Some Recent Advances in Multivariate Analysis Applied to Anthropometry

With fossil hominids, skeletal evidence is often fragmentary. Certain regions of the skull may be missing for whole populations. Missing populations are fatal to the use of some methods but others, discussed below, can cope with this difficulty. With fossil material it is common for some populations to be represented by a single example - or at most very few. Whether it is admissible to calculate generalised (or any other) distance based on such small samples, and using a covariance matrix calculated from modern data, is noted but not otherwise discussed here. But it may be possible to evaluate generalised distances for some parts of the skull - the lower jaw or the articular region, for example. The question immediately arises as to how generalised distances between n populations, based on measurements from one region of the skull, relate to generalised distances between the same n populations based on measurements from another region of the skull. If the two sets of generalised distances seem to agree well, how should they be combined to give a joint analysis? Such questions immediately generalise to more than two skull regions, and in the following, m denotes the number of different regions. Of course problems of this kind need not relate only to fossil material. For example, it may be of general interest to investigate the stability of generalised distances based on different sets of measurements or different definitions of distance; the techniques discussed below are also appropriate in such circumstances. Of course all estimated distances are subject to sampling fluctuations and one would like to be able to compare sampling errors of distances evaluated from different regions of the skull.