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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: 2,961 Registered: 12/13/04
Re: kolmogov-smirnov, 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

Date Subject Author
12/22/12 czytaczgrup@gmail.com
12/23/12 Ray Koopman
12/23/12 czytaczgrup@gmail.com
12/23/12 Richard Ulrich
12/23/12 Ray Koopman
12/23/12 Luis A. Afonso
12/24/12 Luis A. Afonso
12/29/12 illywhacker
12/29/12 Richard Ulrich
12/30/12 czytaczgrup@gmail.com
12/30/12 Richard Ulrich
12/31/12 Herman Rubin
12/31/12 Richard Ulrich
12/31/12 Herman Rubin
12/31/12 illywhacker