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

[Berton Gunter]

Folks:

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.

-- Bert Gunter
Genentech Non-Clinical Statistics
South San Francisco, CA
 
"The business of the statistician is to catalyze the scientific learning
process."  - George E. P. Box
 
 

> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Ted Harding
> Sent: Wednesday, April 20, 2005 8:54 AM
> To: michael watson (IAH-C)
> Cc: bates at wisc.edu; r-help at stat.math.ethz.ch
> 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) <Ted.Harding at nessie.mcc.ac.uk>
> Fax-to-email: +44 (0)870 094 0861
> Date: 20-Apr-05                                       Time: 16:54:21
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