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AN ANALYSIS OF PAIRED COMPARISON DESIGNS WITH INCOMPLETE REPETITIONS

1957; Oxford University Press; Volume: 44; Issue: 1-2 Linguagem: Inglês

10.1093/biomet/44.1-2.97

1464-3510

John Wilkinson,

Optimal Experimental Design Methods

Experiments involving paired comparisons have mainly concerned the situation where each judge compares all possible pairs of treatments or objects. In certain types of experiments, this may require an excessive number of comparisons to be made by any observer. To overcome this handicap, Bose (1956) and Kendall (1955) constructed certain designs, symmetrical with respect to objects and judges, which do not require each judge to compare all possible pairs of objects. However, neither Bose nor Kendall proposed any procedure of analysis in their respective papers. The purpose of this paper is to consider the problem of analysis of the Bose-Kendall paired comparison designs. This analysis is carried out in the tradition of the fundamental Bradley-Terry (1952) paper concerning the situation where all possible pairs are compared by each judge. Using the Bradley-Terry mathematical model, likelihood ratio tests are constructed in detail for certain classes of hypotheses, and are stated for some additional situations of interest. To exemplify the test procedures, the proposed analysis is applied to an experiment involving pairwise comparison of handwriting specimens.