Recently, the levels of correct classifications due to chance that were attainable by nonparametric linear discriminant functions (NLDFs) were studied. The previous work dealt with easily generated, idealized data. Because of this, the application of those results to actual studies using nonideal data may not be warranted. The studies reported here analyze the effects of zero values, indicator values, and multicollinearities: variations that occur in actual data and that could affect the levels of random classifications. Three structure-activity relationship studies that were performed with NLDFs are also examined.