I am comparing measures of a DV x with two group factors (2-way ANOVA) - y (with 2 levels) and k (with 3 levels). Both present significant main effects (p<.001) and high partial eta squared (above 0.6). The interaction effect is also significant (p<0.001) but the partial eta squared is 0.029. Post-hoc testing for the interaction of y*k yields significant differences on the DV for all comparisons. In this case, shouldn't the effect size be greater? How do I interpret this? Thank you for your help!
P.S. - Note: (I have a big sample; N>600)