Date: Dec 23, 2012 2:01 PM
Author: Luis A. Afonso
Subject: Re: kolmogov-smirnov, wilcoxon and kruskal tests

Ray Kooper is right: a test where its statistics does not fall in the rejection interval only means that, given data, one was failed to assert a sufficient difference (of the two samples, at the case) between the two data sets in analysis. It was pointed out that each of the three tests analyses data under a specific (proper) point of view, so, one should not expect that all tests lead to conclude the same way: reject/not reject. The choice of a test in what all sample values are called, on the empirical distribution function, as KS, is preferable than those analysing some particular Population parameter?s set (such the Jarque- Bera, Skewness and Kurtosis). 
Not inconsistent, Ray Kooper used wisely, is the term we prefer to say when one is lead to not reject the Null Hypotheses. We should always keep in mind that Significance Tests (by its own nature) are necessary, not sufficient tools subject to decision errors: to reject when H0 is true (Type I) and to accept when false (Type II).

Luis A. Afonso