Chance factors in pattern recognition studies utilizing nonparametric linear discriminant functions are examined. The relationship between complete linear separation of a data set and the dimensionality of the study is well-known. Also, due to the nature of the inequalities from which these numerical techniques are derived, 50% separation is always assured. The paper investigates the probability of achieving less than 100% but greater than 50% chance separations as a function of the dimensionality and class membership distribution. It is shown that the fraction of correct classifications due to chance factors increases dramatically as the dimensionality of the study increases. These results serve to redefine the level of expected chance classifications as a function of the number of observations, the dimensionality, and the class membership distributions. The results can be used to assess the classification results obtained with a given linear discriminant function.