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Topic: kolmogov-smirnov, wilcoxon and kruskal tests
Replies: 14   Last Post: Dec 31, 2012 6:38 PM

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Richard Ulrich

Posts: 2,940
Registered: 12/13/04
Re: kolmogov-smirnov, wilcoxon and kruskal tests
Posted: Dec 23, 2012 4:31 PM
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On Sat, 22 Dec 2012 21:27:54 -0800 (PST), Ray Koopman <>

>On Dec 22, 5:22 pm, 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 so-called non-parametric 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 Monte-carlo test of KS, done by generating 10,000 samples
with the same margins, would show that the KS test-outcome
*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 non-fit.

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 t-test for comparison.

Rich Ulrich

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