RE: [R] Anova - adjusted or sequential sums of squares? - An example

From: Berton Gunter <>
Date: Thu 21 Apr 2005 - 05:21:58 EST


At the great risk of having my ignorance publicly displayed, let me say:

  1. I enjoyed and learned from the discussion;
  2. I especially enjoyed WNV's paper linked by BDR -- I enjoyed both the wisdom of the content and the elegance and humor of style. Good writing is a rare gift.

Anyway, I would like to add what I hope is just a bit of useful perspective on WNV's comment in his paper that:(p.14) "... there are some very special occasions where some clearly defined estimable function of the parameters that would qualify as a definition of a main effect to be tested, even when there is an interaction in place, but like the regression through the origin case, such instances are extremely rare and special."

Well, maybe not so rare and special: Consider a two factor model with one factor representing, say process type and the other, say, type of raw materials. The situation is that we have several different process types each of which can use one of the several sources of raw materials. We are interested in seeing whether the sources of raw materials can be used interchangeably for the different processes. We are interested both in the issue of whether the sources of raw materials are assoicated with some consistent effect over **all ** processes and also in the more likely issue of whether only some processes might be sensitive and others not. This latter issue can be explored -- with the caveats expressed in this discussion -- by testing for interactions in a simple 2-way model. However, it seems to me to be both reasonable and of interest to test for the main effect term given the interactions. This expresses the view that the interactions are in fact more likely than main effects; i.e. one expects perhaps a few of the processes to be sensitive in different ways, but not most of them and not in a consistent direction. I think that this is, in fact, not so uncommon a situation in many different contexts.

Of course, whether under imbalance one can actually test a hypothesis that meaningfully expresses this notion is another story ...

As always, I would appreciate other perspectives and corrections, either on list or privately.

"The business of the statistician is to catalyze the scientific learning process." - George E. P. Box    

> -----Original Message-----
> From:
> [] On Behalf Of Ted Harding
> Sent: Wednesday, April 20, 2005 8:54 AM
> To: michael watson (IAH-C)
> Cc:;
> Subject: RE: [R] Anova - adjusted or sequential sums of squares?
> On 20-Apr-05 michael watson \(IAH-C\) wrote:
> > I guess the real problem is this:
> >
> > As I have a different number of observations in each of the
> > groups, the results *change* depending on which order I
> > specify the factors in the model. This unnerves me. With a
> > completely balanced design, this doesn't happen - the results
> > are the same no matter which order I specify the factors.
> >
> > It's this reason that I have been given for using the so-called
> > type III adjusted sums of squares...
> This is inevitable. It's not for nothing that unbalanced "designs"
> are called "non-orthogonal".
> What are the "E" and "NE" effects corresponding to the
> observations plotted at "+" in the following diagram?
> NE
> /
> /
> /
> /
> / +
> /
> o------------------>E
> Best wishes,
> Ted.
> --------------------------------------------------------------------
> E-Mail: (Ted Harding) <>
> Fax-to-email: +44 (0)870 094 0861
> Date: 20-Apr-05 Time: 16:54:21
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> mailing list PLEASE do read the posting guide! Received on Thu Apr 21 06:09:17 2005

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