# Which stats should I use when samples are uneven and data are not normally distributed?

My data have four groups: "A" normal group (AN), "B" normal group (BN), "A" group with a clinical diagnosis (AC) and "B" group with a clinical diagnosis (BC). They were tested on a task that included 2 different conditions. I plan to analyze the groups' error rates and reaction times separately.

The data are non-normally distributed (mostly in the groups with clinical diagnosis). I'd like to conduct analyses between AN (N=35) and BN (N=22), and between AC (N=15) and BC (N=10). Also, I'd like to conduct analyses between AN (N=35) and AC (N=15), and between BN (N=22) and BC (N=10). Because the task included 2 different conditions, I want to use repeated measures analysis such as condition, group, and condition x group.

Initially, I thought that I could use the repeated measures of ANOVA to do group comparisons. However, due to unequal sample size and smaller sample sizes in the clinical groups, I am not sure whether the repeated measures of ANOVA would be appropriate. I checked some website suggesting that if the sample size within each group is smaller than 20, nonparametric analyses would be more appropriate. As far as I know, I do not think there is a nonparametric equivalent of the repeated measures of ANOVA. If I am wrong, please let me know! I also heard that linear mixed models are better than the repeated measures of ANOVA for unequal sample sizes. But, I am wondering whether the small sample sizes (AC, N = 15 and BC, N = 10) may influence the results of the linear mixed models.

In regard to the non-normally distributed data, I may just do data transformation. Still, I am not sure what would be the best statistical analysis to fit my data. I would appreciate all experts' feedback!