Eta-Squared

Defining Eta-Squared

Etasquared (η2) is a common measure of effect size used in t tests as well as univariate and multivariate analysis of variance (ANOVA and MANOVA, respectively). An etasquared value reflects the strength or magnitude related to a main or interaction effect. Etasquared quantifies the percentage of variance in the dependent variable (Y) that is explained by one or more independent variables (X). This effect tells the researcher what percentage of the variability in participants’ individual differences on the dependent variable can be explained by the group or cell membership of the participants. This statistic is analogous to r-squared values in bivariate correlation (r2) and regression analysis (R2). Etasquared is considered an additive measure of the unique variation in a dependent variable, such that nonerror variation is not accounted for by other factors in the analysis.

Interpreting the Size of Effects

The value of η2 is interpretable only if the F ratio for a particular effect is statistically significant. Without a significant F ratio, the etasquared value is essentially zero and the effect does not account for any significant proportion of the total variance. Furthermore, some researchers have suggested cutoff values for interpreting etasquared values in terms of the magnitude of the association between the independent and dependent measures. Generally, assuming a moderate sample size, etasquared values of .09, .14, and .22 or greater could be described in the behavioral sciences as small, medium, and large. This index of the strength of association between variables has been referred to as practical significance. Determination of the size of effect based on an etasquared value is largely a function of the variables under investigation. In behavioral science, large effects may be a relative term.

Partial etasquared (η2p), a second estimate of effect size, is the ratio of variance due to an effect to the sum of the error variance and the effect variance. In a one-way ANOVA design that has just one factor, the etasquared and partial etasquared values are the same. Typically, partial etasquared values are greater than etasquared estimates, and this difference becomes more pronounced with the addition of independent factors to the design. Some critics have argued that researchers incorrectly use these statistics interchangeably. Generally, η2 is preferred to η2p for ease of interpretation.

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