Nonparametric Methods of Ranking from Paired Comparisons

Ranking by row-sum scores in the case of balanced paired-comparison experiments was generalized to unbalanced experiments in David [7]. Statistical properties of the proposed scores and associated tests of significance are developed in Andrews and David [2], where extensions to unbalanced ranked data are also treated. A brief account of this work is given and a possible generalization is introduced and examined. The simple methods here advanced make no assumptions on the pairwise preference probabilities. A secondary aim of this paper is to provide a critical review of competing methods also involving no such assumptions as well as of related methods requiring only mild assumptions. Many of the procedures discussed are illustrated on a worked example.