21:08 Tuesday, March 28, 1995 General Linear Models Procedure Class Level Information Class Levels Values T 3 1 2 3 B 3 1 2 3 Number of observations in data set = 10 21:08 Tuesday, March 28, 1995 General Linear Models Procedure Type IV Estimable Functions for: T Effect Coefficients INTERCEPT 0 T 1 L2 2 L3 3 -L2-L3 B 1 0 2 0 3 0 T*B 1 1 L2 1 3 0 2 1 0.5*L3 2 2 0.5*L3 2 3 0 3 1 -L2-0.5*L3 3 2 -0.5*L3 NOTE: Other Type IV estimable functions exist. 21:08 Tuesday, March 28, 1995 General Linear Models Procedure Type IV Estimable Functions for: B Effect Coefficients INTERCEPT 0 T 1 0 2 0 3 0 B 1 L5 2 L6 3 -L5-L6 T*B 1 1 0.5*L5 1 3 -0.5*L5 2 1 0.5*L5 2 2 L6 2 3 -0.5*L5-L6 3 1 0 3 2 0 NOTE: Other Type IV estimable functions exist. 21:08 Tuesday, March 28, 1995 General Linear Models Procedure Type IV Estimable Functions for: T*B Effect Coefficients INTERCEPT 0 T 1 0 2 0 3 0 B 1 0 2 0 3 0 T*B 1 1 L8 1 3 -L8 2 1 L10 2 2 -L8-L10 2 3 L8 3 1 -L8-L10 3 2 L8+L10 21:08 Tuesday, March 28, 1995 General Linear Models Procedure Dependent Variable: Y Sum of Mean Source DF Squares Square F Value Pr > F Model 6 110.00000000 18.33333333 3.79 0.1506 Error 3 14.50000000 4.83333333 Corrected Total 9 124.50000000 R-Square C.V. Root MSE Y Mean 0.883534 29.31312 2.1984843 7.5000000 Source DF Type I SS Mean Square F Value Pr > F T 2 32.00000000 16.00000000 3.31 0.1741 B 2 59.22222222 29.61111111 6.13 0.0872 T*B 2 18.77777778 9.38888889 1.94 0.2876 Source DF Type II SS Mean Square F Value Pr > F T 2 10.72222222 5.36111111 1.11 0.4359 B 2 59.22222222 29.61111111 6.13 0.0872 T*B 2 18.77777778 9.38888889 1.94 0.2876 Source DF Type III SS Mean Square F Value Pr > F T 2 8.41346154 4.20673077 0.87 0.5034 B 2 61.96153846 30.98076923 6.41 0.0826 T*B 2 18.77777778 9.38888889 1.94 0.2876 Source DF Type IV SS Mean Square F Value Pr > F T 2* 6.00000000 3.00000000 0.62 0.5949 B 2* 66.50000000 33.25000000 6.88 0.0757 T*B 2 18.77777778 9.38888889 1.94 0.2876 * NOTE: Other Type IV Testable Hypotheses exist which may yield different SS. 21:08 Tuesday, March 28, 1995 General Linear Models Procedure Dependent Variable: Y T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT 5.500000000 B 1.58 0.2117 3.47610894 T 1 1.500000000 B 0.39 0.7200 3.80788655 2 5.000000000 B 1.61 0.2062 3.10912635 3 0.000000000 B . . . B 1 0.500000000 B 0.12 0.9109 4.11298756 2 3.500000000 B 1.30 0.2845 2.69258240 3 0.000000000 B . . . T*B 1 1 -3.500000000 B -0.75 0.5075 4.66368953 1 3 0.000000000 B . . . 2 1 -8.000000000 B -1.82 0.1664 4.39696865 2 2 0.000000000 B . . . 2 3 0.000000000 B . . . 3 1 0.000000000 B . . . 3 2 0.000000000 B . . . NOTE: The X'X matrix has been found to be singular and a generalized inverse was used to solve the normal equations. Estimates followed by the letter 'B' are biased, and are not unique estimators of the parameters. 21:08 Tuesday, March 28, 1995 General Linear Models Procedure Least Squares Means T B Y Std Err Pr > |T| LSMEAN LSMEAN LSMEAN H0:LSMEAN=0 Number 1 1 4.0000000 1.5545632 0.0823 1 1 3 7.0000000 1.5545632 0.0205 2 2 1 3.0000000 2.1984843 0.2657 3 2 2 14.0000000 2.1984843 0.0078 4 2 3 10.5000000 1.5545632 0.0066 5 3 1 6.0000000 2.1984843 0.0720 6 3 2 9.0000000 2.1984843 0.0264 7 Pr > |T| H0: LSMEAN(i)=LSMEAN(j) i/j 1 2 3 4 5 6 7 1 . 0.2657 0.7350 0.0339 0.0597 0.5115 0.1603 2 0.2657 . 0.2341 0.0804 0.2096 0.7350 0.5115 3 0.7350 0.2341 . 0.0384 0.0687 0.4058 0.1492 4 0.0339 0.0804 0.0384 . 0.2845 0.0823 0.2062 5 0.0597 0.2096 0.0687 0.2845 . 