A thurstone-type model for paired comparisons with unequal numbers of repetitions

In paired comparison experiments t objects are ranked for any particular characteristic x by offering the objects in all possible pairs to a judge, each pair being repeated a certain number of times. The judge is to express his preference by giving a score 1 to the preferred object and a score 0 to the non-preferred object. A modification of Thurstone Model for analysis of data from such experiments has been given by Mosteller ‘1951a,b,c’. In this paper angular transformation is used to generalize Mosteller1s model in order to make the preference proportions independent and incidentally ensure homo-scedastlcity of variances and correlations and additivlty of scale in the subjective continuum for the stimuli." The model is extended to unequal numbers of repetitions of the pairs. Using the model two different types of treatment ratings are obtained along with the respective standard errors for moderately large numbers of repetitions, one setting the location parameter S, "0 and the other using the constraint S1 + S2 +…,+ St = 0.