SCIENCE, STATISTICS, AND PAIRED COMPARISONS

The role of statistics in science is discussed. Statisticians must be trained as scientists and to meet the needs of science. Those needs involve the formulation, modification and verification of stochastic models designed to represent natural phenomena. The method of paired comparisons provides a simple experimental technique but one with a literature rich in model development. A method of paired comparisons proposed originally by Zermelo and rediscovered by Bradley and Terry, Ford and others is discussed. The basic model is reviewed with emphasis on various approaches that lead to the model. Applications and uses of the model are reviewed along with tests of appropriateness of the model. Extensions of the model discussed include adjustment for ties, triple comparisons, use of factorial treatment combinations and the multivariate case for which a numerical example is included. Methodology is omitted that does not relate to the basic approach of this paper unless introduced for comparison. Nothing is included on details of experimental design or the design of tournaments. The development of statistical methodology can benefit from the use of the mathematics of statistics and probability.