KS test is like T test; but it tests not only the mean but also the distribution. The null hypothesis for this test is that the two data sets are drawn from the same continuous distribution. In matlab, you can use function kstest2 to perform two-sample KS test.
[H,P,ksstat] = kstest2(x1, x2);
While T test requires the sample to come from a normal distribution, KS test doesn’t require that. It’s a non-parametric test (or distribution free). The process is:
1. plot cumulative distribution of the two datasets on a single figure
2. find the max vertical distance between the two curves
3. find the p-value based on the max distance and Kolmogorov distribution.
KS on wiki | KS online test