Specifying the Error() term in repeated measures ANOVA in R

Question

I am having problems with defining the error terms for a two way repeated measures ANOVA in R. My data consists of wood density estimates for three radial positions (inner, middle, and outer) along a core extracted from a tree. There are a total of 20 tree species, 6 individuals of each species, and two cores from each tree.

To test the effect of radial position on wood density, I use the following two way ANOVA model with an error term that accounts for variability across individuals:

radpos.aov <- aov(WD ~ Species*Radialposition + Error(Individual), data=Radpos)

However, I am not sure if my specification of the error term is adequate. Am I also supposed to account for the variability within a core? To me this variability is the same as that due to radial position which is the main factor I am interested in.

Although I have devoted some time to reading about specifying the error term in Repeated measures ANOVA, I still have problems with practically specifying the error term. I will appreciate some help with this.

Answer 1

It would be

 radpos.aov <- aov(WD ~ Species*Radialposition + Error(Individual/(Radialposition)), data=Radpos)
 summary(radpos.aov, type=3)

That accounts for the within subject error of Radialposition. If you have other within-subject factors, throw them in (in an interaction) with Radialposition in the Error denominator, like + Error(Individual/(Radialpostion*wiFactorA)). That's my understanding of it. That matches up with SPSS's repeated measures GLM if you have no missing data.