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

michael watson (IAH-C) michael.watson at bbsrc.ac.uk
Wed Apr 20 15:40:03 CEST 2005


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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