The SAS System 1 20:47 Monday, November 24, 2003 General Linear Models Procedure Class Level Information Class Levels Values DESIGN 4 1 2 3 4 Number of observations in data set = 19 The SAS System 2 20:47 Monday, November 24, 2003 General Linear Models Procedure Dependent Variable: Y Sum of Mean Source DF Squares Square F Value Pr > F Model 3 588.22105263 196.07368421 18.59 0.0001 Error 15 158.20000000 10.54666667 Corrected Total 18 746.42105263 R-Square C.V. Root MSE Y Mean 0.788055 17.43042 3.2475632 18.631579 Source DF Type I SS Mean Square F Value Pr > F DESIGN 3 588.22105263 196.07368421 18.59 0.0001 Source DF Type III SS Mean Square F Value Pr > F DESIGN 3 588.22105263 196.07368421 18.59 0.0001 Contrast DF Contrast SS Mean Square F Value Pr > F Design 1 vs Design 2 1 3.60000000 3.60000000 0.34 0.5677 Design 1 vs Design 3 1 53.35555556 53.35555556 5.06 0.0399 Design 2 vs Design 4 1 476.10000000 476.10000000 45.14 0.0001 Design 3 vs Design 4 1 131.75555556 131.75555556 12.49 0.0030 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate LSM overall 18.6750000 24.95 0.0001 0.74852633 LSM design 1 14.6000000 10.05 0.0001 1.45235441 LSM design 2 13.4000000 9.23 0.0001 1.45235441 LSM design 3 19.5000000 12.01 0.0001 1.62378159 LSM design 4 27.2000000 18.73 0.0001 1.45235441 LSM design 1-2 1.2000000 0.58 0.5677 2.05393930 LSM design 1-3 -4.9000000 -2.25 0.0399 2.17853162 LSM design 2-4 -13.8000000 -6.72 0.0001 2.05393930 LSM design 3-4 -7.7000000 -3.53 0.0030 2.17853162 LSM (1+2)-(3+4) -18.7000000 -6.25 0.0001 2.99410532 LSM (1+2)-(3+4) -9.3500000 -6.25 0.0001 1.49705266 LSM (1+3)-(2+4) -3.2500000 -2.17 0.0464 1.49705266 The SAS System 3 20:47 Monday, November 24, 2003 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= 15 MSE= 10.54667 F= 18.59106 Critical Value of T= 2.00599 Minimum Significant Difference= 4.247 WARNING: Cell sizes are not equal. Harmonic Mean of cell sizes= 4.705882 Means with the same letter are not significantly different. Waller Grouping Mean N DESIGN A 27.200 5 4 B 19.500 4 3 C 14.600 5 1 C C 13.400 5 2 The SAS System 4 20:47 Monday, November 24, 2003 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= 15 MSE= 10.54667 Critical Value of T= 2.13 Least Significant Difference= 4.5126 WARNING: Cell sizes are not equal. Harmonic Mean of cell sizes= 4.705882 Means with the same letter are not significantly different. T Grouping Mean N DESIGN A 27.200 5 4 B 19.500 4 3 C 14.600 5 1 C C 13.400 5 2 The SAS System 5 20:47 Monday, November 24, 2003 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= 15 MSE= 10.54667 WARNING: Cell sizes are not equal. Harmonic Mean of cell sizes= 4.705882 Number of Means 2 3 4 Critical Range 4.513 4.730 4.866 Means with the same letter are not significantly different. Duncan Grouping Mean N DESIGN A 27.200 5 4 B 19.500 4 3 C 14.600 5 1 C C 13.400 5 2 The SAS System 6 20:47 Monday, November 24, 2003 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= 15 MSE= 10.54667 Critical Value of Studentized Range= 4.076 Minimum Significant Difference= 6.1019 WARNING: Cell sizes are not equal. Harmonic Mean of cell sizes= 4.705882 Means with the same letter are not significantly different. Tukey Grouping Mean N DESIGN A 27.200 5 4 B 19.500 4 3 B B 14.600 5 1 B B 13.400 5 2 The SAS System 7 20:47 Monday, November 24, 2003 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= 15 MSE= 10.54667 Critical Value of T= 3.04 Minimum Significant Difference= 6.4283 WARNING: Cell sizes are not equal. Harmonic Mean of cell sizes= 4.705882 Means with the same letter are not significantly different. Bon Grouping Mean N DESIGN A 27.200 5 4 B 19.500 4 3 B B 14.600 5 1 B B 13.400 5 2 The SAS System 8 20:47 Monday, November 24, 2003 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= 15 MSE= 10.54667 Critical Value of F= 3.28738 Minimum Significant Difference= 6.6487 WARNING: Cell sizes are not equal. Harmonic Mean of cell sizes= 4.705882 Means with the same letter are not significantly different. Scheffe Grouping Mean N DESIGN A 27.200 5 4 B 19.500 4 3 B B 14.600 5 1 B B 13.400 5 2 The SAS System 9 20:47 Monday, November 24, 2003 General Linear Models Procedure Tukey's Studentized Range (HSD) Test for variable: Y NOTE: This test controls the type I experimentwise error rate. Alpha= 0.1 Confidence= 0.9 df= 15 MSE= 10.54667 Critical Value of Studentized Range= 3.540 Comparisons significant at the 0.1 level are indicated by '***'. Simultaneous Simultaneous Lower Difference Upper DESIGN Confidence Between Confidence Comparison Limit Means Limit 4 - 3 2.247 7.700 13.153 *** 4 - 1 7.459 12.600 17.741 *** 4 - 2 8.659 13.800 18.941 *** 3 - 4 -13.153 -7.700 -2.247 *** 3 - 1 -0.553 4.900 10.353 3 - 2 0.647 6.100 11.553 *** 1 - 4 -17.741 -12.600 -7.459 *** 1 - 3 -10.353 -4.900 0.553 1 - 2 -3.941 1.200 6.341 2 - 4 -18.941 -13.800 -8.659 *** 2 - 3 -11.553 -6.100 -0.647 *** 2 - 1 -6.341 -1.200 3.941 The SAS System 10 20:47 Monday, November 24, 2003 General Linear Models Procedure Class Level Information Class Levels Values DESIGN 4 1 2 3 4 Number of observations in data set = 19 The SAS System 11 20:47 Monday, November 24, 2003 General Linear Models Procedure Dependent Variable: Y Sum of Mean Source DF Squares Square F Value Pr > F Model 3 588.22105263 196.07368421 18.59 0.0001 Error 15 158.20000000 10.54666667 Corrected Total 18 746.42105263 R-Square C.V. Root MSE Y Mean 0.788055 17.43042 3.2475632 18.631579 Source DF Type I SS Mean Square F Value Pr > F DESIGN 3 588.22105263 196.07368421 18.59 0.0001 Source DF Type III SS Mean Square F Value Pr > F DESIGN 3 588.22105263 196.07368421 18.59 0.0001 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate Test 1: 1.2000000 0.58 0.5677 2.05393930 Test 2: -4.9000000 -2.25 0.0399 2.17853162 Test 3: -13.8000000 -6.72 0.0001 2.05393930 Test 4: -7.7000000 -3.53 0.0030 2.17853162 Test 5: -9.3500000 -6.25 0.0001 1.49705266 Test 6: -3.2500000 -2.17 0.0464 1.49705266