Introduction

So far, all the analyses discussed in this book have been for either univariate or bivariate data. Often, however, earth scientists need to analyze samples of multivariate data – where more than two variables are measured on each sampling or experimental unit – because univariate or bivariate data do not give enough detail to realistically describe the material or the environment being investigated.

For example, a large ore body may contain several different metals, and the concentrations of each of these may vary considerably within it. It would be useful to have a good estimate of this variation because some parts of the deposit may be particularly worth mining, others may not be worth mining at all, or certain parts may have to be mined and processed in different ways. Data for only one or two metals (e.g. copper and silver) are unlikely to be sufficient to estimate the full variation in composition and value within a deposit that also includes lead and zinc.

Samples on which multivariate data have been measured are often difficult to compare with one another because there are so many variables. In contrast, samples where only univariate data are available can easily be visualized and compared (e.g. by summary statistics such as the mean and standard error). Bivariate data can be displayed on a two-dimensional graph, with one axis for each variable. Even data for three variables can be displayed in a three-dimensional graph.