This dialog provides rudimentary power analysis for a test
of a coefficient of multiple determination (R-square).
The underlying model is that we have a sample of N iid
multivariate random vectors of length p, and that the pth
variable is regressed on the first p-1 variables.  
R^2 = 1 - SS(error) / SS(total) is the coefficient of 
multiple determination.

The usual way to test a hypothesis about R^2 is to 
transform it to an F statistic:

             (n - k - 1) R^2
        F = -----------------
               k (1 - R^2)

This is the usual ANOVA F.  The distinction that makes 
this dialog different from the one for regular ANOVA is 
that the predictors are random.  The power computed here
is unconditional, rather than conditional.

The GUI components are as follows:

Alpha: The desired significance level of the test

True rho^2 value: The population value of R^2 at which 
we want to compute the power.

Sample size: The number of N multivariate observations
in the data set.

No, of regressors: The value of k = p - 1.

Power (output only):  The power of the test.

References:

Gatsonis, C. and Sampson, A. (1989),  Multiple 
correlation: Exact power and sample size calculations.  
Psychological Bulletin, 106, 516--524.

Benton, D. and Krishnamoorthy, K. (2003),  Computing
discrete mixtures of continuous distributions...,
Computational Statistics and Data Analysis, 43, 249--267.

Note (9-18-06): This may still have some rough edges; the 
values obtained by my algorithms seem to differ slightly 
from those provided in the Gatsonis and Sampson paper.