The SAS System 09:04 Thursday, February 14, 2002 30 Obs stimulus brand scent soft oz pr subj1 subj2 subj3 subj4 subj5 x1 status scen sof bran 1 1 complete fresh n 48 4.99 1 3 3 2 2 1 active 2 0 1 2 2 complete fresh y 32 2.99 1 3 3 5 5 1 active 2 1 1 3 3 complete lemon n 32 2.99 1 2 7 5 1 1 active 1 0 1 4 4 Complete lemon y 64 3.99 1 9 5 8 1 1 active 1 1 1 5 5 complete U n 64 3.99 1 9 7 8 7 1 active 3 0 1 6 6 complete U y 48 4.99 1 3 3 2 3 1 active 3 1 1 7 7 Smile fresh n 64 2.99 1 9 9 9 6 1 active 2 0 2 8 8 Smile fresh y 48 3.99 1 7 7 6 5 1 active 2 1 2 9 9 Smile lemon n 48 3.99 1 7 7 6 1 1 active 1 0 2 10 10 Smile lemon y 32 4.99 1 1 1 1 1 1 active 1 1 2 11 11 Smile U n 32 4.99 1 1 3 1 2 1 active 3 0 2 12 12 Smile U y 64 2.99 1 9 3 9 9 1 active 3 1 2 13 13 Wave fresh n 32 3.99 7 1 7 4 5 1 active 2 0 3 14 14 Wave fresh y 64 4.99 5 5 3 3 2 1 active 2 1 3 15 15 Wave lemon n 64 4.99 5 5 5 3 1 1 active 1 0 3 16 16 Wave lemon y 48 2.99 9 9 5 7 1 1 active 1 1 3 17 17 Wave U n 48 2.99 9 9 5 7 7 1 active 3 0 3 18 18 Wave U y 32 3.99 7 1 5 4 5 1 active 3 1 3 19 19 Wave lemon n 64 2.99 8 9 6 9 3 0 holdout 1 0 3 20 20 Smile lemon n 32 4.99 2 1 3 2 1 0 holdout 1 0 2 21 21 Smile fresh y 48 2.99 2 8 4 5 5 0 holdout 2 1 2 22 22 Complete U y 32 2.99 2 4 2 5 6 0 holdout 3 1 1 23 23 Complete lemon y 48 3.99 2 6 6 6 1 0 holdout 1 1 1 24 24 complete lemon y 64 2.99 . . . . . -1 simulati 1 1 1 25 25 Smile fresh y 48 2.99 . . . . . -1 simulati 2 1 2 26 26 Smile u y 48 3.99 . . . . . -1 simulati 3 1 2 27 27 Wave u y 48 2.99 . . . . . -1 simulati 3 1 3 28 28 Smile u n 48 2.99 . . . . . -1 simulati 3 0 2 The SAS System 09:04 Thursday, February 14, 2002 31 The TRANSREG Procedure Linear(subj1) Algorithm converged. The TRANSREG Procedure Hypothesis Tests for Linear(subj1) Univariate ANOVA Table Based on the Usual Degrees of Freedom Sum of Mean Source DF Squares Square F Value Liberal p Model 9 225.2701 25.03001 67.94 >= <.0001 Error 18 6.6311 0.36839 Corrected Total 27 231.9012 The above statistics are not adjusted for the fact that the dependent variable was transformed and so are generally liberal. Root MSE 0.60695 R-Square 0.9714 Dependent Mean 3.04348 Adj R-Sq 0.9571 Coeff Var 19.94278 The SAS System 09:04 Thursday, February 14, 2002 32 The TRANSREG Procedure Adjusted Multivariate ANOVA Table Based on the Usual Degrees of Freedom Dependent Variable Scoring Parameters=6 S=6 M=1 N=5.5 Statistic Value F Value Num DF Den DF p Wilks' Lambda 0.028594 1.32 54 70.881 <= 0.1339 Pillai's Trace 0.971406 0.39 54 108 <= 0.9999 Hotelling-Lawley Trace 33.97185 7.41 54 30.069 <= <.0001 Roy's Greatest Root 33.97185 67.94 9 18 >= <.0001 The Wilks' Lambda, Pillai's Trace, and Hotelling-Lawley Trace statistics are a conservative adjustment of the normal statistics. Roy's Greatest Root is liberal. These statistics are normally defined in terms of the squared canonical correlations which are the eigenvalues of the matrix H*inv(H+E). Here the R-Square is used for the first eigenvalue and all other eigenvalues are set to zero since only one linear combination is used. Degrees of freedom are computed assuming all linear combinations contribute to the Lambda and Trace statistics, so the F tests for those statistics are conservative. The p values for the liberal and conservative statistics provide approximate lower and upper bounds on p. A liberal test statistic with conservative degrees of freedom