The SAS System 1 10:26 Thursday, February 19, 1998 TABLE OF HEIGHT BY WIDTH HEIGHT(Display Height) WIDTH(Display Width) Frequency|Regular |Wide | Total ---------+--------+--------+ Bottom | 2 | 2 | 4 ---------+--------+--------+ Middle | 2 | 2 | 4 ---------+--------+--------+ Top | 2 | 2 | 4 ---------+--------+--------+ Total 6 6 12 TABLE OF HWCOMBO BY HEIGHT HWCOMBO HEIGHT(Display Height) Frequency|Bottom |Middle |Top | Total ---------+--------+--------+--------+ 11 | 2 | 0 | 0 | 2 ---------+--------+--------+--------+ 12 | 2 | 0 | 0 | 2 ---------+--------+--------+--------+ 21 | 0 | 2 | 0 | 2 ---------+--------+--------+--------+ 22 | 0 | 2 | 0 | 2 ---------+--------+--------+--------+ 31 | 0 | 0 | 2 | 2 ---------+--------+--------+--------+ 32 | 0 | 0 | 2 | 2 ---------+--------+--------+--------+ Total 4 4 4 12 The SAS System 2 10:26 Thursday, February 19, 1998 TABLE OF HWCOMBO BY WIDTH HWCOMBO WIDTH(Display Width) Frequency|Regular |Wide | Total ---------+--------+--------+ 11 | 2 | 0 | 2 ---------+--------+--------+ 12 | 0 | 2 | 2 ---------+--------+--------+ 21 | 2 | 0 | 2 ---------+--------+--------+ 22 | 0 | 2 | 2 ---------+--------+--------+ 31 | 2 | 0 | 2 ---------+--------+--------+ 32 | 0 | 2 | 2 ---------+--------+--------+ Total 6 6 12 The SAS System 3 10:26 Thursday, February 19, 1998 General Linear Models Procedure Class Level Information Class Levels Values HEIGHT 3 Bottom Middle Top WIDTH 2 Regular Wide Number of observations in data set = 12 The SAS System 4 10:26 Thursday, February 19, 1998 General Linear Models Procedure Dependent Variable: SALES Sales in cases Sum of Mean Source DF Squares Square F Value Pr > F Model 5 1580.0000000 316.0000000 30.58 0.0003 Error 6 62.0000000 10.3333333 Corrected Total 11 1642.0000000 R-Square C.V. Root MSE SALES Mean 0.962241 6.303040 3.2145503 51.000000 Source DF Type I SS Mean Square F Value Pr > F HEIGHT 2 1544.0000000 772.0000000 74.71 0.0001 WIDTH 1 12.0000000 12.0000000 1.16 0.3226 HEIGHT*WIDTH 2 24.0000000 12.0000000 1.16 0.3747 Source DF Type III SS Mean Square F Value Pr > F HEIGHT 2 1544.0000000 772.0000000 74.71 0.0001 WIDTH 1 12.0000000 12.0000000 1.16 0.3226 HEIGHT*WIDTH 2 24.0000000 12.0000000 1.16 0.3747 The SAS System 5 10:26 Thursday, February 19, 1998 General Linear Models Procedure Level of ------------SALES------------ HEIGHT N Mean SD Bottom 4 44.0000000 3.16227766 Middle 4 67.0000000 3.74165739 Top 4 42.0000000 2.94392029 Level of ------------SALES------------ WIDTH N Mean SD Regular 6 50.0000000 12.0664825 Wide 6 52.0000000 13.4313067 Level of Level of ------------SALES------------ HEIGHT WIDTH N Mean SD Bottom Regular 2 45.0000000 2.82842712 Bottom Wide 2 43.0000000 4.24264069 Middle Regular 2 65.0000000 4.24264069 Middle Wide 2 69.0000000 2.82842712 Top Regular 2 40.0000000 1.41421356 Top Wide 2 44.0000000 2.82842712 The SAS System 6 10:26 Thursday, February 19, 1998 General Linear Models Procedure Tukey's Studentized Range (HSD) Test for variable: SALES NOTE: This test controls the type I experimentwise error rate. Alpha= 0.05 Confidence= 0.95 df= 6 MSE= 10.33333 Critical Value of Studentized Range= 4.339 Minimum Significant Difference= 6.9743 Comparisons significant at the 0.05 level are indicated by '***'. Simultaneous Simultaneous Lower Difference Upper HEIGHT Confidence Between Confidence Comparison Limit Means Limit Middle - Bottom 16.026 23.000 29.974 *** Middle - Top 18.026 25.000 31.974 *** Bottom - Middle -29.974 -23.000 -16.026 *** Bottom - Top -4.974 2.000 8.974 Top - Middle -31.974 -25.000 -18.026 *** Top - Bottom -8.974 -2.000 4.974 The SAS System 7 10:26 Thursday, February 19, 1998 General Linear Models Procedure Bonferroni (Dunn) T tests for variable: SALES NOTE: This test controls the type I experimentwise error rate but generally has a higher type II error rate than Tukey's for all pairwise comparisons. Alpha= 0.05 Confidence= 0.95 df= 6 MSE= 10.33333 Critical Value of T= 3.28746 Minimum Significant Difference= 7.4725 Comparisons significant at the 0.05 level are indicated by '***'. Simultaneous Simultaneous Lower Difference Upper HEIGHT Confidence Between Confidence Comparison Limit Means Limit Middle - Bottom 15.528 23.000 30.472 *** Middle - Top 17.528 25.000 32.472 *** Bottom - Middle -30.472 -23.000 -15.528 *** Bottom - Top -5.472 2.000 9.472 Top - Middle -32.472 -25.000 -17.528 *** Top - Bottom -9.472 -2.000 5.472 The SAS System 8 10:26 Thursday, February 19, 1998 General