Abstract
In the previous chapter, statistical designs and analyses were presented for mixtures of n of m cultivars when the individual crop responses were available. In this chapter, statistical procedures are given for mixtures of n of m cultivars when there is a single response for the mixture. The methods presented here represent a generalization of those in Chapter 7 of Volume I. The general topic of this chapter has been considered by Federer and Raghavarao (1987), where they develop some of the required theoretical results. Their minimal designs are for m items taken t + 1 at a time, where t is the order of specific mixing effect being considered; a t th-order effect involves t +1 of the m items. The number of cultivars must exceed 2t + 1. They present solutions for general mixing ability effects, for bi-specific mixing ability effects, and for t = 2 or tri-specific mixing ability effects. Their definition of general combining ability (GMA) is denoted as cultivar effect in the following. The definition of GMA used herein removes the sole crop effect from the cultivar effect. As in the previous chapter, their notation will be followed in most cases.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Literature Cited
Balaam, L.N. (1986). Intercropping—past and present. In Statistical Design. Theory and Practice, Proceedings of Conference in Honor of Walter T. Federer (Editors: C. E. McCulloch, S. J. Schwager, G. Casella, and S. R. Searle), Biometrics Unit, Cornell University, Ithaca, NY, pp. 141–159.
Bush, K. A., W. T. Federer, H. Pesotan, and D. Raghavarao (1984). New combinatorial designs and their application to group testing. J. Statist. Plan. Inference 10, 335–343.
Denes, J. and A. D. Keedwell (1974). Latin Squares and Their Applications. Halstead Press, New York.
Federer, W. T. (1967). Experimental Design-Theory and Application. Oxford & IBH Publishing Co., Bombay. (First published by Macmillan, 1955.)
Federer, W. T. (1979). Statistical design and analysis for mixtures of cultivars. Agron. J. 71, 701–706.
Federer, W. T. (1991). Statistics and Society—Data Collection and Interpretation. Marcel Dekker, Inc., New York, Chapter 5.
Federer, W. T. (1995). A simple procedure for constructing experiment designs with incomplete blocks of sizes 2 and 3. Biometr. J. 37, 899–907.
Federer, W. T. and K. E. Basford (1991). Competing effects designs and models for two-dimensional layouts. Biometrics 47, 1461–1472.
Federer, W. T., A. Hedayat, C. C. Lowe, and D. Raghavarao (1976). Application of statistical design theory to crop estimation with special reference to legumes and mixtures of cultivars. Agron. J. 68, 914–919.
Federer, W. T. and D. Raghavarao (1987). Response models and minimal designs for mixtures of n of m items useful for intercropping and other investigations. Biometrika 74, 571–577.
Fisher, R. A. and F. Yates (1938). Statistical Tables for Biological, Agricultural and Medical Research. Oliver and Boyd Ltd, Edinburgh (5fh edn. 1957.)
Hall, D. A. (1976). Mixing design: A general model, simplifications, and some minimal designs. M.S. Thesis, Cornell University, Ithaca, NY
Hedayat, A. and W. T. Federer (1970). On the equivalence of Mann’s group automorphism method of constructing 0(n, n-1) set and Raktoe’s collineation method of constructing a balanced set of l-restrictional prime-powered lattice designs. Ann. Math. Statist. 41, 1530–1540.
Hedayat, A. and W. T. Federer (1974). Pairwise and variance balanced incomplete block designs. Ann. Inst. Statist. Math. 26, 331–338.
Hedayat, A. and W. T. Federer (1984). Orthogonal F-rectangles for all even n. Calcutta Statist. Assoc. Bull. 33, 85–92.
Jensen, N. F. and W. T. Federer (1965). Competing ability in wheat. Crop Sci. 5, 449–452.
Khare, M. and W. T. Federer (1981). A simple construction procedure for resolvable incomplete block designs for any number of treatments. Biometr. J. 23, 121–132.
Martin, K. J. (1980). A partition of a two-factor interaction, with an agricultural example. Appl. Statist. 29, 149–155.
Raghavarao, D. (1971). Constructions and Combinatorial Problems in Design of Experiments. John Wiley & Sons, Inc., New York.
Raghavarao, D. and W. T. Federer (1979). Block total response as an alternative to the randomized response method in surveys. J. Roy. Statist. Soc, Series B 41, 40–45.
Raghavarao, D., W. T. Federer, and S. J. Schwager (1986). Characteristics distinguishing among balanced incomplete block designs with respect to repeated blocks. J. Statist. Plan. Inference 13, 151–163.
Raghavarao, D. and J.B. Wiley (1986). Testing competing effects among soft drink brands. In Statistical Design. Theory and Practice, Proceedings of Conference in Honor of Walter T. Federer (Editors: C. E. McCulloch, S. J. Schwager, G. Casella, and S. R. Searle). Biometrics Unit, Cornell University, Ithaca, NY, pp. 161–176.
Searle, S. R. (1979). On inverting circulant matrices. Linear Alg. Applic. 25, 77–89.
Smith, L. L., W. T. Federer, and D. Raghavarao (1975). A comparison of three techniques for eliciting truthful answers to sensitive questions. Proceedings, American Statistical Association, Social Statistics Section, pp. 447–452.
Snedecor, G. W. and W. G. Cochran (1980). Statistical Methods, 7th edn., Iowa State University Press, Ames, IA.
Rights and permissions
Copyright information
© 1999 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
(1999). Intercrop Mixtures When Individual Crop Responses Are Not Available. In: Statistical Design and Analysis for Intercropping Experiments. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22647-7_6
Download citation
DOI: https://doi.org/10.1007/978-0-387-22647-7_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98533-6
Online ISBN: 978-0-387-22647-7
eBook Packages: Springer Book Archive