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Canonical correlation analysis is an extremely useful technique, especially in biomedical investigations where a large number of variables of distinct types, e.g., physical and psychological, are studied simultaneously. Discriminant analysis and regression analysis are particular cases of this general technique. In this dissertation the following aspects of canonical correlation analysis are investigated: (i) Anderson's classification statistic, (ii) assignment of optimum scores to the categories of a multidimensional contingency table, by using a stepwise method for completing canonical analysis for more than two vector variables, and (iii) the predictive ability of scores in contingency tables. Anderson's classification statistic is expressed in a simpler form by using a series of random orthogonal transformations. Its first two exact moments are derived which are then utilized in obtaining a normal approximation to its distribution. The usefulness of this statistic in estimation of relative potency of a new drug or test preparation is illustrated. Assignment of scores to the categories of a contingency table by use of a stepwise method of canonical correlations is proposed and illustrated for the well known blood serological data of Taylor, first analyzed by Fisher. The efficiency of this method is investigated using redundancy analysis indices. The stepwise method also provides a technique for eliminating categories that do not contribute significantly to the relationship. The predictive ability of the optimum scores obtained by using the canonical variables is investigated for the Taylor data, wherein predicted and observed values agreed in almost 80% of the cases.