Nearest Neighbour (NN) Analysis of Field Experiments

• Published in: Journal of the Royal Statistical Society. Series B, Methodological Vol. 45; no. 2; pp. 151 - 211
• Main Authors: Wilkinson, G. N., Eckert, S. R., Hancock, T. W., Mayo, O.
• Format: Journal Article
• Language: English
• Published: London Royal Statistical Society 01-01-1983
• Subjects: analysis of field experiments; Analytical estimating; bias in f ratio; Correlations; Design analysis; efficiency; Estimation methods; Exact sciences and technology; Experiment design; Experimental design; Field experiments; intra‐n analysis; Least squares; Mathematics; Modeling; monte carlo; nearest neighbour methods; nn analysis; nn‐balanced designs; papadakis's method; Probability and statistics; Random allocation; randomization distributions; Sciences and techniques of general use; spatial models; Statistical discrepancies; Statistics; Spatial analysis; Nearest neighbour; Randomization; Experimental design
• ISSN: 0035-9246; 2517-6161
• DOI: 10.1111/j.2517-6161.1983.tb01240.x

The paper is in two parts. Part I presents results of a Monte Carlo randomization study of Papadakis's covariance method of NN analysis which show that (i) a non-iterated Papadakis analysis tends to be conservatively biassed; (ii) iteration of the analysis as suggested by Bartlett (1978) leads to substantial positive bias in the treatment F ratio; (iii) the method is very inefficient when there are substantial trend effects in the data. A theoretical explanation of these results is given. Part II describes a new method of NN analysis discovered by the first author and developed in collaboration with the co-authors. The method is essentially a "moving-block" analogue of classical forms of analysis for "fixed" blocks (or rows, columns). It avoids the defects of Papadakis's method and leads to approximately unbiased analyses. It is nearly always and often substantially more efficient on average than classical analyses of complete or incomplete block experiments, and also more efficient than standard analyses of Latin or lattice square designs if there are appreciable row × column interactions in the data. New criteria of design for NN balance are described. Validity of the new method under randomization is demonstrated empirically with Monte Carlo studies.