This article reports an empirical study of the nannull distribution of Kendall's coefficient of concordanceWwhen used in estimation and hypothesis testing procedures for the coefficient of reliability,p.This was based on data satisfying the assumption of a normal component of variance model formretests on each ofnsubjects or marginal transformations of such data. For the range of parameters studied,Km, n(ρ*)(m− 1)W/(1 −W) is approximately distributed asFv1,v2for a properly chosen constantKm, n(ρ*),v1= n− 1 − 2/m,v2= (m− 1)v1.