一般线性模型中的Yates MWSM SS
Yates's MWSM SS in the General Linear Model
摘要：
1934年，F. Yates描述了用于检验两个因子效应的饱和非平衡模型中因子主效应的平方和。他声称没有特别的属性，这一总和的平方以外，它提供了一个“有效估计的方差从A手段的子类手段. .虽然它被广泛认为是双因子模型中的黄金标准，但它的基本性质以及与同一模型的其他平方和的关系直到几十年后才建立起来。它的方法还没有扩展到更一般的设置。本文介绍如何将Yates的方法推广到一般线性模型中线性假设的检验统计量的分子平方和的构造。它表明，耶茨的平方和是等效的限制模型-全模型误差平方和的差异，这反过来又被证明是唯一的平方和，测试正是假设的问题。
英文摘要：
In 1934, F. Yates described a sum of squares for testing factor main effects in saturated unbalanced models for effects of two factors. He claimed no particular properties of this sum of squares other than that it provided an "efficient estimate of the variance from the A means of the sub-class means... ." Although it became widely regarded as the gold standard in the two-factor model, its fundamental properties and relations to other sums of squares for the same model were not established until decades later. Its method has not been extended to more general settings. This paper shows how Yates's approach can be extended to construct numerator sums of squares for test statistics for linear hypotheses in general linear models. It is shown that Yates's sum of squares is equivalent to the restricted model - full model difference in error sum of squares, which in turn is shown to be the unique sum of squares that tests exactly the hypothesis in question.
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