Eta-squared

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

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

$$\eta^2$$
 * = SSbetween / SStotal = SSB / SST
 * = proportion of variance in Y explained by X
 * = squared non-linear correlation coefficient

$$\eta^2$$ 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 $$\eta^2$$.