252solngr4-072s 11/5/07 Str Tester 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str 1 Str 3 2 830 743 652 885 814 733 770 829 847 878 728 693 807 901 647 840 747 639 943 916 923 903 760 856 878 990 871 980 630 786 730 617 632 410 727 726 648 668 670 825 564 719 630 786 730 617 632 410 727 726 648 668 670 825 564 719 Anova: Single Factor SUMMARY Groups Str 1 Str 2 Str 3 Count 14 14 14 ANOVA Source of Variation SS Sum 11110 11893 9352 df Between Groups Within Groups 241912.7 372728.9 2 39 Total 614641.6 41 Average 793.5714 849.5 668 Variance 5715.495 12572.27 10383.69 MS F 120956.4 9557.152 12.65611 P-value 5.81E05 F crit 3.238096 Anova: Two-Factor Without Replication SUMMARY Count 1 2 3 4 5 6 7 8 9 10 11 3 3 3 3 3 3 3 3 3 3 3 Sum 2107 2369 2129 2141 2389 2059 2420 2458 2255 2402 2276 Average 702.3333 789.6667 709.6667 713.6667 796.3333 686.3333 806.6667 819.3333 751.6667 800.6667 758.6667 Variance 12296.33 2362.333 2566.333 22137.33 24414.33 65642.33 10612.33 7902.333 9952.333 13321.33 11521.33 1 252solngr4-072s 11/5/07 12 13 14 3 3 3 2508 2242 2600 836 747.3333 866.6667 22143 26232.33 17914.33 14 14 14 11110 11893 9352 793.5714 849.5 668 5715.495 12572.27 10383.69 ANOVA Source of Variation Rows Columns Error SS 116605 241912.7 256124 df 13 2 26 MS 8969.614 120956.4 9850.921 F 0.910536 12.27868 Total 614641.6 41 Str 1 Str 2 Str 3 Str Tester 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 Str 2 830 743 652 885 814 733 770 829 847 878 728 693 807 901 P-value 0.554751 0.000176 F crit 2.119166 3.369016 Str 305 647 840 747 639 943 916 923 903 760 856 878 990 871 980 635 791 735 622 637 415 732 731 653 673 675 830 569 724 630 786 730 617 632 410 727 726 648 668 670 825 564 719 Anova: Single Factor SUMMARY Groups Str 1 Str 2 Str 305 ANOVA Source of Variation Between Groups Count 14 14 14 SS 227816 Sum 11110 11893 9422 df 2 Average 793.5714 849.5 673 Variance 5715.495 12572.27 10383.69 MS F 113908 11.91862 P-value 9.13E05 F crit 3.238096 2 252solngr4-072s 11/5/07 Within Groups Total 372728.9 39 600545 41 9557.152 3 252solngr4-072s 11/5/07 ————— 11/5/2007 6:38:57 PM ———————————————————— Welcome to Minitab, press F1 for help. MTB > Stack c1 c2 c3 c11; SUBC> Subscripts c12; SUBC> UseNames. MTB > Vartest c11 c12; SUBC> Confidence 95.0. Test for Equal Variances: C11 versus C12 95% Bonferroni confidence intervals for standard deviations C12 N Lower StDev Upper Str1 14 51.2792 75.601 137.075 Str2 14 76.0538 112.126 203.300 Str3 14 69.1178 101.900 184.759 Bartlett's Test (normal distribution) Test statistic = 1.97, p-value = 0.373 Levene's Test (any continuous distribution) Test statistic = 0.43, p-value = 0.654 Test for Equal Variances: C11 versus C12 MTB > NormTest c1; SUBC> KSTest. Probability Plot of Str1 MTB > NormTest c2; SUBC> KSTest. Probability Plot of Str2 MTB > NormTest c3; SUBC> KSTest. Probability Plot of Str3 Results for: 2gr3-0712-00.MTW MTB > WSave "C:\Documents and Settings\RBOVE\My Documents\Minitab\2gr3-071200.MTW"; SUBC> Replace. Saving file as: 'C:\Documents and Settings\RBOVE\My Documents\Minitab\2gr3-0712-00.MTW' MTB > AOVOneway c1 c2 c3; SUBC> Tukey 5; SUBC> Fisher 5; SUBC> Dunnett 5 c3; SUBC> MCB 5 +1. One-way ANOVA: Str1, Str2, Str3 Source Factor Error Total DF 2 39 41 S = 97.76 Level Str1 Str2 Str3 N 14 14 14 SS 241913 372729 614642 MS 120956 9557 R-Sq = 39.36% Mean 793.57 849.50 668.00 StDev 75.60 112.13 101.90 F 12.66 P 0.000 R-Sq(adj) = 36.25% Individual 95% CIs For Mean Based on Pooled StDev ---+---------+---------+---------+-----(-----*------) (-----*------) (------*-----) ---+---------+---------+---------+-----640 720 800 880 4 252solngr4-072s 11/5/07 Pooled StDev = 97.76 Dunnett's comparisons with a control Family error rate = 0.05 Individual error rate = 0.0272 Critical value = 2.29 Control = Str3 Intervals for treatment mean minus control mean Level Str1 Str2 Lower 40.77 96.70 Center 125.57 181.50 Upper 210.37 266.30 ---+---------+---------+---------+-----(-------------*-------------) (-------------*-------------) ---+---------+---------+---------+-----60 120 180 240 Hsu's MCB (Multiple Comparisons with the Best) Family error rate = 0.05 Critical value = 1.97 Intervals for level mean minus largest of other level means Level Str1 Str2 Str3 Lower -128.79 -16.93 -254.36 Center -55.93 55.93 -181.50 Upper 16.93 128.79 0.00 -----+---------+---------+---------+---(------*-------) (-------*------) (------*-----------------) -----+---------+---------+---------+----200 -100 0 100 Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons Individual confidence level = 98.06% Str1 subtracted from: Str2 Str3 Lower -34.21 -215.71 Center 55.93 -125.57 Upper 146.07 -35.43 --------+---------+---------+---------+(-----*-----) (-----*-----) --------+---------+---------+---------+-150 0 150 300 Upper -91.36 --------+---------+---------+---------+(-----*-----) --------+---------+---------+---------+-150 0 150 300 Str2 subtracted from: Str3 Lower -271.64 Center -181.50 Fisher 95% Individual Confidence Intervals All Pairwise Comparisons Simultaneous confidence level = 87.98% Str1 subtracted from: Lower Center Str2 -18.81 55.93 Str3 -200.31 -125.57 Upper 130.67 -50.83 Str2 subtracted from: Lower Center Str3 -256.24 -181.50 Upper -106.76 -------+---------+---------+---------+-(----*----) (----*----) -------+---------+---------+---------+--150 0 150 300 -------+---------+---------+---------+-(----*----) -------+---------+---------+---------+--150 0 150 300 5 252solngr4-072s 11/5/07 MTB > Twoway c11 c13 c12; SUBC> Means c13 c12. Two-way ANOVA: Rating versus Customer, Store Source Customer Store Error Total S = 99.25 Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Store Str1 Str2 Str3 MTB MTB MTB MTB MTB MTB MTB MTB MTB MTB MTB MTB > > > > > > > > > > > > DF 13 2 26 41 SS MS F P 116605 8970 0.91 0.555 241913 120956 12.28 0.000 256124 9851 614642 R-Sq = 58.33% R-Sq(adj) = 34.29% Mean 702.333 789.667 709.667 713.667 796.333 686.333 806.667 819.333 751.667 800.667 758.667 836.000 747.333 866.667 Individual 95% CIs For Mean Based on Pooled StDev ---+---------+---------+---------+-----(---------*--------) (---------*---------) (---------*---------) (--------*---------) (--------*---------) (---------*---------) (---------*---------) (---------*---------) (---------*--------) (---------*---------) (---------*---------) (---------*--------) (---------*---------) (---------*---------) ---+---------+---------+---------+-----600 