Can I test the effect of Block in a split plot design in R? I have been confused with the problem for a very long time, and hope that somebody here can help me out.
I have a experiment installed in split-plot design, with 3 temporal groups as blocks, and 2 factors (each have 3 fixed levels) combinations in each of the block, and I have 4 replicates in each treatments. I used to build the model like this:
model <- aov(Var ~ Block+A*B+Error(Block/A/B), data)

where A and B are fixed factors of my focus. It seems that R will calculate the Block as an error term, where only DF, SS and MS were reported, but not F-ratio and p-value. My question is: is it make sense for me to estimate the effect of block (i.e. different time period) in R?
Actually, the 4 replication were sampled in four continuous days to develop a temporal sequence for another analysis. I would like to know how could I test the sampling effect, is it another block, or could be treated as a fixed factor nested within the treatment? 
 A: I think you know this already, but you can calculate the F Statistic by the ratio of MS and the F Statistic follows $F_{df1, df2}$ where df1 and df2 are degrees of freedom of the numerator and denominator.
About your estimating the block effect question: 
First, I don't understand what is your block effect? Normally in split plot design time is not the block, but sometimes it does introduce correlation (like block). Generally, the blocks are the subjects (but if they are blocks as in RBD or samples as in CRD depends on the design)
If I understand your question correctly:
your whole plot treatment is the fixed factor treatment and your split plot treatment is t and you have four observation per individual (lets assume a block). You have got a longitudinal mixed effects model (aka repeated measures). If you have access to SAS can easily handle that using the glimmix (or mixed procedure). All you need to do is impose a temporal correlation (generally AR (1)). If you want to use R, please refer to George Casella's website, an incredible resource for R related experimental design programs. The relevant example for you will be Hypertension.R His book's 5th chapter is my favorite piece on split plot design.
Please let me know if I misunderstood you.
