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Statistics 601, Fall 2006
Lab 1 Notes
This lab concerns the analysis of a nutrient enrichment experiment conducted in
Sinagarind Reservoir in Thailand that also constitutes Example 4.3 in the lecture
notes. The data are given in the table on page 99 of the notes. The design of the
experiment will be explained in lab. The treatments of concern are C: control, P:
phosphorus, N: nitrogen, and NP: both nitrogen and phosphorus. The lecture notes
contain a description of a randomization test conducted using all permutations of
experimental units assigned the C, P, and N treatments. In this lab we wish to
conduct a similar test using all four treatments. The following points are relevant.
1. In the example of the notes, 3 treatments with 3 experimental units each
resulted in 1, 680 possible treatment assignments. With 4 treatments each
having 3 experimental units, the number of possible treatment assignments is
increased substantially, to 369, 600.
2. Given that we will use random selection of permuted treatment assignments,
one question of interest might be the number of such permutations selected.
Does it matter, for example, if the number of randomly selected permutations
(of treatment assignments) is greater than the number of possible permutations?
3. We would also like to examine two algorithms for permuting treatment assignments. One is a “switching” algorithm, in which successive switches are made
among pairs of observations. The other is to simply sample treatment groups
without replacement from the entire set of data.