[R] Paritioning of Interaction SS in ANOVA - Gomez and Gomez(1984) example

peter dalgaard pdalgd at gmail.com
Thu May 9 18:01:13 CEST 2013

On May 9, 2013, at 13:58 , Lundrigan, Cyril wrote:

> Hello
> I'm a new user of R and I'm using Deducer as the interface but also
> making use of the command interface where necessary.  I'm trying to
> replicate Table 6.18 on page 262 in Statistical Procedures in
> Agricultural Research, by K. A. Gomez and A. A. Gomez. New York,
> Chichester, etc.: Wiley (1984).
> http://pdf.usaid.gov/pdf_docs/PNAAR208.pdf.  This example is highly
> relevant to the type of data we will be analyzing in our department but
> nobody here has experience doing partitioning of interactions with
> software.

(Did you _have_ to give us a 600 page book to download to look at one table??)

This was likely done manually, and the syntax therefore may be a bit idiosyncratic, but according to what I _think_ is going on, you could set up Ta, Tb,..., Te as vectors or matrices with specific contrasts and then replace the term T:P in the model by


As far as I can tell, 

Ta is a vector which is 1 when T=7, 0 elsewhere
Tb is 1 when T=8
Tc is 1 when T=2 or T=5
Td is 1 when T=2
Te is a matrix with three columns
 one is 1 when T=3
 one is 1 when T=4
 one is 1 when T=6

(you can probably also do this via releveled versions of the T factor in which certain levels are combined.)

> I've managed to replicate all previous steps for that particular
> exercise up to this point. If I interpret the syntax correctly, the
> table is showing comparisons of specific treatment combinations within
> the time variable P. Is this the correct interpretation?  If so, I don't
> know how to achieve that with R.  I had initially used SYSTAT for this
> exercise and had sent the problem along to their support person and
> after a few days the response was that he did not understand the syntax
> and, thus, could not replicate the table results. Unfortunately, it's
> also one of the few Gomez and Gomez examples not covered in the
> "agridat" package. I was trying to do the partiioning with
> interactionMeans and testInteractions functions in phia package but made
> no headway.  Greatly appreciate any help or direction with this.
> Thanks!
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Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

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