0.1933 0.6163 6 0.5115 0.7350 0.4058 0.0823 0.1933 . 0.4058 7 0.1603 0.5115 0.1492 0.2062 0.6163 0.4058 . NOTE: To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used. 21:08 Tuesday, March 28, 1995 General Linear Models Procedure Dependent Variable: Y Contrast DF Contrast SS Mean Square F Value Pr > F T1 vs. T2 ave over B 1 2.50000000 2.50000000 0.52 0.5240 T2 vs. T3 ave over B 1 1.00000000 1.00000000 0.21 0.6801 T1 vs. T3 at B1 1 2.66666667 2.66666667 0.55 0.5115 B1 vs. B2 ave over T 1 49.00000000 49.00000000 10.14 0.0499 B1 vs. B3 ave over T 1 44.10000000 44.10000000 9.12 0.0567 B2 vs. B3 at T2 1 8.16666667 8.16666667 1.69 0.2845 21:08 Tuesday, March 28, 1995 General Linear Models Procedure Class Level Information Class Levels Values TT 3 1 2 3 BB 3 1 2 3 Number of observations in data set = 10 21:08 Tuesday, March 28, 1995 General Linear Models Procedure Type IV Estimable Functions for: TT Effect Coefficients INTERCEPT 0 TT 1 L2 2 L3 3 -L2-L3 BB 1 0 2 0 3 0 TT*BB 1 2 0 1 3 L2 2 1 0.5*L3 2 2 0 2 3 0.5*L3 3 1 -0.5*L3 3 3 -L2-0.5*L3 NOTE: Other Type IV estimable functions exist. 21:08 Tuesday, March 28, 1995 General Linear Models Procedure Type IV Estimable Functions for: BB Effect Coefficients INTERCEPT 0 TT 1 0 2 0 3 0 BB 1 L5 2 L6 3 -L5-L6 TT*BB 1 2 0.5*L6 1 3 -0.5*L6 2 1 0.5*L5 2 2 0.5*L6 2 3 -0.5*L5-0.5*L6 3 1 0.5*L5 3 3 -0.5*L5 NOTE: Other Type IV estimable functions exist. 21:08 Tuesday, March 28, 1995 General Linear Models Procedure Type IV Estimable Functions for: TT*BB Effect Coefficients INTERCEPT 0 TT 1 0 2 0 3 0 BB 1 0 2 0 3 0 TT*BB 1 2 L8 1 3 -L8 2 1 L10 2 2 -L8 2 3 L8-L10 3 1 -L10 3 3 L10 21:08 Tuesday, March 28, 1995 General Linear Models Procedure Dependent Variable: Y Sum of Mean Source DF Squares Square F Value Pr > F Model 6 110.00000000 18.33333333 3.79 0.1506 Error 3 14.50000000 4.83333333 Corrected Total 9 124.50000000 R-Square C.V. Root MSE Y Mean 0.883534 29.31312 2.1984843 7.5000000 Source DF Type I SS Mean Square F Value Pr > F TT 2 32.00000000 16.00000000 3.31 0.1741 BB 2 59.22222222 29.61111111 6.13 0.0872 TT*BB 2 18.77777778 9.38888889 1.94 0.2876 Source DF Type II SS Mean Square F Value Pr > F TT 2 10.72222222 5.36111111 1.11 0.4359 BB 2 59.22222222 29.61111111 6.13 0.0872 TT*BB 2 18.77777778 9.38888889 1.94 0.2876 Source DF Type III SS Mean Square F Value Pr > F TT 2 8.41346154 4.20673077 0.87 0.5034 BB 2 61.96153846 30.98076923 6.41 0.0826 TT*BB 2 18.77777778 9.38888889 1.94 0.2876 Source DF Type IV SS Mean Square F Value Pr > F TT 2* 4.10714286 2.05357143 0.42 0.6879 BB 2* 70.77777778 35.38888889 7.32 0.0701 TT*BB 2 18.77777778 9.38888889 1.94 0.2876 * NOTE: Other Type IV Testable Hypotheses exist which may yield different SS. 21:08 Tuesday, March 28, 1995 General Linear Models Procedure Dependent Variable: Y T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT 4.00000000 B 2.57 0.0823 1.55456318 TT 1 2.00000000 B 0.74 0.5115 2.69258240 2 -1.00000000 B -0.37 0.7350 2.69258240 3 0.00000000 B . . . BB 1 3.00000000 B 1.36 0.2657 2.19848433 2 11.00000000 B 3.54 0.0384 3.10912635 3 0.00000000 B . . . TT*BB 1 2 -8.00000000 B -1.82 0.1664 4.39696865 1 3 0.00000000 B . . . 2 1 4.50000000 B 1.29 0.2861 3.47610894 2 2 0.00000000 B . . . 2 3 0.00000000 B . . . 3 1 0.00000000 B . . . 3 3 0.00000000 B . . . NOTE: The X'X matrix has been found to be singular and a generalized inverse was used to solve the normal equations. Estimates followed by the letter 'B' are biased, and are not unique estimators of the parameters.