Partial Eta Squared in APA 7: Reporting ANOVA and Repeated Measures

In APA 7 the effect size of an ANOVA goes right after the p value, on the same line and separated by commas: F(2, 87) = 5.23, p = .007, η²p = .11. The symbol is not italicised (it is a Greek letter), it takes two decimals, and it carries no leading zero, because partial eta squared cannot exceed 1. And it is not optional: APA 7 asks for an effect size for every test you report, so an ANOVA with no η²p (or no generalized eta squared, omega squared or the matching confidence interval) is incomplete.

Reporting an ANOVA in APA 7 format seems simple until a reviewer flags that the effect size is missing, that the degrees of freedom are wrong, or that you didn't state the post hoc method. Here's exactly what it should include, copy-ready examples for one-way, factorial and repeated-measures designs, and the mistakes that get penalised most. If your design is within-subjects, go straight to the repeated-measures section: the η²p that SPSS prints there is built on a different error term and does not mean the same thing as the η²p of a between-groups ANOVA. If you want the general guide, it's in how to report results in APA 7.

If what you have is a loose F and all it needs is formatting, the APA 7 results formatter turns it into the full string. And if you already have the result written out in a paragraph and need to pull the η²p out of it without doing the arithmetic by hand, effect size from text computes it for you.

What an ANOVA report must include

A well-reported ANOVA in APA 7 always includes the F statistic with its two degrees of freedom (numerator and denominator), the p-value, and the effect size (usually partial eta squared, η²p, or generalized eta squared, η²G). If the effect is significant and there are more than two groups, you add the post hoc comparisons stating the method (Bonferroni, Tukey, Games-Howell). Group means and standard deviations go in the text or, better, in a table.

Example: one-way ANOVA

For a one-way ANOVA with three groups, the standard format would be:

"A significant effect of therapy type on symptom reduction was found, F(2, 87) = 5.23, p = .007, η²p = .11. Bonferroni-corrected post hoc comparisons indicated that the CBT group (M = 12.4, SD = 3.1) showed greater reduction than the control group (M = 8.9, SD = 2.8), p = .005."

Note the details that make the difference: F carries its two degrees of freedom in parentheses, separated by a comma; the p-value is reported exactly (not "p < .05") unless it's below .001; and the effect size always accompanies the test. Formatting matters: F, p, M and SD are italicised, but η² is not (Greek letters are not italicised in APA). If you are still one step earlier, at the point of getting the output table out of your software, the full walkthrough is in one-way ANOVA in SPSS step by step.

Partial eta squared: what counts as large, and when it fails you

The benchmarks almost everyone uses come from Cohen (1988): η²p around .01 is a small effect, .06 medium and .14 large. Treat them as orientation, not as a verdict. In a tightly controlled experiment a .06 can be trivial, and in a noisy field study a .03 can be the most interesting thing in the paper. What a reviewer wants to read after the number is what that effect means in the units of your outcome, not just the label "medium". If you want the full map of effect size indices and how they convert into each other, it is in effect size: Cohen's d, eta² and r.

Partial, generalized or plain: they are not the same thing

Eta squared (η²) splits the total variability of the study across every effect in the model. Partial eta squared (η²p) compares your effect only against its own error term and ignores the variance explained by the other factors. That is why SPSS returns η²p by default, and why that value goes up as you add factors to the design: in a factorial design the η²p values can add up to more than 1, which is impossible with η². The practical consequence is awkward but worth knowing: two studies with η²p = .14 are not comparable if their designs differ. So the minimum is to state explicitly which of the three you are reporting, and if the design is factorial, within-subjects or mixed, to add generalized eta squared as well. That gap is widest in repeated measures, so it gets its own section below. A good share of the arguments with reviewers about effect sizes are settled by that one sentence.

The confidence interval (and why it is 90%)

APA 7 recommends pairing the effect size with its confidence interval. For partial eta squared the convention is a 90% interval rather than 95%: because the F test is one-tailed, the 90% CI is the one that matches a test at the 5% level and it keeps the lower bound from going negative (Steiger, 2004). It reads like this: η²p = .11, 90% CI [.02, .22]. If your software does not give it directly, in R you get it with effectsize::eta_squared(model, ci = .90), and in Jamovi or JASP it usually sits in the effect size options of the ANOVA itself. Reporting the interval is the fastest way to show that an η²p = .11 with a CI of [.00, .26] is not the solid evidence it looks like. In repeated-measures designs the interval is built from the noncentral F distribution with the degrees of freedom of that model, so give it the same degrees of freedom you report in the text and name the package you used, because implementations differ in how they handle the sphericity correction.

