Use of inter-block information to obtain uniformly better estimators of treatment contrasts

Abstract

In this paper the problem of combining the estimates is reexamined by making use of the theory of basic contrasts. For some basic contrasts, called partially confounded, a general method of finding uniformly better combined estimators of treatment contrast is derived, The method is applicable for all proper block designs, not necessarily connected, with equal or different treatment replications, for which there are multiple efficiency factors ∊ε of multiplicity q> 2and if ν _e > 2, where ν _e is the number of the error degrees of freedom in the intra-block analysis.