Partial eta squared (ηp2) is the proportion of variance in your outcome that one factor explains once the other factors are removed from the denominator, and you get it from the Partial Eta Squared column of your SPSS Tests of Between-Subjects Effects table. The calculation is a single division: ηp2 = SSeffect / (SSeffect + SSerror). It takes about five minutes if SPSS already printed the column, and about fifteen if you have to work it out by hand.
Both halves matter. The calculation tells you the number, and the reporting tells your reader what it means in a sentence that survives peer review. Get the second half wrong and the analysis was fine anyway.
This guide covers the SPSS menu path, the hand calculation, the interpretation benchmarks people actually argue about, and the APA 7 sentence templates for both significant and non-significant results. It also covers the design-specific error term, which is where most wrong numbers come from.
Table of Contents
- 1What You Need
- 2Step-by-Step: How to Calculate and Report Partial Eta Squared
- 3Find the Correct SPSS Test Output
- 4Use the Partial Eta Squared Column
- 5Calculate It Manually When Needed
- 6Interpret the Effect Size
- 7Report the Result in APA Style
- 8Type the Symbol So It Survives Formatting
- 9Common Mistakes
- 10Frequently Asked Questions
- 11What does partial eta squared actually mean?
- 12Why do my partial eta squared values add up to more than 1?
- 13What is the difference between eta squared and partial eta squared?
- 14How do I interpret a value like 0.045?
- 15Should I report an effect size when the F-test is not significant?
- 16How do I get partial eta squared for a repeated-measures or mixed design?
- 17Conclusion
What You Need
Before you calculate anything, line up four things. Missing one of them is how people end up with a value that is mathematically neat and statistically wrong.
- The ANOVA or general linear model output. For a one-way design it sits under Tests of Between-Subjects Effects in the One-Way ANOVA output. For two or more factors it sits in the same table under the GLM Univariate output. Mixed designs split across two tables, and I cover which row to use below.
- The row for the effect you care about. A two-way ANOVA prints rows for Factor A, Factor B, and their interaction. Each one has its own partial eta squared. Decide which one your hypothesis is about before you start reading numbers.
- The correct error sum of squares for your design. Between-subjects designs use the Error row in the same table. Repeated-measures and mixed designs use the within-subjects error row, and picking the wrong one changes the answer.
- The APA 7 reference for your discipline. Most psychology and education programs want effect sizes with every F-test. Check your department’s thesis or journal guidelines, because a handful of fields still report only the F and p values.
Optional but useful: the effectsize package in R. It gives you a confidence interval alongside the value, which lets you cross-check the SPSS number and, if you want one, report a 95% interval rather than a bare value.
Step-by-Step: How to Calculate and Report Partial Eta Squared
Find the Correct SPSS Test Output
For a one-way between-subjects design, the path is Analyze > Compare Means > One-Way ANOVA. Click Options in the dialog, tick Effects size, then Continue and OK. Forgot that checkbox is the single most common reason a student cannot find the column at all.
For two or more factors use Analyze > General Linear Model > Univariate, move your outcome to the Dependent Variable box and your factors to Fixed Factors, then hit Options and tick Effects size and Partial eta squared. The second checkbox is the one that distinguishes the partial measure from the ordinary eta squared measure. In the Model dialog, uncheck Intercept if your output convention is to do so, since the intercept inflates the total sum of squares and changes the ordinary eta squared.
Scan down the output to the Tests of Between-Subjects Effects table. It has columns for Type III Sum of Squares, the Mean Square, the F statistic, the Sig. value, and the effect size columns. The effect you want is a row, not a column. Do not mix those up.
Use the Partial Eta Squared Column
SPSS prints two effect size columns side by side, and this trips up nearly everyone the first time. Eta Squared divides by the total sum of squares, so it answers how much of all the variability in the outcome the effect accounts for. Partial Eta Squared divides by the effect plus its own error term, so it answers how much of the variance the effect accounts for after the other factors are held out. In a one-way design the two are identical. In a multi-factor design they diverge, and partial eta squared is always the larger of the two.
