Aspects of multivariate statistical analysis in geology

Multivariate statistical methods have become commonplace in the Earth Sciences. What was once an exclusive area of activity is now within the reach of Everyman, owing to the ubiquitousness of mini-computers and the ready availability of software for doing the computing. In the days when one was required to do one's own programming, it was necessary to acquire considerable proficiency in linear algebra and one or more programming languages. Today, the vast majority of the people who use multivariate methods to analyse geological data have little or no idea of the matrix operations underlying a particular method, nor, for that matter, what the program is actually supposed to be doing. This situation can be both good and bad. It can do no harm if everything goes according to schedule, the program being used is competently constructed, which, alas, is far from being the general case, and there are no strong deviations from standard statistical theory in the data under examination. It is bad if the data do not fit the theoretical requirements of a particular method and even worse if the method of computation used is inappropriate. It is an inescapable and sad fact of life that much geological and biological material deviates in some manner or other from the theoretical requirements of a multivariate statistical procedure. The immediate relevance of this observation is that there are many sources of error in doing an analysis of geological data by means of standard statistical software.

The spread of multivariate statistics in the Natural Sciences has, therefore, taken place at a cost - the risk of doing something quite wrong and yet never knowing that a mistake can have been committed, or worse, that a blunder is even possible.

Books on multivariate statistics aimed at all levels of sophistication abound, from abstruse algebraically loaded treatises, through practically oriented texts, to volumes of computing recipes such as are profusely available for biologists. The special justification for this book is that it is concerned with the elementary consideration of the special types of multidimensional problems that occur in Geology and which are never, or are only summarily, considered in other places (e.g., textbooks dealing with multivariate statistics) and which cannot always be correctly analysed by commercially available software. There is an attached compact disk of compiled programs and trial data for doing the most commonly occurring computations, the files for running Graph Server and a file summarizing the steps involved in activating the various routines, but we lay no claims to perfection nor to elegance in the appearance of the computational output.