Problem 9.24 in Ott and Longnecker 215 Obs dog treatment fat 1 1 A 2.64 2 1 B 3.24 3 1 C 2.90 4 1 D 2.91 5 2 A 2.56 6 2 B 3.71 7 2 C 3.02 8 2 D 2.89 9 3 A 3.30 10 3 B 2.95 11 3 C 3.78 12 3 D 3.21 13 4 A 2.19 14 4 B 3.01 15 4 C 2.96 16 4 D 2.89 17 5 A 2.45 18 5 B 3.08 19 5 C 2.87 20 5 D 2.68 ' Problem 9.24,page 465 Ott and Longnecker 216 The GLM Procedure Class Level Information Class Levels Values treatment 4 A B C D Number of observations 20 ' Problem 9.24,page 465 Ott and Longnecker 217 The GLM Procedure Dependent Variable: fat Sum of Source DF Squares Mean Square F Value Pr > F Model 3 0.95052000 0.31684000 2.85 0.0703 Error 16 1.77920000 0.11120000 Corrected Total 19 2.72972000 R-Square Coeff Var Root MSE fat Mean 0.348212 11.25816 0.333467 2.962000 Source DF Type I SS Mean Square F Value Pr > F treatment 3 0.95052000 0.31684000 2.85 0.0703 Source DF Type III SS Mean Square F Value Pr > F treatment 3 0.95052000 0.31684000 2.85 0.0703 Standard Parameter Estimate Error t Value Pr > |t| Intercept 2.916000000 B 0.14913082 19.55 <.0001 treatment A -0.288000000 B 0.21090282 -1.37 0.1910 treatment B 0.282000000 B 0.21090282 1.34 0.1999 treatment C 0.190000000 B 0.21090282 0.90 0.3810 treatment D 0.000000000 B . . . NOTE: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable. ' Problem 9.24,page 465 Ott and Longnecker 218 The GLM Procedure Bartlett's Test for Homogeneity of fat Variance Source DF Chi-Square Pr > ChiSq treatment 3 2.2137 0.5293 ' Problem 9.24,page 465 Ott and Longnecker 219 The GLM Procedure Level of -------------fat------------- treatment N Mean Std Dev A 5 2.62800000 0.41227418 B 5 3.19800000 0.30605555 C 5 3.10600000 0.38115614 D 5 2.91600000 0.18942017 ' Problem 9.24,page 465 Ott and Longnecker 220 The GLM Procedure Brown and Forsythe's Test for Homogeneity of fat Variance ANOVA of Absolute Deviations from Group Medians Sum of Mean Source DF Squares Square F Value Pr > F treatment 3 0.0579 0.0193 0.26 0.8513 Error 16 1.1752 0.0734 ' Problem 9.24,page 465 Ott and Longnecker 221 The GLM Procedure Level of -------------fat------------- treatment N Mean Std Dev A 5 2.62800000 0.41227418 B 5 3.19800000 0.30605555 C 5 3.10600000 0.38115614 D 5 2.91600000 0.18942017 ' Analysis of Residuals 222 The CAPABILITY Procedure Variable: rfat Moments N 20 Sum Weights 20 Mean -2.665E-16 Sum Observations -5.329E-15 Std Deviation 0.30600998 Variance 0.09364211 Skewness 1.25919617 Kurtosis 0.89341511 Uncorrected SS 1.7792 Corrected SS 1.7792 Coeff Variation -1.1485E17 Std Error Mean 0.06842591 Basic Statistical Measures Location Variability Mean -0.00000 Std Deviation 0.30601 Median -0.07700 Variance 0.09364 Mode -0.02600 Range 1.11200 Interquartile Range 0.22400 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t -389E-17 Pr > |t| 1.0000 Sign M -4 Pr >= |M| 0.1153 Signed Rank S -25 Pr >= |S| 0.3633 Tests for Normality Test --Statistic--- -----p Value----- Shapiro-Wilk W 0.840287 Pr < W 0.004 Kolmogorov-Smirnov D 0.245416 Pr > D <0.010 Cramer-von Mises W-Sq 0.240502 Pr > W-Sq <0.005 Anderson-Darling A-Sq 1.351514 Pr > A-Sq <0.005 ' Analysis of Residuals 223 The CAPABILITY Procedure Variable: rfat Quantiles (Definition 5) Quantile Estimate 100% Max 0.674 99% 0.674 95% 0.673 90% 0.592 75% Q3 0.027 50% Median -0.077 25% Q1 -0.197 10% -0.242 5% -0.343 1% -0.438 0% Min -0.438 Extreme Observations -----Lowest---- ----Highest---- Value Obs Value Obs -0.438 13 0.042 2 -0.248 10 0.294 12 -0.236 20 0.512 6 -0.236 19 0.672 9 -0.206 3 0.674 11 ' Kruskal-Wallis one way analysis of variance 224 for 2-year dog fat data for Problem 9.24 The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable fat Classified by Variable treatment Sum of Expected Std Dev Mean treatment N Scores Under H0 Under H0 Score ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ A 5 28.0 52.50 11.452131 5.60 B 5 75.0 52.50 11.452131 15.00 C 5 61.0 52.50 11.452131 12.20 D 5 46.0 52.50 11.452131 9.20 Average scores were used for ties. Kruskal-Wallis Test Chi-Square 6.9824 DF 3 Pr > Chi-Square 0.0725 '