Theory of Cyclic Rotation Experiments

The paper reviews some of the statistical problems arising in the design and analysis of long-term cyclic experiments comparing different crop rotations. Three types of design are distinguished and their properties considered. These are basic designs with all phases of the rotations in each block, reduced designs with mutually exclusive groups of phases kept in separate blocks and phase-confounded designs in which some contrasts between test crops are partially confounded with block differences. Methods of analysing the yields of test crops by estimating the mean effects of the rotations over the years and regressions on seasonal and time variates are discussed theoretically for replicated experiments of basic or reduced design. The analysis is complicated by correlations between yield values recurring on the same plots and by lack of homogeneity in residual year-to-year variations in rotation effects. The main topics considered are (1) the estimation of errors, (2) the losses of information due to using unweighted means and regressions ignoring the correlations, (3) methods for recovering this information.