VARIABLES that you listed are called discrete data, i.e. (verbal, numeric, group exercise, interviews etc). Normality should have been tested by the DeMoivre-Laplace Theorem:

Z = (Sn - np)/sqrt(npq)

where Sn = number of success; n = number of observation, p = probability of success determine by p = (s + 1) / (n + 2); and q = 1 -p.

VALIDITY TEST is a test of accuracy between what is expected and what is actually observed. In this case, the expected value of your discrete variable is E[x] = np; this value could be obtained through simulation. Compare E[x] to your actual observed values for np. You will get series of residual values: Residual = E[x] - Actual. Now set confidence interval for your error testing, say 10% for 90% accuracy; then, the residual series should have the probability F(z) < 0.10 in a form of H(a): F(z) < 0.10 and H(o): F(z) = > 0.10.

Hello Ioana,

The issue of normality in hypothesis tests really applies to residuals from a fitted model (e.g., from a multiple linear regression), not the original scores on a specific independent or dependent variable. So, go ahead and try good old Pearson correlations and see where that takes you. It's always a good idea to plot the data (as in scatterplots) to see whether the form of the relationship is essentially linear between a pair of variables under investigation.

As a purely descriptive statistic, you need not assume (bivariate) normality to describe the observed linear association between any pair of variables. Of course, if you are concerned about whether either of the variables is at least interval strength, you could use Spearman (rank order) correlations.

Good luck with your work.

Validity is no where concerned with data to be normally distributed. If not normally distributed try with non parametric methods

Instead non-parametric analyses could be done or else data could be transformed or use bootstrapping...