Date: Tue, 15 Sep 1998 06:33:22 -0400
Reply-To: William Dudley <wdudley@SPH.EMORY.EDU>
Sender: "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From: William Dudley <wdudley@SPH.EMORY.EDU>
Subject: Re: Homogeneity of variance in OneWay ANOVA
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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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