Eta Squared vs Partial Eta Squared: Which Effect Size Should You Report?
Eta squared and partial eta squared both summarize the relative amount of variation associated with an ANOVA effect. They are not interchangeable because their denominators answer different questions.
What is eta squared?
Eta squared uses total sum of squares in the denominator:
It describes the proportion of total observed variation associated with the effect in the analyzed sample. In a simple one-way ANOVA, eta squared is easy to calculate from the standard ANOVA table.
What is partial eta squared?
Partial eta squared compares the effect sum of squares with the effect plus its associated error:
Variation assigned to other modeled effects is excluded from the denominator. Partial eta squared is therefore often larger than eta squared in factorial or repeated-measures designs.
When are the two values equal?
In a one-way between-subjects ANOVA with one factor, eta squared and partial eta squared are commonly equal because there are no other modeled effects to remove from the denominator. They diverge when the model contains multiple factors, interactions, covariates, or repeated components.
Worked example
Suppose a factorial ANOVA reports:
- Factor A sum of squares = 30
- Factor B sum of squares = 20
- Interaction sum of squares = 10
- Error sum of squares = 90
- Total sum of squares = 150
For Factor A:
Both calculations are correct, but they describe different denominators. Reporting only “the effect size was .25” hides that distinction.
Which measure should you report?
Use the measure expected in your field and supported by the design, but label it precisely. Consider these questions:
- Does your audience need the effect relative to total observed variation?
- Are you comparing effects across models with different factors?
- Does your software output partial eta squared by default?
- Would omega squared provide a less biased estimate for the intended interpretation?
For a complex ANOVA, partial eta squared is widely available and useful within the fitted model. Eta squared may be easier to interpret as a total-variation proportion, but comparisons across designs still require care.
Can you compare partial eta squared across studies?
Only cautiously. The denominator changes with the model, included effects, design, and error structure. Two studies can estimate similar substantive effects but report different partial eta squared values because their models differ.
How should the result be written?
Name the statistic and provide the ANOVA result:
The treatment effect was statistically significant, F(2, 57) = 6.31, p = .003, partial η² = .18.
Do not switch between η² and partial η² in the table and narrative. If you calculate the value from sums of squares, preserve the formula and source values in the analysis record.
Use the DataStatPro effect-size calculator and the eta-squared tutorial to check the calculation. For a wider reporting context, see the effect-size interpretation guide.
Frequently asked questions
Is partial eta squared always larger than eta squared?
It is often equal to or larger because other modeled variation is excluded from its denominator. The exact relationship depends on the design and sums of squares.
Is eta squared the same as R squared?
They can coincide in some simple models, but the interpretation and decomposition depend on the fitted model. Do not assume they are universally identical.
Should I use benchmark labels such as small, medium, and large?
Use generic benchmarks cautiously. Interpret the estimate against subject-matter importance, measurement scale, prior evidence, and uncertainty.
Should confidence intervals be reported for eta squared?
An interval can communicate uncertainty more effectively than a point estimate alone. Report one when your method and software provide a defensible interval.