How to Report Partial Eta Squared in APA 7

Most ANOVAs that reach a reviewer carry the same partial eta squared: lifted straight from the SPSS column, set in italics, with a zero in front of the decimal point, and then translated in the text as "the factor explained 9% of the variance". All three are wrong, and the third one changes what the paper claims. This is what the number actually measures, how it is written, and when you should be reporting something else instead. The full write-up of the test itself is in how to report an ANOVA in APA 7.

What partial eta squared measures, and what it does not

The two indices share a numerator and differ in the denominator. Eta squared is SS_effect / SS_total: the share of all the variability in the study that this factor accounts for. Partial eta squared is SS_effect / (SS_effect + SS_error): the share it accounts for once the variance explained by the other effects has been taken out of the pot. With a single between-subjects factor the denominators coincide and the two numbers are identical. The moment a second factor enters, they part company.

Numbers make it concrete. A 2 × 3 between-subjects design with 96 undergraduates, 16 per cell, analyzing errors on a working-memory task by framing (gain or loss) and time pressure (low, medium, high), gives these sums of squares: framing 200, time pressure 160, interaction 40, error 1600, total 2000. Eta squared for time pressure is 160 / 2000 = .08. Partial eta squared is 160 / (160 + 1600) = .09. The gap is small here because the other effects are modest; with a factor soaking up half the variance, the partial would climb without the time-pressure effect having changed at all.

This is where the most expensive mistranslation happens. "Time pressure explained 9% of the variance" is false: 9% is a partial eta squared, and the variance it refers to is not the total but what the other effects had left unexplained. The accurate sentence for that index is "time pressure accounted for 9% of the variance not explained by the other effects in the model", and if what you meant was the first version, the number you want is the non-partial η², .08. When the two are this close the distinction looks cosmetic, but it is the same distinction that lets two studies with an identical real effect publish different effect sizes.

There is a labeling trap that slips into a lot of manuscripts. In a one-way ANOVA, η²_p and η² are exactly equal, because SS_effect + SS_error = SS_total. SPSS still heads the column "Partial Eta Squared" there. Copying the number is fine; copying the label and calling it partial in a design where "partial" has nothing to partial out is what makes a reviewer start checking everything else. State which index you are reporting, and keep it the same in every row of the table.

Partial eta squared follows exactly from the F: convert F to partial eta squared. And for G*Power, convert eta squared to Cohen’s f.

Writing it: upright, no leading zero, two decimals

The rule that gets broken most often is also the easiest: eta is set upright, not in italics. In APA 7 italics mark statistical symbols from the Latin alphabet, not Greek letters. Upright: η, ω, β, α, χ, ε. Italic: F, p, M, SD, N, t, d. Written in full: F(2, 90) = 4.50, p = .014, η²_p = .09. If your word processor italicized the eta because the rest of the line was italicized, fix it by hand.

No leading zero, because partial eta squared is bounded between 0 and 1 and can never go above it. Same rule as p, r and alpha: η²_p = .09, not 0.09. Two decimals are enough; if the value drops below .01 you can give three (η²_p = .004) or write η²_p < .01, but do not mix precisions within a table.

The subscript identifies the index: η²_p for partial, plain η² for the non-partial version, η²_G for the generalized one. Spell it out on first mention ("effect sizes are partial eta squared") and put it in the table note. A reviewer who sees a bare "η²" above a column of suspiciously large values will ask which of the three it is, and that question costs a full round.

The effect size belongs in the same sentence as the test, right after the p value, and it goes with every effect, non-significant ones included. Reporting η²_p only where the result came out significant is selective reporting, it leaves the reader unable to tell whether your null interaction was tiny or simply underpowered, and it is precisely the number anyone meta-analyzing your study will need.

Why partial etas never add up to 100%

The non-partial etas do carve up the whole pie. In the example above: framing .10, time pressure .08, interaction .02, error .80. They sum to exactly 1.00, and they have to, because every one of them divides by the same total sum of squares. That additivity is why η² can safely be read as a percentage of variance.

The partial ones carve up nothing, because each has its own denominator. Here they are .11, .09 and .02, which sum to .22, and that .22 means nothing at all — it does not say that 78% is left over. In a design with large effects and little error the sum sails past 1. If the sums of squares were 900 for factor A, 700 for B, 400 for the interaction and 500 for error out of a total of 2500, the eta squareds would be .36, .28 and .16 (plus .20 error, total 1.00) and the partials would be .64, .58 and .44: 1.66 in total. Nothing has gone wrong; you have three ratios answering three different questions.

