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Date:         Mon, 14 Sep 1998 21:22:15 GMT
Reply-To:     Richard F Ulrich <wpilib+@PITT.EDU>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From:         Richard F Ulrich <wpilib+@PITT.EDU>
Organization: University of Pittsburgh
Subject:      Re: Homogeneity of variance in OneWay ANOVA

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 Univ. of Pittsburgh

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