On the Analysis of Variance of a Two-Way Classification with Unequal Sub-Class Numbers

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Abstract
In a two-way classification where interaction can be assumed absent or negligible, a new method of analysis is proposed for the main effects that usually will be more efficient and will be a better approximation to the method of fitting constants than Yates'' weighted squares of means, which has been proposed by various writers. This new method tends to give weight to sub-class means more in proportion to the numbers on which they are based. A set of inequalities is given which depends only on the numbers of observations that can be evaluated to be sure that the new method will be more efficient than Yates'' method. A numerical example is worked out to show the required calculations involved.