The influence of design on validity and efficiency of neighbour methods

Neighbour methods have often been shown to be apparently more efficient tha n analysis of variance for the analysis of held experiments. This means tha t the precision of the analysis estimated by the statistical method itself is smaller for the neighbour method than for the classical one. This compar ison is meaningful only if the analysis is valid in the sense that it estim ates its own precision without bias. Although precise validity properties a re known for the analysis of variance of randomized designs, no analogous p roperties are known for neighbour analyses. In this paper, we investigate t he validity and efficiency of some neighbour methods and their relations wi th the design. First, we give precise definitions of the desirable properti es of the combination of design (including randomization) and method of ana lysis; then we report on a simulation study. We show that neighbour methods are often valid or conservative with higher efficiency than classical ones . To better ensure these properties, we advocate the use of randomized neig hbour designs and corrections to degrees of freedom. Finally, we discuss ho w these results can be used to assess neighbour methods for routine trials.