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Suppose an experiment is conducted on pairs of objects with outcome responsesa continuous variable measuring the interactions among the pairs. Furthermore,assume the response variable is hard to measure numerically but easy to becoded into ordered categories such as low, moderate, and high levels ofinteraction. In this paper we estimate the unknown interaction values from theinformation contained in the coded data and the design structure of theexperiment. The method of estimation is shown to enjoy several optimalproperties such as explaining maximum variance in the responses with minimumnumber of parameters and for any probability distribution underlying theresponses. Other properties of the method include: the interactions have thesimple interpretation of correlation, size of error is estimable from theexperiment, and only a single run of each pair is needed to carry out theexperiment. We also explore possible applications of the technique. Threeapplications are presented, one on protein interaction, a second on drugcombination, and the third on computer imaging. The first two applications areillustrated using real life data while for the third application the data aregenerated via binary coding of an image.

The Statistical Analysis of Pairwise Experiments with Qualitative Responses