How to Report Eta Squared and Partial Eta Squared in APA 7

Eta squared (η², "eta quadrado" in Portuguese) is the most common effect size for ANOVA. The confusion starts when SPSS prints "Partial Eta Squared", a colleague reports plain η², and a reviewer asks for ω². These are three different statistics. This guide shows what each measures, why they differ in the same analysis, and how to format them in APA 7.

Eta squared, partial eta squared, and omega squared

All three describe the share of outcome variance associated with an effect. They differ in the denominator.

• Eta squared (η²) divides the effect's sum of squares by the total sum of squares: η² = SS(effect) / SS(total). Every other effect in the model stays in the denominator.
• Partial eta squared (partial η², sometimes written ηₚ²) divides by the effect plus error only: partial η² = SS(effect) / (SS(effect) + SS(error)). Other effects are removed from the denominator, so the value is usually larger.
• Omega squared (ω²) adjusts η² for the fact that sample effect sizes overestimate the population value: ω² = (SS(effect) − df(effect) × MS(error)) / (SS(total) + MS(error)). It is less biased, especially in small samples (Lakens, 2013). A partial version, partial ω², also exists for factorial designs.

In a one-way ANOVA there is only one effect, so SS(total) = SS(effect) + SS(error) and η² and partial η² are the same number. With two or more factors they separate, sometimes a lot, as the worked example below shows. Partial η² values from one model can even add up to more than 1, which plain η² never can.

What SPSS calls "Partial Eta Squared"

In SPSS, ticking "Estimates of effect size" in the GLM Univariate options adds a column labelled Partial Eta Squared. The label is accurate, so if you copy that number, call it partial η², not η².

The APA 7 format template

Put the effect size after the p value in the same parenthetical run:

There was a significant main effect of [factor] on [outcome], F(df1, df2) = X.XX, p = .XXX, partial η² = .XX.

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Formatting rules:

• No leading zero. η², partial η² and ω² cannot exceed 1, so APA 7 drops the zero: η² = .19, not 0.19.
• Greek letters are not italicized. Write η² and ω² in upright type; italicize the Latin statistical symbols (F, p, M, SD).
• Name the statistic you used. "partial η² = .38" and "η² = .38" are different claims.
• Two decimals is the usual precision for effect sizes; report p to two or three decimals, or p < .001.

A worked example

Thirty fictional students were randomly assigned to one of two study methods (rereading or flashcards) and one of three session lengths (15, 30 or 45 minutes), five per cell, then took a quiz scored out of 20.

A 2 × 3 between-subjects ANOVA (balanced, so Type I, II and III sums of squares agree) gives:

Look at the method row. η² says method accounts for 19% of all variance in quiz scores; partial η² says 38% of the variance left once session length and the interaction are set aside. Both are correct; they answer different questions, so say which one you report.

For the method effect, ω² = (48.13 − 1 × 3.30) / (258.00 + 3.30) = .17, a little below η² = .19, which is the bias correction at work.

Now run the same data as a one-way ANOVA with method as the only factor. Session length and the interaction fall into the error term, F(1, 28) = 6.42, p = .017, and η² and partial η² are both .19. Same data, but partial η² halved because the denominator changed, which is why partial η² is hard to compare across designs.

Written up in APA 7, with partial η² as the reported effect size:

A 2 × 3 between-subjects ANOVA showed a significant main effect of study method on quiz score, F(1, 24) = 14.59, p < .001, partial η² = .38, with higher scores after flashcards (M = 14.27, SD = 3.10) than after rereading (M = 11.73, SD = 2.31). The main effect of session length was also significant, F(2, 24) = 18.27, p < .001, partial η² = .60. The interaction was not significant, F(2, 24) = 1.53, p = .24, partial η² = .11.

If you prefer the less biased estimate, swap in ω² and label it: F(1, 24) = 14.59, p < .001, ω² = .17.

Cohen's f and f² (the "f2" effect size)

Two related statistics come up in power analysis and regression:

• Cohen's f for ANOVA: f = √(η² / (1 − η²)), using partial η² for one effect in a factorial design. Power-analysis software usually asks for f. From the partial η² of .38 above, f = 0.78.
• Cohen's f² for regression: f² = R² / (1 − R²). A model with R² = .20 has f² = 0.25. For a single predictor's unique contribution, use the change in R² divided by (1 − R²) of the full model.

Both f and f² can exceed 1, so they keep the leading zero (0.78, 0.25), and as Latin letters they are italicized. See the multiple regression guide for where f² fits in a regression write-up.

Small, medium and large, with caution

Cohen (1988) suggested rough benchmarks:

Cohen offered these as a fallback when nothing better is known. Be careful with partial η² from multi-factor designs: removing other effects from the denominator can make a modest effect look "large", as the method effect above shows. Compare against effects in your own field where you can, and treat the labels as a description, not a verdict.

Mistakes reviewers catch

• Calling partial η² "eta squared". Copying SPSS's "Partial Eta Squared" column and labelling it η² is the most common error.
• A leading zero. η² = 0.38 should be η² = .38.
• Italicizing the Greek letter. η² and ω² stay upright.
• Comparing partial η² across different designs. As the example shows, adding a factor can double partial η² without the effect changing.
• Reading benchmarks as laws. A partial η² of .06 is not automatically "medium".
• Only an omnibus effect size when the finding is a specific contrast. Add a Cohen's d for key pairwise comparisons.

For the full factorial write-up, see how to report a two-way ANOVA; for single-factor designs, the one-way ANOVA guide; and for adjusted designs, the ANCOVA guide.

Let KyroStat do the write-up for you

Choosing between η², partial η² and ω² is easy to get wrong under deadline. KyroStat runs the ANOVA on your data, computes the effect sizes, labels each one correctly, and hands you the finished APA 7 sentences, a table and the underlying Python or R code. Upload your spreadsheet, and the report is done in seconds.

Frequently asked questions

Should I report eta squared or partial eta squared? In a one-way ANOVA they are identical. In factorial designs partial η² is more common, but η² compares better across studies. Either works if you name it.

Is omega squared better than eta squared? It is less biased, especially in small samples (Lakens, 2013). It can come out slightly negative for tiny effects; if you report that as 0, say so.

Does partial eta squared have a leading zero in APA? No. It cannot exceed 1, so write partial η² = .38.

Why is my partial eta squared so much bigger than eta squared? The other effects are removed from its denominator, so the more variance they explain, the bigger the gap.

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

References

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

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.

Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863.