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Topic: Multiple comparisons after a significant Kruskal-Wallis analysis

CAVEAT:
I am not up on recent developments, so those in the know should correct
any outdated information presented below...

I still have on my bookshelf a copy of "The Practical Statistician" by
Marigold Linton and Philip Gallo (Brooks/Cole, 1976).  Besides being a
compendium of example analyses using hand calculator techniques (of
which we have been warned), there is a gem of a section on multiple
comparison methods.  The following is extracted from pp. 305-310.

T. A. Ryan published a series of papers in the late 50's and early 60's
which dealt with post hoc tests for such things as partitioning
Chi-Square tables and following up on Kruskal-Wallis and Freedman
tests.

Ryan, T. A. Multiple comparisons in psychological research. _Psychological
  Bulletin_. 1959, _56_, 26-47.  (Reprinted in Kirk, Roger  _Statistical
  Issues: A Reader for the Behavioral Sciences_. 1972)

Ryan, T. A. Significance tests for multiple comparison of proportions,
  variances and other astatistics.  _Psychological Bulletin_, 1960,
  _57_, 318-328

"To use Ryan's procedure, the medians of the groups or sets of
measurements are ordered.  Ryan's procedure involves computing a series
of familar rank-sums tests and testing them against a tabled value of
Z, whose value is determined by _a_, a, and d, where _a_ is the {alpha}
level we wish for the experiment as a whole, a is the number of levels
of the independent variable, and d is the number of ordered levels
spanned by the comparison."

 An abbreviated table of Z for use with Ryan's procedure for pairwise
comparisons using the rank-sums test is presented as Appendix 6 of
"The Practical Statistician."

                         d - 1
a     7      6      5      4      3      2      1
--|---------------------------------------------------
8 | 3.13   3.09   3.03    2.96   2.86   2.74   2.50
7 |        3.04   2.99    2.92   2.83   2.69   2.45
6 |               2.94    2.87   2.77   2.63   2.40
5 |                       2.81   2.72   2.58   2.33
4 |                              2.64   2.50   2.24
3 |                                     2.40   2.13

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Lary Jones...Computing Services...SUNY-Binghamton...(607) 777-2879
School of Management Research Support ...... LJones@BingVMB.Bitnet