Read across the row for your effect to the Partial Eta Squared column and copy the value. Note two things at the same time: the F value, and the degrees of freedom from the df column, which is printed as two numbers, effect df first and error df second. You will need both for the report sentence.
Two checks confirm you read it right. The value must fall between 0 and 1. And the F value must be statistically significant, because SPSS blanks the effect size column whenever Sig. is above .05. If your effect size cell is empty, look at the Sig. column: that effect simply did not reach significance, and you will not get a number from SPSS for it.
Calculate It Manually When Needed
You need the hand calculation when you are working in R, using a mixed model, reading a published paper, or sitting an exam that gives you an ANOVA table and nothing else.
The formula is:
ηp2 = SSeffect / (SSeffect + SSerror)
SSeffect is the sum of squares for the effect row you care about. SSerror is the residual sum of squares from the error row that belongs to that effect, which is not always the row simply labelled Error. df is degrees of freedom.
Worked example. Suppose a one-way ANOVA compares three conditions and the Group row gives SSeffect = 240.000, df = 2, while the Error row gives SSerror = 168.000, df = 27. The calculation is 240.000 / (240.000 + 168.000) = 240 / 408 = 0.588, which rounds to 0.59.
The mean squares for those two rows are MSeffect = 240 / 2 = 120 and MSerror = 168 / 27 = 6.22, so F = 120 / 6.22 = 19.29. Run the shortcut on the same F and degrees of freedom and you get 2 × 19.29 / (2 × 19.29 + 27) = 38.58 / 65.58 = 0.588. The two routes agree, which is your confirmation that you picked the right rows.
That shortcut, ηp2 = df1F / (df1F + df2), needs only four numbers from the ANOVA table, so it is the fastest route when you have the F and both degrees of freedom in front of you. Use the sums of squares form when you have the table but not the F, which happens with some published reports and most hand-worked exam questions.
Which error row goes in the denominator depends entirely on your design:
| Design | Row to use as SSeffect | Row to use as SSerror |
|---|---|---|
| One-way between-subjects ANOVA | The factor row (for example, Group) | The Error row in the same table |
| Two-way between-subjects ANOVA | Factor A, Factor B, or the A × B interaction row | The single Error row in the same table |
| Repeated-measures ANOVA | The within-subjects effect row | The Error row inside the within-subjects tests table |
| Mixed design (one within, one between factor) | The within-subjects main effect and its interaction with the between factor | The within-subjects error row, never the between-subjects Error row |
| Mixed model fitted in lmer | Not printed by default; compute the term and residual sums of squares yourself | Residual sum of squares from the model output |
The mixed-model row is where people get stuck. In a lmer() output there is no SS column for the fixed effect, so you either request the ANOVA table from car::Anova() with Type III sums of squares, or you compute the term sum of squares by hand from the comparison models. If you fitted the model in R, the effectsize package handles most designs directly.
Interpret the Effect Size
Interpretation is where the confusion starts, because two benchmark sets are in circulation and they do not agree. Cohen’s original values are for eta squared, and partial eta squared values are conventionally read against the same cutoffs.
| Value (ηp2) | Cohen (1988) | Green and Salkind | Plain-language reading |
|---|---|---|---|
| below 0.01 | Negligible | Smallest | The factor barely separates the groups |
| 0.01 to 0.058 | Small | Small | A detectable effect worth reporting |
| 0.059 to 0.137 | Medium | Large | The factor accounts for a meaningful share of variance |
| 0.138 and above | Large | Huge | The factor dominates the model |
Write the interpretation as a claim about variance rather than as a bare label. This sentence states what was tested, gives the statistics, and names the size of the effect in the same breath: a one-way ANOVA showed a significant effect of training condition on quiz scores, F(2, 27) = 19.29, p < .001, ηp2 = .59.
Two things that sound contradictory but are not. A value of .05 can still produce p below .05, because statistical significance depends on sample size as well as effect size. And a non-significant effect can carry a surprisingly large partial eta squared, which usually means the study simply lacked power to detect it. Report the value with a confidence interval in that case rather than pretending it is zero.
