In my previous question (Kolmogorov-Smirnov test - reliability) I misused two-sample KS test for normality testing of one-sample data. I was given an advice that I should use one-sample KS test, also it was recommended to me to use Anderson-Darling test.
If i deal with lets say hundreds of points per cluster, AD gives me satisfactory results. Nevertheless, If I have thousands points in my cluster, I receive large values of A-squared from AD that are far away from AD's critical values.
I have read here that AD fails for large number of points and that it is better to use KS. However, I am not sure, if I did something wrong, but KS is equal to 1.0 in almost every case (cross checked in Matlab too).
Example data are located here. It represents a cluster of gaussian mixture points. I want to test this cluster for normality (and I want to fail in that test for this data). Consequently, I want to split data to sub-clusters, test each sub-cluster again and split again until I end up with "leaf clusters" that are normally distributed.