I have 5 conditions (variables), 13 subjects, data points ranging from about -40.0 to +40.0

Both the Kolmogorov-Smirnov and Shapiro-Wilk tests are significant for some of the variables. Some of the variables are negatively skewed while others are positively skewed.

I have tried log, sqrt, and inverse transforms (after adding a constant), however it depends on the direction of the skew as to whether I reflect them or not to get the best result.

e.g. for the negatively skewed variable, i can improve normality by multiplying by -1, adding a constant to return the set to positive values, and then taking the log transform. However this makes the positively skewed values worse.

I can't do different transforms on different variables and then do a repeated measures ANOVA.

How can I address this problem?

Thanks in advance for any assistance!