Ian The crucial thing about permutation tests is the specific hypothesis they are supposed to test. Permutation is a very general technique for simulating a wide range of null hypotheses that you can compare against your data. Whether or not those make sense or whether or not they are relevant to the particular biological question you are asking depends critically on that question!
There are two broad classes of situations in which one will use permutation tests. a) Shape versus some outside variables. Examples are regression (permutation will randomly rematch the shape vectors and the covariates) and various ANOVA designs (observations will be randomly reallocated to treatments/groups by permutation). In all these cases, you probably don't want to mess around with the covariance structure of shape itself, so you will leave all shape variables of each specimen together and do permutations with the whole vectors. b) Matrix permutation procedures. Here the hypothesis is about the covariance structure of shape itself (e.g. similarity/dissimilarity). Accordingly, you have to simulate a covariance structure appropriate to your null hypothesis. So your units for permutation may be landmarks or sets of landmarks or, although I can't see a biological situation where that would make sense, perhaps individual coordinates. You then randomly permute the sets of rows and columns of the covariance matrices that correspond to those units. Programming this in SAS/IML is actually quite easy once you have figured out the permutation procedure appropriate for your experimental design and question. It will probably be easier to write this from scratch for your problem rather than to adapt someone else's code originally written for a different problem. Whether or not you use the original coordinates or derived variables such as partial warp scores (and uniform components!) depends on the problem again. For the analyses of group a), both approaches should yield the same results (provided you use the full information). For analyses of group b), you will normally use raw variables because that's the way the hypotheses are phrased. I hope this helps. Best wishes, Chris ****************************************************** Christian Peter Klingenberg School of Biological Sciences University of Manchester 3.614 Stopford Building Oxford Road Manchester M13 9PT United Kingdom Telephone: +44 161 2753899 Fax: +44 161 2753938 E-mail: [EMAIL PROTECTED] Web: http://www.sbs.man.ac.uk/chrisk ****************************************************** == Replies will be sent to list. For more information see http://life.bio.sunysb.edu/morph/morphmet.html.
