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# ch14 - Chapter 14 Supplemental Text Material S14-1 The...

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Chapter 14. Supplemental Text Material S14-1. The Staggered, Nested Design In Section 14-1.4 we introduced the staggered, nested design as a useful way to prevent the number of degrees of freedom from “building up” so rapidly at lower levels of the design. In general, these designs are just unbalanced nested designs, and many computer software packages that have the capability to analyze general unbalanced designs can successfully analyze the staggered, nested design. The general linear model routine in Minitab is one of these packages. To illustrate a staggered, nested design, suppose that a pharmaceutical manufacturer is interested in testing the absorption of a drug two hours after the tablet is ingested. The product is manufactured in lots, and specific interest focuses on determining whether there is any significant lot-to-lot variability. Excessive lot-to-lot variability probably indicates problems with the manufacturing process, perhaps at the stage where the coating material that controls tablet absorption is applied. It could also indicate a problem with either the coating formulation, or with other formulation aspects of the tablet itself. The experimenters select a = 10 lots at random from the production process, and decide to use a staggered, nested design to sample from the lots. Two samples are taken at random from each lot. The first sample contains two tablets, and the second sample contains only one tablet. Each tablet is test for the percentage of active drug absorbed after two hours. The data from this experiment is shown in Table 1 below. Table 1. The Drug Absorption Experiment Sample Lot 1 2 1 24.5, 25.9 23.9 2 23.6, 26.1 25.2 3 27.3, 28.1 27.0 4 28.3, 27.5 27.4 5 24.3, 24.1 25.1 6 25.3, 26.0 24.7 7 27.3, 26.8 28.0 8 23.3, 23.9 23.0 9 24.6, 25.1 24.9 10 24.3, 24.9 25.3 The following output is from the Minitab general linear model analysis procedure.

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