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st: kwallis2 and adjusted p-values


From   "Visintainer PhD, Paul" <Paul.Visintainer@baystatehealth.org>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: kwallis2 and adjusted p-values
Date   Thu, 3 Sep 2009 11:53:14 -0400

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

___________________________________
Paul F. Visintainer, PhD
Baystate Medical Center
280 Chestnut Street
Springfield, MA 01199

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