Direct comparison
Eta-Squared vs. Partial Eta-Squared
Eta-squared divides by total variance; partial eta-squared divides by that effect plus error only. Comparing the two across studies is misleading.
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How do Eta-squared (η²), Partial eta-squared (partial η²) compare side by side?
The table below compares Eta-squared (η²), Partial eta-squared (partial η²) across 10 procurement-relevant dimensions, from what it divides by (denominator) through best used for.
Side-by-side comparison
| Dimension | Eta-squared (η²) | Partial eta-squared (partial η²) |
|---|---|---|
| What it divides by (denominator) | Total variance across the whole design (SS_total) | That effect's own sum of squares plus error only (SS_effect + SS_error) |
| Formula | η² = SS_effect / SS_total | partial η² = SS_effect / (SS_effect + SS_error) |
| Value in a one-way (single-factor) ANOVA | Identical to partial eta-squared — SS_total = SS_effect + SS_error when there is only one effect | Identical to eta-squared, for the same reason |
| Value in a multi-factor (factorial) ANOVA | Smaller than partial eta-squared for the same effect — other factors’ variance stays in the denominator | Larger than eta-squared for the same effect — other factors’ variance is excluded from the denominator |
| Sum across every effect + error in one model | Sums to exactly 1 (every effect shares the same SS_total denominator) | Does not sum to anything meaningful — each effect has its own denominator |
| Sensitive to how many other factors are in the model | No, in a balanced orthogonal design — SS_effect and SS_total for a given effect are unaffected by adding unrelated factors | Yes — adding factors that explain residual variance shrinks SS_error, inflating partial eta-squared for effects already in the model |
| Comparable across studies with a different number of factors | More stable, but still strictly comparable only across the same overall design | Not comparable — the value for the same real effect shifts purely from what else was modeled alongside it |
| Typical statistical-software default | Rarely a checkbox default — usually computed by hand from reported SS values | SPSS's built-in GLM “Estimates of Effect Size” option reports this by default, a major reason it dominates the published literature |
| Range | 0 to 1 | 0 to 1 |
| Best used for | Describing how much of the total outcome variance the whole study design accounted for | Comparing one factor's effect against its own error term, within a single specified model |
Common questions
Common questions about Eta-squared (η²) vs Partial eta-squared (partial η²)
Are eta-squared and partial eta-squared ever the same number?
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Yes — in a one-way ANOVA with a single factor, SS_total equals SS_effect + SS_error by definition, so the two formulas produce an identical value. They only diverge once a second factor or an interaction term enters the model.
Why don’t partial eta-squared values for different effects in the same model add up to 1?
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Because each partial eta-squared uses a different denominator — that specific effect’s SS plus error only — rather than the shared SS_total that classical eta-squared values use. Summing values computed against different denominators is not a meaningful operation, unlike classical eta-squared, whose components genuinely partition SS_total and sum to exactly 1.
Which one should I report?
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Report whichever answers your actual question, and name it explicitly. Classical eta-squared answers "how much of the total outcome variance did this whole design explain"; partial eta-squared answers "how large is this one effect relative to its own error term." Many papers report partial eta-squared (often because it is the software default) while calling it simply "eta-squared," which is the specific misreport this page addresses.
Can I compare a partial eta-squared from one study to one from another study?
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Only if both studies used a comparably structured model (similar factors and covariates). A partial eta-squared computed inside a two-factor design is not directly comparable to the "same" effect’s partial eta-squared inside a five-factor design — additional factors that soak up residual variance will inflate partial eta-squared for effects already in the model, even though those effects themselves did not change.
