Split-Plot Factorial Design

A Sample Design

Consider an experiment in which the effect of different types of nitrogen and grain varieties on the grain yield is investigated. Usually, it is convenient to treat entire plots of land (the whole plots) with the same type of nitrogen, whereas different grain varieties can typically be planted on small plots of land (the subplots) obtained by splitting each whole plot that was treated with one kind of nitrogen only. In this experimental setup, the first factor, the type of nitrogen, is called the whole-plot factor because its levels are applied to whole plots. The factor grain variety is called the subplot factor of the experiment because its levels are applied to the subplots. A schematic representation of a split- plot design involving type of nitrogen as the whole-plot factor and grain variety as the subplot factor is displayed in Figure 1. The four levels of the whole-plot factor are denoted by N1 − N4, whereas the three levels of the subplot factor are represented by G1 − G3. The split-plot design in this example has only one whole-plot factor and one subplot factor. Nevertheless, split-plot factorial designs with more than one whole-plot factor and more than one subplot factor can be constructed too. An example of a design with two whole-plot factors is given in the following discussion.

Design Layout

The layout of a split-plot design resembles that of a randomized block design. The key difference between split-plot designs and randomized block designs is that, in randomized block designs, the factor level combinations are randomly assigned to the experimental units in the blocks. In split-plot designs, a completely random assignment is impossible because all the subplots within one whole plot must be treated with the same level of the whole-plot factor(s). Because of this restriction on the assignment of factor-level combinations to the plots, only a restricted form of randomization is possible. The restricted randomization is carried out in [Page 1581]two steps. First, the whole-plot factor-level combinations are randomly assigned to the whole plots. Next, the subplot factor-level combinations are randomly assigned to the subplots within each whole plot. This is done so that each subplot factor-level combination appears once in every whole plot.

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