# How to choose between nested or split-plot analysis of variance?

I am having serious problems understanding the type of design I have, I would appreciate any help you can give me to understand it:

I have 324 data points, and four factors:

• epoch factor, with three levels.
• altitudinal floor factor, with three levels.
• site factor, with nine levels.
• time factor, with three levels.

I have four points at each site, I have nine sites, these nine sites are divided in three, three sites correspond to the highest altitudinal floor, three to the middle altitudinal floor and three to the lower altitudinal floor, that give me a total of 36 points, in each point I took data three different times of day, giving me a total of 108 data points. And I repeated these procedure (the exactly same 36 points) in three epochs of the year.

In other words: Each epoch have 108 data points, these 108 are divided in three (the levels of altitudinal floor factor), 36 to each altitudinal floor, these 36 are divided in three (three levels of the site factor), 12 to each site, and these 12 are divided in three (the levels of time factor) each time have 4 data points.

I want know which anova is appropriate for test if there are differences at each factor: a nested anova:

aov(y ~ (epoch/floor/site/time), data=data)


or a split-plot anova:

aov(y ~ floor*site*time + Error(epoch/floor/site/time), data=data)


From what I've read, I think that is a nested design, but I dont understand why it is not a split-plot. Can anyone help me?

-
Is the three-way interaction term in that second model necessary? I thought that the Error term in the anova call would already take that into account, but I could be mistaken. – Jonathan Thiele Jun 17 '12 at 2:33
Yes, it is necessary, if not, adds the sum of squares of each factor in the residual term. – Juan Jun 17 '12 at 3:12
Your design looks like a 2 repeated-measures factors (3 times X 3 epochs) by 2 between-subject factors where one (site) is nested in the other (floor). – ttnphns Jun 17 '12 at 7:34
thank you, that sounds reasonable. Do you have any idea of how write this in R? – Juan Jun 19 '12 at 19:09