We have a data-set with two variables - gender and education qualification. The data-set is severely unbalanced. The are only ~10 observations from 1 level of the education factor, ~20 from another and ~80 from another. Moreover the sampling of gender is not even within each level of education.
We run an ANOVA in SPSS with Type III SS, there is no significant interaction, and education is significant while gender is not. However, I have read that when datasets are very unbalanced we should be careful that Type III analyses do not overlook effects.
Sure enough, when we run ANOVA with type I SS with gender entered first in the model, it comes out as strongly significant. When education is entered first in the model, it is strongly significant.
What are our options here. Given the absence of an interaction, can we just carry out the ANOVA w/TYpe I SS twice with the re-ordered factors and report the results of each?