Probabilities of Correct Classification in Discriminant Analysis

Using Monte Carlo methods, the relationship is investigated between the actual probability of correct classification using the calculated linear discriminant function and the estimate of this probability which can be easily obtained by estimating the Miahalanobis distance between the two populations. Graphs are given for obtaining conservative confidence intervals for the probabilities of correct classification, given the estimated probability. For a given number of variates used to calculate the discriminant function the estimate of the probability becomes more satisfactory in terms of length of confidence interval as the size of the sample increases. For a given sample size, the estimate of the probability becomes less satisfactory as the number of variates is increased from two to ten. Tables with several percentiles in the distribution of these ratios are also included. Data for graphs and tables were obtained by Monte Carlo methods.