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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!

Many thanks in advance!

Grace

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Your data does not have to be normally distributed!! It is the errors that have to be normally distributed.

You can of course perform ANOVA on groups that do not have equal sample size; the power of the test drops, but the test itself is still valid.

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