Relative Efficiency of The Split-Plot Design

Abstract

Formulae are given to calculate the efficiency of the split-plot design, in which whole-plot treatments are arranged in randomized complete blocks. Efficiency for each of the whole-plot and split-plot treatment comparisons is discussed relative to three simpler designs. Tables are given to facilitate calculations for experiments in which up to five whole-plot treatments and five split-plot treatments are tested, using four, six or eight blocks.Split-plot designs are frequently used in agricultural experiments when two or more factors are studied, with levels of one or more factors representing the whole-plot treatments and those of one or more other factors representing the split-plot treatments. In their simplest form, split-plot designs involve the random assignment of the whole-plot treatments to the whole plots according to the completely randomized, randomized complete-block or Latin-square designs, after which the split-plot treatments are allotted at random to the split plots within each whole plot. The use of split-plot designs is recommended in the following cases:1. If the plots required for one or more of the factors are larger than those for the remaining factor (s), in which case the larger plots (whole plots) are used for whole-plot treatments and the smaller ones (split plots) for split-plot treatments; e.g. irrigation treatments, methods of fertilizer application or land preparation require large plots, whereas varieties, seed rates or seed treatments can be compared using much smaller plots, 2. If the experimenter is interested in comparing the levels of one or more factors more precisely than those of the other factor (s), in which case higher precision is required for comparisons among split-plot treatments as well as the interaction between whole-plot and split-plot treatments; e.g. the experimenter may already have information on the effects of the wholeplot treatments, and is mainly interested in their interaction with the split-plot treatments, expecting variation among adjacent split plots to be less than among adjacent whole plots, and therefore precision to be higher for comparisons involving split-plot treatments, and 3. If the experimenter wishes to introduce one or more extra factors at a later stage of the experiment.Split-plot designs have several disadvantages when compared with ordinary factorial experiments, in which all treatment combinations of the levels of the