I am trying to understand Type I/II/III sums of squares. Take for instance the 2 way Anova with 2 factors A and B.

I do not follow what Type III Sums of Squares are. In type III sums of squares we account for the main effect (say A) AFTER removing the effect of the other main effect(B) + interaction(AB). My query is : IF there is interaction, how can we have a main effect for A ? We would have simple effects for both factors and not a main effect.

Can someone clear my doubt ?

  • $\begingroup$ +1 you seem to be correct. Main effect can not be ascertained in the said manner. $\endgroup$ – Subhash C. Davar Dec 10 '17 at 8:04
  • $\begingroup$ You have not mentioned why do you think like that. It may be useful to know the details. $\endgroup$ – Subhash C. Davar Dec 10 '17 at 10:49
  • $\begingroup$ I think I am incorrect. We can have interaction over and above the main effect of variables A and B. So when we control for B and the interaction we get the main effect of A as if there had there been no interaction or effect of B. I am a little confused myself : ). $\endgroup$ – user2338823 Dec 10 '17 at 11:55
  • $\begingroup$ I understand that the main effect is the direct effect and second or secondary effect is something like second-stage or residual effect once you presume existence of interaction. There is nothing wrong with you. The method to determine main effect - type III is incorrect. $\endgroup$ – Subhash C. Davar Dec 10 '17 at 13:30
  • $\begingroup$ Okay, please allow me to rephrase. We assume that there is no interaction in type II SS. In type III we allow for interaction. This interaction is AFTER controlling for the main effect of A and B. Also the main affect is AFTER allowing for interaction. I think type III is correct. $\endgroup$ – user2338823 Dec 11 '17 at 5:01

I know it's late on this thread, but Wm Venables wrote an essay expressing your suspicion about Type iii SS. For about 10 years after that, I was terrified of type iii anything

Bill Venables Exegeses on Linear Models http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf

That's a lively read.

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