# Eta-squared

(Redirected from Partial 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 ($\eta _{p}^{2}$ ) 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 $\eta ^{2}$ .