The SAS System 1 --------------------------------- group=a ---------------------------------- The UNIVARIATE Procedure Variable: y Moments N 7 Sum Weights 7 Mean 76.8571429 Sum Observations 538 Std Deviation 2.54483604 Variance 6.47619048 Skewness -0.0329387 Kurtosis -0.6276384 Uncorrected SS 41388 Corrected SS 38.8571429 Coeff Variation 3.31112496 Std Error Mean 0.96185761 Basic Statistical Measures Location Variability Mean 76.85714 Std Deviation 2.54484 Median 77.00000 Variance 6.47619 Mode 77.00000 Range 7.00000 Interquartile Range 5.00000 NOTE: The mode displayed is the smallest of 2 modes with a count of 2. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 79.90491 Pr > |t| <.0001 Sign M 3.5 Pr >= |M| 0.0156 Signed Rank S 14 Pr >= |S| 0.0156 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.932031 Pr < W 0.5683 Kolmogorov-Smirnov D 0.191902 Pr > D >0.1500 Cramer-von Mises W-Sq 0.040002 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.274522 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 80 99% 80 95% 80 90% 80 75% Q3 80 50% Median 77 25% Q1 75 --------------------------------- group=a ---------------------------------- The UNIVARIATE Procedure Variable: y Quantiles (Definition 5) Quantile Estimate 10% 73 5% 73 1% 73 0% Min 73 Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 73 7 76 2 75 1 77 4 76 2 77 6 77 6 80 3 77 4 80 5 --------------------------------- group=b ---------------------------------- The UNIVARIATE Procedure Variable: y Moments N 7 Sum Weights 7 Mean 82.7142857 Sum Observations 579 Std Deviation 3.14718317 Variance 9.9047619 Skewness -0.1713987 Kurtosis -0.9253513 Uncorrected SS 47951 Corrected SS 59.4285714 Coeff Variation 3.80488466 Std Error Mean 1.18952343 Basic Statistical Measures Location Variability Mean 82.71429 Std Deviation 3.14718 Median 82.00000 Variance 9.90476 Mode 82.00000 Range 9.00000 Interquartile Range 5.00000 NOTE: The mode displayed is the smallest of 2 modes with a count of 2. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 69.53565 Pr > |t| <.0001 Sign M 3.5 Pr >= |M| 0.0156 Signed Rank S 14 Pr >= |S| 0.0156 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.958273 Pr < W 0.8038 Kolmogorov-Smirnov D 0.194736 Pr > D >0.1500 Cramer-von Mises W-Sq 0.039022 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.230488 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 87 99% 87 95% 87 90% 87 75% Q3 85 50% Median 82 25% Q1 80 --------------------------------- group=b ---------------------------------- The UNIVARIATE Procedure Variable: y Quantiles (Definition 5) Quantile Estimate 10% 78 5% 78 1% 78 0% Min 78 Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 78 5 82 1 80 2 82 7 82 7 85 3 82 1 85 4 85 4 87 6 The TTEST Procedure Statistics Lower CL Upper CL Lower CL Variable group N Mean Mean Mean Std Dev Std Dev y a 7 74.504 76.857 79.211 1.6399 2.5448 y b 7 79.804 82.714 85.625 2.028 3.1472 y Diff (1-2) -9.19 -5.857 -2.524 2.0522 2.8619 Statistics Upper CL Variable group Std Dev Std Err Minimum Maximum y a 5.6039 0.9619 73 80 y b 6.9303 1.1895 78 87 y Diff (1-2) 4.7242 1.5298 T-Tests Variable Method Variances DF t Value Pr > |t| y Pooled Equal 12 -3.83 0.0024 y Satterthwaite Unequal 11.5 -3.83 0.0026 Equality of Variances Variable Method Num DF Den DF F Value Pr > F y Folded F 6 6 1.53 0.6189 The REG Procedure Model: MODEL1 Dependent Variable: y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 120.07143 120.07143 14.66 0.0024 Error 12 98.28571 8.19048 Corrected Total 13 218.35714 Root MSE 2.86190 R-Square 0.5499 Dependent Mean 79.78571 Adj R-Sq 0.5124 Coeff Var 3.58698 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 76.85714 1.08170 71.05 <.0001 x 1 5.85714 1.52975 3.83 0.0024 The UNIVARIATE Procedure Variable: resid (Residual) Moments N 14 Sum Weights 14 Mean 0 Sum Observations 0 Std Deviation 2.74962535 Variance 7.56043956 Skewness -0.1088943 Kurtosis -0.9086845 Uncorrected SS 98.2857143 Corrected SS 98.2857143 Coeff Variation . Std Error Mean 0.73486829 Basic Statistical Measures Location Variability Mean 0.00000 Std Deviation 2.74963 Median -0.28571 Variance 7.56044 Mode -0.71429 Range 9.00000 Interquartile Range 4.14286 NOTE: The mode displayed is the smallest of 4 modes with a count of 2. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 0 Pr > |t| 1.0000 Sign M 0 Pr >= |M| 1.0000 Signed Rank S -0.5 Pr >= |S| 0.9880 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.958871 Pr < W 0.7045 Kolmogorov-Smirnov D 0.154236 Pr > D >0.1500 Cramer-von Mises W-Sq 0.042258 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.262026 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 4.285714 99% 4.285714 95% 4.285714 90% 3.142857 75% Q3 2.285714 50% Median -0.285714 25% Q1 -1.857143 10% -3.857143 5% -4.714286 The UNIVARIATE Procedure Variable: resid (Residual) Quantiles (Definition 5) Quantile Estimate 1% -4.714286 0% Min -4.714286 Extreme Observations ------Lowest------ -----Highest----- Value Obs Value Obs -4.714286 12 2.28571 10 -3.857143 7 2.28571 11 -2.714286 9 3.14286 3 -1.857143 1 3.14286 5 -0.857143 2 4.28571 13