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Unformatted text preview: Chapter 13 Experimental Design and Analysis of Variance Learning Objectives 1. Understand the basic principles of an experimental study. 2. Understand the difference between a completely randomized design, a randomized block design, and a factorial experiment. 3. Know the assumptions necessary to use the analysis of variance procedure. 4. Understand the use of the F distribution in performing the analysis of variance procedure. 5. Know how to set up an ANOVA table and interpret the entries in the table. 6. Know how to use the analysis of variance procedure to determine if the means of more than two populations are equal for a completely randomized design, a randomized block design, and a factorial experiment. 7. Know how to use the analysis of variance procedure to determine if the means of more than two populations are equal for an observational study. 8. Be able to use output from Excel to solve experimental design problems. 9. Know how to use Fishers least significant difference (LSD) procedure and Fishers LSD with the Bonferroni adjustment to conduct statistical comparisons between pairs of population means. 13  1 Chapter 13 Solutions: 1. a. x = (156 + 142 + 134)/3 = 144 ( 29 2 1 SSTR k j j j n x x = = = 6(156  144) 2 + 6(142  144) 2 + 6(134  144) 2 = 1,488 b. MSTR = SSTR /( k 1) = 1488/2 = 744 c. 2 1 s = 164.4 2 2 s = 131.2 2 3 s = 110.4 2 1 SSE ( 1) k j j j n s = = = 5(164.4) + 5(131.2) +5(110.4) = 2030 d. MSE = SSE /( n T k ) = 2030/(12  3) = 135.3 e. Source of Variation Sum of Squares Degrees of Freedom Mean Square F p value Treatments 1488 2 744 5.50 .0162 Error 2030 15 135.3 Total 3518 17 f. F = MSTR /MSE = 744/135.3 = 5.50 Using F table (2 degrees of freedom numerator and 15 denominator), pvalue is between .01 and . 025 Using Excel, the pvalue corresponding to F = 5.50 is .0162. Because pvalue = .05, we reject the hypothesis that the means for the three treatments are equal. 2. Source of Variation Sum of Squares Degrees of Freedom Mean Square F p value Treatments 300 4 75 14.07 .0000 Error 160 30 5.33 Total 460 34 3. a. H : u 1 = u 2 = u 3 = u 4 = u 5 H a : Not all the population means are equal b. Using F table (4 degrees of freedom numerator and 30 denominator), pvalue is less than .01 Using Excel, the pvalue corresponding to F = 14.07 is .0000. Because pvalue = .05, we reject H 13  2 Experimental Design and Analysis of Variance 4. Source of Variation Sum of Squares Degrees of Freedom Mean Square F p value Treatments 150 2 75 4.80 .0233 Error 250 16 15.63 Total 400 18 Using F table (2 degrees of freedom numerator and 16 denominator), pvalue is between .01 and . 025 Using Excel, the pvalue corresponding to F = 4.80 is .0233....
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 Fall '09

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