and a conservative test statistic with liberal degrees of freedom yield at best an approximate p value, which is indicated by a "~" before the p value. Utilities Table Based on the Usual Degrees of Freedom Importance Standard (% Utility Label Utility Error Range) Variable Intercept 3.0730 0.12303 Intercept bran 1 -2.0897 0.16947 64.010 Class.bran1 bran 2 -1.9568 0.16262 Class.bran2 bran 3 4.0465 0.17178 Class.bran3 scen 1 0.2051 0.16646 7.261 Class.scen1 scen 2 -0.4506 0.17210 Class.scen2 scen 3 0.2455 0.16218 Class.scen3 sof 0 0.0718 0.12067 1.499 Class.sof0 sof 1 -0.0718 0.12067 Class.sof1 oz 32 0.0713 0.17410 13.776 Class.oz32 oz 48 0.6247 0.16400 Class.oz48 oz 64 -0.6959 0.17654 Class.oz64 pr 2.99 0.6827 0.15597 13.455 Class.pr2D99 The standard errors are not adjusted for the fact that the dependent variable was transformed and so are generally liberal (too small). The SAS System 09:04 Thursday, February 14, 2002 33 The TRANSREG Procedure Utilities Table Based on the Usual Degrees of Freedom Importance Standard (% Utility Label Utility Error Range) Variable pr 3.99 -0.0755 0.17417 Class.pr3D99 pr 4.99 -0.6071 0.18435 Class.pr4D99 The standard errors are not adjusted for the fact that the dependent variable was transformed and so are generally liberal (too small). The SAS System 09:04 Thursday, February 14, 2002 34 The TRANSREG Procedure Linear(subj2) Algorithm converged. The TRANSREG Procedure Hypothesis Tests for Linear(subj2) Univariate ANOVA Table Based on the Usual Degrees of Freedom Sum of Mean Source DF Squares Square F Value Liberal p Model 9 269.4687 29.94097 40.41 >= <.0001 Error 18 13.3376 0.74098 Corrected Total 27 282.8063 The above statistics are not adjusted for the fact that the dependent variable was transformed and so are generally liberal. Root MSE 0.86080 R-Square 0.9528 Dependent Mean 5.26087 Adj R-Sq 0.9293 Coeff Var 16.36232 The SAS System 09:04 Thursday, February 14, 2002 35 The TRANSREG Procedure Adjusted Multivariate ANOVA Table Based on the Usual Degrees of Freedom Dependent Variable Scoring Parameters=6 S=6 M=1 N=5.5 Statistic Value F Value Num DF Den DF p Wilks' Lambda 0.047162 1.08 54 70.881 <= 0.3821 Pillai's Trace 0.952838 0.38 54 108 <= 0.9999 Hotelling-Lawley Trace 20.2037 4.41 54 30.069 <= <.0001 Roy's Greatest Root 20.2037 40.41 9 18 >= <.0001 The Wilks' Lambda, Pillai's Trace, and Hotelling-Lawley Trace statistics are a conservative adjustment of the normal statistics. Roy's Greatest Root is liberal. These statistics are normally defined in terms of the squared canonical correlations which are the eigenvalues of the matrix H*inv(H+E). Here the R-Square is used for the first eigenvalue and all other eigenvalues are set to zero since only one linear combination is used. Degrees of freedom are computed assuming all linear combinations contribute to the Lambda and Trace statistics, so the F tests for those statistics are conservative. The p values for the liberal and conservative statistics provide approximate lower and upper bounds on p. A liberal test statistic with conservative degrees of freedom and a conservative test statistic with liberal degrees of freedom yield at best an approximate p value, which is indicated by a "~" before the p value. Utilities Table Based on the Usual Degrees of Freedom Importance Standard (% Utility Label Utility Error Range) Variable Intercept 4.6167 0.17449 Intercept bran 1 -0.3549 