I have data that has eta squared values and partial eta squared values calculated as a measure of effect size for group mean differences.
What is the difference between eta squared and partial eta squared? Can they both be interpreted using the same Cohen's guidelines (1988 I think: 0.01 = small, 0.06 = medium, 0.13 = large)?
Also, is there use in reporting effect size if the comparison test (ie t-test or one-way ANOVA) is non-significant? In my head, this is like saying "the mean difference did not reach statistical significance but is still of particular note because the effect size indicated from the eta squared is medium". Or, is effect size a replacement value for significance testing, rather than complementary?