Distribution-free analysis of a replicated latin square design by the method of weighted rankings and generalized weighted rankings

Abstract

We propose a class of completely distribution-free rank tests for the analysis of a replicated latin square design. This class is seen to be based on the method of weighted rankings. We establish the asymptotic distribution of any statistic belonging to the class under the null hypothesis of no treatment effects, as well as under a sequence of nearby alternatives, when the number of replications tends to infinity. This enables us to compute the asymptotic Pitman efficiency of any member of our class relative to the asymptotic mimmax test for the problem. It is noticed that this efficiency is a function of three components entering the definition of any statistic in our class. We then proceed in finding the intrinsically optimal efficiency when some or none of the components are fixed and the others are arbitrary. A numerical evaluation of the above findings is given in the presence of latin squares of size three with normal observations. Finally, a generalized weighted ranking method is suggested