Statistical Index Of Relative Performance In Two-Sample Problem

Abstract This paper proposes and develops a statistic here termed the relative performance index or the index of relative performance for rank-ordering subjects by their relative performance both within and between two sampled populations in a contest for preferential selection as the need arises. The proposed method enables the estimation of the median and other tiles of not only each of the sampled populations but also the common median of the two populations as functions of the relative performance indices. The method unlike some other methods used for the analysis of two sample data is based mostly on the individual subjects rather than on only summary indices or averages. Test statistics also based on the relative performance indices are developed to test desired hypotheses concerning the medians and other tiles of each and the common population. The proposed indices being subject specific rather than merely summary averages easily enables one more clearly and succinctly examine individual subjects relative performance or level of seriousness in a condition in comparison with other subjects from the sampled populations thereby providing subject targeted information to better guide any interventionist actions on a condition of research interest. The method is illustrated with some data and shown to compare favorably with some existing methods.