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ANOVA for unbalanced data: Use Type Ⅱ instead of Type Ⅲ sums of squares

机译:不平衡数据的ANOVA:使用Ⅱ型而不是Ⅲ型平方和

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摘要

Methods for analyzing unbalanced factorial designs can be traced back to Yates (1934). Today, most major statistical programs perform, by default, unbalanced ANOVA based on Type Ⅲ sums of squares (Yates's weighted squares of means). As criticized by Nelder and Lane (1995), this analysis is founded on unrealistic models―models with interactions, but without all corresponding main effects. The Type Ⅱ analysis (Yates's method of fitting constants) is usually not preferred because of the underlying assumption of no interactions. This argument is, however, also founded on unrealistic models. Furthermore, by considering the power of the two methods, it is clear that Type Ⅱ is preferable.
机译:分析不平衡阶乘设计的方法可以追溯到Yates(1934)。今天,大多数主要的统计程序默认都基于Ⅲ类平方和(Yates的均值加权平方)执行不平衡ANOVA。正如Nelder和Lane(1995)所批评的那样,这种分析是建立在不现实的模型之上的,即具有相互作用但没有所有相应主要影响的模型。通常不推荐使用Ⅱ型分析(Yates的拟合常数方法),因为其基本假设是没有相互作用。但是,该论点也建立在不现实的模型上。此外,考虑到两种方法的功效,很明显Ⅱ型是优选的。

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