The SAS System Obs symp act sleep eat app skin 1 0.889 1.389 1.555 2.222 1.945 1 2 2.813 1.437 0.999 2.312 2.312 2 3 1.454 1.091 2.364 2.455 2.909 3 4 0.294 0.941 1.059 2.000 1.000 1 5 2.727 2.545 2.819 2.727 4.091 0 6 3.937 1.250 1.937 2.937 3.749 1 7 2.786 1.714 2.357 2.071 2.000 2 8 5.231 2.692 1.077 1.846 2.539 1 9 1.150 1.100 0.950 2.000 1.000 1 10 6.500 2.562 1.749 2.562 2.499 1 11 0.800 1.000 2.200 2.267 2.466 2 12 4.600 2.000 3.000 2.500 3.400 1 13 3.500 1.286 2.714 1.286 1.252 3 14 3.444 2.556 2.388 2.389 3.000 1 15 4.071 1.000 1.000 2.357 1.572 1 16 3.692 1.000 2.538 2.154 2.615 1 17 5.167 3.000 1.000 2.667 3.666 0 18 0.500 1.000 1.000 2.000 1.000 0 19 2.385 1.923 2.539 2.154 2.461 1 20 2.100 1.300 1.300 1.800 2.600 1 21 5.000 3.250 3.125 2.375 3.375 0 22 4.571 1.214 3.286 2.571 3.572 1 23 2.733 1.133 2.600 1.933 1.667 1 24 4.235 2.294 2.706 2.176 1.883 1 25 0.000 1.000 1.941 2.000 2.000 0 26 0.750 1.125 3.000 1.875 2.000 3 27 3.077 1.462 2.384 2.000 1.846 2 28 1.600 1.200 2.950 2.000 2.750 1 29 6.273 3.636 1.182 2.545 3.364 0 30 2.625 1.000 2.438 1.937 2.062 2 31 1.250 1.000 2.000 2.000 3.000 1 32 2.437 2.062 1.687 1.875 1.375 1 33 4.454 1.727 2.637 2.636 3.546 1 34 0.133 1.000 1.000 2.000 1.000 0 35 0.222 1.222 1.445 2.000 1.000 1 36 2.467 2.667 2.200 1.933 1.800 3 37 4.000 1.000 4.000 2.167 2.500 0 38 5.385 3.154 2.384 2.846 2.539 1 39 0.773 1.000 2.273 1.909 2.091 0 40 3.786 2.000 1.571 1.786 1.285 3 41 1.923 1.615 1.693 2.000 1.846 1 42 1.000 1.333 1.834 2.000 1.917 1 43 5.800 2.600 3.000 2.800 4.200 1 44 6.062 1.000 1.562 2.375 1.750 0 45 3.706 1.235 1.530 2.118 2.294 1 46 2.444 2.333 1.223 2.444 1.776 3 47 6.111 2.222 2.889 2.889 3.555 2 48 2.533 1.067 1.600 2.000 1.333 1 49 2.167 1.000 2.167 2.000 2.500 1 50 2.375 1.062 2.375 2.000 2.125 3 51 1.875 1.312 2.188 2.125 2.062 2 52 1.750 1.333 1.167 1.750 1.000 1 53 7.333 1.333 1.459 1.958 1.542 3 54 5.250 1.375 2.812 2.125 2.563 3 The SAS System Obs symp act sleep eat app skin 55 5.182 2.000 2.727 2.818 4.000 2 56 1.875 2.000 2.250 2.813 2.437 2 57 5.400 2.000 1.200 1.800 1.400 2 58 1.154 1.000 1.923 1.846 2.462 1 59 6.375 2.250 2.500 2.125 3.000 1 60 9.454 2.727 3.818 2.455 3.272 3 61 1.000 1.000 1.917 1.833 2.167 1 62 1.444 1.111 2.000 2.111 2.000 1 63 1.800 1.100 3.100 2.200 2.600 1 64 2.818 2.000 1.955 2.045 2.546 2 65 10.461 2.154 2.769 2.000 2.923 0 66 4.143 1.929 2.642 2.429 3.142 3 67 1.227 1.182 1.091 2.227 3.182 1 68 5.667 3.000 1.667 2.667 5.000 1 69 4.111 2.556 2.222 2.778 3.778 1 70 4.444 1.667 2.222 2.000 2.444 0 71 3.714 3.857 2.643 2.286 3.285 0 72 7.400 3.700 3.100 2.500 4.200 1 73 3.182 2.455 1.636 2.273 3.000 1 74 5.200 2.600 0.800 1.800 2.000 0 75 2.333 1.667 0.666 1.667 2.166 0 76 3.333 1.917 2.083 1.917 3.000 1 77 5.250 2.750 2.500 2.000 4.000 0 78 7.714 4.000 3.071 2.929 4.428 3 79 3.846 2.615 3.000 2.692 3.693 2 80 2.444 1.111 1.000 2.111 1.667 2 81 5.333 1.917 3.000 2.250 1.917 1 82 1.556 1.778 3.444 2.667 3.333 1 83 3.182 1.545 1.910 2.273 3.000 1 84 6.222 2.444 3.689 2.444 3.445 1 85 7.231 1.000 3.154 2.308 4.384 2 86 3.857 1.071 3.000 2.071 2.286 1 87 3.778 1.944 1.612 1.611 1.945 1 88 6.000 1.400 2.067 2.267 2.866 2 89 2.333 3.583 2.334 2.333 2.667 2 90 7.571 2.143 3.143 2.571 3.929 1 91 3.667 2.000 2.111 2.778 4.000 3 92 3.600 2.933 2.067 2.200 2.867 0 93 3.364 1.273 1.810 2.000 2.273 0 94 4.100 1.900 2.800 2.000 2.600 2 95 0.125 1.062 1.437 1.875 1.563 0 96 6.231 2.769 1.462 2.385 4.000 2 97 3.000 1.455 2.090 2.273 3.272 2 98 0.889 1.000 1.000 2.000 1.000 2 The SAS System The UNIVARIATE Procedure Variable: symp Moments N 98 Sum Weights 98 Mean 3.54234694 Sum Observations 347.15 Std Deviation 2.15748717 Variance 4.65475089 Skewness 0.6080727 Kurtosis 0.25171616 Uncorrected SS 1681.23658 Corrected SS 451.510836 Coeff Variation 60.9055862 Std Error Mean 0.21793912 Basic Statistical Measures Location Variability Mean 3.542347 Std Deviation 2.15749 Median 3.404000 Variance 4.65475 Mode 0.889000 Range 10.46100 Interquartile Range 3.30700 NOTE: The mode displayed is the smallest of 7 modes with a count of 2. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 16.25384 Pr > |t| <.0001 Sign M 48.5 Pr >= |M| <.0001 Signed Rank S 2376.5 Pr >= |S| <.0001 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.968537 Pr < W 0.0189 Kolmogorov-Smirnov D 0.070241 Pr > D >0.1500 Cramer-von Mises W-Sq 0.086864 Pr > W-Sq 0.1717 Anderson-Darling A-Sq 0.609475 Pr > A-Sq 0.1119 Quantiles (Definition 5) Quantile Estimate 100% Max 10.461 99% 10.461 95% 7.400 90% 6.273 75% Q3 5.182 50% Median 3.404 25% Q1 1.875 10% 0.889 The SAS System The UNIVARIATE Procedure Variable: symp Quantiles (Definition 5) Quantile Estimate 5% 0.294 1% 0.000 0% Min 0.000 Extreme Observations -----Lowest---- -----Highest---- Value Obs Value Obs 0.000 25 7.400 72 0.125 95 7.571 90 0.133 34 7.714 78 0.222 35 9.454 60 0.294 4 10.461 65 Stem Leaf # Boxplot 10 5 1 0 10 9 5 1 | 9 | 8 | 8 | 7 67 2 | 7 234 3 | 6 5 1 | 6 0112234 7 | 5 78 2 | 5 0222222344 10 +-----+ 4 566 3 | | 4 0111124 7 | | 3 56777788899 11 | + | 3 0122344 7 *-----* 2 55677888 8 | | 2 123344444 9 | | 1 56688999 8 +-----+ 1 0022224 7 | 0 588899 6 | 0 01123 5 | ----+----+----+----+ The SAS System The UNIVARIATE Procedure Variable: symp Normal Probability Plot 10.75+ | * | | * | +++ | ++ | **+ 7.25+ ***+ | *++ | ***** | *+ | **** | ** | *** 3.75+ **** | +** | +** | +*** | +*** | **** | ****+ 0.25+* * ***++ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 The SAS System The UNIVARIATE Procedure Variable: act Moments N 98 Sum Weights 98 Mean 1.80935714 Sum Observations 177.317 Std Deviation 0.78282895 Variance 0.61282116 Skewness 0.87984501 Kurtosis -0.006011 Uncorrected SS 380.273433 Corrected SS 59.4436525 Coeff Variation 43.2655847 Std Error Mean 0.07907767 Basic Statistical Measures Location Variability Mean 1.809357 Std Deviation 0.78283 Median 1.641000 Variance 0.61282 Mode 1.000000 Range 3.05900 Interquartile Range 1.22200 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 22.88076 Pr > |t| <.0001 Sign M 49 Pr >= |M| <.0001 Signed Rank S 2425.5 Pr >= |S| <.0001 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.890331 Pr < W <0.0001 Kolmogorov-Smirnov D 0.150969 Pr > D <0.0100 Cramer-von Mises W-Sq 0.508161 Pr > W-Sq <0.0050 Anderson-Darling A-Sq 3.265859 Pr > A-Sq <0.0050 Quantiles (Definition 5) Quantile Estimate 100% Max 4.000 99% 4.000 95% 3.583 90% 2.933 75% Q3 2.333 50% Median 1.641 25% Q1 1.111 10% 1.000 5% 1.000 1% 0.941 The SAS System The UNIVARIATE Procedure Variable: act Quantiles (Definition 5) Quantile Estimate 0% Min 0.941 Extreme Observations -----Lowest---- ----Highest---- Value Obs Value Obs 0.941 4 3.583 89 1.000 98 3.636 29 1.000 85 3.700 72 1.000 61 3.857 71 1.000 58 4.000 78 Stem Leaf # Boxplot 40 0 1 | 38 6 1 | 36 40 2 | 34 8 1 | 32 5 1 | 30 005 3 | 28 3 1 | 26 00279357 8 | 24 464666 6 | 22 2593 4 +-----+ 20 0000000645 10 | | 18 022234 6 | + | 16 277138 6 *-----* 14 04664 5 | | 12 01245790133389 14 | | 10 0000000000000000667790011238 28 +-----+ 8 4 1 | ----+----+----+----+----+--- Multiply Stem.Leaf by 10**-1 The SAS System The UNIVARIATE Procedure Variable: act Normal Probability Plot 4.1+ * | * | ** +++ | * ++ | * +++ | **++ | *++ | **** 2.5+ ***+ | +** | *** | +*** | ++** | +++ ** | ++**** | * *************** 0.9+* ++ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 The SAS System The UNIVARIATE Procedure Variable: sleep Moments N 98 Sum Weights 98 Mean 2.13760204 Sum Observations 209.485 Std Deviation 0.75592914 Variance 0.57142886 Skewness 0.08725467 Kurtosis -0.6641326 Uncorrected SS 503.224163 Corrected SS 55.4285995 Coeff Variation 35.3634176 Std Error Mean 0.07636037 Basic Statistical Measures Location Variability Mean 2.137602 Std Deviation 0.75593 Median 2.177500 Variance 0.57143 Mode 1.000000 Range 3.33400 Interquartile Range 1.15200 NOTE: The mode displayed is the smallest of 2 modes with a count of 6. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 27.9936 Pr > |t| <.0001 Sign M 49 Pr >= |M| <.0001 Signed Rank S 2425.5 Pr >= |S| <.0001 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.979061 Pr < W 0.1198 Kolmogorov-Smirnov D 0.060312 Pr > D >0.1500 Cramer-von Mises W-Sq 0.058053 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.512633 Pr > A-Sq 0.1987 Quantiles (Definition 5) Quantile Estimate 100% Max 4.0000 99% 4.0000 95% 3.2860 90% 3.1000 75% Q3 2.7140 50% Median 2.1775 25% Q1 1.5620 10% 1.0000 The SAS System The UNIVARIATE Procedure Variable: sleep Quantiles (Definition 5) Quantile Estimate 5% 1.0000 1% 0.6660 0% Min 0.6660 Extreme Observations -----Lowest---- ----Highest---- