Some comments on gerechte designs. II. Randomization analysis, and other methods that allow for inter-plot dependence

In a companion paper we derived the correct analysis for gerechte designs with uncorrelated errors. Here we show that this correct analysis cannot be justified by the usual randomization argument. However, when the regions are rectangular there is a randomization procedure which validates an analysis with three separate error terms. We also outline other developments in design and analysis that may be more satisfactory.