The SAS System --------------------------------- method=a --------------------------------- The UNIVARIATE Procedure Variable: y Moments N 11 Sum Weights 11 Mean 50.0909091 Sum Observations 551 Std Deviation 10.9677212 Variance 120.290909 Skewness 0.57278942 Kurtosis -0.4984168 Uncorrected SS 28803 Corrected SS 1202.90909 Coeff Variation 21.8956322 Std Error Mean 3.30689238 Basic Statistical Measures Location Variability Mean 50.09091 Std Deviation 10.96772 Median 49.00000 Variance 120.29091 Mode . Range 35.00000 Interquartile Range 16.00000 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 15.14743 Pr > |t| <.0001 Sign M 5.5 Pr >= |M| 0.0010 Signed Rank S 33 Pr >= |S| 0.0010 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.950123 Pr < W 0.6455 Kolmogorov-Smirnov D 0.165217 Pr > D >0.1500 Cramer-von Mises W-Sq 0.037737 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.251615 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 71 99% 71 95% 71 --------------------------------- method=a --------------------------------- The UNIVARIATE Procedure Variable: y Quantiles (Definition 5) Quantile Estimate 90% 63 75% Q3 57 50% Median 49 25% Q1 41 10% 39 5% 36 1% 36 0% Min 36 Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 36 11 53 4 39 1 56 8 41 5 57 2 42 3 63 10 44 6 71 7 Stem Leaf # Boxplot 7 1 1 | 6 | 6 3 1 | 5 67 2 +-----+ 5 3 1 | + | 4 9 1 *-----* 4 124 3 +-----+ 3 69 2 | ----+----+----+----+ Multiply Stem.Leaf by 10**+1 --------------------------------- method=a --------------------------------- The UNIVARIATE Procedure Variable: y Normal Probability Plot 72.5+ * ++++ | +++++ | +*++ | *+*++ | ++*++ | ++++* | ++*+* * 37.5+ * ++*+ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 --------------------------------- method=b --------------------------------- The UNIVARIATE Procedure Variable: y Moments N 10 Sum Weights 10 Mean 39.9 Sum Observations 399 Std Deviation 8.38583462 Variance 70.3222222 Skewness 0.20416797 Kurtosis -0.5644825 Uncorrected SS 16553 Corrected SS 632.9 Coeff Variation 21.0171294 Std Error Mean 2.65183375 Basic Statistical Measures Location Variability Mean 39.90000 Std Deviation 8.38583 Median 39.00000 Variance 70.32222 Mode . Range 26.00000 Interquartile Range 10.00000 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 15.04619 Pr > |t| <.0001 Sign M 5 Pr >= |M| 0.0020 Signed Rank S 27.5 Pr >= |S| 0.0020 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.970634 Pr < W 0.8967 Kolmogorov-Smirnov D 0.103167 Pr > D >0.1500 Cramer-von Mises W-Sq 0.018437 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.151552 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 54.0 99% 54.0 95% 54.0 --------------------------------- method=b --------------------------------- The UNIVARIATE Procedure Variable: y Quantiles (Definition 5) Quantile Estimate 90% 52.0 75% Q3 45.0 50% Median 39.0 25% Q1 35.0 10% 28.5 5% 28.0 1% 28.0 0% Min 28.0 Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 28 6 40 5 29 10 43 1 35 3 45 4 37 9 50 7 38 2 54 8 Stem Leaf # Boxplot 5 04 2 | 4 5 1 +-----+ 4 03 2 | + | 3 578 3 *-----* 3 | 2 89 2 | ----+----+----+----+ Multiply Stem.Leaf by 10**+1 --------------------------------- method=b --------------------------------- The UNIVARIATE Procedure Variable: y Normal Probability Plot 52.5+ * ++*+++ | *+++++ | *++*++ | * +*++*+ | ++++++ 27.5+ ++*+++ * +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 The UNIVARIATE Procedure Variable: y Schematic Plots | 75 + | | | | 70 + | | | | | | | 65 + | | | | | | | 60 + | | | | +-----+ | | | 55 + | | | | | | | | | | | | | | 50 + | + | | | *-----* | | | | | | | | | 45 + | | +-----+ | | | | | | | | | | | +-----+ | | 40 + | | + | | | *-----* | | | | | | | | 35 + +-----+ | | | | | | 30 + | | | | | | 25 + ------------+-----------+----------- method a b The TTEST Procedure Statistics Lower CL Upper CL Lower CL Variable method N Mean Mean Mean Std Dev Std Dev y a 11 42.723 50.091 57.459 7.6633 10.968 y b 10 33.901 39.9 45.899 5.7681 8.3858 y Diff (1-2) 1.2016 10.191 19.18 7.4753 9.8296 Statistics Upper CL Variable method Std Dev Std Err Minimum Maximum y a 19.248 3.3069 36 71 y b 15.309 2.6518 28 54 y Diff (1-2) 14.357 4.2949 T-Tests Variable Method Variances DF t Value Pr > |t| y Pooled Equal 19 2.37 0.0284 y Satterthwaite Unequal 18.5 2.40 0.0269 Equality of Variances Variable Method Num DF Den DF F Value Pr > F y Folded F 10 9 1.71 0.4325 The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable y Classified by Variable method Sum of Expected Std Dev Mean method N Scores Under H0 Under H0 Score ---------------------------------------------------------------------- a 11 150.0 121.0 14.200939 13.636364 b 10 81.0 110.0 14.200939 8.100000 Wilcoxon Two-Sample Test Statistic 81.0000 Normal Approximation Z -2.0069 One-Sided Pr < Z 0.0224 Two-Sided Pr > |Z| 0.0448 t Approximation One-Sided Pr < Z 0.0292 Two-Sided Pr > |Z| 0.0585 Z includes a continuity correction of 0.5. Kruskal-Wallis Test Chi-Square 4.1702 DF 1 Pr > Chi-Square 0.0411