720 840 960 Mean 793.571 849.500 668.000 Individual 95% CIs For Mean Based on Pooled StDev ---+---------+---------+---------+-----(------*------) (------*------) (------*-----) ---+---------+---------+---------+-----640 720 800 880 let c20 = c3 let c21=c20+1 let c22 = c21+1 let c23 = c22+1 let c24 = c23+1 let c25 = c24+1 let c26 = c25+1 let c27 = c26+1 let c28 = c27+1 let c29 = c28+1 let c30 = c29 +1 describe c20-c30 Descriptive Statistics: C20, C21, C22, C23, C24, C25, C26, C27, C28, C29, C30 Variable C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 N 14 14 14 14 14 14 14 14 14 14 14 N* 0 0 0 0 0 0 0 0 0 0 0 Mean 668.0 669.0 670.0 671.0 672.0 673.0 674.0 675.0 676.0 677.0 678.0 SE Mean 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.2 StDev 101.9 101.9 101.9 101.9 101.9 101.9 101.9 101.9 101.9 101.9 101.9 Minimum 410.0 411.0 412.0 413.0 414.0 415.0 416.0 417.0 418.0 419.0 420.0 Q1 626.8 627.8 628.8 629.8 630.8 631.8 632.8 633.8 634.8 635.8 636.8 Median 669.0 670.0 671.0 672.0 673.0 674.0 675.0 676.0 677.0 678.0 679.0 Q3 727.8 728.8 729.8 730.8 731.8 732.8 733.8 734.8 735.8 736.8 737.8 Maximum 825.0 826.0 827.0 828.0 829.0 830.0 831.0 832.0 833.0 834.0 835.0 6 252solngr4-072s 11/5/07 MTB > AOVOneway c1 c2 c30; SUBC> Tukey 5; SUBC> Fisher 5; SUBC> Dunnett 5 c30; SUBC> MCB 5 +1. One-way ANOVA: Str1, Str2, C30 Source DF Factor 2 Error 39 Total 41 S = 97.76 Level Str1 Str2 C30 N 14 14 14 SS MS 214186 107093 372729 9557 586915 R-Sq = 36.49% Mean 793.57 849.50 678.00 StDev 75.60 112.13 101.90 F 11.21 P 0.000 R-Sq(adj) = 33.24% Individual 95% CIs For Mean Based on Pooled StDev -+---------+---------+---------+-------(------*-------) (------*-------) (-------*------) -+---------+---------+---------+-------630 700 770 840 Pooled StDev = 97.76 Dunnett's comparisons with a control Family error rate = 0.05 Individual error rate = 0.0272 Critical value = 2.29 Control = C30 Intervals for Level Lower Str1 30.77 Str2 86.70 treatment mean minus control mean Center Upper -----+---------+---------+---------+---115.57 200.37 (-------------*-------------) 171.50 256.30 (--------------*-------------) -----+---------+---------+---------+---60 120 180 240 Hsu's MCB (Multiple Comparisons with the Best) Family error rate = 0.05 Critical value = 1.97 Intervals for level mean minus largest of other level means Level Lower Center Upper ----+---------+---------+---------+----Str1 -128.79 -55.93 16.93 (------*-------) Str2 -16.93 55.93 128.79 (-------*------) C30 -244.36 -171.50 0.00 (------*----------------) ----+---------+---------+---------+-----200 -100 0 100 Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons Individual confidence level = 98.06% Str1 subtracted from: Lower Center Str2 -34.21 55.93 C30 -205.71 -115.57 Str2 subtracted from: Lower Center C30 -261.64 -171.50 Upper 146.07 -25.43 Upper -81.36 -------+---------+---------+---------+-(-----*-----) (-----*-----) -------+---------+---------+---------+--150 0 150 300 -------+---------+---------+---------+-(-----*-----) -------+---------+---------+---------+--150 0 150 300 7 252solngr4-072s 