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Unformatted text preview: STAT 8200 Design of Experiments for Research Workers Lab 5 Due: Friday, Oct. 22 This lab is intended to highlight several ideas in the analysis of two-way layouts: 1. For unbalanced data, there are three distinct types of sums of squares whose values are not the same. Type III Sums of Squares are typically the ones to base inference on. 2. For understanding interaction, and for determining whether or not interaction undermines the appropriateness of main effect comparisons, profile plots are useful. In addition, it is often helpful to produce profile plots in both of the possible forms: (i) plot separate profiles for each level of factor A, with the levels of factor B running along the horizontal axis; and (ii) plot separate profiles for each level of factor B, with the levels of factor A running along the horizontal axis. In particular, profile plots of type (i) can be helpful for understanding main effects of factor A, and whether or not such comparisons are meaningful; and profile plots of type (ii) can be helpful for understanding main effects of factor B, and whether or not such comparisons are meaningful. 3. Model diagnostics are just as important in the two-way layout (and other designs) as they were in the one-way layout. In particular, it may be necessary to transform the response. 4. Transformations can affect whether or not interactions are present. Sometimes (but, as it turns out, not in this example), the data interact on the original scale, but do not on the transformed scale (or vice versa). 5. Contrasts in the joint means are not always interaction contrasts. Sometimes, it is interesting to make such comparisons. In particular, in the presence of interaction, we may want to make comparisons across the levels of factor A (B) separately within each of the levels of factor B (A). Example/Exercise: An experiment was conducted to study the effects of bleach concentration (factor A) and type of stain (factor B) on the speed of stain removal from a piece of cloth. The bleach concentrations chosen for the experiment were 3, 5, and 7 teaspoonfuls of bleach per cup of water, and the types of stains were blue ink, jam, and tomato sauce. All 3 3 combinations of the levels of the two factors were observed, for a total of 9 treatments. The experimenter planned on a balanced design with n = 5 replicates per treatment, but there were some problems during data collection that led to the loss of data from some replicates in some treatments. The result was an unbalanced two-way layout, the data for which are displayed below: Amount of Stain Bleach Type Time until Stain Removal (seconds) 3 ink 3600 3920 3340 3173 . 3 jam 495 236 515 573 555 3 tomato 733 525 793 1026 510 5 ink 2029 2271 2156 2493 2805 5 jam 428 432 335 288 ....
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This note was uploaded on 11/13/2011 for the course STAT 8200 taught by Professor Staff during the Fall '08 term at University of Georgia Athens.
- Fall '08