Further Analysis of Spatial Patterns: A Re-Examination of the Papadakis Method of Improving the Accuracy of Randomized Block Experiments

In contrast with the expository nature of my introductory contribution, I would like in my second paper to present some material prepared more especially for this conference. This consists of a re-examination of earlier proposals (Papadakis (1937), Bartlett (1938)) to adjust plot values in field experiments by means of neighbouring values, considering in particular the relevance of conditional nearest-neighbour models in assessing the efficiency of this procedure. (This topic was mentioned by D. R. Cox in the discussion to Besag (1974), and also arose in conversation with S. C. Pearce.) The use of the Papadakis method was considered by Atkinson (1969) in the one-dimensional case, but mainly in relation to the semi-systematic designs introduced by Williams (1952). The greater generality of the Papadakis method (and the absence to date of suitable semi-systematic two-dimensional designs) suggests that the use of the Papadakis method as an auxiliary empirical device in the analysis of randomized block experiments, as previously recommended (Bartlett (1938)) is still perhaps the most reasonable. There are nevertheless several complications arising in the method which need detailed discussion. Let me remind you of the appropriate models.