Do Eta Squared and Partial Eta Squared Coincide in One-Way Repeated-Measures ANOVA?

Question

In one-way anova, do eta squared and partial eta squared always coincide, both in between- and within-subjects designs, i.e. both in independent and repeated measures designs?

I have been discussing about this with professors, who published about statistics and effect sizes. Some of them claim, providing demonstrations, that eta squared and partial eta squared coincide only in one-way between-subjects (independent) anova, but NOT in one-way within-subjects (repeated measures) anova. But I have also found publications and websites saying that, in one-way anova, eta squared and partial eta squared always coincide, without specifying the type of design, and thus I suppose including both.

What's your opinion?

Answer 1

They don't coincide in one way ANOVA repeated since the SSTotal is a sum of SSsubjects + SSinteraction + SSeffect and therefore eta square (which is SSeffect/SStotal) will be smaller than the partial eta square which is (SSeffect/ SSeffect+SSerror) in other words it doesn't count the subjects within the calculation