[Moderator's note: For unknown technical reasons (or, perhaps, moderator incompetence), this message never made it to the list yesterday. This problem is compounded by the fact that a follow-up to this message by Rohlf WAS posted earlier this morning. I apologize and hope most of you aren't too terribly confused this situation. -ds]
I enjoyed seeing morphmet suddenly come to life! Sorry I was not able to comment earlier about MANOVA, permutation tests, etc. (I was busy preparing for a seminar). I agree with a lot of what has been said but I will try making a few points in my own words. 1) I agree with Fred that one has to be very skeptical about analyses that involve maximizing ratios of variances. The problems are well-known for multiple regression. Less well-known is that one can view MANOVA as just a special case. If one is not careful computations can blow-up and interpretations may not be very straight-forward when the tests are not close to being orthogonal. 2) There is a very important distinction to be made between the relations one sees in statistical spaces (such as CVA ordinations) versus those in shape spaces (the tangent space in practice). Distances in the CVA space are generalized distances that measure the amount of difference between two points relative to the amount of within-group variation in that direction. Procrustes distance measures just the amount of difference. Generalized distances are designed to measure the extent one can expect to distinguish members of the two populations. Procrustes distances tell how different they look. They give you fundamentally different answers: does one have evidence that the difference is greater than zero versus the question of the amount of shape difference. To know which to use requires a decision about the question you are asking. Fred's strategy gives priority to the possibility of biological meaning - it is difficult to criticize that! One the other hand, some times one does want to distinguish two populations even if the differences are very minor in the traits you are studying. 3) A statistical test for a difference in means is usually a test of whether two samples are consistent with having been drawn from the same population versus their having been drawn from populations displaced by having different means. It is close to the question of ability to discriminate. With the usual assumptions, MANOVA etc. seem appropriate. Of course, lots can go wrong - especially the assumption of homogeneity of covariance matrices. For some sets of data one may be able to make even more stringent assumptions (isotropic errors such as in Goodall's test). 3) Regarding shape visualizations, one can transform points in tangent space into points in a CVA space and then apply the inverse transformation to get back to the original tangent space so I don't think visualization of shapes should be an issue. At present, it is not a standard option in my software - but now that more people are developing morphometric software that problem will probably be quickly solved. Jim ----------------------- F. James Rohlf State University of New York, Stony Brook, NY 11794-5245 www: http://life.bio.sunysb.edu/ee/rohlf == Replies will be sent to list. For more information see http://life.bio.sunysb.edu/morph/morphmet.html.
