Roger W. Payne, Rothamsted Research, Harpenden, Herts, AL5 2JQ, United Kingdom
Unreplicated experiments have presented a challenge to statisticians throughout their involvement in agricultural research. At Rothamsted this began in 1919, when R.A. Fisher was appointed to analyse the accumulated data from the classical field experiments. Fisher's experiences with the classicals, which had virtually no replication, must have contributed to his inclusion of Replication as one of one of the three "R's" of experimental design (the other two being Randomization and Blocking)! Nevertheless, Fisher made good use of the classical data, for example in his study of the influence of rainfall on yields from the Broadbalk experiment. The over-160 years of data from Broadbalk is recognised as a unique resource for studying long-term issues such as sustainability and climate change. In particular, I shall describe its use for assessing various ways of measuring sustainability, and discuss how the conclusions from such analyses should take account of the deficiencies of the original design. In traditional experimental designs where several treatment factors are studied, it is not essential to include every combination of the factor levels, provided you are willing to make assumptions about which factors may interact with one another. Well-established theory is available to construct effective designs. These have proved very popular particular in industrial applications, and could perhaps be used more often in biology. More recent developments have been concerned to find alternatives to use, instead of blocking, to take account of the spatial variation within an experiment. The resulting methods for modelling spatial correlations have allowed experimenters to obtain more precise estimates of treatment effects - or to decrease numbers of replicates - and they can often provide reliable analyses of unreplicated data. Other useful methods include randomization and bootstrap tests, originally developed to avoid assumptions about the distribution of the data.
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