Design and Analysis of Large Variety Trials.

Variety trials present rather different problems to the statistician from ordinary factorial experiments. They have thus provided the impetus for some very interesting research that has greatly benefitted the practical biologist. This talk will review the resulting methods, and show how design and analysis methodology and computing technology continue to improve the facilities that statisticians can offer.

The key characteristic of these trials is that the main treatment factor (variety or genotype) generally has too many levels for conventional blocking to be used successfully. This led to the development of "incomplete-block" designs that lack the balance required for ordinary analysis of variance. These in turn led to the development of the REML (residual, or restricted, maximum likelihood) algorithm by Patterson and Thompson (1971) to analyze the resulting unbalanced linear mixed models. Best practice in incomplete-block designs for analysis by ordinary REML is probably now achieved by the use of alpha designs and Latinized alpha designs, which can be generated by programs like CycDesigN.

More recent advances in the REML algorithm, however, allow patterns of fertility in the field to be modeled by the fitting of spatial covariance models, and these can provide much more precise and efficient estimates than ordinary blocking. These have led to the development of new design algorithms, involving methods like simulated annealing and Tabu search (Coombes, Payne & Lisboa 2002), that have the aim not only of giving good estimates of varietal effects, but also of providing good estimates of the parameters in the spatial correlation models.

The talk will show how these methods are made easily available by menus in computer programs like CycDesigN (see http://www.cycdesign.co.nz/), Digger and GenStat (see http://www.genstat.co.uk/), and encourage the audience to try them in their future experiments.

References

Coombes, Payne & Lisboa (2002). COMPSTAT 2002, 249-254.

Patterson & Thompson (1971). Biometrika, 58, 545-554