The reason for the rule I gave in my earlier note is that analyses such as canonical variates requires the inversion of the pooled within-groups covariance matrix. It does not invert the individual covariance matrices so there is no minimum sample size for them (well, you have to have n > 0 or else you have no data!).
However, analyses such as CVA assume equal covariance matrices for the different groups. You cannot test for that assumption unless you have sufficient sample sizes so that each covariance matrix is non-singular (i.e., you need n greater than the number of shape variables). Goodall's test was mentioned earlier. It avoids this problem by not inverting a covariance matrix. On the other hand, it makes _many_ more assumptions that are not likely to be true for real biological data. ---------------------------------------------- F. James Rohlf, Distinguished Professor Dept. Ecology & Evolution, Stony Brook University Stony Brook, NY 11794-5245 http://life.bio.sunysb.edu/ee/rohlf > -----Original Message----- > From: morphmet [mailto:[EMAIL PROTECTED] > Sent: Wednesday, February 14, 2007 7:10 AM > To: morphmet > Subject: Re: Advice on IMP > > ok, but are there any requirements regarding sample size of > individual groups? > ______________________________________ > Paul Van Daele > Ghent University > Evolutionary Morphology of vertebrates > K.L. Ledeganckstr 35 > 9000 Gent > T + 32 9 2645233 > F + 32 9 2645344 > > Dance like nobody is watching > Kiss like you have never been loved before > ----- Original Message ----- > From: "morphmet" <[EMAIL PROTECTED]> > To: "morphmet" <[email protected]> > Sent: Tuesday, February 13, 2007 10:12 PM > Subject: RE: Advice on IMP > > > > For a conventional multivariate test of significance you > need to have > > a sufficient sample size so that the degrees of freedom of the > > covariance matrix are equal to or larger (preferably much > larger) than > > the number of variables. With 17 landmarks you will have > 2*17-4 shape > > variables so you will need more than just 15 specimens (3 > groups of 5 > > give you just 3*(5-1) = 12 degrees of freedom). > > > > ========================= > > F. James Rohlf > > Distinguished Professor, Stony Brook University > > http://life.bio.sunysb.edu/ee/rohlf > > > >> -----Original Message----- > >> From: morphmet [mailto:[EMAIL PROTECTED] > >> Sent: Tuesday, February 13, 2007 3:17 PM > >> To: morphmet > >> Subject: RE: Advice on IMP > >> > >> Hi, > >> > >> I was going to post the same question regarding problem > number 1 last > >> week. I was working with a small data set (N = 5 for each > of three > >> species within one species group of a genus) with 17 > landmarks on fly > >> wings. Two of the species are sibling species, so very > similar. I > >> worked around the problem by either reducing the number of > landmarks > >> to > >> 5 (deleting "noisy" and very similar landmarks) or by > increasing the > >> sample size. > >> > >> I am curious about what is causing the problem, too. > >> > >> Ed > >> > >> ************************************* > >> Edward A. Lisowski, Ph.D. > >> WA Department of Agriculture > >> Plant Protection, Pest Division > >> [EMAIL PROTECTED] > >> 509-225-2603 (ph) 509-454-7858 (fax) > >> > >> > >> > >> > >> > >> -----Original Message----- > >> From: morphmet [mailto:[EMAIL PROTECTED] > >> Sent: Tuesday, February 13, 2007 11:36 AM > >> To: morphmet > >> Subject: Advice on IMP > >> > >> Hi everybody! > >> I am using geometric morphometrics in a study on mandibles of mice. > >> I > >> have encountered problems using programs in the IMP series, and I > >> would be very grateful if somebody more experienced with > these could > >> give me a hint on what to do here: > >> > >> 1)I load an output file from CoordGen and a GroupList file into > >> CVAGen. > >> The program displays the landmarks but does not finish the > analysis, > >> instead posting an error message: ?The within-group sum of squares > >> and cross products matrix is singular?. I have inspected > both input > >> files several times; I cannot find any error; they do also perform > >> well in PCAGen. What does the message tell me about my data? > >> > >> > >> > >> > >> -- > >> Replies will be sent to the list. > >> For more information visit http://www.morphometrics.org > > > > > > > > > > -- > > Replies will be sent to the list. > > For more information visit http://www.morphometrics.org > > > > > > -- > Replies will be sent to the list. > For more information visit http://www.morphometrics.org > -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
