Abstract
In a randomized block design with n blocks, c treatments and nij observations in the (i, j) cell, we consider two classes of rank tests for homogeneity against ordered alternatives. Both classes consist of weighted sums of n block statistics based on rankings within blocks, but one uses the simple linear rank statistics based on ranks of the whole observations in i-th block as the i-th block statistic [Simple linear type], the other uses the sum of c(c-1)/2 two sample rank statistics based on ranks of combined observations of two cells in the i-th block [Two sample type]. We consider asymptotic properties of these statistics and compare the two types by their Pitman efficiencies. It is shown that Simple linear type is n-asymptotically more efficient than Two sample type and that Simple linear type and Two sample type are nij- or c-asymptotically equally efficient.
