Problem 8.30 in Ott and Longnecker 185 Obs shield machine diameter sdia 1 1 a 18.1 4.2544 2 2 a 2.4 1.5492 3 3 a 2.7 1.6432 4 4 a 7.5 2.7386 5 5 a 11.0 3.3166 6 1 b 8.7 2.9496 7 2 b 56.8 7.5366 8 3 b 4.4 2.0976 9 4 b 8.3 2.8810 10 5 b 5.8 2.4083 11 1 c 29.7 5.4498 12 2 c 18.7 4.3243 13 3 c 16.5 4.0620 14 4 c 63.7 7.9812 15 5 c 18.9 4.3474 16 6 c 107.2 10.3537 17 7 c 19.7 4.4385 18 8 c 93.4 9.6644 19 9 c 21.6 4.6476 20 10 c 17.8 4.2190 ' Problem 8.30,page 424 Ott and Longnecker 186 The GLM Procedure Class Level Information Class Levels Values machine 3 a b c Number of observations 20 ' Problem 8.30,page 424 Ott and Longnecker 187 The GLM Procedure Dependent Variable: diameter Sum of Source DF Squares Mean Square F Value Pr > F Model 2 4141.04150 2070.52075 2.73 0.0939 Error 17 12907.38800 759.25812 Corrected Total 19 17048.42950 R-Square Coeff Var Root MSE diameter Mean 0.242899 103.4139 27.55464 26.64500 Source DF Type I SS Mean Square F Value Pr > F machine 2 4141.041500 2070.520750 2.73 0.0939 Source DF Type III SS Mean Square F Value Pr > F machine 2 4141.041500 2070.520750 2.73 0.0939 Standard Parameter Estimate Error t Value Pr > |t| Intercept 40.72000000 B 8.71354186 4.67 0.0002 machine a -32.38000000 B 15.09229722 -2.15 0.0467 machine b -23.92000000 B 15.09229722 -1.58 0.1314 machine c 0.00000000 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 8.30,page 424 Ott and Longnecker 188 The GLM Procedure Bartlett's Test for Homogeneity of diameter Variance Source DF Chi-Square Pr > ChiSq machine 2 8.3489 0.0154 ' Problem 8.30,page 424 Ott and Longnecker 189 The GLM Procedure Level of -----------diameter---------- machine N Mean Std Dev a 5 8.3400000 6.5217329 b 5 16.8000000 22.4311168 c 10 40.7200000 34.5199395 ' Problem 8.30,page 424 Ott and Longnecker 190 The GLM Procedure Brown and Forsythe's Test for Homogeneity of diameter Variance ANOVA of Absolute Deviations from Group Medians Sum of Mean Source DF Squares Square F Value Pr > F machine 2 1144.9 572.4 0.84 0.4480 Error 17 11555.8 679.8 ' Problem 8.30,page 424 Ott and Longnecker 191 The GLM Procedure Level of -----------diameter---------- machine N Mean Std Dev a 5 8.3400000 6.5217329 b 5 16.8000000 22.4311168 c 10 40.7200000 34.5199395 ' Analysis of Residuals 192 The CAPABILITY Procedure Variable: rdia Moments N 20 Sum Weights 20 Mean 3.3751E-15 Sum Observations 6.7502E-14 Std Deviation 26.0640789 Variance 679.336211 Skewness 1.47762916 Kurtosis 1.40063302 Uncorrected SS 12907.388 Corrected SS 12907.388 Coeff Variation 7.72251E17 Std Error Mean 5.82810523 Basic Statistical Measures Location Variability Mean 0.00000 Std Deviation 26.06408 Median -8.30000 Variance 679.33621 Mode . Range 90.70000 Interquartile Range 26.28000 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 5.79E-16 Pr > |t| 1.0000 Sign M -4 Pr >= |M| 0.1153 Signed Rank S -23 Pr >= |S| 0.4091 Tests for Normality Test --Statistic--- -----p Value----- Shapiro-Wilk W 0.811160 Pr < W 0.001 Kolmogorov-Smirnov D 0.235658 Pr > D <0.010 Cramer-von Mises W-Sq 0.255007 Pr > W-Sq <0.005 Anderson-Darling A-Sq 1.438729 Pr > A-Sq <0.005 ' Analysis of Residuals 193 The CAPABILITY Procedure Variable: rdia Quantiles (Definition 5) Quantile Estimate 100% Max 66.48 99% 66.48 95% 59.58 90% 46.34 75% Q3 6.21 50% Median -8.30 25% Q1 -20.07 10% -22.47 5% -23.57 1% -24.22 0% Min -24.22 Extreme Observations -----Lowest---- ----Highest---- Value Obs Value Obs -24.22 13 9.76 1 -22.92 20 22.98 14 -22.02 12 40.00 7 -21.82 15 52.68 18 -21.02 17 66.48 16 ' Problem 8.30,page 424 Ott and Longnecker 194 Square Root transformed response The GLM Procedure Class Level Information Class Levels Values machine 3 a b c Number of observations 20 ' Problem 8.30,page 424 Ott