--------------------------------- group=a ---------------------------------- The UNIVARIATE Procedure Variable: x Moments N 9 Sum Weights 9 Mean 86.5555556 Sum Observations 779 Std Deviation 18.5816516 Variance 345.277778 Skewness 1.94925683 Kurtosis 3.71605113 Uncorrected SS 70189 Corrected SS 2762.22222 Coeff Variation 21.4678902 Std Error Mean 6.19388388 Basic Statistical Measures Location Variability Mean 86.55556 Std Deviation 18.58165 Median 77.00000 Variance 345.27778 Mode 77.00000 Range 57.00000 Interquartile Range 14.00000 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 13.97436 Pr > |t| <.0001 Sign M 4.5 Pr >= |M| 0.0039 Signed Rank S 22.5 Pr >= |S| 0.0039 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.734567 Pr < W 0.0036 Kolmogorov-Smirnov D 0.304546 Pr > D 0.0171 Cramer-von Mises W-Sq 0.185586 Pr > W-Sq 0.0061 Anderson-Darling A-Sq 1.044943 Pr > A-Sq <0.0050 Quantiles (Definition 5) Quantile Estimate 100% Max 130 99% 130 95% 130 90% 130 75% Q3 90 50% Median 77 25% Q1 76 10% 73 5% 73 --------------------------------- group=a ---------------------------------- The UNIVARIATE Procedure Variable: x Quantiles (Definition 5) Quantile Estimate 1% 73 0% Min 73 Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 73 7 77 6 75 1 80 5 76 2 90 9 77 6 101 8 77 4 130 3 Stem Leaf # Boxplot 13 0 1 0 12 11 10 1 1 | 9 0 1 +-----+ 8 0 1 | + | 7 35677 5 *-----* ----+----+----+----+ Multiply Stem.Leaf by 10**+1 Normal Probability Plot 135+ * ++ | ++++++ | +++++ 105+ +*+++ | ++++*+ | +++++ * 75+ * *++*++* +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 --------------------------------- group=b ---------------------------------- The UNIVARIATE Procedure Variable: x Moments N 8 Sum Weights 8 Mean 93.25 Sum Observations 746 Std Deviation 21.6316567 Variance 467.928571 Skewness 1.64267639 Kurtosis 1.53258612 Uncorrected SS 72840 Corrected SS 3275.5 Coeff Variation 23.1974871 Std Error Mean 7.64794557 Basic Statistical Measures Location Variability Mean 93.25000 Std Deviation 21.63166 Median 83.50000 Variance 467.92857 Mode 82.00000 Range 59.00000 Interquartile Range 20.00000 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 12.19282 Pr > |t| <.0001 Sign M 4 Pr >= |M| 0.0078 Signed Rank S 18 Pr >= |S| 0.0078 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.706237 Pr < W 0.0026 Kolmogorov-Smirnov D 0.398541 Pr > D <0.0100 Cramer-von Mises W-Sq 0.229284 Pr > W-Sq <0.0050 Anderson-Darling A-Sq 1.161539 Pr > A-Sq <0.0050 Quantiles (Definition 5) Quantile Estimate 100% Max 137.0 99% 137.0 95% 137.0 90% 137.0 75% Q3 101.0 50% Median 83.5 25% Q1 81.0 --------------------------------- group=b ---------------------------------- The UNIVARIATE Procedure Variable: x Quantiles (Definition 5) Quantile Estimate 10% 78.0 5% 78.0 1% 78.0 0% Min 78.0 Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 78 5 82 7 80 2 85 3 82 7 85 4 82 1 117 8 85 4 137 6 Stem Leaf # Boxplot 13 7 1 0 12 11 7 1 | 10 +-----+ 9 | + | 8 02255 5 *-----* 7 8 1 | ----+----+----+----+ Multiply Stem.Leaf by 10**+1 Normal Probability Plot 135+ * +++++ | ++++ | +*+++ 105+ ++++ | +++++ | * +*+++ * 75+ * ++++ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 The UNIVARIATE Procedure Variable: x Schematic Plots | 140 + | 0 | | 130 + 0 | | | 120 + | | | | | | 110 + | | | | | | | 100 + | +-----+ | | | | | | | | | | | + | 90 + +-----+ | | | | + | | | | | | | | | | | *-----* 80 + | | +-----+ | *-----* | | +-----+ | | 70 + ------------+-----------+----------- group a b The TTEST Procedure Statistics Lower CL Upper CL Lower CL Variable group N Mean Mean Mean Std Dev Std Dev x a 9 72.272 86.556 100.84 12.551 18.582 x b 8 75.165 93.25 111.33 14.302 21.632 x Diff (1-2) -27.47 -6.694 14.085 14.82 20.063 Statistics Upper CL Variable group Std Dev Std Err Minimum Maximum x a 35.598 6.1939 73 130 x b 44.026 7.6479 78 137 x Diff (1-2) 31.051 9.7488 T-Tests Variable Method Variances DF t Value Pr > |t| x Pooled Equal 15 -0.69 0.5028 x Satterthwaite Unequal 13.9 -0.68 0.5075 Equality of Variances Variable Method Num DF Den DF F Value Pr > F x Folded F 7 8 1.36 0.6753 The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable x Classified by Variable group Sum of Expected Std Dev Mean group N Scores Under H0 Under H0 Score --------------------------------------------------------------------- a 9 65.50 81.0 10.366802 7.277778 b 8 87.50 72.0 10.366802 10.937500 Average scores were used for ties. Wilcoxon Two-Sample Test Statistic 87.5000 Normal Approximation Z 1.4469 One-Sided Pr > Z 0.0740 Two-Sided Pr > |Z| 0.1479 t Approximation One-Sided Pr > Z 0.0836 Two-Sided Pr > |Z| 0.1672 Z includes a continuity correction of 0.5. Kruskal-Wallis Test Chi-Square 2.2355 DF 1 Pr > Chi-Square 0.1349