A mixed ANOVA (also called a split-plot ANOVA) combines a between-subjects factor, such as treatment group, with a within-subjects factor, such as time. It is the standard analysis for a pre-test/post-test design with a control group. The question it answers is usually the interaction: did the groups change differently over time? This guide gives you the APA 7 format for every part of the output and a worked example.
What you need before you write a single word
- Each cell's mean (M) and standard deviation (SD): every group at every time point.
- Mauchly's test of sphericity for the within-subjects factor (and a Greenhouse-Geisser correction if it fails).
- The interaction: F, both degrees of freedom, exact p, partial η².
- The main effect of the within factor (time) and the main effect of the between factor (group), each with the same statistics.
- Simple effects that explain a significant interaction.
The APA 7 format template
A [2] × [3] mixed ANOVA with [group] as the between-subjects factor and [time] as the within-subjects factor showed a significant [group] × [time] interaction, F(df1, df2) = X.XX, p = .XXX, partial η² = .XX. There was [a significant] main effect of [time], F(df1, df2) = X.XX, p = .XXX, partial η² = .XX, and [no significant] main effect of [group], F(df1, df2) = X.XX, p = .XXX, partial η² = .XX.
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Formatting rules reviewers actually check:
- Lead with the interaction: if it is significant, the main effects cannot be read on their own.
- Give each effect its own degrees of freedom; the between-subjects effect uses a different error term (here 38) from the within-subjects effects (here 76).
- Report Mauchly's test, and the Greenhouse-Geisser corrected df if sphericity is violated.
- No leading zero on p or partial η².
A worked example
Suppose 40 adults with anxiety were randomised to CBT or a waiting-list control, and anxiety was measured before, after, and at a three-month follow-up.
| Group | Pre M (SD) | Post M (SD) | Follow-up M (SD) |
|---|---|---|---|
| CBT (n = 20) | 48.54 (11.56) | 39.58 (8.44) | 37.22 (10.46) |
| Control (n = 20) | 48.61 (9.05) | 44.88 (8.24) | 47.90 (10.75) |
Mauchly's test showed that sphericity held, W = .86, χ²(2) = 5.84, p = .054. Written up in APA 7:
A 2 (group: CBT, control) × 3 (time: pre, post, follow-up) mixed ANOVA showed a significant group × time interaction, F(2, 76) = 12.31, p < .001, partial η² = .24. There was a significant main effect of time, F(2, 76) = 22.33, p < .001, partial η² = .37, and no significant main effect of group, F(1, 38) = 3.52, p = .068, partial η² = .08. Simple effects showed that the groups did not differ before treatment, t(38) = −0.02, p = .983, but the CBT group reported lower anxiety than the control group at follow-up, t(38) = −3.19, p = .003. Anxiety fell significantly over time in the CBT group, F(2, 38) = 25.87, p < .001, and changed less, though still significantly, in the control group, F(2, 38) = 4.33, p = .020.
Mistakes reviewers catch
- Interpreting the main effect of group when the interaction is significant. Here the groups differ only after treatment; "no group effect" alone would be misleading.
- One set of df for everything. The between-subjects effect has its own error df.
- Skipping sphericity. Report Mauchly's test whenever the within factor has three or more levels.
- No simple effects. A significant interaction needs to be broken down: which groups differ at which time points.
- Running separate t-tests instead. That ignores the design and inflates the error rate.
Let KyroStat do the write-up for you
KyroStat recognises when the same people are measured more than once, runs the mixed ANOVA with the sphericity check and simple effects, and writes this paragraph and the table from your data.
Frequently asked questions
What is the difference between a mixed ANOVA and a repeated-measures ANOVA? A repeated-measures ANOVA has only within-subjects factors. A mixed ANOVA adds at least one between-subjects factor, such as treatment group.
How do I report Mauchly's test? W, χ² with its df, and p, before the ANOVA itself. If it is significant, report Greenhouse-Geisser corrected df. See how to report Mauchly's test.
Which effect size do I use? Partial η² for each effect. See eta squared vs partial eta squared.
Could I use ANCOVA with the pre-test as a covariate instead? Yes, for a pre/post design with two time points an ANCOVA on the post-test, adjusting for the pre-test, is often more powerful.