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STATISTICS

Combining Results from Augmented Designs over Sites

^a Dep. of Biometrics, 434 Warren Hall, Cornell Univ., Ithaca, NY 14853
^b Wheat Program, CIMMYT, Lisboa 27, Apdo. Postal 6-641, Mexico D.F., Mexico
^c Biometrics and Statistics Unit, CIMMYT, Lisboa 27, Apdo. Postal 6-641, 06600 Mexico D.F., Mexico

Corresponding author (wtf1{at}cornell.edu)

The class of augmented designs contains two kinds of treatments, standard or check and new or augmented. The latter are usually considered to be random effects while the check treatments are considered as fixed effects. New treatments are usually not replicated and the checks are replicated as points of reference. An augmented experiment design is a screening design. It is obtained by selecting any experiment design for the check treatments and then enlarging the blocks or increasing the number of rows and/or columns to accommodate the new treatments. The new treatments are randomly distributed among the blocks or among the rows and columns. An augmented design has many advantages over systematic check arrangements and is useful for shortening the selection cycle over standard methods. Statistical procedures are available for recovering inter-block or inter-row-column and inter-variety information at each site. Procedures are presented herein for combining the results from single experiments over sites. Inter-site information may be recovered for random site effects. The method recommended for combining results is invariant to experiment design changes, variance heterogeneity, changes in checks from site to site, and different response models for each site. An experiment involving 120 new wheat genotypes and checks was conducted at three sites. It is used to illustrate the statistical procedure for combining results over sites. The new wheat genotypes exhibited a relatively large genotype x site interaction, indicating their site and environmental specificity.

Abbreviations: RCBD, randomized complete block • ICBD, an incomplete block • ANOVA, analysis of variance • REML, restricted maximum likelihood • smean, standardized means

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