This study investigates the statistical properties of a variety of discriminant functions and determines how well they differentiate between alcoholic, other diseased, and normal populations using standard batteries of blood chemistries. Blood chemistry variables that are used to discriminate between diseased and normal groups have been found to have skewed distributions. Using computer simulations, the properties of parametric (linear and quadratic) and nonparametric (fixed and variable kernel) discriminant methods have been investigated when the data comes from a skewed multivariate lognormal distribution. In addition, rank and inverse normal score transformations were applied to the data from the simulation in order to determine if they could improve upon the accuracy of the discriminant functions. It was found that the nonparametric methods were less accurate than the parametric methods when the data came from a multivariate lognormal distribution. The rank and inverse normal score transformations greatly improved the classification accuracy of the parametric methods. The rank and inverse normal score transformations have been applied to data from multivariate repeated measure designs in order to remedy the effect nonsphericity and non-normality has upon classical repeated measure analyses. It was shown through simulations that the inverse normal scores does improve the performance of certain classical tests used with repeated measures.
