exact wilcox test and Bonferroni correction
(i) you EITHER correct the p value (by multiplying by 8 in your case) OR you use the Bonferroni-threshold of 0.05/8, not both. If you correct the p values, your threshold remains 0.05. If you use 0.05/8, you use the original p values. (ii) Yes, if the p value is 0.15, then the corrected one for 8 tests is min(0.15*8, 1)=1 (i.e. all p values of 1/8 and higher will be 1 after correction) (iii) No, you can NOT AT ALL conclude that your samples are from the same distribution. You have no evidence that they are from different ones, but that does not imply that they come from the same (or a similar) one. In particular as the power of the test can be assumed to be pretty low. Regarding (i), it might be helpful to search the web for some information on Bonferroni correction, you could start with wikipedia, but there are other resources around. Regarding (iii), I would strongly recommend (re-)reading a good introduction into stats or consulting an expert statistician. I'm afraid you are missing some of the basics of statistical hypothesis testing here. To conclude "similarity", you'd have to define first what exactly that means (you can NEVER show exact equality), and then construct some appropriate test for that. NB: I am sure that you won't succeed to show similarity with a reasonable definition if you have just 10 observations, though. And for completeness: If you were aiming at similarity, you should rather NOT correct for multiplicity (while that depends again on what exactly you want to show). But I think this goes far beyond the scope of this post now. HTH, Michael
-----Original Message----- From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of netrunner Sent: Freitag, 22. Januar 2010 15:25 To: r-help at r-project.org Subject: Re: [R] exact wilcox test and Bonferroni correction Dear Michael, thank you very much for your help. I perfomed the wilcox.exact function on each of the 8 items for the two groups that I am analysing (that is, I performed 8 times the wilcox test). Here an example for the values (ratings from a questionnaire) of one of the 8 items: a1=5 9 10 10 10 10 10 10 10 10 b1=7 5 10 NaN 10 10 8 10 10 8 9 9 wilcox.exact(a1,b1, alternative="two.sided", mu=0, paired=FALSE, exact=TRUE, conf.level=0.95) I obtained: data: a1 and b1 W = 73.5, p-value = 0.1514 alternative hypothesis: true mu is not equal to 0 Then I adjusted p-values using p.adjust. For the example above the p-bonferroni value was 1. The threshold p-value is 0.00625 (that is 0.05/8) Finally, because p-bonferroni > 0.00625 can I conclude that for each item my samples are from the same distribution? I am a little bit confused.... thank you! netrunner -- View this message in context: http://n4.nabble.com/exact-wilcox-test-and-Bonferroni-correcti
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