The influence of design on validity and efficiency of neighbour methods

Neighbour methods have often been shown to be apparently more efficient than analysis of variance for the analysis of field experiments. This means that the precision of the analysis estimated by the statistical method itself is smaller for the neighbour method than for the classical one. This comparison is meaningful only if the analysis is valid in the sense that it estimates its own precision without bias. Although precise validity properties are known for the analysis of variance of randomized designs, no analogous properties are known for neighbour analyses. In this paper, we investigate the validity and efficiency of some neighbour methods and their relations with the design. First, we give precise definitions of the desirable properties of the combination of design (including randomization) and method of analysis; 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 neighbour designs and corrections to degrees of freedom. Finally, we discuss how these results can be used to assess neighbour methods for routine trials.