Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-19T21:36:21.450Z Has data issue: false hasContentIssue false

Block designs for variety trials

Published online by Cambridge University Press:  27 March 2009

H. D. Patterson
Affiliation:
A.R.C. Unit of Statistics, University of Edinburgh
E. R. Williams
Affiliation:
C.S.I.R.O. Division of Mathematics and Statistics, Canberra
E. A. Hunter
Affiliation:
A.R.C. Unit of Statistics, University of Edinburgh

Summary

In this paper we present a series of resolvable incomplete block designs suitable for variety trials with any number of varieties v in the range 20 ≤v ≤ 100. These designs usefully supplement existing square and rectangular lattices. They are not necessarily optimal in the sense of having smallest possible variances but their efficiencies are known to be high.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Clatworthy, W. H. (1973). Tables of Two-Associate- Class Partially Balanced Designs. Applied Mathematics Series, no. 63. Washington: National Bureau of Standards.Google Scholar
Cochran, W. G. & Cox, G. M. (1957). Experimental Designs, 2nd ed.New York: Wiley.Google Scholar
Harshbarger, B. (1949). Triple rectangular lattices. Biometrics 5, 113.CrossRefGoogle ScholarPubMed
Hedayat, A. (1973). Self orthogonal Latin squares and their importance. Biometrics 29, 393–6.CrossRefGoogle Scholar
Patterson, H. D. & Williams, E. R. (1976). A new class of resolvable incomplete block designs. Biometrika 63, 8392.CrossRefGoogle Scholar
Williams, E. R. (1977). Iterative analysis of generalized lattice designs. Australian Journal of Statistics 19, 3942.CrossRefGoogle Scholar
Williams, E. R. & Patterson, H. D. (1977). Upper bounds for efficiency factors in block designs. Australian Journal of Statistics (in the Press).CrossRefGoogle Scholar
Yates, F. (1936). A new method of arranging variety trials involving a large number of varieties. Journal of Agricultural Science, Cambridge 26, 424–55.CrossRefGoogle Scholar
Yates, F. (1939). The recovery of inter-block information in variety trials arranged in three dimensional lattices. Annals of Eugenics 9, 136–56.CrossRefGoogle Scholar
Yates, F. (1940). The recovery of inter-block information in balanced incomplete block designs. Annals of Eugenics 10, 317–25.CrossRefGoogle Scholar