Determination of optimum plot size has been regarded as an important and useful area of study for agriculturists and statisticians since the first remarkable contribution on this problem came to light in a paper by Smith (1938). As we explore the scientific literature relating to this problem, we may note a number of contributions, including those of Modjeska and Rawlings (1983), Webster and Burgess (1984), Sethi (1985), Zhang et al. (1990, 1994), Bhatti et al.(1991), Fagroud and Meirvenne (2002), etc. In Pal et al. (2007), a general method was presented by means of which the optimum plot size can be determined through a systematic analytical procedure. The importance of the procedure stems from the fact that even with Fisherian blocking, the correlation among the residuals is not eliminated (as such the residuals remain correlated). The method is based on an application of an empirical variogram constructed on real-life data sets (obtained from uniformity trials) wherein the data are serially correlated. This paper presents a deep and extensive investigation (involving theoretical exploration of the effect of different plot sizes and shapes in discovering the point – actually the minimum radius of curvature of the variogram at that point – beyond which the theoretical variogram assumes stationary values with further increase in lags) in the case of the most commonly employed model (incorporating a correlation structure) assumed to represent real-life data situations (uniformity trial or designed experiments, RBD/LSD).
@article{bwmeta1.element.doi-10_1515_bile-2015-0002,
author = {Satyabrata Pal and Goutam Mandal and Kajal Dihidar},
title = {Determination of robust optimum plot size and shape -- a model-based approach},
journal = {Biometrical Letters},
volume = {52},
year = {2015},
pages = {13-22},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_bile-2015-0002}
}
Satyabrata Pal; Goutam Mandal; Kajal Dihidar. Determination of robust optimum plot size and shape – a model-based approach. Biometrical Letters, Tome 52 (2015) pp. 13-22. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_bile-2015-0002/
Bhatti A.U., Mulla D.J., Koehler F.E., Gurmani A.H. (1991): Identifying and removing spatial correlation from yield experiments. Soil Sci. Soc. Am. J. 55: 1523-1528.
Cressie N.A.C. (1993): Statistics for Spatial Data. John Wiley, New York. | Zbl 06439472
Cressie N., Wikle C.K. (2011): Statistics for Spatio-Temporal Data. Pub. A John Wiley & Sons. Inc. | Zbl 1273.62017
Faground M., Meirvenne M. Van (2002): Accounting for Soil Spatial Autocorrelation in the design of experimental trials. Soil Sci. Soc. Am. J. 66: 1134-1142.
Matheron G. (1963): Principles of geostatistics. Economic geology 58: 1246-1266.
Modjeska J.S., Rawlings J.O. (1983): Spatial correlation analysis of uniformity data. Biometrics 39: 373-384. | Zbl 0527.62097
Pal S., Basak S., Pal S., Kageyama S. (2007): On determination of optimum size and shape of plots in field trials. Biometrical Letters 44(1): 23-31.
Sethi A.S. (1985): A modified approach to determine the optimum size and shape of plots in field experiments on maize grown on terraced land. Indian Jour. of Agric. Sci. 55 (1): 48-51.
Smith H.F. (1938): An empirical law describing heterogeneity in the yields of agricultural crops. Jour. of Agricultural Science, Cambridge 28: 1-29.[Crossref]
Webster R., Burgess T.M. (1984): Sampling and bulking strategies for estimating soil properties in small regions. J. Soil Sci. 35: 127-140.
Zhang R, Warrick A.W., Myers D.E. (1990): Variance as a function of sample support size. Math. Geol. 22(1): 107-121.[Crossref]
Zhang R, Warrick A.W., Myers D.E. (1994): Heterogeneity, plot shape effect and optimum plot size. Geoderma 62: 183-197.