Estimate of Subject Specific Index of Relative Performance in ‘K’ Samples

Abstract

This paper proposes and develops a statistic here termed the ‘relative performance index’ or the index of relative performance’ by subjects both within and between several sampled populations for preferentially rank-ordering subjects by their relative performance in comparison with other subjects from these populations involved in a test or contest. The proposed index would enable decisions on the preferential selection of subjects both within and between various classifications for management purposes. 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 several populations as functions of the relative performance indices. The method unlike some other methods used for the analysis of many samples is based mostly on individual subjects rather than on only summary indices or averages. Test statistics also based on subject specific relative performance indices are developed to test desired hypothesis concerning population. The proposed indices being subject specific rather than merely summary averages easily enables one to 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.