[R] exact wilcox test and Bonferroni correction

[Peter Dalgaard]

netrunner wrote:
> 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....

Yes...

First, you need to EITHER adjust the p-value OR the threshold, not both.
 So coompare the p-bonferroni to 0.05, or the 0.1514 to 0.00625. In both
cases, not significant, of course.

Secondly, you NEVER conclude from statistics that samples are from the
same distribution, only that this is an acceptable hypothesis, not
contradicted by data.

Third, it you have 8 separate items comparing two groups, how would
pairwise.wilcox.test have worked? That function is designed to compare
more than two groups pairwise (A vs B, B vs C, A vs C, etc.) with
respect to a single outcome measure.


-- 
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907