I couldn't find this situation described somewhere, though I think it's pretty common so I post it here. I have data from survey that is asking repondents to evaluate their color preferences across different types of webpages. There are 10 colors and 10 webpages, every person gives Likert type answer (5 choices) for each combination.
I would like to do two things:
1) For each website determine whether there is significant difference among color preferences (and ideally group similar colors together).
2) Test differences in count distributions of Likert categories across websites.
I end up using Friedman test for 1), because I consider questions as repeated measures on the same sample. Is this appropriate here? Or is there a better choice, because Friedman test is reported to be of low power?
What about post-hoc after Friedman in my case when there is 45 hypothesis for each website?