A question about how -kwallis2- computes the adjusted critical level pops up occasionally (see http://www.stata.com/statalist/archive/2009-02/msg00379.html). It seems as if the adjusted critical level is too conservative for a usual Bonferroni's adjustment, using alpha/(k(k-1)) rather than alpha/k. (I even modified kwallis2 to use alpha/k adjustment). Now, however, I believe that -kwallis2- is indeed using the correct adjustment.
Recently I had some data which I gave to a colleague who uses BMDP (remember BMDP?). His output was virtually identical to -kwallis2-, using the alpha/(k(k-1)) adjustment. The old BMDP manual (1992) states that the observed "Z is compared with the tabled Z[alpha*/2], where alpha* = 2alpha/(k(k-1)). So, alpha*/2 = alpha/(k(k-1)), which is what -kwallis2- uses.
My interpretation of this is that the global K-W test is one-sided (e.g., a chi-square test where all squared deviations are positive), but the post-hoc pairwise comparisons are two-sided, either positive or negative deviations. Another way of thinking about it is that if the conventional Bonferroni's adjustment were applied (alpha/k), the global test would be conducted at a critical level of 5%, but the post-hoc tests would be equivalent to computing adjusted 90% confidence intervals.
-p
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Paul F. Visintainer, PhD
Baystate Medical Center
280 Chestnut Street
Springfield, MA 01199
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