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Abstract:
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Split plot designs and, more generally, multistratum designs arise due to restrictions in the randomization, so that different factors are randomized to different-sized experimental units. Thus, it is natural to explore how far randomization-based analysis, based on minimal model assumptions, can lead. For orthogonal multistratum designs, randomization-based methods give an essentially complete analysis, such as the usual split plot analysis. In response surface experiments, however, the designs are usually nonorthogonal. In this paper, it will be shown that randomization leads naturally to separate analyses in each stratum, but that there is no obvious way to combine them. Combination of information usually is done using REML and GLS. A modified method, which uses the estimates of pure error variance in each stratum, and GLS will be recommended instead as being more robust.
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