Question

why we use type 3 sum of square in SPSS program for two way ANOVA?

Answer 1

Type III sum of squares :

i) First compare the full model with both factors and interaction to the model with only factor 2 and the interaction.

ii) Then, compare the full model with both factors and interaction to the model with only factor 1 and the interaction.

iii) Finally, compare the full model with both factors and interaction to the model with only factor 1 and factor 2.

Type III sum of squares always takes into account an interaction term.

Type I sum of squares are appropriate if you are interested in the incremental effects of adding terms to a model. However, the conclusions will depend on the order in which the terms are entered. If there is really no interaction, Type-II and Type-III are the same for the main effects, and Type-II will have more power.

But, the interaction effect was added for a reason, so in the end, you will use the Type-III sum of squares.