BATCHES from 3 different vendors 00:26 Thursday, December 1, 2005 1 BATCHES ARE NESTED WITHIN VENDORS THE DATA AS SAS SEES IT Obs Supplier Batch Qual 1 AcmeInd B11 94 2 AcmeInd B11 92 3 AcmeInd B11 93 4 AcmeInd B11 91 5 AcmeInd B12 91 6 AcmeInd B12 90 7 AcmeInd B12 89 8 AcmeInd B12 88 9 AcmeInd B13 91 10 AcmeInd B13 93 11 AcmeInd B13 94 12 AcmeInd B13 93 13 AcmeInd B14 94 14 AcmeInd B14 97 15 AcmeInd B14 93 16 AcmeInd B14 93 17 WHSupply B21 94 18 WHSupply B21 91 19 WHSupply B21 90 20 WHSupply B21 92 21 WHSupply B22 93 22 WHSupply B22 97 23 WHSupply B22 95 24 WHSupply B22 94 25 WHSupply B23 92 26 WHSupply B23 93 27 WHSupply B23 91 28 WHSupply B23 90 29 WHSupply B24 93 30 WHSupply B24 96 31 WHSupply B24 95 32 WHSupply B24 94 33 GenWidge B31 96 34 GenWidge B31 94 35 GenWidge B31 92 36 GenWidge B31 93 37 GenWidge B32 90 38 GenWidge B32 92 39 GenWidge B32 94 40 GenWidge B32 91 41 GenWidge B33 93 42 GenWidge B33 91 43 GenWidge B33 94 44 GenWidge B33 93 45 GenWidge B34 95 46 GenWidge B34 94 47 GenWidge B34 93 48 GenWidge B34 92 BATCHES from 3 different vendors 00:26 Thursday, December 1, 2005 2 BATCHES ARE NESTED WITHIN VENDORS CORRECT NESTED GLM ANALYSIS A FULL-FACTORIAL MODEL WITH TWO EFFECTS The GLM Procedure Class Level Information Class Levels Values Supplier 3 AcmeInd GenWidge WHSupply Batch 12 B11 B12 B13 B14 B21 B22 B23 B24 B31 B32 B33 B34 Number of Observations Read 48 Number of Observations Used 48 BATCHES from 3 different vendors 00:26 Thursday, December 1, 2005 3 BATCHES ARE NESTED WITHIN VENDORS CORRECT NESTED GLM ANALYSIS A FULL-FACTORIAL MODEL WITH TWO EFFECTS The GLM Procedure Dependent Variable: Qual Sum of Source DF Squares Mean Square F Value Pr > F Model 11 100.2291667 9.1117424 4.09 0.0006 Error 36 80.2500000 2.2291667 Corrected Total 47 180.4791667 R-Square Coeff Var Root MSE Qual Mean 0.555350 1.609384 1.493039 92.77083 Source DF Type I SS Mean Square F Value Pr > F Supplier 2 6.79166667 3.39583333 1.52 0.2317 Batch(Supplier) 9 93.43750000 10.38194444 4.66 0.0004 Source DF Type III SS Mean Square F Value Pr > F Supplier 2 6.79166667 3.39583333 1.52 0.2317 Batch(Supplier) 9 93.43750000 10.38194444 4.66 0.0004 BATCHES from 3 different vendors 00:26 Thursday, December 1, 2005 4 BATCHES ARE NESTED WITHIN VENDORS INCORRECT CROSSED ANOVA ANALYSIS The GLM Procedure Class Level Information Class Levels Values Supplier 3 AcmeInd GenWidge WHSupply Batch 12 B11 B12 B13 B14 B21 B22 B23 B24 B31 B32 B33 B34 Number of Observations Read 48 Number of Observations Used 48 BATCHES from 3 different vendors 00:26 Thursday, December 1, 2005 5 BATCHES ARE NESTED WITHIN VENDORS INCORRECT CROSSED ANOVA ANALYSIS The GLM Procedure Dependent Variable: Qual Sum of Source DF Squares Mean Square F Value Pr > F Model 11 100.2291667 9.1117424 4.09 0.0006 Error 36 80.2500000 2.2291667 Corrected Total 47 180.4791667 R-Square Coeff Var Root MSE Qual Mean 0.555350 1.609384 1.493039 92.77083 Source DF Type I SS Mean Square F Value Pr > F Supplier 2 6.79166667 3.39583333 1.52 0.2317 Batch 9 93.43750000 10.38194444 4.66 0.0004 Supplier*Batch 0 0.00000000 . . . Source DF Type III SS Mean Square F Value Pr > F Supplier 0 0.00000000 . . . Batch 9 93.43750000 10.38194444 4.66 0.0004 Supplier*Batch 0 0.00000000 . . . BATCHES from 3 different vendors 00:26 Thursday, December 1, 2005 6 BATCHES ARE NESTED WITHIN VENDORS CROSSED-EFFECT ANOVA ANALYSIS OF SUPPLIER AND BATCH-ORDER The GLM Procedure Class Level Information Class Levels Values Supplier 3 AcmeInd GenWidge WHSupply Order 4 T1 T2 T3 T4 Number of Observations Read 48 Number of Observations Used 48 BATCHES from 3 different vendors 00:26 Thursday, December 1, 2005 7 BATCHES ARE NESTED WITHIN VENDORS CROSSED-EFFECT ANOVA ANALYSIS OF SUPPLIER AND BATCH-ORDER The GLM Procedure Dependent Variable: Qual Sum of Source DF Squares Mean