0.24035 8.126 Class.bran1 bran 2 0.6033 0.23064 Class.bran2 bran 3 -0.2484 0.24363 Class.bran3 scen 1 0.2649 0.23608 7.070 Class.scen1 scen 2 -0.5493 0.24408 Class.scen2 scen 3 0.2844 0.23000 Class.scen3 sof 0 -0.0514 0.17114 0.871 Class.sof0 sof 1 0.0514 0.17114 Class.sof1 oz 32 -3.5503 0.24692 50.962 Class.oz32 oz 48 1.0909 0.23259 Class.oz48 oz 64 2.4594 0.25038 Class.oz64 pr 2.99 1.7567 0.22120 32.971 Class.pr2D99 The standard errors are not adjusted for the fact that the dependent variable was transformed and so are generally liberal (too small). The SAS System 09:04 Thursday, February 14, 2002 36 The TRANSREG Procedure Utilities Table Based on the Usual Degrees of Freedom Importance Standard (% Utility Label Utility Error Range) Variable pr 3.99 0.3749 0.24702 Class.pr3D99 pr 4.99 -2.1315 0.26146 Class.pr4D99 The standard errors are not adjusted for the fact that the dependent variable was transformed and so are generally liberal (too small). The SAS System 09:04 Thursday, February 14, 2002 37 The TRANSREG Procedure Linear(subj3) Algorithm converged. The TRANSREG Procedure Hypothesis Tests for Linear(subj3) Univariate ANOVA Table Based on the Usual Degrees of Freedom Sum of Mean Source DF Squares Square F Value Liberal p Model 9 88.8496 9.872177 8.03 >= 0.0001 Error 18 22.1385 1.229919 Corrected Total 27 110.9881 The above statistics are not adjusted for the fact that the dependent variable was transformed and so are generally liberal. Root MSE 1.10902 R-Square 0.8005 Dependent Mean 4.73913 Adj R-Sq 0.7008 Coeff Var 23.40128 The SAS System 09:04 Thursday, February 14, 2002 38 The TRANSREG Procedure Adjusted Multivariate ANOVA Table Based on the Usual Degrees of Freedom Dependent Variable Scoring Parameters=6 S=6 M=1 N=5.5 Statistic Value F Value Num DF Den DF p Wilks' Lambda 0.199468 0.49 54 70.881 <= 0.9967 Pillai's Trace 0.800532 0.31 54 108 <= 1.0000 Hotelling-Lawley Trace 4.013344 0.88 54 30.069 <= 0.6710 Roy's Greatest Root 4.013344 8.03 9 18 >= 0.0001 The Wilks' Lambda, Pillai's Trace, and Hotelling-Lawley Trace statistics are a conservative adjustment of the normal statistics. Roy's Greatest Root is liberal. These statistics are normally defined in terms of the squared canonical correlations which are the eigenvalues of the matrix H*inv(H+E). Here the R-Square is used for the first eigenvalue and all other eigenvalues are set to zero since only one linear combination is used. Degrees of freedom are computed assuming all linear combinations contribute to the Lambda and Trace statistics, so the F tests for those statistics are conservative. The p values for the liberal and conservative statistics provide approximate lower and upper bounds on p. A liberal test statistic with conservative degrees of freedom and a conservative test statistic with liberal degrees of freedom yield at best an approximate p value, which is indicated by a "~" before the p value. Utilities Table Based on the Usual Degrees of Freedom Importance Standard (% Utility Label Utility Error Range) Variable Intercept 4.7837 0.22481 Intercept bran 1 -0.1732 0.30966 3.103 Class.bran1 bran 2 0.0904 0.29714 Class.bran2 bran 3 0.0828 0.31388 Class.bran3 scen 1 0.1063 0.30416 12.441 Class.scen1 scen 2 0.4753 0.31446 Class.scen2 scen 3 -0.5815 0.29632 Class.scen3 sof 0 1.1032 0.22048 25.976 Class.sof0 sof 1 -1.1032 0.22048 Class.sof1 oz 32 -0.6872 0.31811 13.663 Class.oz32 oz 48 