Restricted Randomization: A Practical Example

Abstract A method of restricted randomization, which avoids bad patterns in the treatments but retains validity in the analysis, is demonstrated on an example that exhibits many features of real agricultural experiments, such as untidy treatment structure and uncertainty about blocking. The method uses permutation groups. Modern farming methods force agricultural experimenters to use long thin lines of plots for blocking, rather than more compact areas. Ordinary randomization of a long thin block can produce a plan with, say, all low levels of nitrogen at one end of the block. The first section of the article discusses why simple rerandomization is not a satisfactory method of avoiding poor layouts. Restricted randomization has been developed as a method of avoiding badly patterned plans while ensuring validity of the usual analysis. One method of restricted randomization uses special groups of permutations of the plots. Catalogs of good restricted randomizations have been given for symmetric factorial de...

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