Normality tests and Shape statistics contradictory

#1
Hello.

I am testing for normality on a number of repeated measures variables in a sample of 29 people.

Both the Kolmogorov-Smirnov test and the Shapiro-Wilk test statistics say that all of these variables are significantly non-normal. However, observations of skew and kurtosis (as well as normality plots on histograms) suggests that the data are normally distributed.

In the end, I am looking to do repeated measures ANOVAs if this helps with any advice.

Anyway, I am wondering why the apparent contradiction? And what may be the solution?

I am very grateful for any help. I did find similar forums but they always dealt with very large samples hence why I am posting a new thread.

Thanks,

capn_kangaroo