Dear All,

I have the following problem to ponder over:

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Assume 3 groups with parameters mu1, mu2, and mu3 respectively.

I want to test the global hypothesis

H0: mu1 = mu2 =mu3

against the alternative hypothesis

H1: mu1 ne mu2 ne mu3

using non-parametric mehods such as Kruskal-Wallis or Jonckheere tests.
I am also interested in the pairwise comparisons in the following order

mu1 = mu3
mu2 = mu3
mu1 = mu2

using e.g. Wilcoxon, where I will use the simple step-down procedure to
control my type 1 error rate whereby I will only proceed to the first
pairwise comparison if the global hypothesis is rejected and so on....

My question is now the following: It is not always of interest to know the
result of the global hypothesis test (i.e. mu1 = mu2 =mu3) but rather that
of the first pairwise comparison test (i.e. mu1 = mu3, e.g. highest dose
against placebo). I therefore propose to use the following global
hypothesis

H0: mu1 = mu3
vs
H0: mu1 ne mu3

and then proceed to test the further two pairwise comparisons using the
familar step-down procedure. Afterall, if I reject the hypothesis that mu1
= mu3 then I must also be able to reject the original hypothesis, namely mu1
= mu2 =mu3. Furthermore, if I use the step-down procedure I will still
control my Type I error rate.

This all seems correct to me but something keeps tapping me on my shoulder
telling me to beware......

I would appreciate your comments.

Thanks

Martin Scott.
 


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