MODELS FOR PAIRED COMPARISONS.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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A central concept in this paper is that of linear model. A model is called linear if the frequency probability with which a subject reports the stimulus X sub 1 as greater than X sub 2 has the form HtX sub 1-tX sub 2. Interrelations among various models for paired comparisons are studied. The Thurstone, Bradley-Terry, and Scheffe models are treated as special cases of the general linear model. It is shown that all of these special cases introduce a concept of psychological distance between stimuli. The increase or decrease of the probability of detecting the larger stimulus for linearmodels is shown to depend primarily on t rather than H. The uniqueness of the linear representation of a Bradley-Terry model is discussed. A final section proposes a general model allowing for the response of no apparent difference. Author
- Statistics and Probability