Write up this ANOVA
An APA-style results paragraph from the table above, flagging whether Welch's F should be reported instead.
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How one-way ANOVA works
ANOVA splits the total variability of all scores into two parts: how far each group mean sits from the grand mean (between-groups) and how far individual scores sit from their own group mean (within-groups). Dividing each sum of squares by its degrees of freedom gives mean squares, and F = MSbetween / MSwithin. If the groups share one true mean, F should hover around 1.
After a significant F
F tells you that some difference exists, not which. Run post-hoc tests that control the family-wise error rate: Tukey HSD when variances are similar, Games–Howell when they are not. If you planned specific comparisons in advance, use contrasts with a Bonferroni or Holm correction.
Planning the sample
Cohen's f from this page can be entered in the power analysis calculator. Three groups need 53 per group to detect a medium effect (f = 0.25) with 80% power.
Frequently asked questions
What does a one-way ANOVA test?
Whether the means of three or more independent groups are all equal. It compares variation between group means with variation within groups; the ratio is the F statistic.
Why not run several t-tests?
Each test carries a 5% false-positive risk, so three pairwise tests push the family-wise error rate to about 14%. ANOVA tests all groups at once; follow up with corrected post-hoc comparisons such as Tukey HSD.
What is eta squared?
η² = SS_between / SS_total, the proportion of variance in the outcome explained by group membership. Rough guides: .01 small, .06 medium, .14 large (Cohen, 1988). ω² is a less biased alternative, also shown.
What if the group variances are unequal?
Use Welch’s ANOVA, which this calculator also reports. It is robust to unequal variances and unequal group sizes and is recommended as the default by Delacre et al. (2019).