Date: Tue, 15 Sep 1998 06:33:22 -0400 William Dudley "SPSSX(r) Discussion" William Dudley Re: Homogeneity of variance in OneWay ANOVA text/plain; charset="us-ascii"

Thanks to Rick for an interesting and useful discussion on heterogeneity of variance in ANOVA. I was especially interested in his comments re the assumptions of non parametric tests - because on the bus this am I just happend to read an interesting article by :

Vargha and Delaney (1998). The Kruskal-Wallis Test and Stochastic, Journal of Educational and Behavioral Statistics, 1998 23(2), p 170-192.

They make similar point regarding assumptions of non parametric tests. Those who use the KW test may find this article useful as well.

Bill

on HomogeneityAt 09:22 PM 9/14/1998 GMT, you wrote: >Jocelyn Bisson (Jocelyn.Bisson@UMONTREAL.CA) wrote: >: Different approach have been offered to remedy for the heterogeneity of >: variances in ANOVA models, such as the use of Weighted least squares, >: the transformation of the response variable and the use of >: non-parametric test. > > - The non-parametric test has the disadvantage of either rescoring the >data dramatically, or having assumptions that are nearly as stringent >as the ANOVA. If simpler transforming works, where you gain both >homogeneity and a metric that still seems proper for what you were >measureing, then the simple transformation is what you ought to do. > > >: I would like to know about the role of post hoc comparison tests that do >: not require the assumption of homogeneity of variance. Can these tests, >: such as Tamhane s T2, Dunnett s T3, Games-Howell, and Dunnett s C, can >: be used as an alternative to the other means of correction (i.e. the >: transformation of Y) for the heterogeneity of variance ? > >Well, why were they invented, if not to serve as a poor substitute >for actual homogeneity? Yes, that is what they do, they serve as poor >substitutes for actual homogeneity, especially when you try to generalize >across several groups with very different Ns and variances. > >: Would it be legitimate to use post hoc comparison tests without first >: making an appropriate omnibus test which respects all assumtions ? > >No -- "post" means "after". Read your textbook. Now, what the chapter >describes may include a procedure such as Scheffe's, which is *not* a >post-hoc test; in the case of Scheffe's, the overall test would be >redundant because Scheffe's is at the limit of conservativeness. >There are tests without prior omnibus testing, but (by definition) they >are not post-hoc tests. > >: Maybe, in a more general way, what is the usual pratice with respect to >: one way ANOVA with unequal sample sizes and quite heterogeneous >: variances ? > >Cynically, I might guess that the usual practice is to mis-state things >badly. The good-practice is to admit that you have those features. >Do "quite heterogeneous variances" exist for continuous variables >despite attempts to re-scale? Is that more important that the simple >difference in means? > >Under the assumption that variances do have vast differences, too, the >honest approach is to perform pair-wise tests, using the actual Ns. > > >-- >Rich Ulrich, biostatistician wpilib+@pitt.edu >http://www.pitt.edu/~wpilib/index.html Univ. of Pittsburgh > > William N Dudley, PhD Asst Professor Dept Behavioral Science and Health Education Rollins School of Public Health Emory University Atlanta 30322 Phone 404 727 2447 FAX 404 727 1369

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