I want to do non-parametric test on my data using Rstudio in a data frame called Data. My data is repeated measures. Each participant did the experiment in two modes (Arcade and Challenge). They did the experiment over 3 latencies in each mode (1,2,3). We obtained their Accuracy which is ordinal from 0 to 9. this means there are 6 rows per participant (ID). They were either monolingual or multilingual (Language_Group variable). They either used a verbal strategy or a nonverbal strategy (Main_Strategy Variable). I want to test Accuracy differences across the board. How to do non-paramteric testing since my data is not normal? how to capture possible interactions? Please note transformations are not possible for my data as this beats the purpose of the results and my experimental purpose. I am confused as nothing seems to work or capture what I want. It seems Kruskal-Wallis is not appropriate for repeated measures design and the Friedman test wants factors but even that did not work in R. Please also note that outliers are highly important in my study and I do not wish to remove them as they are very meaningful. Is there a certain procedure of steps I need to take to simplify the analysis? Perhaps I can't capture all interactions like in lmer model and then do Anova if data was normal :(
this is important as it is for my PhD. I am assuming I might have to calculate means for each interaction of the variables and then do kruskal wallis?
Please see an excerpt of my DataFrame. I have 291 participants (138 monolinguals and 153 bilinguals). enter image description here
I tried the kruskal wallis and friedman tests. I also tried box cox transformation but transforming my data tomake it normal did not make sense for the purposes of this experiment. Here is what my resulting boxplot looks like for my data. enter image description here
From the boxplot, we can see the medians are different. This is why i used kruskal wallis but it seems it is not proper for repeated measures :(. Also, I have a floor effect where participants perform really bad in the challenge mode (or really well).