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Unformatted text preview: Chapter 13 Exercise Solutions Notes: 1. New exercises are denoted with an “ ”. 2. To analyze an experiment in MINITAB, the initial experimental layout must be created in MINITAB or defined by the user. The Excel data sets contain only the data given in the textbook; therefore some information required by MINITAB is not included. Detailed MINITAB instructions are provided for Exercises 13.1 and 13.2 to define and create designs. The remaining exercises are worked in a similar manner, and only the solutions are provided. 13.1. This experiment is three replicates of a factorial design in two factors—two levels of glass type and three levels of phosphor type—to investigate brightness. Enter the data into the MINITAB worksheet using the first three columns: one column for glass type, one column for phosphor type, and one column for brightness. This is how the Excel file is structured ( Chap13.xls ). Since the experiment layout was not created in MINITAB, the design must be defined before the results can be analyzed. After entering the data in MINITAB, select Stat > DOE > Factorial > Define Custom Factorial Design . Select the two factors (Glass Type and Phosphor Type), then for this exercise, check “ General full factorial ”. The dialog box should look: 131 Chapter 13 Exercise Solutions 13.1 continued Next, select “ Designs ”. For this exercise, no information is provided on standard order, run order, point type, or blocks, so leave the selections as below, and click “ OK ” twice. Note that MINITAB added four new columns (4 through 7) to the worksheet. DO NOT insert or delete columns between columns 1 through 7. MINITAB recognizes these contiguous seven columns as a designed experiment; inserting or deleting columns will cause the design layout to become corrupt. The design and data are in the MINITAB worksheet Ex13.1.MTW . 132 Chapter 13 Exercise Solutions 13.1 continued Select Stat > DOE > Factorial > Analyze Factorial Design . Select the response (Brightness), then click on “ Terms ”, verify that the selected terms are Glass Type, Phosphor Type, and their interaction, click “ OK ”. Click on “ Graphs ”, select “ Residuals Plots : Four in one ”. The option to plot residuals versus variables is for continuous factor levels; since the factor levels in this experiment are categorical, do not select this option. Click “ OK ”. Click on “ Storage ”, select “ Fits ” and “ Residuals ”, and click “ OK ” twice. General Linear Model: Ex13.1Bright versus Ex13.1Glass, Ex13.1Phosphor Factor Type Levels Values Ex13.1Glass fixed 2 1, 2 Ex13.1Phosphor fixed 3 1, 2, 3 Analysis of Variance for Ex13.1Bright, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Ex13.1Glass 1 14450.0 14450.0 14450.0 273.79 0.000 Ex13.1Phosphor 2 933.3 933.3 466.7 8.84 0.004 Ex13.1Glass*Ex13.1Phosphor 2 133.3 133.3 66.7 1.26 0.318 Error 12 633.3 633.3 52.8 Total 17 16150.0 S = 7.26483 RSq = 96.08% RSq(adj) = 94.44% No indication of significant interaction (...
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 Spring '11
 SCHUR
 Normal Distribution, Variance, Analyze Factorial Design

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