A note on optimum grouping and the relative discriminating power of qualitative to continuous normal variates

Abstract

Ogawa (1951) considered the efficiency of estimation of the population mean from suitably chosen order statistics in large samples. Cox (1957) has considered the relative amount of information retained by grouping the normal curve. Cochran and Hopkins (1961) determined the discriminating power retained after partitioning normally distributed variates into qualitative ones in multivariate classification problems. And Connor (1972) discussed the asymptotic efficiencies of the test for the trend using m groups formed from a continuous variable. The same expression appears in all these investigations. This note throws some more light on the occurrence of the same expression in these seemingly unrelated problems.