chap4 - Chapter 4 The Randomized Block Design 4.1 Study...

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Unformatted text preview: Chapter 4 The Randomized Block Design 4.1 Study Suggestions Chapter 1 of the text introduced the CRD as a device for comparing two treatments. Chapter 2 introduced the hypothesis test for analyzing data from a CRD. Chapter 3 gave two methods, computer simulation and mathematical theory, for obtaining an approxi- mate P-value. With this solid background, Chapter 4 presents a new design, the randomized block design (RBD), a hypothesis test for this new designs data, and an easy way to obtain an approximate P-value for the test. In an RBD the pool of subjects is divided into blocks, and within each block a CRD is performed. Thus, you already know a great deal about RBDs since you have studied CRDs extensively. In an RBD the researcher must choose a factor for creating blocks. For example, in the AIDS-IP study in the text, the researcher used the T-cell count to form blocks. I do not attempt to give rules for choos- ing blocks, but the following argument may provide you with some guidance. The goal of a CRD is to learn whether the treatments differ. This goal is difficult to achieve because subjects are so variable. More precisely, there are factors other than treatment that influence a subjects response. Any factor whose value both influences the response, and can be deter- mined without too much trouble provides a good cri- terion for forming blocks. Thus, obtaining expertise in the subject area is the best way to become good at choosing blocks! There are two major new methods developed in Chapter 4: the interaction graph, and the Mantel- Haenszel (MH) test. Make sure you can draw an interaction graph for an RBD. Remember that there are two possible in- teraction graphs, one for the proportion of successes and one for the proportion of failures. Recall the two examples of the RBD design in the textthe AIDS-IP study and the eight Infidelity studies. The AIDS-IP study has a natural ordering to its blocks, but the blocks corresponding to the dif- ferent Infidelity studies are not ordered. If the blocks are ordered, then the interaction graph should present the blocks in their natural order. If the blocks are not ordered, however, then there is no natural way to present the blocks in the interaction graph, and you should remember this fact when you interpret the graph. The two treatments can be compared within each block of an RBD. If there is a consistent direction to the differences between treatments across blocks (that is, if one of the treatments is better than the other treatment in every block) then the MH test is a good way to obtain an overall (that is, across blocks) comparison of the treatments. This sounds fairly simple, but there are two difficulties....
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This note was uploaded on 10/23/2009 for the course STAT STATS 371 taught by Professor Professorwardrop during the Fall '09 term at Wisconsin.

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chap4 - Chapter 4 The Randomized Block Design 4.1 Study...

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