Two practical consequences. First: if you need a decomposition that adds up, report η² or η²_G, never the partials, and never draw a pie chart of partial etas. Second, and more serious: η²_p values are not comparable across designs. Adding a covariate, a second factor or a blocking variable shrinks the error term, which lifts the partial eta of every other effect without any of them having changed. An η²_p of .20 from a two-factor design and an η²_p of .20 from a four-factor design are not the same claim, and comparing them in the discussion is an argument that does not hold.

When a reviewer adds your partials up and asks — it happens more often than you would think — the answer fits in one line of the table note: "Values are partial eta squared and, by definition, do not sum to 1". Give the non-partial η² in a neighboring column and the question never gets asked.

When to switch to omega squared

Both η² and η²_p are biased upwards: they describe the variance explained in your sample, and in a sample the effect always looks slightly bigger than it is in the population, because part of what the model captures is noise. Omega squared subtracts that expected noise. The formula is ω² = (SS_effect − df_effect × MS_error) / (SS_total + MS_error), and it needs four numbers that are already in your ANOVA table.

With the example data, MS_error = 1600 / 90 = 17.78. For time pressure: (160 − 2 × 17.78) / (2000 + 17.78) = .06, against an η² of .08. For the interaction: (40 − 35.56) / 2017.78 = .00, against an η² of .02 — almost all of that interaction's apparent effect is what you would expect from noise alone, which the eta squared cheerfully hides. With 96 participants the correction is modest. With 10 per cell it is not, and that is where eta squared starts publishing effects nobody replicates.

There is a partial version too: ω²_p = (SS_effect − df_effect × MS_error) / (SS_effect + (N − df_effect) × MS_error), which gives .07 for time pressure against an η²_p of .09. One quirk worth knowing: omega squared can come out negative when the effect is essentially null. That is not a software bug, it is the correction doing its job. The convention is to report it as .00 and say that it was truncated.

Use omega squared when the sample is small, when the result is heading for a meta-analysis, or when you are comparing your effect against another study. Use partial eta squared when the journal or the field expects it, which is still the majority in psychology, and then report both — it costs one column. On software: the SPSS GLM procedure offers only the partial (recent versions add eta and omega in the one-way procedure), jamovi and JASP have the omega checkbox sitting right next to the eta one, and in R you get both from effectsize::eta_squared() and effectsize::omega_squared(). If all you have is an F with its degrees of freedom, the effect size calculator will convert it for you.

Repeated measures: why your partial eta looks enormous

In a repeated-measures ANOVA the error term is not the leftover variability of the whole study but the factor-by-participants interaction. The variability between people — usually the largest source of all — sits outside the denominator. The upshot is that η²_p values from within-subjects designs are systematically far larger than the same effect measured between subjects, and not because the effect is larger.

A worked case: 32 participants measured across four weekly sessions of an app-delivered mindfulness program, with SS_session = 180, SS_error = 420 and SS_participants = 1500. Partial eta squared is 180 / (180 + 420) = .30. Generalized eta squared, which puts between-participant variability back into the denominator, is 180 / (180 + 1500 + 420) = .09. Same effect, two ways of counting it, and only the second can be placed beside a study with independent groups. Olejnik and Algina (2003) and Bakeman (2005) proposed it for exactly this reason, several journals now ask for it, and in R the afex package returns η²_G by default.

The sphericity correction does not touch the effect size, and this trips people up. If Mauchly's test is significant and you apply Greenhouse-Geisser with ε = .74, the degrees of freedom become 2.22 and 68.82 and the p value gets more conservative, but the sums of squares are unchanged, so η²_p stays exactly where it was: F(2.22, 68.82) = 13.29, p < .001, η²_p = .30. Corrected degrees of freedom are written to two decimals, and you have to name the correction you used.

The most damaging use of a within-subjects η²_p is sample size planning. Feed that .30 into G*Power for a between-subjects design and the f it produces is √(.30 / .70) = 0.65, a huge effect, and the software will tell you a handful of participants will do. The study is then born with half the power you think it has. The effect size that feeds a power calculation has to come from a design like the one you are about to run; there is more on this in the article on statistical power.

