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Re: st: Very small sample and multivariate analysis?

From   "JVerkuilen (Gmail)" <>
Subject   Re: st: Very small sample and multivariate analysis?
Date   Mon, 17 Sep 2012 16:54:12 -0400

On Mon, Sep 17, 2012 at 3:41 PM, Yupa <> wrote:

> Dear Statalisters,
> I need an advice. I have a dataset with 25 observations and three
> variables: a biomarker (continuous variable), a first dummy coded 0/1
> (group) and a second dummy coded 0/1.
> The distribution of the biomarker isn't normal. I found a statistical
> difference in the biomarker level between group 0 and group 1 with the
> Mann Whitney test, but not with the t test.
> A referee asked for a multivariate analysis to account for the
> contribution of the second dummy variable...
> Which approach/analysis may I consider?

In my view rarely is it the case that a classical nonparametric analysis is
what you really want.

It's quite possible to do a regression analysis with the two dummies and
their interaction in this case. The question is what to do about the
non-normality. The answer to the latter question might well be "nothing."
What characterizes it?

With a dataset this small you should boxplot (or -qplot-) all four
possible conditions
and see what you get. The non-normality you observe in the biomarker itself
may go away when you condition on the predictors. Regression has an issue
with errors that are not reasonably normal, not the response variable

You can always try the robust regression program implemented in -rreg- or
quantile regresion -qreg-. -rreg- might be a good check on the validity of
an ordinary regression analysis. Even if you do stick with ordinary
regression and chances are good that you probably will, I'd suggest using
bootstrapped standard errors.

(Apologies if there's a double post. Rich formatting got turned on

JVVerkuilen, PhD

"Out beyond ideas of wrong-doing and right-doing there is a field. I'll
meet you there. When the soul lies down in that grass the world is too full
to talk about." ---Rumi
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