# Eta-squared

(Redirected from Partial eta-squared)
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Eta-squared (${\displaystyle \eta ^{2}}$) is a measure of effect size for use in ANOVA (Analysis of variance).

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

${\displaystyle \eta ^{2}}$

= SSbetween / SStotal = SSB / SST
= proportion of variance in Y explained by X
= squared non-linear correlation coefficient

${\displaystyle \eta ^{2}}$ ranges between 0 and 1.

Interpret ${\displaystyle \eta ^{2}}$ 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 (${\displaystyle \eta _{p}^{2}}$) in versions of SPSS prior to V 11.0. [1]

${\displaystyle \eta ^{2}}$ was not previously provided by SPSS, however, it is available in V 18.0. It can also be calculated manually: ${\displaystyle \eta ^{2}}$ = 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 ${\displaystyle \eta ^{2}}$.

## 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.