On the asymptotic theory of rank order tests for experiments involving paired comparisons

Summary The problem of testing the hypothesis of no difference among several treatments for the case when the comparisons between the treatments is possible only in pairs has been considered by Durbin [3], Bradley and Terry [1], Elteren and Noether [4], and Mehra and Puri [6], among others. Following the lines of Sen and Puri [9], a new approach to the asymptotic theory of rank order tests for this problem is developed. This avoids the unnecessarily complicated and lengthy conditional approach of Mehra and Puri [6] and also simplifies the proofs considerably. Prepared under contract Nonr-285 (38) with the Office of Naval Research, and Research Grant GM-12868 with the National Institutes of Health, Public Health Service.