An Approach for Quantifying Paired Comparisons and Rank Order

PAIRED COMPARISONS FOR MULTIPLE CHARACTERISTICS: AN ANOCOVA APPROACH by PRANAB

An analysis of covariance model is developed for paired comparisons to situations in which responses (on a preference order) to paired comparisons are obtained on some primary as well as concomitant traits. Along with the general rationality of the proposed test, its asymptotic properties are studied.

An impossibility theorem for paired comparisons

In several decision-making problems, alternatives should be ranked on the basis of paired comparisons between them. We present an axiomatic approach for the universal ranking problem with arbitrary preference intensities, incomplete and multiple comparisons. In particular, two basic properties – independence of irrelevant matches and self-consistency – are considered. It is revealed that there ...

Comparability of Multiple Rank Order and Paired Comparison Methods

Optimal Scaling of Paired Comparison and Rank Order Data: an Alternative to Guttman’s Formulation

A formulation, which is different from Guttman’s is presented. The two formulations are both called the optimal scaling approach, and are proven to provide identical scale values. The proposed formulation has at least two advantages over Guttman’s. Namely, (i) the former serves to clarify close relations of the optimal scaling approach to those of Slater and the vector model of preferential cho...

The Wilcoxon signed rank test for paired comparisons of clustered data.

The Wilcoxon signed rank test is a frequently used nonparametric test for paired data (e.g., consisting of pre- and posttreatment measurements) based on independent units of analysis. This test cannot be used for paired comparisons arising from clustered data (e.g., if paired comparisons are available for each of two eyes of an individual). To incorporate clustering, a generalization of the ran...