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

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Øyvind Langsrud at Statistisk sentralbyrå
Øyvind Langsrud
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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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Statistics and Computing
April 2003, Volume 13, Issue 2, pp 163-167
ANOVA for unbalanced data:
Use Type II instead of Type III
sums of squares
Øyvind Langsrud
According to the policy of Springer this is an accepted manuscript version of the article.
The final publication is available at Springer via
http://dx.doi.org/10.1023/A:1023260610025
... Thus, the mice with locomotor values falling into the first quartile were classified as non-sensitized and those with locomotor activity values falling above the first quartile were considered sensitized animals. Given the distinct number of mice in the sensitized and non-sensitized groups we used sums of square type II in the ANOVA model (Langsrud 2003). This analysis was conducted using the software R version 4.3.2 ...
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