One more expectation to set correctly: in a factorial design, the partial eta squared values for Factor A, Factor B, and the interaction do not have to sum to 1, and often they will not. Each uses its own error term in the denominator, so they are not pieces of a single whole. Users on r/AskStatistics and Cross Validated ask about this constantly, and the arithmetic is not broken. If you need values that are comparable across studies and sum meaningfully, generalized eta squared is the measure built for that job, and it is a legitimate second report alongside partial eta squared.
Report the Result in APA Style
APA 7th edition wants the effect size in the same sentence as the F statistic and the p value, in that order: F with its two degrees of freedom, then p, then ηp2. Italicise the F, the p, and the Greek symbols, because they are statistical symbols rather than ordinary letters.
Reusable template:
An n-way ANOVA showed a significant effect of factor on dependent variable, F(df1, df2) = F value, p < .001, ηp2 = .00.
Worked example, significant main effect:
A one-way ANOVA indicated that learning mode significantly affected test scores, F(2, 27) = 4.18, p = .026, ηp2 = .24.
Worked example, a two-way design with a significant interaction:
A two-way ANOVA found a significant interaction between presentation format and time pressure on recall accuracy, F(2, 54) = 3.86, p = .028, ηp2 = .13. The main effect of presentation format was not significant, F(1, 54) = 1.84, p = .180.
Formatting rules that get flagged in journals. Omit the leading zero for values that cannot exceed 1, so write ηp2 = .24, not 0.24. Report to two decimals, three at most. Never write p = .000; use p < .001. Degrees of freedom always put the effect df first and the error df second, and separate them with a comma inside the parentheses.
For a multi-factor design, a table beats a paragraph. Here is the APA layout with a filled example:
| Source | SS | df | MS | F | p | ηp2 |
|---|---|---|---|---|---|---|
| Presentation format | 49.60 | 1 | 49.60 | 1.84 | .180 | .03 |
| Time pressure | 28.32 | 1 | 28.32 | 1.05 | .309 | .02 |
| Format × Pressure | 208.31 | 2 | 104.16 | 3.86 | .028 | .13 |
| Error | 1456.22 | 54 | 26.97 | |||
| Total | 1742.45 | 58 |
Give the table a number, a title, and a note underneath defining the abbreviations. List the effects in the order they appear in the analysis rather than in order of significance.
In practice, APA expects effect sizes for the significant effects, and does not require one for anything else. If you tested several effects and want to show the full picture, give the table and cover every row. If you tested ten things and one crossed .05, a table plus a one-sentence note that the remaining tests were non-significant is a more honest write-up than a single cherry-picked sentence.
Do report the effect size when the F is non-significant but the estimate matters to your argument, for instance when you are defending a null result or justifying a future power analysis. The key is to frame it as an estimate with its uncertainty rather than as a finding.
Type the Symbol So It Survives Formatting
Type the symbol in Word with the Unicode toggle: type 03b7 and press Alt + X. The letter turns into η. Then type p and apply subscript with Ctrl + =, and type 0020 followed by Alt + X for the superscript 2. Or paste these directly: η² for eta squared, ηp² for partial eta squared, ω² for omega squared, ηG² for generalized eta squared.
In Google Docs, use Insert > Special character > Symbol and search for “eta” to get η. Subscript and superscript come from Format > Text > Subscript and Superscript, or Ctrl + , and Ctrl + . . If you paste from a paper or a website, expect the formatting to flatten; set the p and the 2 by hand after pasting rather than trusting the paste.
Common Mistakes
Using the between-subjects error row in a within-subjects design. This is the most damaging error because it usually still produces a number, so nothing warns you. Fix: for repeated-measures and mixed designs, take SSerror from the within-subjects error row.
Reading the wrong row in a multi-factor table. The A × B interaction row is directly under the two main effect rows and looks similar at a glance. Fix: read the label in the leftmost column before you read any number.
Mixing up Eta Squared and Partial Eta Squared. They are identical in a one-way design and differ in every other one. Fix: report partial eta squared unless your field’s convention says otherwise, and never cite the ordinary eta squared value as if it were the partial one.
