How to Interpret Repeated-Measures ANOVA Output in SPSS (and Report It in APA 7)

SPSS's repeated-measures ANOVA (General Linear Model > Repeated Measures) prints up to ten tables, and its main result table gives the same F four times with four different p values. Which one you report depends on a test printed two tables earlier, Mauchly's test of sphericity. This guide walks through the output in the order SPSS prints it, with a worked example in which sphericity is violated, lists the misreadings to avoid, and gives the APA 7 write-up. The reporting format alone is in the repeated-measures ANOVA APA guide.

What SPSS gives you

Analyze > General Linear Model > Repeated Measures, with a within-subjects factor (here Time, 3 levels), Descriptive statistics and Estimates of effect size ticked under Options, and pairwise comparisons with Bonferroni adjustment under EM Means, produces:

1. Within-Subjects Factors: which variable is which level. Check the order.
2. Descriptive Statistics: mean, SD and N at each level.
3. Multivariate Tests: a MANOVA-style test of the same effect.
4. Mauchly's Test of Sphericity: the assumption check that decides which row to report.
5. Tests of Within-Subjects Effects: the result.
6. Tests of Within-Subjects Contrasts: linear and quadratic trends.
7. Tests of Between-Subjects Effects: the intercept; nothing to report in a one-way design.
8. Estimated Marginal Means and Pairwise Comparisons: which levels differ.

Several tables carry the line "Measure: MEASURE_1", SPSS's default name for the outcome.

The worked example

Eighteen adults on an eight-week anxiety programme rated their anxiety (0 to 60) at the start (Week 0), halfway (Week 4) and at the end (Week 8). Time is the within-subjects factor. All numbers below come from one dataset.

Table 1: Within-Subjects Factors (not reproduced)

It lists Time levels 1, 2 and 3 against the variables anx_week0, anx_week4 and anx_week8. If the order is wrong here, every pairwise comparison later is mislabelled.

Table 2: Descriptive Statistics

The means and SDs you report. Anxiety fell from 29.78 to 25.44 to 24.17. Note the much larger SD at Week 8 (9.79): some people improved a lot in the second half and some did not, which is exactly what violates sphericity below.

Table 3: Multivariate Tests

This is a different way of testing the same Time effect (a multivariate test on the differences between levels) that does not assume sphericity. Pillai's Trace, Wilks' Λ, Hotelling's Trace and Roy's Largest Root are four multivariate statistics; with one within-subjects factor they give the same F and p, as here. Footnotes say the design and that the statistic is exact.

Most write-ups use the univariate test (Tests of Within-Subjects Effects) instead. Pick one approach before looking at the results, and report that one; do not choose whichever gives the smaller p.

Table 4: Mauchly's Test of Sphericity

SPSS puts the last three columns under an "Epsilon" heading.

Sphericity means the variances of the differences between every pair of levels are equal. The repeated-measures F assumes it.

• Mauchly's W = .354: 1 would mean perfect sphericity.
• Approx. Chi-Square = 16.625 with df = 2, Sig. = .000: sphericity is violated (p < .001).
• Greenhouse-Geisser ε = .607, Huynh-Feldt ε = .629, Lower-bound ε = .500: three estimates of how far sphericity is violated. 1 means no violation; the lower bound is 1 / (levels − 1). Each one is the factor the dfs are multiplied by in the corresponding row of the next table.

With only two levels there is one difference score and sphericity cannot be violated: SPSS prints W = 1.000 with df = 0 and no Sig. value, and you report the Sphericity Assumed row. More on the test itself in the Mauchly's test guide.

Table 5: Tests of Within-Subjects Effects

The four rows for Time are the same F (11.626) evaluated against four different sets of degrees of freedom:

• Sphericity Assumed: the uncorrected test, df = 2 and 34. Report it only when Mauchly's test is not significant.
• Greenhouse-Geisser: dfs multiplied by .607, giving 1.215 and 20.653, p = .002. The usual choice when sphericity is violated.
• Huynh-Feldt: dfs multiplied by .629, p = .001. Less conservative; often preferred when ε is above about .75.
• Lower-bound: the most conservative correction possible, rarely reported.

Take the first df from the Time row and the second from the Error(Time) row, on the same correction. With Greenhouse-Geisser here: F(1.21, 20.65) = 11.63, p = .002.

Partial Eta Squared = .406: Time SS / (Time SS + Error SS) = 311.370 / (311.370 + 455.296). It is the same on every row because the correction changes the dfs, not the sums of squares.

