Can you please describe the type of data (categorical/continous scale) you have. As far as the data on continous scale is concerne, it rarely tends to be normally distributed while checking through K-W an so on. But most of the time, skewness and kurtosis are within the range of -1 and +1.

Hello Rachel,

Skewness and kurtosis are two moments of distributions; there are others. Most goodness of fit tests (such as Shapiro-Wilk and Kolmogorov-Smirnov, usually with Lilliefor's modification when normality is the question) test for equality of all moments simultaneously. Therefore, it's quite possible that a test for a single distribution moment shows a different result than a test of all moments.

If you're abandoning parametric tests because of worry about normality, consider using bootstrap/resampling methods within the parametric test instead. The ideal test would be an exact or permutation test, but with designs like manova or mancova, these are not frequently available in software packages.

Good luck with your work.

Thank you Imran and David.

Imran - it's continuous data (scores on the theory of planned behaviour questionnaire and the barriers to help seeking scale).

David - thank you, I will have a look into you suggestions.