How to Report a Repeated-Measures ANOVA in APA 7 (With Example)

A one-way repeated-measures ANOVA compares three or more conditions measured on the same participants. The write-up is harder than for a one-way ANOVA because of one extra assumption, sphericity, and what you do when it fails changes the degrees of freedom you report. This guide covers the APA 7 format, a worked example with every number computed from data you can see, and the mistakes reviewers catch.

What you need before you write a single word

An APA 7 write-up of a one-way repeated-measures ANOVA needs these values from your output:

1. The mean (M) and standard deviation (SD) for each condition.
2. Mauchly's test of sphericity (Mauchly, 1940): W, χ² with its df, and p.
3. If sphericity is violated, the Greenhouse-Geisser ε (Greenhouse & Geisser, 1959) or Huynh-Feldt ε (Huynh & Feldt, 1976).
4. The F value with both degrees of freedom, corrected if needed, and its exact p value.
5. An effect size, usually partial η².
6. Pairwise comparisons with a correction such as Bonferroni.

Sphericity, in one paragraph

Sphericity means the variances of the differences between every pair of conditions are equal. When they are not, the ordinary F test produces too many false positives. Epsilon measures the departure: ε = 1 is perfect sphericity, and the lowest possible value is 1/(k - 1) for k conditions (.50 for three). The correction multiplies both degrees of freedom by ε. The F value itself does not change, only its p.

The APA 7 format template

A one-way repeated-measures ANOVA showed a significant effect of [factor] on [dependent variable], F(df1, df2) = X.XX, p = .XXX, partial η² = .XX.

boltAll 53 templates, ready to paste with the italics set: the Rescue Vault, $27 →

When sphericity is violated, add one sentence before it:

Mauchly's test indicated that the assumption of sphericity was violated, W = .XX, χ²(df) = X.XX, p = .XXX, so Greenhouse-Geisser corrected degrees of freedom are reported (ε = .XX).

Formatting rules reviewers actually check:

• Italicise statistical symbols that use Latin letters: M, SD, F, p, W. Greek letters such as ε, η² and χ² are not italicised.
• No leading zero on values that cannot exceed 1: p, partial η², ε, and Mauchly's W.
• Report p exactly to two or three decimals; below .001, write p < .001.
• Corrected degrees of freedom are not whole numbers. Report them to two decimals, for example F(1.29, 14.18), and keep the decimals rather than rounding them to integers.

A worked example

Twelve participants (fictional data) studied 40-word lists under three conditions in counterbalanced order: silence, instrumental music, and music with lyrics. The dependent variable is the number of words recalled.

Running the analysis on these 36 scores gives:

• Descriptives: Silence M = 23.42, SD = 3.80; Instrumental M = 22.50, SD = 3.37; Lyrics M = 19.25, SD = 5.96.
• Mauchly's test: W = .45, χ²(2) = 8.01, p = .018. Sphericity is violated: participant 4 recalled more words with lyrics and participant 10 far fewer, so differences involving the Lyrics condition vary much more than the others.
• Greenhouse-Geisser ε = .64, so the degrees of freedom become 2 × ε and 22 × ε.
• Corrected test: F(1.29, 14.18) = 9.97, p = .005, partial η² = .48.
• Bonferroni-corrected pairwise comparisons (paired t-tests, each p multiplied by 3): Silence versus Instrumental, mean difference 0.92, p = .281; Silence versus Lyrics, mean difference 4.17, p = .013; Instrumental versus Lyrics, mean difference 3.25, p = .045.

Written up in APA 7, that becomes:

A one-way repeated-measures ANOVA examined the effect of study condition on the number of words recalled. Mauchly's test indicated that the assumption of sphericity was violated, W = .45, χ²(2) = 8.01, p = .018, so Greenhouse-Geisser corrected degrees of freedom are reported (ε = .64). Recall differed significantly across conditions, F(1.29, 14.18) = 9.97, p = .005, partial η² = .48. Bonferroni-corrected pairwise comparisons showed that participants recalled fewer words with lyrical music (M = 19.25, SD = 5.96) than in silence (M = 23.42, SD = 3.80), p = .013, and than with instrumental music (M = 22.50, SD = 3.37), p = .045. Recall in silence and with instrumental music did not differ significantly, p = .281.

Greenhouse-Geisser or Huynh-Feldt?

Greenhouse-Geisser tends to over-correct when ε is close to 1; Huynh-Feldt is less conservative. A common rule of thumb is Greenhouse-Geisser when ε is below about .75 and Huynh-Feldt above that. Here the original Huynh and Feldt (1976) formula gives ε = .69 and F(1.39, 15.26) = 9.97, p = .004, the same conclusion. Some software uses a modified Huynh-Feldt formula, so your value may differ slightly. Whichever you use, name it and report its ε.

The APA 7 table (optional)

Note. N = 12; words recalled out of 40. Greenhouse-Geisser corrected effect of condition, F(1.29, 14.18) = 9.97, p = .005, partial η² = .48.

Mistakes reviewers catch

• Reporting the uncorrected test after Mauchly's test was significant. The uncorrected result here is F(2, 22) = 9.97, p < .001. It looks stronger than the corrected p = .005, and that is exactly why reviewers check.
• Correcting without saying so. Name the correction and give ε, otherwise F(1.29, 14.18) looks like a typo.
• Rounding corrected df to whole numbers. F(1, 14) is a different test.
• Leaving Mauchly's test out. Report it, or state that you corrected regardless (it has little power in small samples, so some researchers always correct).
• Uncorrected pairwise comparisons. Three comparisons at .05 each inflate the false positive rate.
• Analysing repeated data as independent groups. A between-subjects ANOVA uses the wrong error term.
• A leading zero on p, ε, W or partial η². None of them can exceed 1.

When to use the Friedman test instead

If the dependent variable is ordinal, or the scores are badly non-normal in a small sample, use the Friedman test, the non-parametric alternative. On the data above it gives χ²(2) = 12.33, p = .002, Kendall's W = .51. See how to report a Friedman test. With only two conditions sphericity cannot be violated; use a paired t-test or the Wilcoxon signed-rank test. The assumptions guide and the effect size guide cover the checks and partial η².

Let KyroStat do the write-up for you

Mauchly's test, an epsilon, corrected degrees of freedom and Bonferroni comparisons are four places for a number to slip. KyroStat runs the repeated-measures ANOVA, checks sphericity, applies the correction when needed, and hands you the finished APA 7 sentences, the means table and the underlying Python or R code. Upload your spreadsheet, and the report is done in seconds.

Frequently asked questions

Do I report Mauchly's test if sphericity was not violated? A short clause is enough, for example "Mauchly's test indicated that sphericity was not violated, W = .XX, χ²(2) = X.XX, p = .XXX". Then report the uncorrected F.

Which effect size should I report? Partial η², without a leading zero. It divides the condition sum of squares by the condition plus error sums of squares, leaving out individual differences between participants.

Which related guides might I need? Often these: Mauchly's test, mixed ANOVA and post hoc tests.

References

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.).

Greenhouse, S. W., & Geisser, S. (1959). On methods in the analysis of profile data. Psychometrika, 24, 95-112.

Huynh, H., & Feldt, L. S. (1976). Estimation of the Box correction for degrees of freedom from sample data in randomized block and split-plot designs. Journal of Educational Statistics, 1, 69-82.

Mauchly, J. W. (1940). Significance test for sphericity of a normal n-variate distribution. Annals of Mathematical Statistics, 11, 204-209.