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Stochastic models and field trials

Published online by Cambridge University Press:  14 July 2016

M. S. Bartlett
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Abstract

A survey of the development of statistical techniques of field experimentation refers to the unified approach of R. A. Fisher, in which analysis and design were closely linked. Randomization of treatment positions bypassed the need for a precise stochastic model, but sometimes at the cost of diminished accuracy.

Alternative covariance methods associated with the name of J. S. Papadakis, taking note of the yields of neighbouring plots, have stimulated much research in recent years. The results to date suggest that, while improved accuracy can often be achieved, the assessment of accuracy is more dependent on the stochastic model. Robust methods for such assessment still need to be finalized; with these alternative methods a closer link between analysis and design is also advocated.

Keywords

COVARIANCEPAPADAKIS METHODRANDOMIZATIONSEMI-SYSTEMATIC DESIGNS
Type
Part 3 - Stochastic Models in Biology and Field Trials
Information
Journal of Applied Probability , Volume 25 , Issue A , 1988 , pp. 79 - 89
Copyright
Copyright © Applied Probability Trust 1988 

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References

Atkinson, A. C. (1969) The use of residuals as a concomitant variable. Biometrika 56, 33–41.Google Scholar
Bartlett, M. S. (1934) The vector representation of a sample. Proc. Camb. Phil. Soc. 30, 327–340.Google Scholar
Bartlett, M. S. (1938) The approximate recovery of information from replicated field experiments with large blocks. J. Agric. Sci. 28, 418–427.Google Scholar
Bartlett, M. S. (1965) R. A. Fisher and the last fifty years of statistical methodology. J. Amer. Statist. Assoc. 60, 395–409.Google Scholar
Bartlett, M. S. (1978a) Further analysis of spatial patterns: a re-examination of the Papadakis method of improving the accuracy of randomized block experiments. Suppl. Adv. Appl. Prob. 10, 133–143.Google Scholar
Bartlett, M. S. (1978b) Nearest neighbour models in the analysis of field experiments. J.R. Statist. Soc. B 43, 140–174.Google Scholar
Bartlett, M. S. (1984) Recent investigations involving stochastic population models. Adv. Appl. Prob. 16, 449–470.Google Scholar
Besag, J. and Kempton, R. (1986) Statistical analysis of field experiments using neighbouring plots. Biometrics 42, 231–251.Google Scholar
Brewer, A. C. and Mead, R. (1986) Continuous second order models of spatial variation with application to the efficiency of field crop experiments. J.R. Statist. Soc. A 149, 314–348.Google Scholar
Constantine, G. (1984) Workshop on design and analysis of field-type experiments. CSIRO., DMS Newsletter 101.Google Scholar
Crowther, F. and Bartlett, M. S. (1938) Experimental and statistical technique of some complex cotton experiments in Egypt. J. Exp. Agric. 6, 53–68.Google Scholar
Dagnelie, P. (1987) La méthode de Papadakis en expérimentation agronomique: considérations historiques et bibliographiques Biom.—Praxim. 27, 49–64.Google Scholar
Gleeson, A. C. and Wilkinson, G. N. (1985) Comparison of nearest-neighbour methods for field experiments. Int. Statist. Inst. 45th Session, Contributed Papers, Book 2, 535–536.Google Scholar
Green, P. J., Jennison, C. and Seheult, A. U. (1985) Analysis of field experiments by least squares smoothing. J.R. Statist. Soc. B 47, 299–315.Google Scholar
Kempton, R. A., (ed.) (1984) Spatial methods in field experiments (Papers presented at a Biometric Society Workshop, Univ. of Durham—available on application).Google Scholar
Kempton, R. A. and Howes, C. W. (1981) The use of neighbouring plot values in the analysis of variety trials. Appl. Statist. 30, 159–170.Google Scholar
Martin, R. J. (1986) Design of experiments under spatial correlation. Biometrika 73, 247–277.Google Scholar
Papadakis, J. S. (1937) Méthode statistique pour des expériences sur champ. Bull. Inst. Amél. Plantes à Salonique No. 23.Google Scholar
Papadakis, J. S. (1940) Comparaison de différentes méthodes d'experimentation phytotechnique. Revista Argentina de Agronomia 7, 297–362.Google Scholar
Papadakis, J. S. (1954) Ecologia de los cultivos (2 vol.) Buenos Aires.Google Scholar
Papadakis, J. S. (1970) Agricultural Research. Buenos Aires.Google Scholar
Papadakis, J. S. (1984) Advances in the analysis of field experiments. Proc. Acad. Athens 59, 326–362.Google Scholar
Pearce, S. C. (1980) Randomized blocks and some alternatives: a study in tropical conditions. Trop. Agric. 57, 1–10.Google Scholar
Pearce, S. C. and Moore, C. S. (1976) Reduction of experimental error in perennial crops, using adjustment by neighbouring plots. Exp. Agric. 12, 267–272.Google Scholar
Stigler, S. M. (1986) The History of Statistics. Harvard University Press, Cambridge, Mass.Google Scholar
Wilkinson, G. N. (1984) Nearest neighbour methodology for design and analysis of field experiments. Proc. XIIth Inter. Biom. Conf., Tokyo, 69–79.Google Scholar
Wilkinson, G. N. and Mayo, O. (1982) Control of variability in field trials: an essay on the controversy between ‘Student’ and Fisher, and a resolution of it. Utilitas Math. 21B, 169–188.Google Scholar
Wilkinson, G. N., Eckert, S. R., Hancock, T. W. and Mayo, O. (1983) Nearest neighbour (NN) analysis of field experiments. J.R. Statist. Soc. B 44, 151–211.Google Scholar
Williams, R. M. (1952) Experimental designs for serially correlated observations. Biometrika, 39, 151–167.Google Scholar
Yates, F. and Mather, K. (1963) Ronald Aylmer Fisher. Biog. Mem. of Fellows of the Royal Society, 9, 91–129.Google Scholar