Abstract
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.
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Langsrud, Ø. ANOVA for unbalanced data: Use Type II instead of Type III sums of squares. Statistics and Computing 13, 163–167 (2003). https://doi.org/10.1023/A:1023260610025
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- unbalanced factorial design
- linear model
- fixed effect
- nonorthogonal
- fitting constants
- constraint