11/5/07 Fisher 95% Individual Confidence Intervals All Pairwise Comparisons Simultaneous confidence level = 87.98% Str1 subtracted from: Lower Center Upper ------+---------+---------+---------+--Str2 -18.81 55.93 130.67 (----*----) C30 -190.31 -115.57 -40.83 (----*----) ------+---------+---------+---------+---150 0 150 300 Str2 subtracted from: Lower Center Upper ------+---------+---------+---------+--C30 -246.24 -171.50 -96.76 (----*----) ------+---------+---------+---------+---150 0 150 300 MTB > Save "C:\Documents and Settings\RBOVE\My Documents\Minitab\2gr3-071200.MTW"; SUBC> Replace. Saving file as: 'C:\Documents and Settings\RBOVE\My Documents\Minitab\2gr3-0712-00.MTW' Existing file replaced. MTB > Print c1-c3 Data Display Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str1 830 743 652 885 814 733 770 829 847 878 728 693 807 901 Str2 647 840 747 639 943 916 923 903 760 856 878 990 871 980 Str3 630 786 730 617 632 410 727 726 648 668 670 825 564 719 Extra Credit ————— 11/5/2007 9:42:54 PM ———————————————————— Welcome to Minitab, press F1 for help. MTB > WOpen "C:\Documents and Settings\RBOVE\My Documents\Minitab\2gr3-07200.MTW". Retrieving worksheet from file: 'C:\Documents and Settings\RBOVE\My Documents\Minitab\2gr3-072-00.MTW' Worksheet was saved on Mon Nov 05 2007 Results for: 2gr3-072-00.MTW MTB > erase c11-c100 Results for: 2gr3-072-01.MTW MTB > WSave "C:\Documents and Settings\RBOVE\My Documents\Minitab\2gr3-07201.MTW"; SUBC> Replace. Saving file as: 'C:\Documents and Settings\RBOVE\My Documents\Minitab\2gr3-072-01.MTW' 8 252solngr4-072s 11/5/07 MTB > print c1-c4 Data Display Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Tester 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str1 830 743 652 885 814 733 770 829 847 878 728 693 807 901 Str2 647 840 747 639 943 916 923 903 760 856 878 990 871 980 Str3 630 786 730 617 632 410 727 726 648 668 670 825 564 719 MTB > AOVO c2-c4; SUBC> tukey 5; SUBC> fisher 5. One-way ANOVA: Str1, Str2, Str3 Source DF Factor 2 Error 39 Total 41 S = 97.76 Level Str1 Str2 Str3 N 14 14 14 SS MS 241913 120956 372729 9557 614642 R-Sq = 39.36% Mean 793.57 849.50 668.00 StDev 75.60 112.13 101.90 F 12.66 P 0.000 R-Sq(adj) = 36.25% Individual 95% CIs For Mean Based on Pooled StDev ---+---------+---------+---------+-----(-----*------) (-----*------) (------*-----) ---+---------+---------+---------+-----640 720 800 880 Pooled StDev = 97.76 Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons Individual confidence level = 98.06% Str1 subtracted from: Lower Center Str2 -34.21 55.93 Str3 -215.71 -125.57 Upper 146.07 -35.43 --------+---------+---------+---------+(-----*-----) (-----*-----) --------+---------+---------+---------+-150 0 150 300 Str2 subtracted from: Lower Center Str3 -271.64 -181.50 Upper -91.36 --------+---------+---------+---------+(-----*-----) --------+---------+---------+---------+-150 0 150 300 Fisher 95% Individual Confidence Intervals All Pairwise Comparisons Simultaneous confidence level = 87.98% Str1 subtracted from: Lower Center Upper -------+---------+---------+---------+-Str2 -18.81 55.93 130.67 (----*----) Str3 -200.31 -125.57 -50.83 (----*----) -------+---------+---------+---------+--150 0 150 300 9 252solngr4-072s 11/5/07 Str2 subtracted from: Lower Center Str3 -256.24 -181.50 MTB > SUBC> SUBC> MTB > Upper -106.76 -------+---------+---------+---------+-(----*----) -------+---------+---------+---------+--150 0 150 300 stack c2 c3 c4 c11; subscripts c12; UseNames. print c11 c12 c13 Data Display Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 rating 830 743 652 885 814 733 770 829 847 878 728 693 807 901 647 840 747 639 943 916 923 903 760 856 878 990 871 980 630 786 730 617 632 410 727 726 648 668 670 825 564 719 store Str1 Str1 Str1 Str1 Str1 Str1 Str1 Str1 Str1 Str1 Str1 Str1 Str1 Str1 Str2 Str2 Str2 Str2 Str2 Str2 Str2 Str2 Str2 Str2 Str2 Str2 Str2 Str2 Str3 Str3 Str3 Str3 Str3 Str3 Str3 Str3 Str3 Str3 Str3 Str3 Str3 Str3 tester1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 This is just to show you what the data looks like in stacked form. MTB > table c13 c12; SUBC> data rating. Tabulated statistics: tester1, store Rows: tester1 Columns: store Str1 Str2 Str3 1 830 647 630 2 743 840 786 3 652 747 730 4 885 639 617 5 814 943 632 6 733 916 410 10 252solngr4-072s 11/5/07 7 770 923 727 8 829 903 726 9 847 760 648 10 878 856 668 11 728 878 670 12 693 990 825 13 807 871 564 14 901 980 719 Cell Contents: rating : DATA MTB > MTB > twoway c11 c13 c12; SUBC> means c13 c12. Two-way ANOVA: rating versus tester1, store Source DF SS MS F P tester1 13 116605 8970 0.91 0.555 store 2 241913 120956 12.28 0.000 Error 26 256124 9851 Total 41 614642 S = 99.25 R-Sq = 58.33% R-Sq(adj) = 34.29% Individual 95% CIs For Mean Based on Pooled StDev tester1 Mean ---+---------+---------+---------+-----1 702.333 (---------*--------) 2 789.667 (---------*---------) 3 709.667 (---------*---------) 4 713.667 (--------*---------) 5 796.333 (--------*---------) 6 686.333 (---------*---------) 7 806.667 (---------*---------) 8 819.333 (---------*---------) 9 751.667 (---------*--------) 10 800.667 (---------*---------) 11 758.667 (---------*---------) 12 836.000 (---------*--------) 13 747.333 (---------*---------) 14 866.667 (---------*---------) ---+---------+---------+---------+-----600 720 840 960 Individual 95% CIs For Mean Based on Pooled StDev store Mean ---+---------+---------+---------+-----Str1 793.571 (------*------) Str2 849.500 (------*------) Str3 668.000 (------*-----) ---+---------+---------+---------+-----640 720 800 880 MTB > vartest c2-c4; SUBC> unstacked. Test for Equal Variances: Str1, Str2, Str3 95% Bonferroni confidence intervals for standard deviations N Lower StDev Upper Str1 14 51.2792 75.601 137.075 Str2 14 76.0538 112.126 203.300 Str3 14 69.1178 101.900 184.759 Bartlett's Test (normal distribution) Test statistic = 1.97, p-value = 0.373 Levene's Test (any continuous distribution) Test statistic = 0.43, p-value = 0.654 Test for Equal Variances: Str1, Str2, Str3 11 252solngr4-072s 11/5/07 MTB > vartest c11 c12. Test for Equal Variances: rating versus store 95% Bonferroni confidence intervals for standard deviations store N Lower StDev Upper Str1 14 51.2792 75.601 137.075 Str2 14 76.0538 112.126 203.300 Str3 14 69.1178 101.900 184.759 Bartlett's Test (normal