Question

The partial eta squared for the ANOVA test was .135. What does this statistic mean?

Answer 1

Partial eta squared is the ratio of variance associated with an effect, plus that effect and it's associated error variance.

Ie,partial eta squared = SS effect/ ( SSeffect + SSerror)

In summary if we have more than one predictor , then partial eta squared is the variance explained by the given variable of variance remaining after excluding variance by other predictors.

Suppose we are interested in the effect of X in Y.(say). Then

Partial eta square = 0.135 implies some 13.5% of all variance in Y is attributable to X. The percentage is very small but certainly it is not negligible.