Rank Analysis of Incomplete Block Designs: A Method of Paired Comparisons Employing Unequal Repetitions on Pairs

Abstract

The paired comparisons method developed by Bradley and Terry is modified by dropping the assumption that there are equal repetitions on all possible pairs. Analysis procedures are developed which are analogous to those developed by Bradley and Terry and by Bradley alone, including estimation of the sample parameters, the test of the hypothesis that all samples are equally preferred, the test of the appropriateness of the paired comparisons model, and the precision of the estimates of the sample parameters. A number of partially balanced incomplete block designs are given. These are a special case of unequal repetitions on the pairs, in that equal repetitions are obtained on those pairs which are compared, but no repetitions are obtained on some pairs. The methods are completely illustrated for an experiment in which 4 samples were compared.