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Unformatted text preview: Read Chapter 13. See Blackboard for assignment. This homework is due 1 April. Chapter 13: Homework You should be able to recall: The meaning of each of the components in the ANOVA table Assumptions required of the data for the ANOVA to be valid The recommended set of options for running an ANOVA in Minitab What each of the recommended plots should look like You should be able to accomplish: Given a set of treatments of a single factor, design an experiment to test differences in some response for those treatments Given data from a single factor experiment, run an ANOVA using Minitab Interpret output from Minitab, including the recommended plots You should be able to understand: Why certain plots should be examined and what is expected of them How to randomize to ensure independence of observations The difference between a fixed factor and a random factor Chapter 13: Objectives The last chapter was about multiple linear regression. We had one response (y), and we were using a line to create predictions of y for different values of several x variables. In this chapter we go back to there being one x, but this time instead of assuming x is continuous (regression) or having only 2 levels (hypothesis testing on two populations), x may have many levels. The method well use is called Analysis of Variance , or ANOVA. It uses the same type of math and logic we used for hypothesis testing and regression. In ANOVA, each x is called a factor . Each level of x is called a treatment . Chapter 13: Overview of ANOVA and DOE We are testing whether a new saw blade lasts as long as the old blade. This tests H0: 1 2 = 0 vs. 1 2 0 (or < 0, or > 0). Two population ttest We are trying to determine the relationship of saw blade life to saw RPM. Simple linear regression We are trying to determine the relationship of saw blade life to saw RPM and density of material. Multiple linear regression We want to know which of four blades lasts the longest. ANOVA Why ANOVA? Why not just a bunch of comparisons between each combination of blades? Chapter 13: Comparison of ANOVA with previous chapters Consider the following data: Chapter 13: ANOVA example Blade 1 Blade 2 Blade 3 Blade 4 149.3 153.8 155.0 180.2 196.3 210.0 228.9 258.9 198.1 222.6 221.1 226.8 250.2 216.2 255.1 231.2 178.3 203.0 216.4 248.7 240.9 237.8 214.1 201.7 213.4 209.5 250.4 243.5 254.0 228.6 233.8 252.2 211.4 232.5 221.8 232.2 231.9 209.8 270.3 228.4 191.2 186.5 196.4 213.8 248.6 233.0 261.6 263.3 193.3 228.2 257.4 238.7 182.7 213.7 193.4 209.2 237.2 206.5 227.5 213.0 244.4 203.1 274.9 265.2 187.1 237.1 220.9 251.9 223.1 185.7 252.6 248.5 237.8 228.1 288.9 263.0 181.7 225.5 270.8 238.9 242.9 190.8 208.6 239.9 229.1 186.0 232.2 243.6 195.1 216.0 295.5 208.9 211.0 213.7 208.8 255.8 253.7 202.7 243.7 256.9 Lets see how we could do this in Minitab using multiple comparisons....
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This document was uploaded on 09/19/2011.
 Spring '08

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