0.2139 0.29966 Class.oz48 oz 64 0.4734 0.32258 Class.oz64 pr 2.99 0.2290 0.28498 44.816 Class.pr2D99 The standard errors are not adjusted for the fact that the dependent variable was transformed and so are generally liberal (too small). The SAS System 09:04 Thursday, February 14, 2002 39 The TRANSREG Procedure Utilities Table Based on the Usual Degrees of Freedom Importance Standard (% Utility Label Utility Error Range) Variable pr 3.99 1.7889 0.31825 Class.pr3D99 pr 4.99 -2.0180 0.33685 Class.pr4D99 The standard errors are not adjusted for the fact that the dependent variable was transformed and so are generally liberal (too small). The SAS System 09:04 Thursday, February 14, 2002 40 The TRANSREG Procedure Linear(subj4) Algorithm converged. The TRANSREG Procedure Hypothesis Tests for Linear(subj4) Univariate ANOVA Table Based on the Usual Degrees of Freedom Sum of Mean Source DF Squares Square F Value Liberal p Model 9 173.1782 19.24202 59.82 >= <.0001 Error 18 5.7902 0.32168 Corrected Total 27 178.9684 The above statistics are not adjusted for the fact that the dependent variable was transformed and so are generally liberal. Root MSE 0.56717 R-Square 0.9676 Dependent Mean 5.08696 Adj R-Sq 0.9515 Coeff Var 11.14944 The SAS System 09:04 Thursday, February 14, 2002 41 The TRANSREG Procedure Adjusted Multivariate ANOVA Table Based on the Usual Degrees of Freedom Dependent Variable Scoring Parameters=6 S=6 M=1 N=5.5 Statistic Value F Value Num DF Den DF p Wilks' Lambda 0.032353 1.26 54 70.881 <= 0.1798 Pillai's Trace 0.967647 0.38 54 108 <= 0.9999 Hotelling-Lawley Trace 29.90879 6.53 54 30.069 <= <.0001 Roy's Greatest Root 29.90879 59.82 9 18 >= <.0001 The Wilks' Lambda, Pillai's Trace, and Hotelling-Lawley Trace statistics are a conservative adjustment of the normal statistics. Roy's Greatest Root is liberal. These statistics are normally defined in terms of the squared canonical correlations which are the eigenvalues of the matrix H*inv(H+E). Here the R-Square is used for the first eigenvalue and all other eigenvalues are set to zero since only one linear combination is used. Degrees of freedom are computed assuming all linear combinations contribute to the Lambda and Trace statistics, so the F tests for those statistics are conservative. The p values for the liberal and conservative statistics provide approximate lower and upper bounds on p. A liberal test statistic with conservative degrees of freedom and a conservative test statistic with liberal degrees of freedom yield at best an approximate p value, which is indicated by a "~" before the p value. Utilities Table Based on the Usual Degrees of Freedom Importance Standard (% Utility Label Utility Error Range) Variable Intercept 4.6313 0.11497 Intercept bran 1 -0.0020 0.15836 5.615 Class.bran1 bran 2 0.2762 0.15196 Class.bran2 bran 3 -0.2742 0.16052 Class.bran3 scen 1 0.2379 0.15555 6.471 Class.scen1 scen 2 -0.3964 0.16082 Class.scen2 scen 3 0.1585 0.15154 Class.scen3 sof 0 0.1473 0.11276 3.005 Class.sof0 sof 1 -0.1473 0.11276 Class.sof1 oz 32 -1.6300 0.16269 35.186 Class.oz32 oz 48 -0.1895 0.15325 Class.oz48 oz 64 1.8194 0.16497 Class.oz64 pr 2.99 1.9030 0.14574 49.724 Class.pr2D99 The standard errors are not adjusted for the fact that the dependent variable was transformed and so are generally liberal (too small). The SAS System 09:04 Thursday, February 14, 2002 42 The TRANSREG Procedure Utilities