A comparison of two scaling procedures in paired-comparison experiments involving ties
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A recently-proposed modification of the Thurstone- Mosteller method of paired comparisons makes possible the analysis of data involving tied observations. The modification includes the postulating of an angular response law such that the response proportions are scaled with arc sine transforms instead of with normal deviates.
In this paper a comparison is made of the arc sine and normal curve scaling procedures in paired comparisons involving ties. This is done by applying both methods to data from to important fields of application. Comparisons are also made on several series of hypothetical data. The criterion of comparison is the goodness of fit between the observations and the expected numbers computed from the solution, as measured by means of a chi-square statistic. Computations of parameter estimates and chi-square statistics are made with the aid of an IBM-650, for which the necessary programs have been written.
It is concluded that for data conforming well to the model as proposed, both scaling procedures tend to give results in satisfactory agreement with the observations. There is some evidence that, for the cases considered, the preference, if any, is for the normal curve procedure.
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