Overview of split-plot designs

Split-plot designs occur in a wide range of applications of experimental design. One application area for split-plot designs is when there are some variables that can be applied only to experimental units that are larger than the units to which the other variables can be applied. 

A second application area is when there is a variable that is difficult or expensive to change and so the randomization is restricted to limit the number of changes of that variable. This is accomplished by conducting the experiment in blocks with the restricted variable held constant within a block, but changed randomly between blocks. In this case the large experimental units are the blocks and the smaller experimental units are the individual runs within a block. 

An excellent exposition of split-plot experimental designs can be found in D.R. Cox s book, Planning of Experiments [42]. He states that split-plot designs are particularly useful when one (or more) factors are what he calls classification factors. These factors are included in the experiment to determine whether they modify the effect of the other factors or indicate how the other factors work. The classification factors are included to examine their possible interaction with the other factors. Lower precision is tolerated for comparisons of the classification factors, in order that the precision of the other factors and the interactions can be increased. In the standard terminology associated with split-plot experiments, the classification factors are called whole-plot factors and are applied to the larger experimental units. The smaller experimental units are called subplots. 

In the following subsections several alternative experimental arrangements of split-plot experiments will be considered. The tablet formulation data given in the example of Table 2.1 in Section 2.1.1 will be 

Design (I) environmental factors as whole-plot factors Using Cox s concept of classification factors, it seems most reasonable to have the classification factors, that is the whole-plot factors, associated with the environmental variables, since they are in fact included primarily to examine their possible interaction with the design variables. Thus, the first arrangement considered is one in which the whole plots contain the environmental variables and the subplots contain the design variables. 

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