On Sunday, December 30, 2012 12:38:41 AM UTC+1, Rich Ulrich wrote: > By the way, OP -- WHY could you imagine, at the start, > without knowing their properties, that the KS test would > have more power than the other tests for testing a shift? > - The Wilcox and Kruskal tests do assume that distributions > have a similar form, for those tests to be valid. > - That is what the KS tests, if you follow an explicit assumption > that the distributions are "of the same form", so you are not > testing for shape. >
First of all I'd like to thanks for all the comments and hints.
So far, I was considering a KS test as a kind of ultimate test, because equality of (cumulative) distributions means equality of all moments and characteristics. Now, I know that it is not the logic of hypothesis testing (thanks for pointing that).
When I was searching for online resources on Wilcox and Kruskal tests I found various formulation of these test, more precisely various null hypothesis which sometimes seems to be inconsistent. They claim that the null hypothesis is equality of distributions or the the null hypothesis is that the distributions of ?x? and ?y? differ by a location shift. Unfortunately, it was hard to find what are the conditions when these tests can be performed meaningfully. Thus, forgetting about the similar shape assumption one can be testing location (shift) of two very different distributions, e.g. uniform on [-1,1] and normal N(0,1). In such a case KS test rejects the null hypothesis while Wilcoxon and Kruskal prove the null hypothesis. When both distributions have the same functional dependence (except the location parameter) the equality of location parameters is equivalent to the equality of distributions but if the distributions are of the different type mentioned null hypothesis seems to be not equivalent. This shows that knowledge of assumptions when those tests are meaningful is crucial.
Making the story short, I am missing detailed cookbook description of test saying clearly what are the assumptions and what are the null and alternative hypothesis.
> >This just shows the total mess (meaningless concepts, ad hoc tests, unclarified assumptions, contradictory results with no explanation, "I would be willing to use...", confusion on the part of the user) that arises from the nonsensical nature of classical statistical hypothesis testing. The best advice here is: learn Bayesian methods. > > >
> > By the way, Ray showed that the KS test does reject these data, too, > despite the different test properties.
Thanks, I have noticed that.
The data which I gave were ranks attributed to some answers in the ordinal scale.