Remarks on the Method of Paired Comparisons: the Effect of Non-Normality in Thurstone's Comparative Judgment Model

Abstract

Scale values of stimulus-objects O_j (j = 1, 2 ... n) are calculated in Thurstone's comparative judgment model under the assumption that the perceived difference between each pair (O_j , O_k ), with respect to the attribute being scaled, is normally distributed across a population of subjects. The present study considered the amount of error introduced into Thurstone scale values when difference distributions are not normal. Non-normal distributions were simulated for objects O_j , having known true scale values; and corresponding scale values were derived from this aberrant data. The discrepancy between true and derived scale values thus provided a measure of error. As expected, the amount of error in derived values increased as the degree of non-normality increased. However, the magnitude of error did not reach serious proportions except for distributions that were both extremely non-normal and heterogeneous in shape.

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