A full example, and interpreting without overreaching

Here is the paragraph in full, ready to copy and swap the numbers: "Framing had a significant effect on the number of errors, F(1, 90) = 11.25, p = .001, η²_p = .11, 90% CI [.03, .21], as did time pressure, F(2, 90) = 4.50, p = .014, η²_p = .09, 90% CI [.01, .18]. The framing × time pressure interaction was not significant, F(2, 90) = 1.13, p = .329, η²_p = .02, 90% CI [.00, .08]. Effect sizes are partial eta squared; the corresponding non-partial values, which do partition total variance, were .10, .08 and .02, and omega squared for time pressure was .06." Four lines, and no reasonable question left unanswered.

The confidence interval deserves its own paragraph. APA 7 asks for effect sizes with intervals wherever possible, and for η²_p the convention is a 90% interval rather than a 95% one: because the F test is one-tailed, a 90% interval is the one that lines up with a test at .05, so an effect is significant exactly when the lower bound clears zero. The interval is asymmetric and SPSS does not produce it by default; jamovi, JASP and the R package effectsize do. Its width is the information missing from almost every manuscript: an η²_p of .09 with an interval running from .01 to .18 is an effect estimated with almost no precision, and saying so protects you from the discussion section that writes itself.

On benchmarks: the convention everyone cites (η² of .01 small, .06 medium, .14 large) comes from Cohen's (1988) equivalences and was derived for eta squared, not for the partial version. Applying it as-is to an η²_p from a factorial or within-subjects design, where the partial is larger by construction, inflates the reading. Present it as what it is — a rough reference — say which index you are applying it to, and add what genuinely helps the reader: how much the outcome moved on the scale of the instrument. Three points on a standardized measure communicate more than a .09, exactly as they do with Cohen's d: the benchmark orients, the scale of the instrument informs.

Four sentences worth not writing: "explained 9% of the variance" about a partial index, "a large effect" with no index and no threshold named, any comparison of η²_p across different designs, and an effect size reported only where the result came out well. If you are staring at ANOVA output and cannot tell which column feeds which sentence, paste it into the results interpreter and come out with the paragraph already built.

Already drafted it? Paste your Results section into Review one section before it goes to your supervisor or the journal. You get the first thing a reviewer would object to, with your own sentence quoted.

Frequently asked questions

How do you report partial eta squared in APA 7?

In the same sentence as the test and immediately after the p value, set upright because eta is a Greek letter, and with no leading zero: F(2, 90) = 4.50, p = .014, η²_p = .09. Report it for every effect, including the non-significant ones, and give a 90% confidence interval alongside it wherever your software can produce one.

What is the difference between eta squared and partial eta squared?

Same numerator, different denominator. Eta squared divides the effect sum of squares by the total sum of squares, so it is a proportion of all the variance in the study. Partial eta squared divides it by the effect plus the error, that is, by what was left once the other effects were removed. In a one-way ANOVA the two are identical; as soon as there are two factors, the partial is larger.

Why do my partial eta squared values add up to more than 1?

Because each one has its own denominator and they are not carving up a shared pie. Only the non-partial etas sum to 1 alongside the error term. Three partials summing to 1.66 is not an arithmetic error and not a problem with the model: it just means they cannot be read as percentages of total variance or plotted as a pie chart.

What counts as a large partial eta squared?

The usual convention (.01 small, .06 medium, .14 large) comes from Cohen's (1988) equivalences and was derived for eta squared, not the partial version. Since the partial is larger by construction in factorial and repeated-measures designs, applying those same cut-offs inflates the interpretation. Treat them as a rough reference, name the index you are interpreting, and add the change on the scale of the outcome measure.

When should I use omega squared instead of eta squared?

When the sample is small, when the result is going into a meta-analysis, or when you are comparing against other studies, because eta squared overestimates the population effect and omega removes that bias. It is (SS effect − df effect × MS error) / (SS total + MS error). It can come out negative when the effect is essentially null, and the convention then is to report .00 and say it was truncated.

How is partial eta squared reported in a repeated-measures ANOVA?

The same way as in a between-subjects design, with two caveats. If you applied Greenhouse-Geisser, the degrees of freedom are corrected and written to two decimals — F(2.22, 68.82) = 13.29, p < .001, η²_p = .30 — and the partial eta squared itself does not change, because the sums of squares do not. And since the within-subjects error term excludes between-participant variability, the partial runs high: add generalized eta squared (here η²_G = .09), which is the value comparable with independent-groups studies.

With eta upright, no leading zero, the index named and an interval beside it, your effect size is reported the way APA 7 expects. If the harder question is the one that comes earlier — which design supports the question you are actually asking, which effect size you have to commit to before collecting a single data point — that is cheaper to settle in advance: in my statistical consulting we go through the analysis plan and write down what gets reported in each table.