Significant differences on the basis of stable rankings analyzed by the SD technique
AuthorsGeorge A. Baker
Burton J. Hoyle
Authors AffiliationsGeorge A. Baker was Professor of Mathematics and Statistician in the Experiment Station, Davis; Burton J. Hoyle was Specialist in Field Station Administration and Superintendent of the Tulelake Field Station, Tulelake.
Hilgardia 35(22):627-646. DOI:10.3733/hilg.v35n22p627. November 1964.
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.
Hoyle B. J. Tulelake field station, 13th annual report—research 1959. p.20. Mimeo
Hoyle B. J., Baker G. A. Determining the most efficient plot size for potato trials 1960. Amer. Soc. Hort. Sci. Western Meetings, Eugene, Ore., Mimeo.
Hoyle B. J., Baker G. A. Stability of variety response to extensive variations of environment and field plot design. Hilgardia. 1961. 30:365-94E. DOI: 10.3733/hilg.v30n13p365 [CrossRef]
Baker G. A. Fundamental distributions of errors for agricultural field trials. Nat. Math. Mag. 1941. 16:7-19. DOI: 10.2307/3028105 [CrossRef]
Baker G. A. F values for samples of four and four from populations which are the sum of two normal populations. Nat. Math. Mag. 1944. 19:62-63. DOI: 10.2307/3030009 [CrossRef]
Baker G. A. Test of the significance of the differences of per cents of emergence of seedlings in multiple field trials. J. Am. Stat. Assn. 1945. 40:93-97. DOI: 10.1080/01621459.1945.10500731 [CrossRef]
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. Field trial problems. Ann. of Math. Stat. 1952. 23:480 Abstract. DOI: 10.1214/aoms/1177729448 [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. Wheat bunt field trials. J. Amer. Soc. Agron. 1945. 37:127-33. DOI: 10.2134/agronj1945.00021962003700020005x [CrossRef]
Baker G. A., Briggs F. N. Wheat bunt field trials. II. Proc. of Berkeley symposium on math. stat. and prob., 1945-46 1949. pp.485-91.
Baker G. A., Briggs F. N. Yield trials with back-cross derived lines of wheat. Ann. Inst. Stat. Math. 1950. 2:61-67. DOI: 10.1007/BF02919502 [CrossRef]
Baker G. A., Hanna G. C. Transformations of split-plot yield trial data to improve analysis of variance. Proc. Amer. Soc. Hort. Sci. 1949. 53:273-75.
Baker G. A., Huberty M. R., Veihmeyer F. J. A uniformity trial on unirrigated barley of ten years duration. Agron. J. 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]
Baker R. E., Baker G. A. Experimental design for studying resistance of strawberry varieties to verticillium wilt. Phytopathology. 1950. 40:477-82.
Hanna G. C., Baker G. A. Analysis of asparagus field trials on the basis of partial records. Proc. Amer. Soc. Hort. Sci. 1951. 57:273-76.
Hoyle B. J. Stress indicators 1957. Ann. Research Review of Agronomy Staff, Davis, January 28.
Hoyle B. J. Islands 1958. Ann. Research Review of Agronomy Staff, Davis, January 28.
Hoyle B. J., Baker G. A. A more efficient barley yield testing method. Barley News Letter. 1959. 2:32-33.
Hoyle B. J., Baker G. A. The SD technique and its use for conducting field trials 1959. p.4. Mimeo.
Hoyle B. J., Baker G. A. The analysis of field trials based on the concept of islands of variation 1959. pp.16-20. Agron. Abstracts, Amer. Soc. Agron. Cleveland Meetings, November
Hoyle B. J., Baker G. A. Factor analysis of twenty-eight independent field trials on nine strains of Hannchen barley. Biometrics. 1960. 16:127-128. Abstract 633.
Hoyle B. J., Baker G. A. Game theory applied to field trials. Biometrics. 1961. 17:167-68. Abstract 693.
Riddle O. C., Baker G. A. Biases encountered in large-scale yield tests. Hilgardia. 1944. 16:1-14. DOI: 10.3733/hilg.v16n01p001 [CrossRef]
Smith F. L. Effects of plot size, plot shape and number of replications on the efficiency of bean yield trials. Hilgardia. 1958. 28:43-63. DOI: 10.3733/hilg.v28n02p043 [CrossRef]
Waynick D. D. Variability in soils and its significance to past and future soil investigations. I. A study of nitrification in soils. Univ. of Calif. Pub. in Agric. Sci. 1919. 3:243-70.
Waynick D. D., Sharp L. T. Variability in soils and its significance to past and future soil investigations. II. Variations in nitrogen and in field soils and their relation to the accuracy of field trials. Univ. of Calif. Pub. in Agric. Sci. 1949. 4:121-39.
Wiebe G. A. Variation and correlation in grain yield among 1,500 wheat nursery plots. Jour. Agric. Research. 1935. 50:331-57.