![]() Let's take \(k = 6\) and \(p = 2\), now we again have to choose two generators with the highest order possible, such that the generalized interaction is also as high as possible. This is a Resolution III design because the smallest word in the generator set has only three letters. Our generator set is: I = ABCD = CDE = ABE. Now we have a design with eight observations, \(2^3\), with five factors. ![]() Although D and E weren't a part of the original design, we were able to construct them from the two generators as shown below: trt Now we can define the new columns D = ABC and E = CD. Note that I = ABCD tells us that D = ABC, and the other generator I = CDE tells us that E = CD. In an example where we have \(k = 3\) treatments factors with \(2^3 = 8\) runs, we select \(2^p = 2 \text = 8\) observations which are constructed from all combinations of A, B, and C, then we'll use our generators to define D and E. In setting up the blocks within the experiment we have been picking the effects we know would be confounded and then using these to determine the layout of the blocks. The treatment combinations in each block of a full factorial can be thought of as a fraction of the full factorial. What we did in the last chapter is consider just one replicate of a full factorial design and run it in blocks.
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