
Re: kolmogovsmirnov, wilcoxon and kruskal tests
Posted:
Dec 29, 2012 6:38 PM


On Sat, 29 Dec 2012 12:21:31 0800 (PST), illywhacker <illywacker@gmail.com> wrote:
>On Sunday, 23 December 2012 01:22:31 UTC, czyta...@gmail.com wrote: >> Hi Everybody, >> >> >> >> I'm trying to do some hypotheses testing in R and I have problems with interpretation of results. >> >> >> >> I have two data sets: >> >> > x<c(2,1,1,2,2,3,2,2,1,2,2,4,1,2,4,1,1,5,2,1,4,2,2,1,1,2,2,1) >> >> > y<c(2,2,1,1,2,2,1,4,1,4,2,4,4,4,3,2,4,4,3,2,4,5) >> >> >> >> according to the KS test they come from the same distribution: >> >> > ks.test(x,y) >> >> >> >> If they come from the same distribution all the characteristics (mean, median, ... ) should be the same. >> >> However, Wicoxon and Kruskal tests indicate that their null hypothesis should be rejected: >> >> > wilcox.test(x,y) >> >> > kruskal.test(list(x,y)) >> >> >> >> Now, I am puzzled with the outcome of the test. >> >> I can simply imagine a situation when Wilcox and Kruskal tests indicate that their null hypothesis should be accepted but the KS test can indicate that samples comes from different distributions. Here, it is the other way round. Does any one has some hints what causes the problems?
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.
>> > >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. >
Are you saying that Bayesian methods are so limited and narrow that you, the Bayesian, cannot apply alternate assumptions and tests? Or get confused by conflicting results? I've stayed away from Baysian because it seemed more confusing, not less.
By the way, Ray showed that the KS test does reject these data, too, despite the different test properties.
 Rich Ulrich

