MANOVA required sample size

[john....@gmail.com]

I would like to run a MANOVA test with 11 IVs. I have a sample size of
52, and keep getting "insufficient degrees of freedom" error, which I
believe is caused by the insufficient data size.

Is there a rule of thumb to estimate the minimum data size requirement
for MANOVA as a function of IVs?

Thank you all
jon

[Richard Ulrich]

On Thu, 24 Jan 2008 14:43:47 -0800 (PST), john....@gmail.com wrote:

> I would like to run a MANOVA test with 11 IVs. I have a sample size of
> 52, and keep getting "insufficient degrees of freedom" error, which I
> believe is caused by the insufficient data size.

Let's see - Your R-squared, by chance, for prediction
of each *single DV* is 11/51 = 0.22 . This MANOVA
will be saturated with capitalization-on-chance
unless you do expect some large effect sizes.

>
> Is there a rule of thumb to estimate the minimum data size requirement
> for MANOVA as a function of IVs?

An approximate guide is to consider the total count of
(Cells minus 1), multiplied by the number of IVs, and that
is a number comparable to the number of predictors
which might be used in a multiple regression. (For two
cells, it *is* multiple regression.) I think I got that
guide by looking at the computations of the tests that
are conventional.

Using the approximation -- you probably need an N
of that size in order to run the analysis at all; and
you possibly need to avoid cells with counts of zero.
And, depending on your effect size, you might need
a total sample that is larger by a factor of 2, 5, 10, ....,
to have reasonable hopes of decent power.

The last edition of Cohen's book on "Power analysis
in the Social Sciences" (circa 1990) has chapters on
multivariate analyses. (The chapters make a pretty good,
implicit argument for avoiding MANOVAs, etc., especially
for Ns that are small.)

--
Rich Ulrich
http://www.pitt.edu/~wpilib/index.html