Explores and extends statistical techniques for evaluating preferential-ranking data. After a brief review of previously used analysis procedures, especially in parapsychological research, a generalized weighted sum approach to the problem is developed whereby weights or scores are assigned to each rank with the sum of these weights over a series of N trials being the test statistic. Three possible weighting schemes are suggested, one of which is designed to test variance. The distributions of these schemes are explored to show how rapidly they approach normality with respect to number of trials and number of stimuli to be ranked. Tables of exact probabilities are provided for the non-normal cases. Continuity corrections are discussed for those cases where the normal approximation is valid. Included are several illustrations of the weighted sum statistics applied to actual data, suggestions for useful variants to parapsychological tests based on the weighted sum statistics, and a discussion of the use of weighted sum statistics in standard parametric analyses.