My background is not mathematics and I do not really understand what this mathematical symbols means: Type I SS: SS(A) SS(B|A) SS (AB|A, B) Type II SS: SS(A|B) SS(B|A) SS (AB|A, B) Type III SS: SS (A|B, AB) SS (B|A, AB) SS (A*B|A, B)?
By reading, as I've understood; Type II is only when we don't have an interaction. But I've not convinced what the difference between TypeI and Type III?
Can you help me to understand above notations and TypeI,II,III SS for ANOVA in a simplified way?
Type $I$ is when the order of including matters. I.e., assume that you have factors $A$ and $B$, hence the sum of squares are $S(A)$, then $S(B|A)$ and finally $S(A\times B|A, B)$. While in Type $III$, the order doesn't matter, i.e., all the sum of squares are conditioned on all the other terms, namely $S(A|B, A\times B)$, $S(B|A, A\times B)$ and $S(A\times B|A, B)$. Hence, in the interaction terms Type $I$ and $III$ are equivalent.