General Solution of the Analysis of Variance and Covariance in the Case of Unequal or Disproportionate Numbers of Observations in the Subclasses

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Abstract
In this paper a preview of the problem is given. Then the mathematical solutions of estimating the sums of squares and products of different sources of variation under different assumptions are presented. Two kinds of populations from which our samples are supposed to be drawn are specified. One is defined as possessing approximately the same stratification as our sample; while the other is defined as having equal frequencies in the subclasses. For the first kind of population, we should use the restrictions of “the weighted means.” For the second kind, we should use the restrictions of “the unweighted means.” The assumptions of zero interactions and significant interactions are also considered. After working out the exact method, two approximate methods with appropriate statistical assumptions to be fulfilled are given.
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