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Homework 7

Split Plot Analysis 
In this assignment you will be looking at the split plot example
given in section 16.3 of Steel et al. Here D.C. Arny of the
University of Wisconsin was measuring the yields of four lots of
oats for three chemical treatments and an untreated check.  The
data are as follows.
    lots: 1)Vicland1     treatments: 1)Check
          2)Vicland2                 2)CeresanM
          3)Clinton                  3)Panogen
          4)Branch                   4)Agrox
1.     For your own visual interpretation, draw a diagram of the split plot setup used in this experiment.  Something similar to the sketch at the top of page 401 will be fine.
2.     First of all, find the ANOVA table we would have obtained if we had not realized that it is a split plot, that is, analyze it just as a factorial in blocks.  What does this analysis say about the significance of the different factors?
3.     For most experiments we sould expect such a mistake to cause the F tests for whole plots to be ... (too big, too small) and those for split plots to be (too big, too small) (pick the right answers and explain your reasoning BRIEFLY)
4.     Now find the ANOVA table for the split plot design which actually was used.  Find the F-statistics for treatments and for lot*treatment.  How do these compare to those in #1?  Also compare the MSE's of the two models.  What can be said of this? Is this comparison what you'd expect in most split plot situations or is this experiment unusual in this regard (i.e. in terms of what happens if you don't realize it's a split plot)
5.     Note that the F value for seed lot is not the same as that found in Steel et al page 407.  Why is the value given by SAS not correct?  Compute the correct F value and explain what the block*lot interaction is representing here.