The SAS System 1 08:17 Wednesday, November 7, 2001 General Linear Models Procedure Class Level Information Class Levels Values BRAND 4 1 2 3 4 Number of observations in data set = 40 The SAS System 2 08:17 Wednesday, November 7, 2001 General Linear Models Procedure Dependent Variable: Y Sum of Mean Source DF Squares Square F Value Pr > F Model 3 15953.466000 5317.822000 866.12 0.0001 Error 36 221.034000 6.139833 Corrected Total 39 16174.500000 R-Square C.V. Root MSE Y Mean 0.986334 4.112645 2.4778687 60.250000 Source DF Type I SS Mean Square F Value Pr > F BRAND 3 15953.466000 5317.822000 866.12 0.0001 Source DF Type III SS Mean Square F Value Pr > F BRAND 3 15953.466000 5317.822000 866.12 0.0001 Contrast DF Contrast SS Mean Square F Value Pr > F Brand 1 vs Brand 4 1 35.64450000 35.64450000 5.81 0.0212 Brand 3 vs Brands 1& 1 18.37066667 18.37066667 2.99 0.0922 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate LSM overall 60.2500000 153.78 0.0001 0.39178544 LSM brand 1 43.1400000 55.06 0.0001 0.78357089 LSM brand 2 89.4400000 114.14 0.0001 0.78357089 LSM brand 3 67.9500000 86.72 0.0001 0.78357089 LSM brand 4 40.4700000 51.65 0.0001 0.78357089 The SAS System 3 08:17 Wednesday, November 7, 2001 General Linear Models Procedure Waller-Duncan K-ratio T test for variable: Y NOTE: This test minimizes the Bayes risk under additive loss and certain other assumptions. Kratio= 100 df= 36 MSE= 6.139833 F= 866.1183 Critical Value of T= 1.79702 Minimum Significant Difference= 1.9913 Means with the same letter are not significantly different. Waller Grouping Mean N BRAND A 89.440 10 2 B 67.950 10 3 C 43.140 10 1 D 40.470 10 4 The SAS System 4 08:17 Wednesday, November 7, 2001 General Linear Models Procedure T tests (LSD) for variable: Y NOTE: This test controls the type I comparisonwise error rate not the experimentwise error rate. Alpha= 0.05 df= 36 MSE= 6.139833 Critical Value of T= 2.03 Least Significant Difference= 2.2474 Means with the same letter are not significantly different. T Grouping Mean N BRAND A 89.440 10 2 B 67.950 10 3 C 43.140 10 1 D 40.470 10 4 The SAS System 5 08:17 Wednesday, November 7, 2001 General Linear Models Procedure Duncan's Multiple Range Test for variable: Y NOTE: This test controls the type I comparisonwise error rate, not the experimentwise error rate Alpha= 0.05 df= 36 MSE= 6.139833 Number of Means 2 3 4 Critical Range 2.247 2.363 2.438 Means with the same letter are not significantly different. Duncan Grouping Mean N BRAND A 89.440 10 2 B 67.950 10 3 C 43.140 10 1 D 40.470 10 4 The SAS System 6 08:17 Wednesday, November 7, 2001 General Linear Models Procedure Tukey's Studentized Range (HSD) Test for variable: Y NOTE: This test controls the type I experimentwise error rate, but generally has a higher type II error rate than REGWQ. Alpha= 0.05 df= 36 MSE= 6.139833 Critical Value of Studentized Range= 3.809 Minimum Significant Difference= 2.9845 Means with the same letter are not significantly different. Tukey Grouping Mean N BRAND A 89.440 10 2 B 67.950 10 3 C 43.140 10 1 C C 40.470 10 4 The SAS System 7 08:17 Wednesday, November 7, 2001 General Linear Models Procedure Bonferroni (Dunn) T tests for variable: Y NOTE: This test controls the type I experimentwise error rate, but generally has a higher type II error rate than REGWQ. Alpha= 0.05 df= 36 MSE= 6.139833 Critical Value of T= 2.79 Minimum Significant Difference= 3.0939 Means with the same letter are not significantly different. Bon Grouping Mean N BRAND A 89.440 10 2 B 67.950 10 3 C 43.140 10 1 C C 40.470 10 4 The SAS System 8 08:17 Wednesday, November 7, 2001 General Linear Models Procedure Scheffe's test for variable: Y NOTE: This test controls the type I experimentwise error rate but generally has a higher type II error rate than REGWF for all pairwise comparisons Alpha= 0.05 df= 36 MSE= 6.139833 Critical Value of F= 2.86627 Minimum Significant Difference= 3.2495 Means with the same letter are not significantly different. Scheffe Grouping Mean N BRAND A 89.440 10 2 B 67.950 10 3 C 43.140 10 1 C C 40.470 10 4 The SAS System 9 08:17 Wednesday, November 7, 2001 OBS BRAND _TYPE_ _FREQ_ MEAN 1 1 0 10 43.14 2 2 0 10 89.44 3 3 0 10 67.95 4 4 0 10 40.47 The SAS System 10 08:17 Wednesday, November 7, 2001 --------------------------------------------------------------------- 90 + | | + | | | | | | | | | | | | | | | 80 + | | | | | | | | | | | | | | | | | 70 + | | | | + | M | | E | | A | | N | | | | | | 60 + | | | | | | | | | | | | | | | | | 50 + | | | | | | | | | | | | + | | | | | 40 + + | +---------------+-----------------+-----------------+---------------+ 10 25 50 75 90 Normal Percentiles