Comparisons of Sum of Squares Methods in ANOVA Models

Ergun G., Aktas S.

KAFKAS UNIVERSITESI VETERINER FAKULTESI DERGISI, vol.15, no.3, pp.481-484, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 3
  • Publication Date: 2009
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.481-484
  • Hacettepe University Affiliated: Yes


The total sum of squares in ANOVA models is decomposed and the significances of the main term and interaction terms are tested. The four different methods called as Type I, II, III, and IV are used for calculating the sum of squares of the main effects and interactions. The model and data structures are crucial in the selection of the most appropriate method for applications. However, Type III method is adapted as the default sum of square method in most of the standard statistical software packages regardless of model and data structures. If the appropriate method is not selected, it directly affects the value of the F statistic and it may cause statistically invalid inferences. In this paper, the use of the sum of squares methods for various cases are indicated and the differences between the methods are discussed on two examples defined by a two-way ANOVA design.