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Re: kolmogovsmirnov, wilcoxon and kruskal tests
Posted:
Dec 23, 2012 4:31 PM


On Sat, 22 Dec 2012 21:27:54 0800 (PST), Ray Koopman <koopman@sfu.ca> wrote:
>On Dec 22, 5:22 pm, czytaczg...@gmail.com wrote: >> [...] >> >> according to the KS test they come from the same distribution: > >NO. You misunderstand the logic of hypothesis testing. Failing to >reject a hypothesis does not mean that it is true or that you should >act as if it were true. It means only that, in the way that the test >looks at data, your data are not inconsistent with the hypothesis. >Other tests, that look at the data differently, may well disagree.
Good statement.
I'll just add that these socalled nonparametric tests are based on ranks, and their usual tests are calculated on the basis of "no ties"  That certainly does not characterize these data, with 50 scores from 1 to 5. It is conceivable that a Montecarlo test of KS, done by generating 10,000 samples with the same margins, would show that the KS testoutcome *is* an unusual one. Or it might not.
It seems to me, though I'm not entirely sure, that the KS test is fundamentally testing the number of "interchanges" in ranks (which is a linear metric), whereas the other two tests are measuring the squared differences in ranks. So, he tests may disagree because they are testing two different ways to measure the nonfit.
For these data, I would be willing to report the means as meaningful ... and thus, using that as a guide, I would be willing to use the ordinary ttest for comparison.
 Rich Ulrich



