Economics Letters 45 (1994) 161-167 01651765/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved 161 Statistical inference for decile means Charles M. Beach”’ zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Department of Economics, Queen’s University, Kingston, Ontario K7L 3N6, Canada K. Victor Chow Department of Finance, College of Business and Economics, University of W est Virginia, P.O. Box 6025, Morgantown, W V 265’066025, USA John P. Forrnby Economics, Finance and Legal Studies, College of Commerce and Business Administration, University of Alabama, P.O. Box 870224, Tuscaloosa, AL 35487- 0024, USA George A. Slotsvet Department of Economics, Vanderbilt University, Nashville, TN 37235, USA Received 30 June 1993 Final revision received 23 November 1993 Accepted 7 December 1993 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Abstract This paper provides a simple set of formulas to compute standard errors, variances, and covariances for a set of decile mean incomes. This facilitates the statistical implementation of the Rank Dominance criterion for comparing two income (or wealth) distributions. JEL classification: C49 1. Introduction Considerable interest in recent years has focused on changes in income inequality in the United States and its implications for economic welfare. At the same time, recent developments in applied welfare theory have allowed one to evaluate relative levels of economic well-being in terms of dominance criteria of one income distribution by another. One such criterion, Rank Dominance (or, equivalently, first-order stochastic dominance), has been used to evaluate the convergence of distributions between the U.S. South and non-South [Bishop et al. (1992)] and to examine changes in the U.S. income inequality and economic well-being since the 1960s [Bishop et al. (1991)]. Statistical application of the Rank Dominance criterion involves comparing the mean incomes of a set of ordered quantile groups - such as deciles - between two distributions. Such decile means computed from a sample of micro data on incomes are subject to sampling * Corresponding author. ’ Beach and Slotsve acknowledge a grant from the Social Sciences and Humanities Research Council of Canada SSDI 0165-1765(94)00409-U