# Uniformity field trials and Monte Carlo simulations

#### Authors

George A. BakerJohn P. Johnson

#### Authors Affiliations

George A. Baker was Professor of Mathematics and Statistician in the Experiment Station, Davis; John P. Johnson was at the time of these studies graduate student at the University of California, Davis, and is at present graduate student in statistics at Iowa State University, Ames.#### Publication Information

Hilgardia 35(22):615-625. DOI:10.3733/hilg.v35n22p615. November 1964.

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#### Abstract

In the first paper, actual uniformity field trials are examined and it is found that analyses based on conventional mathematical models may assess very poorly the probabilities used in detecting significantly different varieties.

Monte Carlo results show changes in the mathematical model of field trials that can give probability distributions that correspond closely to the distributions observed for actual trials.

In the second paper, emphasis is placed on reproducibility of field plot results as the most desirable evaluation. Techniques by which a stable ranking among treatments can be obtained (i.e.: A is better than B) are discussed as a matter of field plot manipulation. Examples are given where reproducibility, as measured by the SD technique in a single year, is applicable to a high degree of certainty to results based on several years’ experience. The SD technique provides a confidence limit depending on design, and the values of the limits are computed.

A reproducible ranking order is held to be desirable and the problems of securing one are discussed. Techniques are offered which simplify obtaining a stable ranking. Mathematical formulas are given by which given cut-off points of confidence can be calculated. Adequate field plot decisions are based on both agronomic usefulness and mathematical confidence. The SD technique is shown to fulfill both of these considerations.

#### Literature Cited

Baker G. A. Distribution of the means divided by the standard deviations of samples from nonhomogeneous populations. Ann. of Math. Stat. 1932. 3:1-9. DOI: 10.1214/aoms/1177732927 [CrossRef]

Baker G. A. Fundamental distribution of errors for agricultural field trials. Nat’l. Math. Mag. 1941. 16:1-13.

Baker G. A. Uniformity field trials when differences in fertility levels of subplots are not included in experimental error. Ann. of Math. Stat. 1952. 23:289-93. DOI: 10.1214/aoms/1177729448 [CrossRef]

Baker G. A. Empiric investigation of a test of homogeneity for populations composed of normal distributions. Jour. of Amer. Stat. Ass’n. 1958. 53:551-57. DOI: 10.1080/01621459.1958.10501459 [CrossRef]

Baker G. A., Baker R. E. Strawberry uniformity yield trials. Biometrics. 1953. 9:412-21. DOI: 10.2307/3001713 [CrossRef]

Baker G. A., Briggs F. N. Yield trials with backcross derived lines of wheat. Ann. of Inst. of Stat. Math. 1950. 2:61-67. DOI: 10.1007/BF02919502 [CrossRef]

Baker G. A., Huberty M. R., Veihmeyer F. J. A uniformity trial on unirrigated barley of ten years’ duration. Agron. Jour. 1952. 44:267-70. DOI: 10.2134/agronj1952.00021962004400050011x [CrossRef]

Baker G. A., Roessler E. B. Implications of a uniformity trial with small plots of wheat. Hilgardia. 1957. 27:183-88. DOI: 10.3733/hilg.v27n05p183 [CrossRef]

Hanna G. C., Baker G. A. Transformation of split-plot yield trial data to improve analysis of variance. Proc. of Amer. Soc. for Hort. Sci. 1949. 53:273-75.

Hoyle B. J., Baker G. A. Stability of variety response to extensive variations of environment and field plot designs. Hilgardia. 1961. 30:365-94E. DOI: 10.3733/hilg.v30n13p365 [CrossRef]

Riddle O. C., Baker G. A. Biases encountered in large-scale yield tests. Hilgardia. 1944. 16:1-14. DOI: 10.3733/hilg.v16n01p001 [CrossRef]