Copying the Sig. value into the effect size slot. p = .026 and ηp2 = .24 look similar in a hurry and are completely different quantities. Fix: the effect size column sits to the right of Sig., so track your eye one column further.
Reversing the degrees of freedom. APA wants effect df first, error df second. SPSS prints them in that order, so copying them out preserves the order, and reversing them by hand is entirely avoidable.
Describing the value as a percentage of total variance. Partial eta squared is not that. It excludes the variance attributable to the other factors, so in a three-factor design the three main effects plus the interaction can add to well over 1. Fix: phrase it as the proportion of variance the effect accounts for in the model, or switch to generalized eta squared if you need a measure that partitions the total.
Rounding to one decimal place. ηp2 = .1 destroys the distinction between a small and a medium effect. Two decimals is the floor; three is the ceiling.
One quick habit catches nearly all of these: after you copy the value, confirm the cell is populated, the number is under 1, and the corresponding Sig. value is below .05. Those three checks take a few seconds and catch the mistakes that end up in a supervisor’s feedback email.
Frequently Asked Questions
What does partial eta squared actually mean?
Partial eta squared is the proportion of variance in the dependent variable explained by one specific factor, calculated after the variance from all other factors in the model has been removed from the denominator. A value of .20 means the factor accounts for 20 percent of the variance that remains once the other factors are held out. It is reported alongside an F-test because the F-test says an effect probably exists, while the effect size says how much it matters.
Why do my partial eta squared values add up to more than 1?
Because each value uses its own error term in the denominator rather than the total sum of squares. The values are therefore not slices of one whole and are not expected to sum to 1, especially when a design has an interaction. Nothing is wrong with your analysis. If you need a measure that genuinely partitions the total variance so the pieces sum correctly, use generalized eta squared, or report ordinary eta squared alongside partial eta squared.
What is the difference between eta squared and partial eta squared?
Eta squared divides the effect sum of squares by the total sum of squares, so it reports the effect’s share of all variability in the outcome. Partial eta squared divides by the effect sum of squares plus its own error term, removing the variance belonging to the other factors in the model. In a one-way ANOVA the two values are identical. In any design with two or more factors, partial eta squared is always the larger of the two.
How do I interpret a value like 0.045?
Read it against the benchmarks rather than reacting to the raw number. Cohen’s cutoffs of .01, .06 and .14 place .045 just under a medium effect, and Green and Salkind’s larger set of .02, .13 and .26 calls the same value small. A modest effect can still reach statistical significance with a large enough sample, so the p value and the effect size are answering different questions. Report the number and let the design and sample size give it context.
Should I report an effect size when the F-test is not significant?
APA 7th edition only requires effect sizes for significant effects, so you are not obliged to include one. You should include it anyway when the estimate carries argumentative weight, such as when you are defending a null result or planning a replication. Report the value with a confidence interval and frame it as an estimate rather than a finding. SPSS leaves the cell blank for non-significant effects, so compute it by hand from the sums of squares if you want it.
How do I get partial eta squared for a repeated-measures or mixed design?
For repeated-measures designs, take the effect sum of squares from the within-subjects effect row and the error sum of squares from the within-subjects error row, not the between-subjects Error row. Mixed designs follow the same rule for the within factor and its interaction with the between factor. SPSS computes the value once you tick Effects size in the Model dialog. For models fitted in R, the effectsize package handles the common designs, and car::Anova supplies the Type III sums of squares you need for a mixed model.
Conclusion
Start in the Tests of Between-Subjects Effects table, find the row for the effect your hypothesis is about, and copy the value from the Partial Eta Squared column along with the F and the two degrees of freedom. If the column is empty, tick Effects size in the SPSS Options dialog and run it again.
If you have to calculate it yourself, divide the effect sum of squares by the effect plus its error sum of squares, using the within-subjects error row whenever your design has one. Check your work with the degrees-of-freedom shortcut, and the two numbers should match to three decimals.
Then paste the figures into the APA template: F(df1, df2) = F value, p < .001, ηp2 = .00, with no leading zero and two decimals. That combination, right row, right denominator, right format, is the whole job.