Because sphericity is violated here, the uncorrected row (p = .000) overstates the evidence; the corrected p = .002 is the honest one. Both are significant in this example, but they will not always agree.

Tables 6 and 7: Within-Subjects Contrasts and Between-Subjects Effects (not reproduced)

Tests of Within-Subjects Contrasts tests a linear and a quadratic trend across the three time points. Report it only if you planned a trend analysis. Tests of Between-Subjects Effects contains the Intercept, which tests whether the overall mean anxiety is zero; ignore it in a design with no between-subjects factor.

Table 8: Pairwise Comparisons

Footnotes: "Based on estimated marginal means", "*. The mean difference is significant at the .05 level" and "b. Adjustment for multiple comparisons: Bonferroni."

• Each pair appears twice, in both directions. Three time points give three comparisons.
• Sig. is already Bonferroni-adjusted (the raw p multiplied by 3, capped at 1), and so is the CI. Do not adjust again.
• Week 0 to Week 4: anxiety fell by 4.33 points, p < .001. Week 0 to Week 8: fell by 5.61, p = .003. Week 4 to Week 8: 1.28 points, p = 1.000 (the adjusted value hit its cap; report p > .999).

Misreadings that cost marks

• Reporting the Sphericity Assumed row after Mauchly's test was significant. Use the Greenhouse-Geisser (or Huynh-Feldt) row and say so.
• Taking both dfs from the Time row, or mixing corrections. The second df comes from Error(Time), on the same correction row.
• Rounding the corrected dfs to whole numbers. Report them to two decimals: F(1.21, 20.65).
• Reporting Mauchly's Sig. as the result. It is the assumption check.
• Writing p = .000 or p = 1.000. Write p < .001 and p > .999.
• Reporting the Multivariate Tests and the univariate test together as if they were two findings. They test the same effect. Report one.
• Adjusting the Bonferroni Sig. again. SPSS has already done it.

The APA 7 format template

A one-way repeated-measures ANOVA examined the effect of [factor] on [dependent variable]. 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). [Dependent variable] differed significantly across [levels], F(X.XX, X.XX) = X.XX, p = .XXX, partial η² = .XX.

The write-up for this example

A one-way repeated-measures ANOVA examined change in anxiety across the programme. Mauchly's test indicated that the assumption of sphericity was violated, W = .35, χ²(2) = 16.63, p < .001, so Greenhouse-Geisser corrected degrees of freedom are reported (ε = .61). Anxiety differed significantly across time points, F(1.21, 20.65) = 11.63, p = .002, partial η² = .41. Bonferroni-corrected pairwise comparisons showed that anxiety was lower at Week 4 (M = 25.44, SD = 5.35) than at Week 0 (M = 29.78, SD = 5.98), p < .001, and lower at Week 8 (M = 24.17, SD = 9.79) than at Week 0, p = .003. Weeks 4 and 8 did not differ significantly, p > .999.

Huynh-Feldt values can differ slightly between programs because some use a corrected version of the Huynh-Feldt formula. Whichever correction you use, name it and report its ε.

Let KyroStat do the write-up for you

Mauchly's test, an epsilon, two dfs from two rows and adjusted comparisons are a lot of places for a number to slip. KyroStat runs the repeated-measures ANOVA on your spreadsheet, checks sphericity, applies the correction when it is needed, and writes the APA 7 sentences and the means table with the code behind every number.

Also useful for the write-up (affiliate links): Proofreading for your thesis or paper (20% off with code PAP20): Paperpal

Frequently asked questions

Which row of Tests of Within-Subjects Effects do I report? Sphericity Assumed if Mauchly's test is not significant (Sig. ≥ .05); Greenhouse-Geisser if it is. Some researchers use Huynh-Feldt when the Greenhouse-Geisser ε is above about .75.

Where do the two degrees of freedom come from? The first from the Time row, the second from the Error(Time) row, both on the row of the correction you are reporting.

Why does Mauchly's test show no Sig. value? Your factor has two levels, so sphericity cannot be violated and there is nothing to test. Report the Sphericity Assumed row.

Should I report the Multivariate Tests? Only if you chose the multivariate approach. Most APA write-ups report the univariate test with a sphericity correction; either way, report one, not both.

Why is the Bonferroni Sig. exactly 1.000? The raw p times the number of comparisons exceeded 1, and SPSS caps it at 1. Report p > .999.

Which related guides might I need? Often these: Mauchly's test, mixed ANOVA and the Friedman test as the non-parametric alternative.