Linear Models Procedure Scheffe's test for variable: SALES NOTE: This test controls the type I experimentwise error rate but generally has a higher type II error rate than Tukey's for all pairwise comparisons. Alpha= 0.05 Confidence= 0.95 df= 6 MSE= 10.33333 Critical Value of F= 5.14325 Minimum Significant Difference= 7.2902 Comparisons significant at the 0.05 level are indicated by '***'. Simultaneous Simultaneous Lower Difference Upper HEIGHT Confidence Between Confidence Comparison Limit Means Limit Middle - Bottom 15.710 23.000 30.290 *** Middle - Top 17.710 25.000 32.290 *** Bottom - Middle -30.290 -23.000 -15.710 *** Bottom - Top -5.290 2.000 9.290 Top - Middle -32.290 -25.000 -17.710 *** Top - Bottom -9.290 -2.000 5.290 The SAS System 9 10:26 Thursday, February 19, 1998 Model: MODEL1 Dependent Variable: SALES Sales in cases Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 5 1580.00000 316.00000 30.581 0.0003 Error 6 62.00000 10.33333 C Total 11 1642.00000 Root MSE 3.21455 R-square 0.9622 Dep Mean 51.00000 Adj R-sq 0.9308 C.V. 6.30304 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 51.000000 0.92796073 54.959 0.0001 H1 1 -7.000000 1.31233465 -5.334 0.0018 H2 1 16.000000 1.31233465 12.192 0.0001 W1 1 -1.000000 0.92796073 -1.078 0.3226 H1W1 1 2.000000 1.31233465 1.524 0.1783 H2W1 1 -1.000000 1.31233465 -0.762 0.4749 Variable Variable DF Label INTERCEP 1 Intercept H1 1 H2 1 W1 1 H1W1 1 H2W1 1 The SAS System 10 10:26 Thursday, February 19, 1998 Dependent Variable: SALES Test: HEIGHT Numerator: 772.0000 DF: 2 F value: 74.7097 Denominator: 10.33333 DF: 6 Prob>F: 0.0001 The SAS System 11 10:26 Thursday, February 19, 1998 Dependent Variable: SALES Test: WIDTH Numerator: 12.0000 DF: 1 F value: 1.1613 Denominator: 10.33333 DF: 6 Prob>F: 0.3226 The SAS System 12 10:26 Thursday, February 19, 1998 Dependent Variable: SALES Test: H_BY_W Numerator: 12.0000 DF: 2 F value: 1.1613 Denominator: 10.33333 DF: 6 Prob>F: 0.3747 The SAS System 13 10:26 Thursday, February 19, 1998 Model: MODEL1 NOTE: No intercept in model. R-square is redefined. Dependent Variable: SALES Sales in cases Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 6 32792.00000 5465.33333 528.903 0.0001 Error 6 62.00000 10.33333 U Total 12 32854.00000 Root MSE 3.21455 R-square 0.9981 Dep Mean 51.00000 Adj R-sq 0.9962 C.V. 6.30304 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| MU11 1 45.000000 2.27303028 19.797 0.0001 MU12 1 43.000000 2.27303028 18.917 0.0001 MU21 1 65.000000 2.27303028 28.596 0.0001 MU22 1 69.000000 2.27303028 30.356 0.0001 MU31 1 40.000000 2.27303028 17.598 0.0001 MU32 1 44.000000 2.27303028 19.357 0.0001 Variable Variable DF Label MU11 1 MU12 1 MU21 1 MU22 1 MU31 1 MU32 1 The SAS System 14 10:26 Thursday, February 19, 1998 Dependent Variable: SALES Test: HEIGHT Numerator: 772.0000 DF: 2 F value: 74.7097 Denominator: 10.33333 DF: 6 Prob>F: 0.0001 The SAS System 15 10:26 Thursday, February 19, 1998 Dependent Variable: SALES Test: WIDTH Numerator: 12.0000 DF: 1 F value: 1.1613 Denominator: 10.33333 DF: 6 Prob>F: 0.3226 The SAS System 16 10:26 Thursday, February 19, 1998 Dependent Variable: SALES Test: H_BY_W Numerator: 12.0000 DF: 2 F value: 1.1613 Denominator: 10.33333 DF: 6 Prob>F: 0.3747 The SAS System 17 10:26 Thursday, February 19, 1998 General Linear Models Procedure Class Level Information Class Levels Values HWCOMBO 6 11 12 21 22 31 32 Number of observations in data set = 12 The SAS System 18 10:26 Thursday, February 19, 1998 General Linear Models Procedure Dependent Variable: SALES Sales in cases Sum of Mean Source DF Squares Square F Value Pr > F Model 5 1580.0000000 316.0000000 30.58 0.0003 Error 6 62.0000000 10.3333333 Corrected Total 11 1642.0000000 R-Square C.V. Root MSE SALES Mean 0.962241 6.303040 3.2145503 51.000000 Source DF Type I SS Mean Square F Value Pr > F HWCOMBO 5 1580.0000000 316.0000000 30.58 0.0003 Source DF Type III SS Mean Square F Value Pr > F HWCOMBO 5 1580.0000000 316.0000000 30.58 0.0003 The SAS System 19 10:26 Thursday, February 19, 1998 General Linear Models Procedure Tukey's Studentized Range (HSD) Test for variable: SALES 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= 6 MSE= 10.33333 Critical Value of Studentized Range= 5.628 Minimum Significant Difference= 12.793 Means with the same letter are not significantly different. Tukey Grouping Mean N HWCOMBO A 69.000 2 22 A A 65.000 2 21 B 45.000 2 11 B B 44.000 2 32 B B 43.000 2 12 B B 40.000 2 31