Paired sample tests with unordered observations

Abstract

The problem of testing equality of means of a bivariate normal distribution on the basis of a sample of size n has been considered when the labels of the observations are not known. Two tests based on the sample moments of absolute values of the differences of the observations in each pair are suggested. Their power properties are investigated. It is interesting to observe that for small values of the parameter one is more powerful than the other while for larger values it is the other way around.