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Re: st: How to perform a non parametric manova

 From "Michael N. Mitchell" To statalist@hsphsun2.harvard.edu Subject Re: st: How to perform a non parametric manova Date Thu, 27 May 2010 09:58:16 -0700

```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
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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
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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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