Relationships between a Three-Way Classification Disproportionate Numbers Analysis of Variance and Several Two-Way Classification and Nested Analyses

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Abstract
A study was made to determine what information on the sources of variation for a three-way classification analysis of variance was extractable from nested and two-way classification analyses of variance. The case of unequal numbers of observations in the subclasses was considered. Although various analyses of variance produced various and different sums of squares, it was not possible to extract all of the information via the analyses considered in this investigation. Thus, if all the sums of squares for a higher-way classification analysis of variance are desired, it will be necessary to perform the complete analyses; if sums only of various sums of squares are suitable then these may be obtained as described herein.

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