distribution) Test statistic = 1.97, p-value = 0.373 Levene's Test (any continuous distribution) Test statistic = 0.43, p-value = 0.654 Test for Equal Variances: rating versus store MTB > normtest c2; SUBC> KStest. Probability Plot of Str1 MTB > normtest c3; SUBC> KStest. Probability Plot of Str2 MTB > normtest c4; SUBC> KStest. Probability Plot of Str3 MTB > name k2 'stdv1' 12 252solngr4-072s 11/5/07 MTB > MTB > name k3 'stdv2' name k4 'stdv3' MTB > stdev c2 k2 Standard Deviation of Str1 Standard deviation of Str1 = 75.6009 MTB > stdev c3 k3 Standard Deviation of Str2 Standard deviation of Str2 = 112.126 MTB > stdev c4 k4 Standard Deviation of Str3 Standard deviation of Str3 = 101.900 MTB > print k2-k4 Data Display stdv1 stdv2 stdv3 MTB MTB MTB MTB MTB MTB > > > > > > 75.6009 112.126 101.900 stack k2-k4 c6 let c7 = c6*c6 let k7 = mean(c7) let k8 = logten (k7) let c8 = logten(c7) print k7-k8 Data Display K7 K8 9557.15 3.98033 MTB > print c6-c8 Data Display Row 1 2 3 MTB MTB MTB MTB MTB MTB MTB MTB MTB MTB MTB MTB MTB MTB C6 75.601 112.126 101.900 > > > > > > > > > > > > > > vars 5715.5 12572.3 10383.7 C8 3.75705 4.09941 4.01635 name k15 'med1' name k16 'med2' name k17 'med3' let c14 = c1 let c15 = c2 let c16 = c3 let c17 = c4 let k15 = median (c15) let k16 = median (c16) let k17 = median(c17) let c15 = c15-k15 let c16 = c16-k16 let c17 = c17-k17 describe c15-c17 Descriptive Statistics: Str1*, Str2*, Str3* Variable Str1* Str2* Str3* N 14 14 14 N* 0 0 0 Mean -16.9 -25.0 -1.0 SE Mean 20.2 30.0 27.2 StDev 75.6 112.1 101.9 Minimum -158.5 -235.5 -259.0 Q1 -78.8 -117.8 -42.3 Median 0.0 0.0 0.0 Q3 44.3 53.5 58.8 Maximum 90.5 115.5 156.0 13 252solngr4-072s 11/5/07 MTB > print c14-c17 Data Display Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 MTB MTB MTB MTB tester2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 > > > > Str1* 19.5 -67.5 -158.5 74.5 3.5 -77.5 -40.5 18.5 36.5 67.5 -82.5 -117.5 -3.5 90.5 Str3* -39 117 61 -52 -37 -259 58 57 -21 -1 1 156 -105 50 let c15 = abs(c15) let c16 = abs(c16) let c17 = abs(c17) print c15-c17 Data Display Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str2* -227.5 -34.5 -127.5 -235.5 68.5 41.5 48.5 28.5 -114.5 -18.5 3.5 115.5 -3.5 105.5 Str1* 19.5 67.5 158.5 74.5 3.5 77.5 40.5 18.5 36.5 67.5 82.5 117.5 3.5 90.5 Str2* 227.5 34.5 127.5 235.5 68.5 41.5 48.5 28.5 114.5 18.5 3.5 115.5 3.5 105.5 Str3* 39 117 61 52 37 259 58 57 21 1 1 156 105 50 MTB > AOVO c15-c17 One-way ANOVA: Str1*, Str2*, Str3* Source Factor Error Total DF 2 39 41 S = 64.29 Level Str1* Str2* Str3* N 14 14 14 SS 3544 161199 164743 MS 1772 4133 R-Sq = 2.15% Mean 61.29 83.79 72.43 StDev 44.49 75.40 68.81 F 0.43 P 0.654 R-Sq(adj) = 0.00% Individual 95% CIs For Mean Based on Pooled StDev ---------+---------+---------+---------+ (-------------*------------) (-------------*------------) (-------------*-------------) ---------+---------+---------+---------+ 50 75 100 125 Pooled StDev = 64.29 MTB > Save "C:\Documents and Settings\RBOVE\My Documents\Minitab\2gr3-07201.MTW"; SUBC> Replace. Saving file as: 'C:\Documents and Settings\RBOVE\My 14 252solngr4-072s 11/5/07 Documents\Minitab\2gr3-072-01.MTW' Existing file replaced. 15