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Unformatted text preview: Two-level designs In this exercise, we will focus on the analysis of an unreplicated full factorial two- level design, typically referred to as a 2 k design–k factors, all crossed, with two levels each. I had discussed replicated designs as well, but unreplicated designs have their own particular methods for inference that are quite different from methods used for replicated factorial completely randomized designs (CRD’s), and I would like to reinforce some of these differences with this exercise. For our data set, we will use a former statistics student’s (Carla Padgett) class project under Prof. Don Edwards, in which the loudness of a violin’s note (measured in deci- bels) was modelled as a function of 4 2-level factors. This experiment was actually replicated (11 times!), but we will study the averages here, and treat it as an unrepli- cated experiment. Table 1. Factors and Factor Levels Factor Factor Label-1 1 A Bow Speed Low High B Bow Angle Low High C Bow Placement Near Far D Pressure Low High Table 2. Responses and Runs Decibels (Y) A B C D 69.3-1-1-1-1 75.3-1-1-1 1 75.9-1-1 1-1 79.3-1-1 1 1 67.4-1 1-1-1 74.9-1 1-1 1 74.4-1 1 1-1 78.8-1 1 1 1 73.4 1-1-1-1 77.5 1-1-1 1 78.8 1-1 1-1 81.6 1-1 1 1 72.3 1 1-1-1 78.8 1 1-1 1 78.1 1 1 1-1 81.5 1 1 1 1 1 Note that Table 2 has the data entered in the “wrong” order, with the levels of Factor A varying the slowest, while the levels of Factor D vary the quickest. When creating the design in Minitab (see “Some notes on factorial designs in Minitab” on the course website for a primer), we could actually modify the way in which we specify the de- sign using...
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- Spring '08
- Normal Distribution, Low Low Low, bow angle, Bow Speed