Factorial ANOVA: one line per effect

In a two-way ANOVA you report each main effect and the interaction separately, each with its F, p and effect size: "The main effect of group was significant, F(1, 120) = 8.40, p = .004, η²p = .07; the group × time interaction was not, F(2, 240) = 1.20, p = .31." Report the non-significant effects too, with their numbers: a design where only the significant effects have an F next to them is the classic sign of a results section written after looking at the output.

Once you are at three or four of those lines, prose stops being readable and the whole thing belongs in a table. The universal APA table generator takes the F, the two degrees of freedom, the p and the η²p of each effect and returns the ANOVA table already formatted, rules and note included, ready to paste into the manuscript.

Repeated-measures ANOVA: what changes when the design is within-subjects

This is where most of the trouble is, because a within-subjects ANOVA needs three things a between-groups ANOVA doesn't: corrected degrees of freedom when sphericity fails, the epsilon you corrected with, and an effect size that you have labelled clearly enough for a reader to know what it is comparable to. A complete one-way repeated-measures report looks like this:

"Depressive symptoms changed across the three assessment points, F(1.44, 84.96) = 14.75, p < .001, η²p = .20, η²G = .07. Mauchly's test indicated that the assumption of sphericity had been violated, χ²(2) = 8.44, p = .015, so degrees of freedom were corrected using the Greenhouse-Geisser estimate of sphericity (ε = .72). Bonferroni-corrected pairwise comparisons showed a reduction between baseline (M = 21.3, SD = 5.2) and post-treatment (M = 17.8, SD = 5.6), p = .002."

Three details in there are the ones reviewers actually catch: the degrees of freedom are decimals and carry two of them (that is what tells the reader you corrected), the epsilon is stated with the correction that used it, and there are two effect sizes because η²p alone is ambiguous in this design. Below is why.

Why partial eta squared comes out bigger in a within-subjects design

Partial eta squared is SS_effect / (SS_effect + SS_error), and in a repeated-measures ANOVA that error term is the effect's own residual, after the stable differences between participants have been pulled out into a separate subjects term. Those individual differences are usually the largest source of variance in a psychological outcome, and in a within-subjects design they are not in the denominator. That is the whole story: SPSS is not doing anything wrong, it is applying the definition, but the resulting η²p answers "how much of what was left over does my effect explain" and not "how much of the variance in the outcome does my effect explain".

The practical consequences are three, and they are not cosmetic. First, η²p values of .30, .50 or higher are routine in within-subject designs and do not mean the manipulation is enormous. Second, Cohen's .01 / .06 / .14 benchmarks were framed for variance explained out of the total, so calling a within-subject η²p = .20 "large" by that yardstick is not an interpretation, it is a category error. Third, the same manipulation run between groups would yield a much smaller η²p, so the value in your table is not comparable to the one in the between-groups paper you are citing next to it, and it should not be pasted into a between-subjects power analysis to justify a sample size.

Generalized eta squared: the one that travels between designs

Generalized eta squared (η²G; Olejnik and Algina, 2003; Bakeman, 2005) exists precisely for this. It puts back into the denominator the variance that the design removed but that would have been there in a different design, so that a within-subjects effect and a between-groups effect become comparable, which is what a meta-analyst or anyone running a power analysis off your paper needs. For a one-way repeated-measures design with a manipulated factor it is simply:

η²G = SS_effect / (SS_effect + SS_subjects + SS_error)

With the sums of squares behind the example above (SS_time = 100 on 2 df, SS_subjects = 1000, SS_error = 400 on 118 df), η²p = 100 / 500 = .20 while η²G = 100 / 1500 = .07. Same effect, same data, one number roughly three times the other. Neither is wrong; what would be wrong is reporting one and letting the reader assume the other. SPSS does not print η²G, but every quantity in that formula is in the output, so you can compute it by hand in thirty seconds. In R it comes for free: afex::aov_ez() returns generalized eta squared by default, and effectsize::eta_squared(model, generalized = TRUE) does the same on an existing model.

The rule of thumb that keeps you out of trouble: report η²p if you want to stay consistent with what your software printed, add η²G whenever the design is within-subjects or mixed, and in either case write the symbol out rather than saying "eta squared" and leaving the reader to guess which of the three you meant.

Sphericity: the correction moves your degrees of freedom, not your effect size

A detail that trips up a lot of manuscripts. The Greenhouse-Geisser and Huynh-Feldt corrections multiply both degrees of freedom by epsilon; they do not touch the sums of squares. So F stays exactly the same, the degrees of freedom shrink, and the p-value grows, but η²p is identical before and after the correction. That is why the "Tests of Within-Subjects Effects" table in SPSS shows the same partial eta squared in all four rows (sphericity assumed, Greenhouse-Geisser, Huynh-Feldt, lower bound) and why you should not go looking for a different effect size to match the corrected line. What changes in your write-up is the degrees of freedom and the p, and you report the epsilon so the reader can reconstruct both.

