Eta-squared

Subject classification: this is a statistics resource .

Educational level: this is a tertiary (university) resource.

Eta-squared ($\eta^2$) is a measure of effect size for use in ANOVA.

$\eta^2$ is analagous to R² from multiple linear regression.

$\eta^2$

= SSbetween / SStotal = SSB / SST

= proportion of variance in Y explained by X

= Non-linear correlation coefficient

= proportion of variance in Y explained by X

$\eta^2$ ranges between 0 and 1.

Interpret $\eta^2$ as for r² or R²; a rule of thumb (Cohen):

• .01 ~ small
• .06 ~ medium
• .14 ~ large

In SAS, eta-squared statistics can be found in semi-partial eta-squared statistics in SAS 9.2.

The eta-squared column in SPSS F-table output is actually partial eta-squared ($\eta^2_p$) in versions of SPSS prior to V 11.0.

$\eta^2$ was not previously provided by SPSS, however, it is available in V 18.0. It can also be calculated manually: $\eta^2$ = Between-Groups Sum of Squares / Total Sum of Squares.

R² is provided at the bottom of SPSS F-tables is the linear effect as per MLR – however, if an IV has 3 or more non-interval levels, this won’t equate with $\eta^2$.

External links

• Eta-squared and partial eta-squared (Wilderdom)
• How are the effect size measures, Cohen’s f and SPSS’s η 2 , related? What is the difference between η 2and partial η 2 that I see in SPSS?