Square F Value Pr > F Model 11 100.2291667 9.1117424 4.09 0.0006 Error 36 80.2500000 2.2291667 Corrected Total 47 180.4791667 R-Square Coeff Var Root MSE Qual Mean 0.555350 1.609384 1.493039 92.77083 Source DF Type I SS Mean Square F Value Pr > F Supplier 2 6.79166667 3.39583333 1.52 0.2317 Order 3 30.22916667 10.07638889 4.52 0.0086 Supplier*Order 6 63.20833333 10.53472222 4.73 0.0012 Source DF Type III SS Mean Square F Value Pr > F Supplier 2 6.79166667 3.39583333 1.52 0.2317 Order 3 30.22916667 10.07638889 4.52 0.0086 Supplier*Order 6 63.20833333 10.53472222 4.73 0.0012 BATCHES from 3 different vendors 00:26 Thursday, December 1, 2005 8 BATCHES ARE NESTED WITHIN VENDORS CROSSED-EFFECT ANOVA ANALYSIS OF SUPPLIER AND BATCH-ORDER Plot of Qual*Order. Symbol is value of Supplier. Qual ‚ ‚ ‚ ‚ ‚ ‚ ‚ 94.75 ˆ W 94.50 ˆ W 94.25 ˆ A 94.00 ˆ 93.75 ˆ G 93.50 ˆ G 93.25 ˆ 93.00 ˆ 92.75 ˆ A 92.50 ˆ A 92.25 ˆ 92.00 ˆ 91.75 ˆ W G 91.50 ˆ W 91.25 ˆ 91.00 ˆ 90.75 ˆ 90.50 ˆ 90.25 ˆ 90.00 ˆ 89.75 ˆ 89.50 ˆ A ‚ Šƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒ T1 T2 T3 T4 Order NOTE: 1 obs hidden. COFFEE QUALITY in 12 cities in 3 states 1 Which is significant: State, City within State, or Both? THE DATA AS SAS SEES IT 00:26 Thursday, December 1, 2005 Obs State City Qual 1 Ohio Columbus 104 2 Ohio Columbus 93 3 Ohio Columbus 98 4 Ohio Cleveland 92 5 Ohio Cleveland 104 6 Ohio Cleveland 98 7 Ohio Cincinnati 102 8 Ohio Cincinnati 99 9 Ohio Cincinnati 100 10 Ohio Oxford 112 11 Ohio Oxford 109 12 Ohio Oxford 106 13 NewYork Brooklyn 104 14 NewYork Brooklyn 100 15 NewYork Brooklyn 102 16 NewYork Buffalo 106 17 NewYork Buffalo 108 18 NewYork Buffalo 113 19 NewYork Albany 104 20 NewYork Albany 104 21 NewYork Albany 98 22 NewYork Oneonta 108 23 NewYork Oneonta 100 24 NewYork Oneonta 95 25 Washington Bellingham 109 26 Washington Bellingham 108 27 Washington Bellingham 101 28 Washington Seattle 114 29 Washington Seattle 111 30 Washington Seattle 109 31 Washington Spokane 100 32 Washington Spokane 98 33 Washington Spokane 101 34 Washington Yakima 97 35 Washington Yakima 104 36 Washington Yakima 109 COFFEE QUALITY in 12 cities in 3 states 2 Which is significant: State, City within State, or Both? NESTED GLM ANALYSIS 00:26 Thursday, December 1, 2005 The GLM Procedure Class Level Information Class Levels Values State 3 NewYork Ohio Washington City 12 Albany Bellingham Brooklyn Buffalo Cincinnati Cleveland Columbus Oneonta Oxford Seattle Spokane Yakima Number of Observations Read 36 Number of Observations Used 36 COFFEE QUALITY in 12 cities in 3 states 3 Which is significant: State, City within State, or Both? NESTED GLM ANALYSIS 00:26 Thursday, December 1, 2005 The GLM Procedure Dependent Variable: Qual Sum of Source DF Squares Mean Square F Value Pr > F Model 11 660.666667 60.060606 3.37 0.0062 Error 24 427.333333 17.805556 Corrected Total 35 1088.000000 R-Square Coeff Var Root MSE Qual Mean 0.607230 4.083545 4.219663 103.3333 Source DF Type I SS Mean Square F Value Pr > F State 2 81.1666667 40.5833333 2.28 0.1241 City(State) 9 579.5000000 64.3888889 3.62 0.0056 Source DF Type III SS Mean Square F Value Pr > F State 2 81.1666667 40.5833333 2.28 0.1241 City(State) 9 579.5000000 64.3888889 3.62 0.0056 COFFEE QUALITY in 12 cities in 3 states 4 Which is significant: State, City within State, or Both? ANALYSES WITHIN STATES 00:26 Thursday, December 1, 2005 State=NewYork The GLM Procedure Class Level Information Class Levels Values City 4 Albany Brooklyn Buffalo Oneonta Number of Observations Read 12 Number of Observations Used 12 COFFEE QUALITY in 12 cities in 3 states 5 Which is significant: State, City within State, or Both? ANALYSES WITHIN STATES 00:26 Thursday, December 1, 2005 State=NewYork The GLM Procedure Dependent Variable: Qual Sum of Source DF Squares Mean Square F Value Pr > F