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The performance of discriminant analysis procedures under non-optimal conditions Lind, John Charles

Abstract

The performance of four discriminant analysis procedures for the classification of observations from unknown populations was examined by Monte Carlo methods. The procedures examined were the Fisher linear discriminant function, the quadratic discriminant function, a polynomial discriminant function and a linear procedure designed for use in situations where covariance matrices are unequal. Each procedure was observed under conditions of unequal sample sizes, unequal covariance matrices, and in conditions where the samples were drawn from populations that did not have a multivariate normal distribution. When the population covariance matrices were equal, or not greatly different, the quadratic discriminant function performed similarly or marginally better than the linear procedures. In all cases the polynomial discriminant function demonstrated the poorest quadratic discriminant function performed much better than the other procedures. All of the procedures were greatly affected by non-normality and tended to make many more errors in the classification of one group than the other, suggesting that data be standardized when non-normality is suspected.

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