A few days ago, Jim Rohlf said, in response to Patrick Arnold's query about how to test the significance of major axis "regression"
> > I don't know about how to do it in PAST, but note that because the slope of > the standard major axis "regression" line is just the signed ratio of two > standard deviations, its square follows the F-distribution if one assumes > that the two variances are based on random samples from two normally > distributed populations. Thus a test for a slope = 1 corresponds to a > 2-tailed test for the equality of variances. One can easily look up > probabilities in an F-table or compute confidence limits using standard > methods. Note that if the samples are across different populations or > species, as in many (most?) morphometric applications, then these assumptions > do not hold. This problem was brought to my attention by Paul Harvey in the late 1970s. I suggested that he look for a rotation angle (theta) that would maximize the likelihood under a model in which the two (new) variables are independent Gaussian variables. This also allows a likelihood ratio test of the assertion that theta is zero. The estimate of theta provides an estimate of the angle of the major axis. These can be easily generalized to multiple populations, even when their variances are unequal. The likelihood ratio test is done with a test for equality of correlation matrices which will be found in a multivariate statistics book by Morrison. I am not sure where Paul published this, but I think he did in an appendix to a paper of his in some multiauthor volume. J.F. ---- Joe Felsenstein j...@gs.washington.edu Department of Genome Sciences and Department of Biology, University of Washington, Box 355065, Seattle, WA 98195-5065 USA _______________________________________________ R-sig-phylo mailing list - R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo Searchable archive at http://www.mail-archive.com/r-sig-phylo@r-project.org/
