We note that the test of hypothesis information shown in the printout (F = and p <.0001) is identical to the information shown in the text. We compare this printout to the information shown in the text. Figure 9.6 The XLSTAT output is shown in Figure 9.7.Ĥ Section 9.2 The Completely Randomized Design: Single Factor 133 Figure 9.7 Analysis of variance (DISTANCE): Source DF Sum of squares Mean squares F Pr > F Model Diff Significant BrandC vs BrandD < Yes BrandC vs BrandA < Yes BrandC vs BrandB Yes BrandB vs BrandD < Yes BrandB vs BrandA < Yes BrandA vs BrandD No Tukey's d critical value: Category Mean Groups BrandC A BrandB B BrandA C BrandD C We see that the printouts above contain both the test of hypothesis and multiple comparison information that we desire. Click OK to conduct the desired analyses. and Pairwise comparisons boxes, and specify the Tukey (HSD) technique by checking the appropriate box. To conduct the Tukey multiple comparisons of the treatment means, we check the Mean, Multiple Comparisons. Figure 9.4 Figure 9.5 Click on the Means tab (shown if Figure 9.6). To conduct the test of hypothesis to compare treatment means, we check the Analysis of variance box. Click on the Outputs tab (shown in Figure 9.5) to specify the type of output desired. We specify the column F data in the Quantitative box and the column E data in the Qualitative box, and check the Variable labels box to in this menu. We note that the data in column A represents brand of club and the data in column B represent the corresponding golf ball distance. In our data set, the data is located in columns A and B, rows 2 41, with row 1 being the variable labels. 130ģ 132 Chapter 9: Design of Experiments and Analysis of Variance Figure 9.3 This opens the ANOVA menu shown in Figures We need to first specify the location of the data that is to be analyzed. The distance is recorded for each hit, and the results are shown in Table 9.1, organized by brand.
XLSTAT CALCULATE CONFIDENCE INTERVAL DRIVER
A completely randomized design is employed, with Iron Byron, the USGA s robotic golfer, using a driver to hit a random sample of 10 balls of each brand in a random sequence. Problem: Suppose the United States Golf Association (USGA) wants to compare the mean distances associated with four different brands of golf balls when struck with a driver.
Exercise 9.1: We use Example 9.4 found in the Statistics for Business and Economics text. We illustrate with the following example. This experimental design is the completely randomized design and can be analyzed in both XLSTAT and Excel. The goal is to compare the means of the response variable for those treatments. Since there is only one factor in the design, the various levels of the factor are the treatments in the design. The simplest of all experimental designs involves using a single factor to compare values of a response variable. Excel Companion Statistics for Business Exercise Page and Economics Text Excel File Name Example 9.4 GLFCRD Example 9.4 GLFCRD Example 9.8 GLRRBD Example 9.10 GLFAC Example 9.10 GLFAC1 9.2 The Completely Randomized Design: Single Factor The goal of analysis of variance is to compare the mean responses of the various treatments in an experimental design, where the treatments are the combinations of the levels of all the factors involved in the design. The following examples from Statistics for Business and Economics are solved with Excel and XLSTAT in this chapter. We will use the chapter examples that are given in the text to illustrate the model building and testing methods discussed above. XLSTAT also provides the analysis of the randomized block design discussed in the text. The XLSTAT technique is preferred over the Excel technique since XLSTAT also performs the multiple comparison procedures shown in Section 9.3 of the text. Both XLSTAT and Excel offer the one-way and two-way studies presented in the text. Once detected, the text presents several methods of comparing the multiple means of the experiment. The combination of levels of the various factors are called treatments and the analysis of variance procedures discussed in the text attempt to detect differences in the mean response variable for the various treatments. The goal of analysis of variance is to identify factors that contribute information to the response variable of interest. The concept of the designed experiment is explained and the completely randomized, the randomized block design, and factorial designs are covered in the text. 1 Chapter 9 Design of Experiments and Analysis of Variance 9.1 Introduction Chapter 9 introduces the topics of design of experiments and analysis of variance (ANOVA) to the reader.
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