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Split-plot designs and nested designs use the same idea. However, the difference is that split-plot designs are used in experimental studies while nested designs are used in observational studies.
If there are two factors (e.g. A & B) and if the experimenter adopts a split-plot design due to some constraints, such as the of lack of experimental units, then factor-A ("main plot factor") levels can be applied to the main plots, and factor-B ("sub-plot factor") levels can be applied to sub plots within each main plot.
This scenario is otherwise called a completely randomized design (CRD). Here, factor-B levels are nested within each level of factor A. Also, the precision for the estimation of factor B is more than that of factor A in split-plot designs. Thus, before starting the experiment, the experimenter needs to consider which factor needs more attention and then label the main factor and the sub factor.
One common mistake that the experimenter makes, when using the split-plot factor, is to ignore the importance of error terms. In split-plot design, there are two errors. The F value that is calculated for factor A uses error A, and the F value that is calculated for factor B, and its interaction, uses error B.
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