I have an experiment to check factors that influence the results of a

measurement which is done like this:

Several pieces of substrate are selected (a kind of paper), on each

substrate a left and a right side area is defined and in each area five

measurement points going from top to bottom. Then the slips are painted with a machine and various quality measures of the painting captured in each point.

So, each substrate receives the same treatment (except for random variation

in the painting process of course) and the results are measured at each

measurement point.

The objective of the exeriment is to investigate whether there are

systematic diferences in the results, due to differences in the

substrate, the side which is measured (i.e. left or right) or the

position of the measurement points (from top to bottom).

So, my questions are:

1. This design needs to be analysed with a nested ANOVA, right?

2. If using R the error term shuld be Error(Substrate/Side/Points)?

and most importantly

3. I do not get a p-value for the highest level (Substrate). I checked

in the Crowley book and the example he uses for split-plot designs also

does not have a p-value for the highest level, however this is not

commented in any way in the book. If I do a nested ANOVA with Minitab

(same data) I get a p-value for the Substrate variable, so my question

is: why do I not get a p value with the evaluation of the nested design

in R ?