The same considerations apply to any multivariate study (conventional variables, partial warp scores, or scores on Fourier harmonics). One can use exploratory methods such as PCA or cluster analysis with any sample size but in order use methods that look at difference among groups relative to within-group variability one needs the degrees of freedom of the within-group covariance matrix to be greater than the number of variables. With fewer observations the within-group covariance matrix will be singular. This rule gives a minimum sample size but for reliable results the sample size should, of course, be much larger. This makes the use of a number of standard multivariate methods impractical when using many harmonics or many landmarks so that less powerful methods have to be used.
------------------------ F. James Rohlf, Distinguished Professor Ecology & Evolution, Stony Brook University www: http://life.bio.sunysb.edu/ee/rohlf > -----Original Message----- > From: morphmet [mailto:[EMAIL PROTECTED] > Sent: Sunday, November 25, 2007 6:44 AM > To: morphmet > Subject: outlines analysis Fourier coefficients > > Dear morphometricians. > > I would like to know, if it is possible... > How to calculate the number of harmonics, for the estimation of Fourier > coefficients, depending the number of individuals sampled. > Some formulae. > I know this formulae (k-1)/2 or (k/2, K=numer of points on the > outlines. > I know that the number of harmonics depends on the degree of > recostrucion of the original structure, but what about the number of > individual. > > Thanks > > Ang�lica Cuevas > > ----------------------------------------------------------------------- > - > > Comparte video en la ventana de tus mensajes (y tambi�n tus fotos de > Flickr). > Usa el nuevo Yahoo! Messenger versi�n Beta. > Visita http://e1.beta.messenger.yahoo.com/ > > -- > 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
