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Abstract The paper contains a description of the extent to which the use of randomization in experimental designs permits evaluation of the experimental results. The case considered is that in which the whole population of treatments is used with particular experimental material. A completely general mathematical specification of the design is given and the procedure by which linear models for the experimental results are derived is exemplified by the cases of the completely randomized design, randomized blocks, Latin squares, and a particular systematic design. The case of the completely randomized design is discussed extensively. An assessment of the present state of randomization theory is given, with a statement of major deficiencies.
Oscar Kempthorne (1955) studied this question.