[R] Anova - adjusted or sequential sums of squares?

From: michael watson (IAH-C) <michael.watson_at_bbsrc.ac.uk>
Date: Wed 20 Apr 2005 - 23:40:03 EST


Hi

I am performing an analysis of variance with two factors, each with two levels. I have differing numbers of observations in each of the four combinations, but all four combinations *are* present (2 of the factor combinations have 3 observations, 1 has 4 and 1 has 5)

I have used both anova(aov(...)) and anova(lm(...)) in R and it gave the same result - as expected. I then plugged this into minitab, performed what minitab called a General Linear Model (I have to use this in minitab as I have an unbalanced data set) and got a different result. After a little mining this is because minitab, by default, uses the type III adjusted SS. Sure enough, if I changed minitab to use the type I sequential SS, I get exactly the same results as aov() and lm() in R.

So which should I use? Type I adjusted SS or Type III sequential SS? Minitab help tells me that I would "usually" want to use type III adjusted SS, as type I sequential "sums of squares can differ when your design is unbalanced" - which mine is. The R functions I am using are clearly using the type I sequential SS.

Any help would be very much appreciated!

Thanks
Mick



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