Choice between Type-I, Type-II, or Type-III ANOVA We have a dataset with three variables (dV: self-reported measure on scale 1-5, assumed to be metric; iV1: factor with 4 levels; iV2: factor with 8 levels). We are interested whether the dV differs in regard to both iVs and whether there is an interaction between the iVs.
Idea: Calculating an ANOVA with both main effects and the interaction between both iVs using R.
The question: What Type of Sum of Squares should be used for this research question?
Using aov() in R calculates Type-I Sum of Squares as standard. SPSS and SAS, on the other hand, calculate Type-III Sum of Squares by default. However, using Anova() {car} in combination with options(contrasts=c("contr.sum", "contr.poly")) in R gives the same Type-III ANOVA tables as calculated in SPSS.
I have already read the following discussions:


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*http://afni.nimh.nih.gov/sscc/gangc/SS.html

*http://myowelt.blogspot.de/2008/05/obtaining-same-anova-results-in-r-as-in.html
However, I am still confused which Type of Sums of Squares is the most adequate for our question. The results (F and p values) differ considerably.
 A: I have recently made a decision : I will never use again an ANOVA sum-of-squares testing, except for the interaction. Why ? 


*

*Because, in general, the hypothesis $H_0$ of the tests of the main effects are diffcult to interpet.

*Because we can do something really more instructive and interpretable: multiple comparisons with confidence intervals. 
A: I realize this is a year old post but its likely to come up again.
There are many factors that play into this, I'd argue the most important is your hypothesis. So there is no clear answer but I generally follow these rules-of-thumb:
1) Type II is only when you don't have an interaction term.
2) Type I vs Type III to test the interaction term...I go Type I all the time reason is this
Type I SS for dv ~ A + B + A*B depends on order so...its sequential
SS(A)
SS(B|A)
SS(A*B|A B) 
This is great to test your interaction...but not great to test the main effects since the effect of B is dependent on A.
Type II gets around this
SS(A|B)
SS(B|A)
Which looks great to test your main effects IF there is no interaction term.
Type III:
SS(A| A*B B)
SS(B| A*B A)
Which given the most common hypotheses...doesn't seem very useful since most people are interested in the interaction term, not the main effects when an interaction term is present.
So in this case I'd use Type-I to test the interaction term.  If not significant I'd refit without the interaction term and use Type-II to test the main effects.
warning: anova() in R is Type-I, to get Type-II (or III) use the Anova() in the car package.
A: I've never been a fan of Type III SS for ANOVA's so this is a biased recommendation.
I believe you should select Type II in this case.  In the Type I ANOVA order matters.  So, whether you include iV1, or iV2 first makes a difference because the first (e.g. iV1) is compared to a model with just an intercept while the second is compared to a model with an intercept and the first.  Try out switching the order they're in and you'll see the difference in main effect outcomes because your predictors are correlated.
The Type III gets around this by assessing each predictor, including the interaction against a model including everything but that predictor.  That sounds like a good idea until you try to consider what an interaction is without one of the main effects included.  You're comparing the predictor to what is essentially a nonsensical model (I think one of your references sort of goes into this).  (Furthermore, my recollection is that Type III is especially sensitive to missing cells (thus Type IV I believe).)
Type II gets around the order issue in Type I and compares sensible models (unlike Type III).  Main effects are tested with all other main effects in the model but not the interaction.  Thus each main effect is easily interpreted as the unique contribution of that predictor.  
Note, all of the SS types discussed would get the same interaction effect in your case because it's assessed with all of the main effects included in each case.
