# Significant differences on the basis of stable rankings analyzed by the SD technique

#### Authors

George A. BakerBurton J. Hoyle

#### Authors Affiliations

George 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.#### Publication Information

Hilgardia 35(22):627-646. DOI:10.3733/hilg.v35n22p627. 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

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]

### References

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