A method is proposed for estimating intra-block and inter-blook weights in the analysis of incomplete block designs with block sizes not necessarily equal. The method consists of maximizing the likelihood, not of all the data, but of a set of selected error contrasts. When block sizes are equal results are identical with those obtained by the method of Nelder (1968) for generally balanced designs. Although mainly concerned with incomplete block designs the paper also gives in outline an extension of the modified maximum likelihood procedure to designs with a more complicated block structure.
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