# Eta-squared

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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):

• .02 ~ small
• .13 ~ medium
• .26 ~ 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. [1]

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

## References

1. CAUTIONARY NOTE ON REPORTING ETA-SQUARED VALUES FROM MULTIFACTOR ANOVA DESIGNS. Pierce C.A., Block, C.A. & Aguinis, H. Educational and Psychological Measurement 64(6), 2004.