Model 3 123.0000000 41.0000000 2.28 0.1566 Error 8 144.0000000 18.0000000 Corrected Total 11 267.0000000 R-Square Coeff Var Root MSE Qual Mean 0.460674 4.099170 4.242641 103.5000 Source DF Type I SS Mean Square F Value Pr > F City 3 123.0000000 41.0000000 2.28 0.1566 Source DF Type III SS Mean Square F Value Pr > F City 3 123.0000000 41.0000000 2.28 0.1566 COFFEE QUALITY in 12 cities in 3 states 6 Which is significant: State, City within State, or Both? ANALYSES WITHIN STATES 00:26 Thursday, December 1, 2005 State=NewYork The GLM Procedure Duncan's Multiple Range Test for Qual NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 8 Error Mean Square 18 Number of Means 2 3 4 Critical Range 7.988 8.324 8.512 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 City A 109.000 3 Buffalo A A 102.000 3 Brooklyn A A 102.000 3 Albany A A 101.000 3 Oneonta COFFEE QUALITY in 12 cities in 3 states 7 Which is significant: State, City within State, or Both? ANALYSES WITHIN STATES 00:26 Thursday, December 1, 2005 State=Ohio The GLM Procedure Class Level Information Class Levels Values City 4 Cincinnati Cleveland Columbus Oxford Number of Observations Read 12 Number of Observations Used 12 COFFEE QUALITY in 12 cities in 3 states 8 Which is significant: State, City within State, or Both? ANALYSES WITHIN STATES 00:26 Thursday, December 1, 2005 State=Ohio The GLM Procedure Dependent Variable: Qual Sum of Source DF Squares Mean Square F Value Pr > F Model 3 239.5833333 79.8611111 4.11 0.0487 Error 8 155.3333333 19.4166667 Corrected Total 11 394.9166667 R-Square Coeff Var Root MSE Qual Mean 0.606668 4.344882 4.406435 101.4167 Source DF Type I SS Mean Square F Value Pr > F City 3 239.5833333 79.8611111 4.11 0.0487 Source DF Type III SS Mean Square F Value Pr > F City 3 239.5833333 79.8611111 4.11 0.0487 COFFEE QUALITY in 12 cities in 3 states 9 Which is significant: State, City within State, or Both? ANALYSES WITHIN STATES 00:26 Thursday, December 1, 2005 State=Ohio The GLM Procedure Duncan's Multiple Range Test for Qual NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 8 Error Mean Square 19.41667 Number of Means 2 3 4 Critical Range 8.297 8.646 8.841 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 City A 109.000 3 Oxford B 100.333 3 Cincinnati B B 98.333 3 Columbus B B 98.000 3 Cleveland COFFEE QUALITY in 12 cities in 3 states 10 Which is significant: State, City within State, or Both? ANALYSES WITHIN STATES 00:26 Thursday, December 1, 2005 State=Washington The GLM Procedure Class Level Information Class Levels Values City 4 Bellingham Seattle Spokane Yakima Number of Observations Read 12 Number of Observations Used 12 COFFEE QUALITY in 12 cities in 3 states 11 Which is significant: State, City within State, or Both? ANALYSES WITHIN STATES 00:26 Thursday, December 1, 2005 State=Washington The GLM Procedure Dependent Variable: Qual Sum of Source DF Squares Mean Square F Value Pr > F Model 3 216.9166667 72.3055556 4.52 0.0391 Error 8 128.0000000 16.0000000 Corrected Total 11 344.9166667 R-Square Coeff Var Root MSE Qual Mean 0.628896 3.806503 4.000000 105.0833 Source DF Type I SS Mean Square F Value Pr > F City 3 216.9166667 72.3055556 4.52 0.0391 Source DF Type III SS Mean Square F Value Pr > F City 3 216.9166667 72.3055556 4.52 0.0391 COFFEE QUALITY in 12 cities in 3 states 12 Which is significant: State, City within State, or Both? ANALYSES WITHIN STATES 00:26 Thursday, December 1, 2005 State=Washington The GLM Procedure Duncan's Multiple Range Test for Qual NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 8 Error Mean Square 16 Number of Means 2 3 4 Critical Range 7.531 7.848 8.026 Means with the same letter are not significantly different. Duncan Groupi ng Mean N City A 111.333 3 Seattle A B A 106.000 3 Bellingham B B 103.333 3 Yakima B B 99.667 3 Spokane