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Online Journal of Bioinformatics©


Volume 8 (1):45-55, 2007.

Unbalanced Factorial Design: Use of Type(s) I,  II and III Sums of Squares


Boyacıoğlu H, Baskan O


Ege University Faculty of Science Department of Statistics Bornova 35100 İzmir TURKEY




Boyacıoğlu H, Baskan O, Unbalanced Factorial Design: Use of Type(s) I, II and III Sums of Squares, Online J Bioinformatics, 8 (1):45-55, 2007. Analysis of variance with unbalanced data in biology often presents difficulties. The history of the analysis of variance with unbalanced data can be traced back to Yates  in 1933 and 1934.  Which types of sums of squares(SS) to use for unbalanced designs is controversial. In this study, a two-way analysis of variance (ANOVA) technique with unbalanced data was examined, and in this sense, Type I (Weighted Means), Type II (Yates’s method of fitting constants), Type III (Yates’s weighted squares of means) methods were evaluated. The purpose of this work is to present meaningful evaluations of unbalanced conditions.


Keywords: fitting Constants, unbalanced data, (Posidonia oceanica(L.), weighted means, weighted squares of means