Degree Type


Date of Award


Degree Name

Doctor of Philosophy




This thesis is directed toward data analysis and analysis of variance for data in a classificatory structure. Different approaches to looking at data by different authors are examined and some of their results extended;An analysis of variance of data is a partial description of the data. The fitted model is an approximating description of the data. P. D. Finch has worked on the quantification of the quality of a description, in particular, the description of a strong ordering by an ordered dichotomy. His ideas have been extended to ordered polychotomous numerical data and data in some basic ANOVA type structures;D. R. Cox looked at one-way, two-way and three-way classifications of data and obtained the expected mean squares under random permutation. These expected mean squares are expressed simply in terms of the quantities (SIGMA) which are defined as certain combinations of the variance components (sigma). The (SIGMA) are easily derived whether or not there is unit-treatment additivity. The derivations of the (SIGMA) are extended, in this thesis, to the general n-way classification of data;Many authors have written about the mixed model. The controversy with respect to the proper error term when testing for the random factor in the mixed model is examined from several viewpoints;References;Cox, D. R. 1958. The interpretation of the effects of non-additivity in the Latin square. Biometrika 45:69-73;Finch, P. D. 1979. Description and analogy in the practice of Statistics and Probability; Biometrics 3:1-21.



Digital Repository @ Iowa State University,

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Lakshmi Rangachari



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117 pages