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

Published 2002

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Publication details

Journal : Statistics and computing , vol. 13 , p. 163–167 , 2002

International Standard Numbers :
Printed : 0960-3174
Electronic : 1573-1375

Publication type : Academic article

Contributors : Langsrud, Øyvind

Issue : 2

Links :
DATA : http://link.springer.com/artic...

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Kjetil Aune
Chief Librarian
kjetil.aune@nofima.no

Summary

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.