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#### Appendix C: Experimental Design Strategies Pages 109-114

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 From page 109...... The main goal of a factorial design is to study the main effects of factors involved in the design. An experimenter may also be interested in studying the two factor interaction effects or even higher-order interactions. Read the entire page → From page 110...... SSE / 8(n − 1) As we see from the previous discussion, if the number of factors k in a 2k factorial design increases, the total number of runs in a complete factorial design outgrows the resources of most experimenters. Read the entire page → From page 111...... 25 ½ fractional replicate designs can estimate unconfounded main effects and two-factor interactions, but three-factor interactions may be confounded Read the entire page → From page 112...... Resolution IV 2k fractional factorial designs include 24-1, 26-2, 27-2, 27-3, 28-3, 28-4, 29-3, 29-4 designs, where for example, a 29-4 design reduces the total number of experimental conditions (i.e., factor level combinations) from 29 = 512 to a far more manageable 25 = 32 and still permits estimates and tests of main effects that are unconfounded by two-factor interactions. Read the entire page → From page 113...... and are also provided online by the National Institute of Standards and Technology at http://www.itl.nist.gov/div898/ handbook/pri/section3/pri3347.htm. Response Surface Methodology The previous discussion of fractional factorial designs is based on discrete levels of each factor (e.g., high or low, experimental or control) Read the entire page → From page 114...... Once the parameters have been estimated, we can use the estimated response surface to evaluate the values of x1 and x2 for a specific targeted value of y0 -- for example, a carcinogenetic threshold. A contour plot may help in this regard to estimate levels of x1 and x2 corresponding to a particular level of carcinogenic risk. Read the entire page →

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