Table Based on the Usual Degrees of Freedom Importance Standard (% Utility Label Utility Error Range) Variable pr 3.99 1.0687 0.16276 Class.pr3D99 pr 4.99 -2.9717 0.17227 Class.pr4D99 The standard errors are not adjusted for the fact that the dependent variable was transformed and so are generally liberal (too small). The SAS System 09:04 Thursday, February 14, 2002 43 The TRANSREG Procedure Linear(subj5) Algorithm converged. The TRANSREG Procedure Hypothesis Tests for Linear(subj5) Univariate ANOVA Table Based on the Usual Degrees of Freedom Sum of Mean Source DF Squares Square F Value Liberal p Model 9 150.4692 16.71880 18.67 >= <.0001 Error 18 16.1197 0.89554 Corrected Total 27 166.5889 The above statistics are not adjusted for the fact that the dependent variable was transformed and so are generally liberal. Root MSE 0.94633 R-Square 0.9032 Dependent Mean 3.47826 Adj R-Sq 0.8549 Coeff Var 27.20697 The SAS System 09:04 Thursday, February 14, 2002 44 The TRANSREG Procedure Adjusted Multivariate ANOVA Table Based on the Usual Degrees of Freedom Dependent Variable Scoring Parameters=6 S=6 M=1 N=5.5 Statistic Value F Value Num DF Den DF p Wilks' Lambda 0.096763 0.76 54 70.881 <= 0.8502 Pillai's Trace 0.903237 0.35 54 108 <= 1.0000 Hotelling-Lawley Trace 9.334492 2.04 54 30.069 <= 0.0189 Roy's Greatest Root 9.334492 18.67 9 18 >= <.0001 The Wilks' Lambda, Pillai's Trace, and Hotelling-Lawley Trace statistics are a conservative adjustment of the normal statistics. Roy's Greatest Root is liberal. These statistics are normally defined in terms of the squared canonical correlations which are the eigenvalues of the matrix H*inv(H+E). Here the R-Square is used for the first eigenvalue and all other eigenvalues are set to zero since only one linear combination is used. Degrees of freedom are computed assuming all linear combinations contribute to the Lambda and Trace statistics, so the F tests for those statistics are conservative. The p values for the liberal and conservative statistics provide approximate lower and upper bounds on p. A liberal test statistic with conservative degrees of freedom and a conservative test statistic with liberal degrees of freedom yield at best an approximate p value, which is indicated by a "~" before the p value. Utilities Table Based on the Usual Degrees of Freedom Importance Standard (% Utility Label Utility Error Range) Variable Intercept 3.2554 0.19183 Intercept bran 1 -0.4617 0.26423 11.079 Class.bran1 bran 2 0.5702 0.25355 Class.bran2 bran 3 -0.1085 0.26783 Class.bran3 scen 1 -2.4142 0.25954 46.949 Class.scen1 scen 2 0.4554 0.26833 Class.scen2 scen 3 1.9588 0.25285 Class.scen3 sof 0 0.0621 0.18814 1.333 Class.sof0 sof 1 -0.0621 0.18814 Class.sof1 oz 32 -0.2992 0.27145 10.637 Class.oz32 oz 48 -0.3458 0.25570 Class.oz48 oz 64 0.6450 0.27526 Class.oz64 pr 2.99 1.1846 0.24318 30.002 Class.pr2D99 The standard errors are not adjusted for the fact that the dependent variable was transformed and so are generally liberal (too small). The SAS System 09:04 Thursday, February 14, 2002 45 The TRANSREG Procedure Utilities Table Based on the Usual Degrees of Freedom Importance Standard (% Utility Label Utility Error Range) Variable pr 3.99 0.4253 0.27156 Class.pr3D99 pr 4.99 -1.6099 0.28743 Class.pr4D99 The standard errors are not adjusted for the fact that the dependent variable was transformed and so are generally liberal (too small).