/* Analysis of Covariance (ANACOVA) */ OPTIONS LS=75 PS=55 NODATE; DATA one; TITLE 'Analysis of Covariance (ANACOVA)'; INPUT sbp group $ 5-13 age grp_ind; DATALINES; 110 Placebo 20 0 118 Placebo 25 0 132 Placebo 30 0 140 Placebo 35 0 120 Treatment 30 1 128 Treatment 35 1 132 Treatment 35 1 138 Treatment 40 1 142 Treatment 40 1 150 Treatment 45 1 ; PROC TABULATE; CLASS group; VAR sbp age; TABLE (sbp age)*group, (N*f=5.0 MEAN STD); RUN; PROC REG; MODEL sbp = grp_ind age; TEST grp_ind=0; RUN; PROC GLM; CLASS group; MODEL sbp = group ; MEANS group / T; RUN; PROC GLM; CLASS group; MODEL sbp = group age / SOLUTION; MEANS group / T; LSMEANS group; RUN; QUIT; *************************************************************************** Analysis of Covariance (ANACOVA) 1 ---------------------------------------------------- N Mean Std ---------------------------------------------------- sbp group ------------ Placebo 4 125.00 13.52 -------------------------------------------- Treatment 6 135.00 10.64 ---------------------------------------------------- age Placebo 4 27.50 6.45 -------------------------------------------- Treatment 6 37.50 5.24 ---------------------------------------------------- Analysis of Covariance (ANACOVA) 2 The REG Procedure Model: MODEL1 Dependent Variable: sbp Number of Observations Read 10 Number of Observations Used 10 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 1330.38095 665.19048 197.14 <.0001 Error 7 23.61905 3.37415 Corrected Total 9 1354.00000 Root MSE 1.83689 R-Square 0.9826 Dependent Mean 131.00000 Adj R-Sq 0.9776 Coeff Var 1.40220 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 68.95238 3.25028 21.21 <.0001 grp_ind 1 -10.38095 1.64051 -6.33 0.0004 age 1 2.03810 0.11338 17.98 <.0001 Analysis of Covariance (ANACOVA) 3 The REG Procedure Model: MODEL1 Test 1 Results for Dependent Variable sbp Mean Source DF Square F Value Pr > F Numerator 1 135.10732 40.04 0.0004 Denominator 7 3.37415 Analysis of Covariance (ANACOVA) 4 The GLM Procedure Class Level Information Class Levels Values group 2 Placebo Treatment Number of Observations Read 10 Number of Observations Used 10 Analysis of Covariance (ANACOVA) 5 The GLM Procedure Dependent Variable: sbp Sum of Source DF Squares Mean Square F Value Pr > F Model 1 240.000000 240.000000 1.72 0.2256 Error 8 1114.000000 139.250000 Corrected Total 9 1354.000000 R-Square Coeff Var Root MSE sbp Mean 0.177253 9.007957 11.80042 131.0000 Source DF Type I SS Mean Square F Value Pr > F group 1 240.0000000 240.0000000 1.72 0.2256 Source DF Type III SS Mean Square F Value Pr > F group 1 240.0000000 240.0000000 1.72 0.2256 Analysis of Covariance (ANACOVA) 6 The GLM Procedure t Tests (LSD) for sbp NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 8 Error Mean Square 139.25 Critical Value of t 2.30600 Least Significant Difference 17.565 Harmonic Mean of Cell Sizes 4.8 NOTE: Cell sizes are not equal. Means with the same letter are not significantly different. t Grouping Mean N group A 135.000 6 Treatment A A 125.000 4 Placebo Analysis of Covariance (ANACOVA) 7 The GLM Procedure Class Level Information Class Levels Values group 2 Placebo Treatment Number of Observations Read 10 Number of Observations Used 10 Analysis of Covariance (ANACOVA) 8 The GLM Procedure Dependent Variable: sbp Sum of Source DF Squares Mean Square F Value Pr > F Model 2 1330.380952 665.190476 197.14 <.0001 Error 7 23.619048 3.374150 Corrected Total 9 1354.000000 R-Square Coeff Var Root MSE sbp Mean 0.982556 1.402203 1.836886 131.0000 Source DF Type I SS Mean Square F Value Pr > F group 1 240.000000 240.000000 71.13 <.0001 age 1 1090.380952 1090.380952 323.16 <.0001 Source DF Type III SS Mean Square F Value Pr > F group 1 135.107321 135.107321 40.04 0.0004 age 1 1090.380952 1090.380952 323.16 <.0001 Standard Parameter Estimate Error t Value Pr > |t| Intercept 58.57142857 B 4.31719354 13.57 <.0001 group Placebo 10.38095238 B 1.64051396 6.33 0.0004 group Treatment 0.00000000 B . . . age 2.03809524 0.11337506 17.98 <.0001 NOTE: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable. Analysis of Covariance (ANACOVA) 9 The GLM Procedure t Tests (LSD) for sbp NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 7 Error Mean Square 3.37415 Critical Value of t 2.36462 Least Significant Difference 2.8037 Harmonic Mean of Cell Sizes 4.8 NOTE: Cell sizes are not equal. Means with the same letter are not significantly different. t Grouping Mean N group A 135.000 6 Treatment B 125.000 4 Placebo Analysis of Covariance (ANACOVA) 10 The GLM Procedure Least Squares Means group sbp LSMEAN Placebo 137.228571 Treatment 126.847619