A least squares solution for successive intervals assuming unequal standard deviations

A least squares solution has been presented for the Law of Categorical Judgment and the Method of Successive Intervals, which is formally equivalent to Horst's solution for the matrix of incomplete data. A simplified approximation which is recommended for use with any matrix of complete data is also given. A procedure, analogous to that originally devised by Thurstone and presented by Saffir, is outlined for the typical experimental matrix of incomplete data. It is essentially a point and slope method of fitting a straight line which comes rather directly from the least squares solution.This study was supported in part by Office of Naval Research Contract N6onr 270-20 with Princeton University.The author wishes to acknowledge helpful suggestions and comments received in discussions of this problem with Max Woodbury, Frederic Lord, Frederick Mosteller, Warren Torgerson, Robert Abelson, and Bert F. Green, Jr. Thanks are due to Mrs. Gertrude Diederich and Irving Abrams for work on the computing necessary for the illustrative applications.