Hello Enttisar,

Remember, normality applies to the distribution of model residuals (difference between observed scores on the DV and those estimated from your fitted model).

If normality is a concern, you may wish to consider one or more of these options:

1. If it makes sense to do so, try transforming scores on both occasions so as to conform more closely to whatever target distribution you desire.

2. Use a method which does not require assumptions of normality. Some of these would include:

a. "Non-parametric" (typically, rank-based tests) methods. Since you have at least one repeated measures dimension, probably something along the lines of Wilcoxon or Friedman methods. ("Probably," because you didn't explain what other variables are included in this analysis.)

b. Exact/permutation tests. While these can be computationally intensive, depending on model complexity and sample size, they allow you to avoid distributional assumptions.

c. Resampling/bootstrap methods. These generally yield very good approximations to the exact tests, but appear more frequently as options in statistical packages.

Good luck with your work.

Please remember that most people that do normality tests get it wrong. For these tests large p-values favor the normal hypothesis not small p-values. See Wikipedia for your test. Best wishes David Booth