# Eta-squared

Subject classification: this is a statistics resource. |

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

Eta-squared () is a measure of effect size for use in ANOVA.

is analogous to *R*^{2} from multiple linear regression.

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

ranges between 0 and 1.

Interpret as for *r*^{2} or *R*^{2}; 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 () in versions of SPSS prior to V 11.0. ^{[1]}

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

*R*^{2} 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 .

## References[edit]

- ↑ 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.