12 - Probabilistic Methods: Multivariate Statistics I: Basic Strategies

Abstract

Multivariate analysis means any statistical analysis involving more than two variables or more than two groupings even if only one dependent variable is being considered at a time. The chapter examines several multivariate techniques, including multiple regression analysis, the analysis of variance, covariance analysis, factor analysis, discriminant function analysis, canonical correlation, chisquare, Cochran's Q, Friedman's two-way analysis, and the Kruskal–Wallis test. Most of the techniques involve great computational complexity and rigorous mathematical justification and require both training and know-how for successful application and interpretation. The greatest emphasis in standard texts is given to the techniques for presenting charts, graphs, and tables for univariate and bivariate data. A sheet of paper presents a two-dimensional surface and therefore, considerable ingenuity is required to deal with three or more variables. The possibilities for graphing and charting are very severely limited. At the heart of the use of multivariate analysis is the notion of multiple causality. Both the theoretical foundation and the practical application or interpretation of every technique reflects an attempt to formulate this notion in a systematic and mathematically manageable way.