I am the sole author of an R package (named “wmpvaer”). This package along with all the R code and extensive documentation are available for download by anyone from the GitHub repository https://github.com/chvrngit/wmpvaer.

It contains four sub-packages.

The first creates high precision power and p-values for the Wilks Lambda Statistic using the Butler/Wood Algorithm (Butler, R.W. and Wood, A.T.A. "Approximation of Power in Multivariate Analysis" in Statistics and Computing Vol. 15,pp. 281-287,2005 doi:10.1007/s11222-005-4071-x).In addition provides an S4 object that computes these same statistics useful in evaluating multiple dependent variables models created by other R programs. The second computes the likelihood ratio statistic for block independence. The third creates a statistic testing equivalence of covariance matrices along with p-values. In a fourth part, computes a sample size estimate for a 1-way MANOVA analysis.

To most people this may seem like pretty obscure stuff. But Butler and Wood’s largely overlooked paper presents a way to solve a number of difficult multivariate analysis problems (which are otherwise intractable, that is, can’t be solved). My package computes these Butler and Wood solutions for, as far as I know, the first time.

I have received no support from anyone for this work. But the fact is, if I had the chance, I could expand the methods I computed. I have invented methods to speed up the R calculations involved using C++ routines and methods that produce more accurate estimates. I have rewritten parts of the R package in Python and could improve the performance of these as well. I have designed ancillary programs programmable in SciPy that could be used to expand the Butler/Woods methods to many otherwise intractable problems in statistics and probability. The problem of computing otherwise intractable probability distributions, for example, is an ongoing roadblock in the development of better machine learning methods

My intention is to distribute these programs as open source using GitHub as a repository. But these programs are unlikely to be created unless I can get financial support. I hope there are GitHub Sponsors out there somewhere who will help me.