Splitplot

Splitplot, in experimental design, refers to a split-plot design or split-plot experiment. It is used when there are two or more factors that cannot be randomized at the same experimental unit size or cost, creating a hierarchical structure of units. Typically, one factor, called the whole-plot factor, is applied to larger units (whole plots) and another factor, the subplot factor, is applied to smaller units within each whole plot.

In a standard two-factor split-plot design, whole plots are assigned to levels of the whole-plot factor. Within each whole plot, subplots are formed and randomized to levels of the subplot factor. Replication is achieved across blocks or other grouping structures to manage variability. The arrangement yields two sources of experimental error: a whole-plot error term for assessing the whole-plot factor (and any interactions involving it) and a subplot error term for the subplot factor and its interactions.

Statistical analysis typically uses an analysis of variance or a mixed-effects model that incorporates both error terms. The whole-plot factor is tested against the whole-plot error, while the subplot factor and any interaction with the whole-plot factor are tested against the subplot error. This framework accounts for the different levels of randomization and preserves valid inferences about factor effects.

Applications are common in agriculture, manufacturing, and other fields where some treatments are easier to apply to larger plots than to individual subunits. Variants include designs with multiple whole-plot factors or extended structures such as split-split-plot designs. Advantages include efficient handling of hard-to-randomize factors; drawbacks include more complex analysis and potentially reduced power for whole-plot effects.