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- Date: Wed, 2 Sep 1992 15:59:29 CDT
- Sender: "STATISTICAL CONSULTING" <STAT-L@MCGILL1.BITNET>
- From: "J. Philip Miller" <phil@WUBIOS.WUSTL.EDU>
- Subject: unequal variances (fwd)
- X-To: "STAT-L Distribution List" <stat-l@vm1.mcgill.ca>
- Lines: 39
-
- Forwarded message:
- > There is another aspect to the unequal variance problem - that of power under
- > alternatives. In a recent study, (Comm. Stat., 1991) I compared the size and
- > power of the F, Kruskal-Wallis, and Normal Scores tests when variances were
- un-
- > equal. The F test was badly hurt, but the KW and NS tests were relatively un-
- > affected. I suspect that the rank transformation will work pretty well in most
- > anova problems.
-
- it is also very important to worry about the sample sizes you are concerned
- with. In papers I gave in 1981 (Proceedings of SUGI and of Stat Computing
- Section of ASA) I looked at 11 different methods of estimating solutions for
- the Behrens-Fisher problem EVEN WHEN THE POPULATION VARIANCES WERE EQUAL. For
- even the case of n1=n2 with n1 < 6 many of the methods provide empirical
- two-sided Type I error rates substantially different than the nomial levels.
- To take an example for n1=n2=2, the method utilized by SAS produces an
- empirical error rate of about .025 for a nominal level of .05. For unequal
- sample sizes, it gets even worse, e.g. for n1=2, n2=50 the SAS method produces
- an empirical error rate of of .12. Even using an F test for the equality of
- the variances as a pretest estimator does not eliminate the problem.
-
- Having said all of that, I think it is important for me to remark that in most
- actual cases of data where there appear to be unequal variances, it is also
- the case that the normal distribution assumption is not reasonable.
- Frequently a transformation of the data either by a analytic function, e.g.
- log or one of the rank transformations will produce better results than any of
- the BF solutions which assume only different variances but still normal
- distributions.
-
- -phil
-
- > Tony
- >
-
-
- --
- J. Philip Miller, Professor, Division of Biostatistics, Box 8067
- Washington University Medical School, St. Louis MO 63110
- phil@wubios.WUstl.edu - Internet (314) 362-3617 [362-2694(FAX)]
-