I'm new to the forum but wanted to ask a question about the appropriateness of using a test such as ANOVA or Mann-Whitney U test on the PC-scores of a Principal Component Analysis. I have recently received the critique on a submitted manuscript that it is problematic that I did multiple (non-independent) testing on the pc-scores of a PCA analysis using an ANOVA. I did an individual ANOVA on the scores of each principal component to test for significance of between group differences.

Although I realize this may not be a good approach, can anyone perhaps explain to me in more detail why this would be problematic? And is it really the case that pc-scores cannot be treated as independent variables?

Thank you,

Jan