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Difference Tests for Distributions of Ratings

Three exact probability tests, counterparts of t tests for single sample, independent samples, and dependent samples, are described for data obtained from ratings on m scales by a single rater or on a single scale by n raters. These tests, which involve computing a difference ratio (D), require fewer assumptions and restrictions than the t test or nonparametric procedures such as the Mann-Whitney and Wilcoxen tests. Tables of one-tail discrete probabilities for 2 to 7 rating categories and 2 to 10 raters or scales are provided. Formulas for computing z scores for estimating the one-tail normal curve probabilities associated with each difference ratio (D 1, D 2, and D 3) and with the means of a sample of such ratios, are also given.