Eta-squared

Subject classification: this is a statistics resource.

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

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 $\eta ^{2}$.

External links

• Eta-squared (η²) and partial eta-squared (ηp²) compared to epsilon squared (ε²) and omega-squared (ω²) including R script to simulate η² bias over ε² and ω².