA: F(2, 48.57) = 17.22, p < .001, η² = .15
- Games-Howell: A vs B p < .001; A vs C p = .007; B vs C p = .826
Written up in APA 7:
Because Levene's test indicated unequal variances, F(2, 87) = 20.34, p < .001, Welch's ANOVA was used. Waiting times differed significantly across the three clinics, F(2, 48.57) = 17.22, p < .001, η² = .15. Games-Howell comparisons showed that patients at Clinic A (M = 21.88, SD = 3.86) waited less than patients at Clinic B (M = 29.65, SD = 7.11), p < .001, and at Clinic C (M = 31.49, SD = 15.54), p = .007. Clinics B and C did not differ significantly, p = .826.
Mistakes reviewers catch
- Reporting the classic F. The ordinary ANOVA here gives F(2, 87) = 7.62; if you ran Welch's test, report Welch's F and its fractional df.
- Tukey post hoc tests after Welch's ANOVA. Tukey assumes equal variances; use Games-Howell.
- No effect size. Report η² or ω² alongside F.
- Listing post hoc p values without the means. Each comparison needs the group means so the direction is clear.
Let KyroStat do the write-up for you
KyroStat checks the variances, switches to Welch's ANOVA and Games-Howell tests when they differ, and writes the APA 7 paragraph from your data, with the effect size and every comparison.
Frequently asked questions
When should I use Welch's ANOVA instead of a one-way ANOVA? When the group variances are unequal, especially with unequal group sizes. Many statisticians recommend it by default, since it loses little when variances are equal. The classic version is covered in how to report a one-way ANOVA.
Which effect size goes with Welch's ANOVA? There is no single standard; η² or ω² from the ordinary ANOVA table is common. Say which one you report. See eta squared vs partial eta squared.
What if the data are also badly non-normal? Consider the rank-based Kruskal-Wallis test.
How do I report the post hoc tests? See how to report post hoc tests for Tukey, Bonferroni and Games-Howell write-ups.