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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?

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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.

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  • $\begingroup$ Thanks very much, Suncoolsu, for the explanation as well as the great resources! Yes, you are right. My split-plot treatment, or subject, should be the 4 individuals within each combination of the two fixed factors, they were sampled 4 times (with one day interval), forming a longitudinal sequences. (But I am totally confused by the terminology of repeated measurement, as I did destructive sampling, but the samples should have temporary correlation in between). $\endgroup$
    – Marco
    Commented Dec 28, 2010 at 1:09
  • $\begingroup$ The BLOCK in my question referred to three whole plots (I call them groups) with 5 days interval (destructive sampling). As a result, all the individuals were sampled in 12 samplings (｛3 groups｝*｛4 samplings in each group｝), the dates from the first sampling is 1-4, 6-9, 11-14 (I also tested the model where all the sampling were taken as one random factor, but it is still not correct, as I only have pseudo-replications, right?). $\endgroup$
    – Marco
    Commented Dec 28, 2010 at 1:10
  • $\begingroup$ The reason for the complicated design is because I have a little bit long term variables (i.e., biomass) which takes effect on the group level, and short term variables (i.e., 14C activity) which could respond quickly within one day. Each group was fertilized, irrigated, and labeled together, and received different water, nutrient, but the same labels. Now, I would like to arrangethe whole experiment like this model<-aov(Var~Group+A*B+Error(Group/A/B/Block),data) But, I do not if it is correct. $\endgroup$
    – Marco
    Commented Dec 28, 2010 at 1:11
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    $\begingroup$ @Marco. Can you please make edits to your original question? This will make it easier to answer similar questions in the future. It will also help me comprehend your design and answer it correctly. Thanks in advance. $\endgroup$
    – suncoolsu
    Commented Jan 16, 2011 at 4:34

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