On which correction to use: Greenhouse-Geisser is conservative and the safe default, Huynh-Feldt is less conservative and usually preferred when epsilon is above roughly .75. Note also that Mauchly's test has poor power in small samples, so failing to reject it is weak evidence that sphericity holds; a defensible alternative that some methodologists prefer is to apply the Greenhouse-Geisser correction by default and say so, instead of letting a non-significant Mauchly decide it for you.

Mixed designs: two error terms, two partial eta squareds

In the group × time design that dominates intervention research, SPSS splits the output in two: the within-subject effects (time, and the group × time interaction) use the residual error term, while the between-subject factor (group) is tested in a separate "Tests of Between-Subjects Effects" table against the subject-level error. Those are two different denominators, so the η²p of your group effect and the η²p of your time effect are not on the same scale, and ranking them against each other ("the effect of time was larger than the effect of group") is not something those numbers support. Report each with its own F and degrees of freedom, and if you want them comparable, that is exactly what η²G is for. And if you have missing data or participants without every time point, consider whether a mixed model beats a repeated-measures ANOVA here, because the ANOVA will drop whole cases and you will be reporting an effect estimated on the completers.

Table and common mistakes

When there are several effects, an APA-format ANOVA table (horizontal lines at the top, below the headers and at the bottom; no vertical lines) is clearer than text. The most penalised mistakes: omitting the effect size, not stating the post hoc method, writing a single degree of freedom instead of two, reporting "marginally significant" for a p between .05 and .10, or not describing group means. In repeated measures, add three more: reporting whole-number degrees of freedom after saying you applied Greenhouse-Geisser, correcting the degrees of freedom without ever giving the epsilon, and calling a within-subject η²p "large" against Cohen's benchmarks. Reporting the ANOVA incompletely is one of the common reasons a reviewer asks you to redo the results section. And if you are stuck one step earlier, with the SPSS output in front of you and no idea which of these rows goes into the manuscript, paste it here and it interprets it for you, APA 7 sentence included.

Frequently asked questions

How do you report an ANOVA in APA 7?

With the F, its two degrees of freedom, the exact p and an effect size on the same line, preceded by the means and standard deviations of the groups: "A significant effect of therapy type on symptom reduction was found, F(2, 87) = 5.23, p = .007, η²p = .11." If the effect is significant and there are more than two groups, add the post hoc comparisons naming the method used.

Is partial eta squared italicized, and does it take a leading zero?

It is not italicised, because η is a Greek letter and APA 7 keeps Greek symbols upright. And it does not take a leading zero, because it is bounded between 0 and 1: η²p = .11, not 0.11. Two decimals. The "p" is a subscript, and it is worth writing it, precisely so the reader knows it is the partial version and not plain η².

What counts as a small, medium or large partial eta squared?

The benchmarks in circulation come from Cohen (1988): about .01 small, .06 medium and .14 large. Two cautions. They were framed for variance explained out of the total, so they do not transfer to a within-subjects η²p, which is inflated by construction. And they are orientation, not a verdict: in a tightly controlled experiment a .06 can be trivial, and in a noisy field study a .03 can be the most interesting result in the paper.

Why is the confidence interval for partial eta squared a 90% one?

Because the F test is one-tailed. A 90% interval is the one that corresponds to a test at the 5% level and it keeps the lower bound from falling below zero, which a 95% interval can do (Steiger, 2004). It reads: η²p = .11, 90% CI [.02, .22].

How do I report the Greenhouse-Geisser correction?

Give the corrected degrees of freedom with their decimals, state the correction and give the epsilon: F(1.44, 84.96) = 14.75, p < .001, with Greenhouse-Geisser correction (ε = .72). Also report Mauchly's test that led you there. The correction changes the degrees of freedom and therefore the p; it does not change F and it does not change η²p, so do not go looking for a different effect size to match the corrected row.

Do I have to report non-significant effects in an ANOVA?

Yes, with their full statistics. A factorial design in which only the significant effects carry an F is the classic sign of a results section written after looking at the output, and it is the kind of thing a reviewer notices immediately.

Which post hoc test should I report?

The one that matches your assumptions, and you have to name it. Tukey's HSD for all pairwise comparisons with homogeneous variances, Bonferroni or Holm when the comparisons are few and planned, Games-Howell when the variances are unequal. For each comparison, report the mean difference with its confidence interval and the adjusted p, not just an asterisk on a graph.

Before you submit: a missing effect size, one that never says whether it is partial or generalized, or one with no interval, is among the most repeated comments in the first review round. If your manuscript is already written, run it through the Q1 Reviewer: a free Reviewer 2 style pre-review that tells you what they will flag in your results before the journal flags it.

That covers the ANOVA. If your design is more complex or you want the report to pass your committee without issues, I'll have it ready in APA 7 format through my statistical consulting for theses and papers.