Good question but the answer is difficult. Fourier coefficients can be viewed as regression coefficients so there is nothing wrong with having many negative coefficients.
The assumption of normality that one worries about is whether the entire set is consistent with sampling from a multivariate normal distribution. One property of a multivariate normal is that all linear combinations of the variables should also be normally distributed thus one could test each coefficient individually as well as linear combinations such as their principal components. Of course the tests must be done for within-population variation not across what you believe are different shapes. If you reject normality then one could consider transformations just for the purpose of significance testing. However, transformations such as raising to even powers would distort the shape differences between populations. Alternatively, one could note that the assumption required for testing differences of means is that the means are normally distributed - not the individual items. Thus the central limit theorem may allow you to use standard methods if sample sizes are large enough and the deviations from normality are not too great. Alternatively, one could use permutation tests that do not require the assumption of a particular statistical distribution. -------------------- F. James Rohlf - Dept. Ecology & Evolution SUNY, Stony Brook, NY 11794-5245 > -----Original Message----- > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] > Sent: Monday, February 09, 2004 11:16 AM > To: [EMAIL PROTECTED] > Subject: normality assumption with respect to elliptic fourier > > > coefficients > Sender: [EMAIL PROTECTED] > Precedence: bulk > Reply-To: [EMAIL PROTECTED] > > Hello, > > I was wondering: how does one deal with the normality > assumption of statistic tests with respect to the > distribution of elliptic fourier coefficients? > > First, as one is performing multivariate analysis, does one > need to consider each of the coefficients separately? And how > does that relate to the 'biological' irrelevance of each > separate coefficient? > > Secondly, what kind of transformation can one perform when > the normal distribution is not obtained. These coefficients > are all close to zero, and almost half of them are of negative value. > > Sincerely, > > Kristel Wautier > Ghent University > Department of Biology > K.-L. Ledeganckstraat 35 > 9000 Ghent > Belgium > > Tel.: +32 9 264 52 31 > Fax: +32 9 264 53 44 > > [EMAIL PROTECTED] > http://allserv.UGent.be/> ~kwautier/VMDB/homepage.html > > > == > > Replies will be sent to > list. > For more information see > http://life.bio.sunysb.edu/morph/morphmet.h> tml. > == Replies will be sent to list. For more information see http://life.bio.sunysb.edu/morph/morphmet.html.
