Nearest Neighbour (Nn) Analysis of Field Experiments

Abstract

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 "movingblock" analogue of classical forms of analysis for "fixed" blocks (or rows, columns). It avoids the defects of Papadakis's method and leads to approximately unbiassed 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 X 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.

Fractal geometry: a tool for describing spatial patterns of plant communities

“…Latin square), and the treatment in one quadrat does not affect adjacent quadrats, spatial dependence will not bias statistical results. However, statistical tests which consider spatial dependence can improve the efficiency of analysis of field experiments (Wilkinson et al 1983). Unfortunately, experimental studies can give only partial answers about vegetation-environment relationships: they may suggest that certain factors might cause variation in vegetation, but they do not directly test the response of vegetation to natural environmental variation.…”

Lack of interplot competition in Swedes (Brassica napus ssp rapifera L.)

“…This can lead to considerable influence from competition between adjacent plots. Several papers have been published on the impact of neighbouring plots in experiments with small plots (Bradshaw & Kempton, 1991) and analytical approaches to deal with this have been proposed (Kempton, 1982;Wilkinson et al, 1983). It seems clear from these papers that the bias in such experiments can be serious and to a large extent reduce the efficiency in the selection work.…”

Local adjustment method for field experiments. 1. The method and its examination by computer simulation

“…Only the main idea of `the nearest neighbour' method will be considered (for details see Bartlett, 1978 ;Bos, 1983 ; Wilkinson et al ., 1983) . The observation on a quantitative character of genotype i (the term 'genotype' will be used for simplicity, but treatment in any field experiment could be used) consists of a genotypic component and environmental effect and can be introduced as xi = p + gi + eri = p + gi + (si + ei) where: xi is the phenotypic value, p is the mean value (mathematical expectation), gi and eri are the genotypic and environmental components of the character, respectively .…”

“…Thus, the environmental index (Ii) for the test plant (Xi) can be calculated as the mean value of those neighbouring plants positioned at the corners of the hexagon (to enhance the accuracy each genotypes' plant must be surrounded by plants of the check variety placed at the corners of the hexagon) : Ii = (XI + X2 + X 3 + X 4 + X5 + X6) /6 . Such an approach for the analysis of single plants in field trials is of good theoretical and practical benefit (Bartlett, 1978 ;Bos, 1983 ;Wilkinson et al ., 1983 ;Stam, 1984 ;Weber & Stam, 1988 ;Fasoulas, 1990 ;Bos & Hennink, 1991) .…”