# [R] Formulating anova for partially nested model

Yves Brostaux brostaux.y at fsagx.ac.be
Tue Nov 20 17:57:47 CET 2001

```Hello,

I'm trying to analyse data from an incomplete design with four factor :
- fr : number of the batch
- op : ID of operator
- meth : method used
- mat : nature of the material used
and one variable
- mv : mesure
- trmv : transformed mesure

str(matvol)
`data.frame':   120 obs. of  6 variables:
\$ fr  : Factor w/ 30 levels "1","2","3","4",..: 1 1 1 1 2 2 2 2 3 3 ...
\$ op  : Factor w/ 3 levels "1","2","3": 3 3 3 3 1 1 1 1 2 2 ...
\$ meth: Factor w/ 2 levels "1","2": 2 2 2 2 1 1 1 1 2 2 ...
\$ mat : Factor w/ 5 levels "1","2","3","4",..: 1 5 2 4 2 1 3 5 2 1 ...
\$ mv  : num  0.761 0.806 0.837 0.264 0.799 ...
\$ trmv: num  2.12 2.23 2.31 1.08 2.21 ...

op, meth and mat are crossed and fr is nested in op*meth interaction. op
and fr are taken as random. For each batch, only 4 on the total 5 matrices
are mesured (oven constraint), and op and meth are constant.

I spent time trying every kind of aov models seeming sensible to me, read
the according chapters in MASS2 and still didn't succeed writing the
formula to obtain the results I expected (e.a. meth tested vs meth*op, mat
vs mat*op, etc.).

Can someone bring some light to my clouded mind ?

Y. Brostaux
=====================================================================
YVES BROSTAUX - Ingénieur agronome Orientation Eaux & Forêts
Assistant - Unité de Statistique et Informatique
Gembloux Agricultural University
8, avenue de la Faculté B-5030 Gembloux (Belgium)
Tél:      +32 (0)81 62 24 69
E-mail :  brostaux.y at fsagx.ac.be
=====================================================================

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```