Q A valid solution was provided by Anderson and Bahadur in 1962 - Annals of Mathematical Statistics. Examples in Blackith and Reyment (1971) Multivariate Morphometrics, Academic Press, London.
Richard A. Reyment uoting morphmet <[EMAIL PROTECTED]>: > Hello all, > I have been struggling the past few days with the results of > elliptical fourier analysis on fossil clams. EFA went well enough; I > used the HAngle and HMatch programs. I have been using PCA for > visualizing the data (by treating the Fourier coefficients as > variables; I have been getting 11 pairs = 22 coefficients = 22 > variables), but I would very much like to run a statistical test on > the "sameness" of the groups that I have, and also be able to place > ungrouped specimens within the framework I develop. > > I have read this entire thread [http://www.mail-archive.com/ > [EMAIL PROTECTED]/msg00328.html] about PCA and multivariate > normality, but I would like to know more about how 'real' > discriminant analyses are actually run. > > Every textbook source I have claims that you need to be able to > assume multivariate normality and equal variance-covariance matrices > to be able to run discriminant analysis and Hotelling's T^2 test. > Unfortunately, both skewness and kurtosis of the data are not normal, > and Box's M tells me that the variance-covariance matrices are unqual > (although I hear that test is rather stingent). > > However, I have found a number of papers where the authors either use > discriminant analysis or do something similar, but I have not found > any mention of meeting these assumptions. So my question is this: > is it okay to run the test without multivariate normality just > because everyone else seems to have done so, or is there something I > am missing? If the latter, is there a way to normalize this > multivariate data? > > (As an aside, it would be best for me to rely on the data from the > original specimens rather than an aggregation of the group, simply > because the question I am trying to ask is 'what group(s) do these > specimens fit into?) > > Thanks for any light you can shed on these problems, > Matt BK > > > > > ----------------------------- > Matthew Burton-Kelly > Graduate Student > Department of Geology and Geological Engineering > University of North Dakota > (802) 922-3696 > [EMAIL PROTECTED] > Web site: http://uweb.und.nodak.edu/~matthew.burton.kelly/ > -------------------------------------------- > "About thirty years ago there was much talk that geologists ought > only to observe and not theorize; and I well remember someone saying > that at this rate a man might as well go into a gravelpit and count > the pebbles and describe the colors. How odd it is that anyone > should not see that all observation must be for or against some view > if it is to be of any service!" > -Charles Darwin, in an 1861 letter to Henry Fawcett. > > > > > -- > Replies will be sent to the list. > For more information visit http://www.morphometrics.org > ---------------------------------------------------------------- This message was sent using IMP, the Internet Messaging Program. -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
