Re: st: How to perform a non parametric manova

["Michael N. Mitchell" <Michael.Norman.Mitchell@gmail.com>]

Dear Ama

  Thanks for your reply. If the concern is regarding "normality", then the next question 
that I would ask is "What are your sample sizes per group?". And, to answer that question 
in advance, if your sample sizes "per group" are 30 or larger, then I think you have 
nothing to worry about, because the central limit theorem saves the day. As you may 
recall, the assumption of ANOVA (and MANOVA) is that the distribution of the SAMPLE MEANS 
is normal (not that the distribution of the individuals is normal). Even with non-normal 
distributions at the person (subject) level, with increasing sample sizes (generally above 
30) the distributions of the sample means become sufficiently normal. There are numerous 
publications in support of this... the one that comes to mind the quickest is

  http://works.bepress.com/cgi/viewcontent.cgi?article=1023&context=paula_diehr

  The greatest concern that I have is homogeneity of variance combined with strongly 
unequal Ns per group. This can play havoc with the p values. There are many publications 
on this more serious issue, including

    *  Browne, M. B. & Forsythe, A. B. (1974). The ANOVA and multiple comparisons for 
data with heterogeneous variances, Biometrics, 719-724.
    * Wilcox, R. (1987). New Designs in Analysis of Variance. Annual Review of 
Psychology, 29-60.
    * Wilcox, R, Charlin, V, Thompson, K. (1986). Communications in Statistical 
Simulation and Computation. 15(4) 933-943.

  I wrote a tool in Stata to help assess the seriousness of this issue called "simanova" 
which is described at

  http://www.ats.ucla.edu/stat/stata/library/homvar.htm

  It allows you to assess the seriousness of the violation of homogeneity of variance 
based on your variances (per group) and sample sizes (per group).

I hope this helps,

Michael N. Mitchell
Data Management Using Stata      - http://www.stata.com/bookstore/dmus.html
A Visual Guide to Stata Graphics - http://www.stata.com/bookstore/vgsg.html
Stata tidbit of the week         - http://www.MichaelNormanMitchell.com



On 2010-05-27 3.44 AM, amatoallah ouchen wrote:
> Dear Michael,
> Thanks a lot for your concern, the reasons are  as you have already
> said it as well as Nick, specially the fear of violating manova
> assumptions of normality and  thus the danger of getting biased
> results.
>
>
>
>
>
> 2010/5/26 Michael N. Mitchell<Michael.Norman.Mitchell@gmail.com>:
> > Dear Ama
> >
> >   There have been some extremely useful answers to your question so far, and
> > it might be completely settled. I don't know if anyone asked about the
> > motivation for doing the non-parametric anova. I could see it being related
> > to at least two different reasons...
> >
> >   1) The outcome variable is not measured on an interval scale (is ordinal).
> >
> >   2) There is question about meeting assumptions of the manova model, in
> > terms of normality, homogeneity of variance, etc... especially if combined
> > with small sample sizes.
> >
> >   Perhaps letting us know about the underlying motivations for the selection
> > of this model could help inform further useful information.
> >
> > Best regards,
> >
> > Michael N. Mitchell
> > Data Management Using Stata      - http://www.stata.com/bookstore/dmus.html
> > A Visual Guide to Stata Graphics - http://www.stata.com/bookstore/vgsg.html
> > Stata tidbit of the week         - http://www.MichaelNormanMitchell.com
> >
> >
> >
> > On 2010-05-26 4.38 AM, amatoallah ouchen wrote:
> > > Good day Stata-listers,
> > > Does anyone have an idea about how to perform a non parametric manova?
> > > an equivalent of the kruskal wallis test for anova?
> > >
> > > Any help would be highly appreciated.
> > >
> > > Ama
> > > I
> > > *
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> >
> > *
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