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On the Analysis of Combined Experiments

Published online by Cambridge University Press:  20 January 2017

David C. Blouin ,
Eric P. Webster  and
Jason A. Bond
David C. Blouin*
Affiliation:
Department of Experimental Statistics, 45 Agricultural Administration Building, Louisiana State University Agricultural Center, Baton Rouge, LA 70803
Eric P. Webster
Affiliation:
School of Plant, Environmental, and Soil Sciences, 104 Sturgis Hall, Louisiana State University Agricultural Center, Baton Rouge, LA 70803
Jason A. Bond
Affiliation:
Delta Research and Extension Center, Mississippi State University, Stoneville, MS 38776
*
Corresponding author's E-mail: dblouin@lsu.edu
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Abstract

The replication of experiments over multiple environments such as locations and years is a common practice in field research. A major reason for the practice is to estimate the effects of treatments over a variety of environments. Environments are frequently classed as random effects in the model for statistical analysis, while treatments are almost always classed as fixed effects. Where environments are random and treatments are fixed, it is not always necessary to include all possible interactions between treatments and environments as random effects in the model. The rationale for decisions about the inclusion or exclusion of fixed by random effects in a mixed model is presented. Where the effects of treatments over broad populations of environments are to be estimated, it is often most appropriate to include only those fixed by random effects that reference experimental units.

La repetición de experimentos en múltiples ambientes, como por ejemplo, lugares y años, es una práctica común en investigaciones de campo. Una de las razones fundamentales para esta práctica es la de estimar los efectos de los tratamientos en una variedad de ambientes. Estos últimos, son frecuentemente clasificados como efectos aleatorios en el modelo de análisis estadístico, mientras que los tratamientos son casi siempre clasificados como efectos fijos. Donde los ambientes son aleatorios y los tratamientos son fijos, no siempre es necesario incluir todas las interacciones posibles entre ellos como efectos aleatorios en el modelo. En este trabajo se presenta la justificación para las decisiones en cuanto a incluir o excluir los efectos fijos por aleatorios, en un modelo mixto. En casos en donde se van a estimar los efectos de los tratamientos sobre poblaciones extensas de ambientes, frecuentemente es más apropiado incluir solamente aquellos efectos fijos por aleatorios que hagan referencia a las unidades experimentales.

Keywords

Fixed effectinteractionmixed modelpredictable functionrandom effect
Type
Education/Extension
Information
Weed Technology , Volume 25 , Issue 1 , March 2011 , pp. 165 - 169
Copyright
Copyright © Weed Science Society of America 

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References

Literature Cited

Blouin, D. C., Taverner, J. D., and Beasley, J. S. 2009. A composite latin rectangle and nonstandard strip block design. J. Agric. Biol. Environ. Stat 14:484–494.Google Scholar
Brien, C. J. and Bailey, R. A. 2006. Multiple randomizations (with discussion). J. R. Stat. Soc. B. 68:571–609.Google Scholar
Brien, C. J. and Demetrio, C. G. B. 2009. Formulating mixed models for experiments, including longitudinal experiments. J. Agric. Biol. Environ. Stat 14:253–280.Google Scholar
Carmer, S. G., Nyquist, W. E., and Walker, W. M. 1989. Least significant differences for combined analyses of experiments with two- or three-factor treatment designs. Agron. J. 81:665–672.Google Scholar
Cochran, W. G. and Cox, G. M. 1957. Experimental Designs. New York Wiley.Google Scholar
Federer, W. T. and King, F. 2007. Variations on split plot and split block experiment designs. Hoboken, NJ Wiley.Google Scholar
Hager, A. G., Wax, L. M., Bollero, G. A., and Stoller, E. W. 2003. Influence of diphenylether herbicide application rate and timing on common waterhemp (Amaranthus rudis) control in soybean (Glycine max). Weed Technol. 17:14–20.Google Scholar
Littell, R. C., Milliken, G. A., Stroup, W. W., Wolfinger, R. D., and Schabenbrger, O. 2006. SAS for Mixed Models. 2nd ed. Cary, NC SAS Institute.Google Scholar
Liu, X. and Raudenbush, S. 2004. A note on the noncentrality parameter and effect size determination for the F test in ANOVA. J. Educ. Behav. Stat 29:251–255.Google Scholar
McIntosh, M. S. 1983. Analysis of combined experiments. Agron. J. 75:153–155.Google Scholar
McLean, R. A. 1989. An introduction to general linear models. Pages. 9–38. in. Applications of Mixed Models in Agriculture and Related Disciplines. Southern Cooperative Series Bulletin No. 343. Baton Rouge Louisiana Agricultural Experiment Station.Google Scholar
McLean, R. A., Sanders, W. L., and Stroup, W. W. 1991. A unified approach to mixed linear models. Am. Statistician 45:54–64.Google Scholar
Milliken, G. A. and Johnson, D. E. 1984. Analysis of Messy Data. Volume I: Designed Experiments. Belmont, CA Lifetime Learning.Google Scholar
Monlezun, C. R., Blouin, D. C., and Malone, L. C. 1984. Contrasting split plot and repeated measures experiments and analyses (with discussion). Am. Statistician 38:21–31.Google Scholar
Redfearn, D. D., Venuto, B. C., Pitman, W. D., Blouin, D. C., and Alison, M. W. 2005. Multilocation annual ryegrass cultivar performance over a twelve-year period. Crop Sci 45:2388–2393.Google Scholar
Sanders, W. L. 1989. Choice of models. Pages. 49–53. in. Applications of Mixed Models in Agriculture and Related Disciplines. Southern Cooperative Series Bulletin No. 343. Baton Rouge Louisiana Agricultural Experiment Station.Google Scholar
SAS 1999. SAS/STAT User's Guide, Version 8, Volume 2. Cary, NC SAS Institute.Google Scholar
SAS 2000. SAS Language Reference: Dictionary, Version 8. Cary, NC SAS Institute.Google Scholar
Schabenberger, O. and Pierce, F. J. 2002. Contemporary statistical models for the plant and soil sciences. New York CRC Press.Google Scholar
Shukla, G. K. 1972. Some statistical aspects of partitioning genotype-environmental components of variability. Heredity 29:237–245.Google Scholar
Steel, R. G. D. and Torrie, J. H. 1980. Principles and Procedures of Statistics: A Biometrical Approach. New York McGraw-Hill.Google Scholar
Stroup, W. W. 1989a. Why mixed models?. Pages. 1–8. in. Applications of Mixed Models in Agriculture and Related Disciplines. Southern Cooperative Series Bulletin No. 343. Baton Rouge Louisiana Agricultural Experiment Station.Google Scholar
Stroup, W. W. 1989b. Predictable functions and prediction space in the mixed model procedure. Pages. 39–48. in. Applications of Mixed Models in Agriculture and Related Disciplines. Southern Cooperative Series Bulletin No. 343. Baton Rouge Louisiana Agricultural Experiment Station.Google Scholar
Yang, R. C. 2007. Mixed-model analysis of crossover genotype-environment interactions. Crop Sci 47:1051–1062.Google Scholar