and Longnecker 195 Square Root transformed response The GLM Procedure Dependent Variable: sdia Sum of Source DF Squares Mean Square F Value Pr > F Model 2 41.4272950 20.7136475 4.48 0.0274 Error 17 78.6683337 4.6275490 Corrected Total 19 120.0956287 R-Square Coeff Var Root MSE sdia Mean 0.344953 47.34982 2.151174 4.543151 Source DF Type I SS Mean Square F Value Pr > F machine 2 41.42729503 20.71364751 4.48 0.0274 Source DF Type III SS Mean Square F Value Pr > F machine 2 41.42729503 20.71364751 4.48 0.0274 Standard Parameter Estimate Error t Value Pr > |t| Intercept 5.948794417 B 0.68026091 8.74 <.0001 machine a -3.248392804 B 1.17824646 -2.76 0.0135 machine b -2.374181940 B 1.17824646 -2.02 0.0600 machine c 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 8.30,page 424 Ott and Longnecker 196 Square Root transformed response The GLM Procedure Bartlett's Test for Homogeneity of sdia Variance Source DF Chi-Square Pr > ChiSq machine 2 2.2835 0.3193 ' Problem 8.30,page 424 Ott and Longnecker 197 Square Root transformed response The GLM Procedure Level of -------------sdia------------ machine N Mean Std Dev a 5 2.70040161 1.14446010 b 5 3.57461248 2.24224933 c 10 5.94879442 2.43398279 ' Problem 8.30,page 424 Ott and Longnecker 198 Square Root transformed response The GLM Procedure Brown and Forsythe's Test for Homogeneity of sdia Variance ANOVA of Absolute Deviations from Group Medians Sum of Mean Source DF Squares Square F Value Pr > F machine 2 2.2704 1.1352 0.31 0.7364 Error 17 61.9489 3.6441 ' Problem 8.30,page 424 Ott and Longnecker 199 Square Root transformed response The GLM Procedure Level of -------------sdia------------ machine N Mean Std Dev a 5 2.70040161 1.14446010 b 5 3.57461248 2.24224933 c 10 5.94879442 2.43398279 ' Problem 8.30,page 424 Ott and Longnecker 200 Square Root transformed response The CAPABILITY Procedure Variable: rdia Moments N 20 Sum Weights 20 Mean -5.773E-16 Sum Observations -1.155E-14 Std Deviation 2.03480678 Variance 4.14043861 Skewness 1.22990247 Kurtosis 0.21040612 Uncorrected SS 78.6683337 Corrected SS 78.6683337 Coeff Variation -3.5246E17 Std Error Mean 0.45499663 Basic Statistical Measures Location Variability Mean -0.00000 Std Deviation 2.03481 Median -0.87544 Variance 4.14044 Mode . Range 6.29172 Interquartile Range 2.57878 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t -127E-17 Pr > |t| 1.0000 Sign M -3 Pr >= |M| 0.2632 Signed Rank S -15 Pr >= |S| 0.5958 Tests for Normality Test --Statistic--- -----p Value----- Shapiro-Wilk W 0.801182 Pr < W 0.001 Kolmogorov-Smirnov D 0.246866 Pr > D <0.010 Cramer-von Mises W-Sq 0.278129 Pr > W-Sq <0.005 Anderson-Darling A-Sq 1.593010 Pr > A-Sq <0.005 ' Problem 8.30,page 424 Ott and Longnecker 201 Square Root transformed response The CAPABILITY Procedure Variable: rdia Quantiles (Definition 5) Quantile Estimate 100% Max 4.40494887 99% 4.40494887 95% 4.18345693 90% 3.83876906 75% Q3 1.08511552 50% Median -0.87543718 25% Q1 -1.49366050 10% -1.67711727 5% -1.80828250 1% -1.88677521 0% Min -1.88677521 Extreme Observations -------Lowest------- -------Highest------ Value Obs Value Obs -1.88677521 13 1.55400786 1 -1.72978980 20 2.03243356 14 -1.62444475 12 3.71557313 18 -1.60138139 15 3.96196500 7 -1.51032621 17 4.40494887 16 ' Kruskal-Wallis one way analysis of variance 202 for diameter data for Problem 8.30 The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable diameter Classified by Variable machine Sum of Expected Std Dev Mean machine N Scores Under H0 Under H0 Score ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ a 5 27.0 52.50 11.456439 5.40 b 5 37.0 52.50 11.456439 7.40 c 10 146.0 105.00 13.228757 14.60 Kruskal-Wallis Test Chi-Square 9.8914 DF 2 Pr > Chi-Square 0.0071 '