One-way ANOVA
One-way ANOVA tests whether the means of three or more independent groups differ. StatLab adds Levene's test, Welch's robust ANOVA and Tukey HSD post-hoc comparisons to show which groups differ.
Menu: Analyze → Compare Means → One-Way ANOVA…
When should I use One-way ANOVA?
- One scale outcome, one factor with three or more groups (e.g. control, programme A, programme B).
What are the assumptions?
- Independent observations; outcome roughly normal in each group.
- Equal variances (Levene). If Levene's Sig. < .05, report Welch's F.
How do I run it in StatLab?
- Choose dependent variable(s) and the factor.
- Keep Welch and Tukey HSD ticked.
How do I read the output?
| Output | Meaning |
|---|---|
| Descriptives | N, mean, SD, SE and 95% CI per group. |
| Homogeneity of Variances | Levene based on the mean (classic) and on the median (robust). |
| ANOVA table | Between- and within-groups sums of squares, df, mean squares, F and Sig. |
| η² and ω² | Proportion of variance explained (ω² is less biased). η² ≈ .01 small, .06 medium, .14 large. |
| Welch | F that does not assume equal variances. |
| Tukey HSD | Every pair of groups: mean difference (* = significant), SE, adjusted Sig. and simultaneous 95% CI (Tukey-Kramer when group sizes differ). |
Worked example
Compare score across the three groups in the bundled sample dataset (File → Sample dataset: 150 survey respondents with gender, programme group, age, pre/post test scores, five satisfaction items, income, smoking and education): F(2, 147) = 4.91, p = .009; Levene p = .333.
How would I report it in APA style?
A one-way ANOVA showed a significant effect of programme group on wellbeing, F(2, 147) = 4.91, p = .009, η² = .06. Tukey HSD tests showed that programme B scored higher than control (mean difference = 4.94, p = .008); other pairs did not differ significantly.
Numbers above were computed by StatLab’s validated engine from the sample dataset when this page was built.
What are common mistakes?
- Interpreting post-hoc tests when the overall F is not significant (and the question was not planned).
- Using one-way ANOVA for repeated measurements on the same people.