THREE-WAY ANOVA FOR STEEL QUALITY - YOURNAME 1 22:19 Wednesday, November 16, 2005 The GLM Procedure Class Level Information Class Levels Values carb 3 C10 C12 C14 pres 3 P25 P35 P45 temp 2 Cool Hot Number of Observations Read 72 Number of Observations Used 72 THREE-WAY ANOVA FOR STEEL QUALITY - YOURNAME 2 22:19 Wednesday, November 16, 2005 The GLM Procedure Dependent Variable: yy Sum of Source DF Squares Mean Square F Value Pr > F Model 17 11034.06944 649.06291 5.38 <.0001 Error 54 6511.25000 120.57870 Corrected Total 71 17545.31944 R-Square Coeff Var Root MSE yy Mean 0.628890 5.479382 10.98083 200.4028 Source DF Type I SS Mean Square F Value Pr > F carb 2 218.361111 109.180556 0.91 0.4104 pres 2 6640.361111 3320.180556 27.54 <.0001 carb*pres 4 1262.472222 315.618056 2.62 0.0450 temp 1 754.013889 754.013889 6.25 0.0155 carb*temp 2 6.194444 3.097222 0.03 0.9747 pres*temp 2 1998.694444 999.347222 8.29 0.0007 carb*pres*temp 4 153.972222 38.493056 0.32 0.8639 Source DF Type III SS Mean Square F Value Pr > F carb 2 218.361111 109.180556 0.91 0.4104 pres 2 6640.361111 3320.180556 27.54 <.0001 carb*pres 4 1262.472222 315.618056 2.62 0.0450 temp 1 754.013889 754.013889 6.25 0.0155 carb*temp 2 6.194444 3.097222 0.03 0.9747 pres*temp 2 1998.694444 999.347222 8.29 0.0007 carb*pres*temp 4 153.972222 38.493056 0.32 0.8639 THREE-WAY ANOVA FOR STEEL QUALITY - YOURNAME 3 22:19 Wednesday, November 16, 2005 The GLM Procedure Duncan's Multiple Range Test for yy NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.01 Error Degrees of Freedom 54 Error Mean Square 120.5787 Number of Means 2 3 Critical Range 8.464 8.824 Means with the same letter are not significantly different. D u n c a n G r o u p i n g Mean N pres A 213.000 24 P45 B 198.500 24 P35 C 189.708 24 P25 THREE-WAY ANOVA FOR STEEL QUALITY - YOURNAME 4 22:19 Wednesday, November 16, 2005 The GLM Procedure Duncan's Multiple Range Test for yy NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 54 Error Mean Square 120.5787 Number of Means 2 Critical Range 5.189 Means with the same letter are not significantly different. D u n c a n G r o u p i n g Mean N temp A 203.639 36 Hot B 197.167 36 Cool THREE-WAY ANOVA FOR STEEL QUALITY - YOURNAME 5 PRES x TEMP INTERACTION PLOT 22:19 Wednesday, November 16, 2005 Plot of yy*pres. Symbol is value of temp. yy | | 230 + | | | H 220 + | | | 210 + | | | H C 200 + | | C | C 190 + | H | | 180 + | ---+----------------------+----------------------+-- P25 P35 P45 Pressure THREE-WAY ANOVA FOR STEEL QUALITY - YOURNAME 6 PRES x CARB INTERACTION PLOT 22:19 Wednesday, November 16, 2005 Plot of yy*pres. Symbol is value of carbsym. yy | | 220 + 4 | | 2 | | 210 + | | | 0 | 200 + 2 | 0 | | 0 | 190 + 4 | | | 2 | 180 + | ---+----------------------+----------------------+-- P25 P35 P45 Pressure NOTE: 1 obs hidden. THREE-WAY ANOVA FOR STEEL QUALITY - YOURNAME 7 RESIDUAL x PREDICTED VALUE PLOT 22:19 Wednesday, November 16, 2005 Plot of resid*predict. Legend: A = 1 obs, B = 2 obs, etc. resid | | 40 + | | | | 20 + A A | A A A A A | A A B A | A A A A A | AAA C B B A A A 0 + A A A BB A A A A B | B B B AAA A B A | A B A A | A A B A A | A A A -20 + A | A | | | -40 + | --+------------+------------+------------+------------+------------+- 180 190 200 210 220 230 predict THREE-WAY ANOVA FOR STEEL QUALITY - YOURNAME 8 RESIDUALS FOR THE THREE-WAY ANOVA 22:19 Wednesday, November 16, 2005 The UNIVARIATE Procedure Variable: resid Moments N 72 Sum Weights 72 Mean 0 Sum Observations 0 Std Deviation 9.57641616 Variance 91.7077465 Skewness -0.0934123 Kurtosis -0.0045781 Uncorrected SS 6511.25 Corrected SS 6511.25 Coeff Variation . Std Error Mean 1.12859147 Basic Statistical Measures Location Variability Mean 0.00000 Std Deviation 9.57642 Median -0.37500 Variance 91.70775 Mode -4.00000 Range 45.50000 Interquartile Range 10.25000 NOTE: The mode displayed is the smallest of 2 modes with a count of 3. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 0 Pr > |t| 1.0000 Sign M -1 Pr >= |M| 0.9063 Signed Rank S 14.5 Pr >= |S| 0.9358 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.990697 Pr < W 0.8779 Kolmogorov-Smirnov D 0.088086 Pr > D >0.1500 Cramer-von Mises W-Sq 0.043815 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.249247 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 21.250 99% 21.250 95% 16.250 90% 11.500 75% Q3 5.375 50% Median -0.375 25% Q1 -4.875 10% -12.750 5% -15.000 THREE-WAY ANOVA FOR STEEL QUALITY - YOURNAME 9 RESIDUALS FOR THE THREE-WAY ANOVA 22:19 Wednesday, November 16, 2005 The UNIVARIATE Procedure Variable: resid Quantiles (Definition 5) Quantile Estimate 1% -24.250 0% Min -24.250 Extreme Observations -----Lowest---- ----Highest---- Value Obs Value Obs -24.25 65 15.25 20 -21.75 46 16.25 45 -17.75 21 17.75 67 -15.00 12 19.75 68 -14.50 51 21.25 22 Stem Leaf # Boxplot 20 2 1 0 18 8 1 | 16 28 2 | 14 022 3 | 12 | 10 00025 5 | 8 00 2 | 6 225 3 | 4 258225 6 +-----+ 2 2222288 7 | | 0 22282 5 | + | -0 528552 6 *-----* -2 8550855200 10 | | -4 88000 5 +-----+ -6 08 2 | -8 28 2 | -10 80 2 | -12 82880 5 | -14 05 2 | -16 8 1 | -18 -20 8 1 0 -22 -24 2 1 0 ----+----+----+----+ THREE-WAY ANOVA FOR STEEL QUALITY - YOURNAME 10 RESIDUALS FOR THE THREE-WAY ANOVA 22:19 Wednesday, November 16, 2005 The UNIVARIATE Procedure Variable: resid Normal Probability Plot 21+ ++ * | +* | *+* | ***+ | ++ | *+** | *+ | ** | *** | *** | +** | *** | ***** | *++ | *+ | ** | +** | *** | ** | *+ | ++ | ++* |+++ -25+ * +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 THREE-WAY ANOVA FOR STEEL QUALITY - YOURNAME 11 ONE-WAY ANOVA ON CELLS 22:19 Wednesday, November 16, 2005 The GLM Procedure Class Level Information Class Levels Values cell 18 P25_C10_Cool P25_C10_Hot P25_C12_Cool P25_C12_Hot P25_C14_Cool P25_C14_Hot P35_C10_Cool P35_C10_Hot P35_C12_Cool P35_C12_Hot P35_C14_Cool P35_C14_Hot P45_C10_Cool P45_C10_Hot P45_C12_Cool P45_C12_Hot P45_C14_Cool P45_C14_Hot Number of Observations Read 72 Number of Observations Used 72 THREE-WAY ANOVA FOR STEEL QUALITY - YOURNAME 12 ONE-WAY ANOVA ON CELLS 22:19 Wednesday, November 16, 2005 The GLM Procedure Dependent Variable: yy Sum of Source DF Squares Mean Square F Value Pr > F Model 17 11034.06944 649.06291 5.38 <.0001 Error 54 6511.25000 120.57870 Corrected Total 71 17545.31944 R-Square Coeff Var Root MSE yy Mean 0.628890 5.479382 10.98083 200.4028 Source DF Type I SS Mean Square F Value Pr > F cell 17 11034.06944 649.06291 5.38 <.0001 Source DF Type III SS Mean Square F Value Pr > F cell 17 11034.06944 649.06291 5.38 <.0001 THREE-WAY ANOVA FOR STEEL QUALITY - YOURNAME 13 ONE-WAY ANOVA ON CELLS 22:19 Wednesday, November 16, 2005 The GLM Procedure Duncan's Multiple Range Test for yy NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 54 Error Mean Square 120.5787 Number of Means 2 3 4 5 6 7 8 9 10 Critical Range 15.57 16.37 16.91 17.29 17.59 17.83 18.02 18.18 18.32 Number of Means 11 12 13 14 15 16 17 18 Critical Range 18.44 18.54 18.63 18.71 18.78 18.85 18.90 18.95 Means with the same letter are not significantly different. Duncan Grouping Mean N cell A 228.750 4 P45_C14_Hot A B A 223.750 4 P45_C12_Hot B A B A C 214.750 4 P45_C10_Hot B C B D C 210.250 4 P45_C14_Cool B D C B E D C 207.750 4 P45_C12_Cool E D C F E D C 204.750 4 P35_C12_Hot F E D C F E D C 203.750 4 P35_C14_Hot F E D C G F E D C 198.250 4 P35_C10_Hot G F E D C G F E D C 197.000 4 P25_C10_Cool G F E D C G F E D C 197.000 4 P35_C10_Cool G F E D G F E D 194.750 4 P35_C12_Cool G F E D G F E D 194.500 4 P25_C14_Cool G F E D G F E D 192.750 4 P45_C10_Cool G F E D G F E D 192.500 4 P35_C14_Cool G F E G F E 191.250 4 P25_C10_Hot G F G F 188.000 4 P25_C12_Cool G F THREE-WAY ANOVA FOR STEEL QUALITY - YOURNAME 14 ONE-WAY ANOVA ON CELLS 22:19 Wednesday, November 16, 2005 The GLM Procedure Duncan's Multiple Range Test for yy Means with the same letter are not significantly different. Duncan Grouping Mean N cell G F 186.500 4 P25_C14_Hot G G 181.000 4 P25_C12_Hot