The estimation of the discriminal dispersion in the method of successive intervals

A new algebraic formula is derived for estimation of the discriminal dispersion in the method of successive intervals. The legitimate use of the formula requires that as many normal deviates as possible be present in the matrix. For this reason, it is recommended that deviates corresponding to the interval (0.01, 0.99) of the cumulative proportions be used, instead of those corresponding to (0.05, 0.95), the interval used by Edwards and Thurstone. Computations on data published by Edwards and Thurstone showed that when adjustment was made for variability in dispersions calculated by the formula of this paper, a reduction of fifty per cent in mean absolute discrepancy was produced. Since the formula is easy to use and avoids the disadvantages of its predecessors, it should have fairly wide applicability in psychological research.This research was supported in part by the United States Air Force under Contract No. AF 33(038)-25726 monitored by Air Force Personnel and Training Research Center. Permission is granted for reproduction, translation, publication, use and disposal in whole and in part by or for the United States Government. The writer is grateful to Dr. A. L. Edwards for a critical reading of an earlier version of this paper, and to Dr. L. H. Lanier and Dr. L. M. Stolurow for editorial advice on the present version, which was written at the University of Illinois. The editors ofPsychometrika have informed the writer that H. J. A. Rimoldi and M. Hormaeche (7) have independently derived the same formula for the discriminal dispersion from a different set of postulates using the law of comparative judgment.