Split-plot is a type of nested design. The phrase comes from Statistics' youth, spent at the agricultural testing station of Rothhamstead, UK, where so many different experimental designs were created. Split-plots really were portions of plots. You might put a particular type of fertilizer over an entire plot, and then plant different varieties of peas on that plot. A different plot would have different fertilizer - but the same varieties of pea. So you envisage 2 or more factors, but different levels of randomization. Fertilizers are randomly assigned to plots - then for each plot, variety is randomly assigned to the split portion. All nested designs have that feature: different levels of randomization, applied to different subjects.
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