The Design and Analysis of Long-Term Rotation Experiments

Rotation experiments are intended to compare different sequences of crop (and possibly husbandry) combinations. To avoid the conclusions being dependent on a specific sequence of years, it is advantageous to phase the start of the experiment, with new replicates of the rotations starting in successive years. Once a complete cycle has taken place, comparisons can then be made between the rotations in every subsequent year. If sufficient resources are available to have more than one replicate in each year, it will be possible to do an interim analysis with the data from a single year. Otherwise meaningful analyses will need several years' data and the assumption, e.g., that higher order interactions can be ignored or that responses over years can be modeled by low-order polynomials. Other analysis complications are that the within-year variances may be unequal and that the correlation between observations on a plot may differ according to the distance in time between them. The old-fashioned method of analysis, feasible if the data are balanced, would be to do a repeated-measurements analysis of variance. A more recent, and more satisfactory, alternative is to do a mixed model analysis by residual (restricted) maximum likelihood estimation, possibly fitting a model to the between-year correlation structure. The issues are illustrated using data from the Woburn Ley-Arable Experiment.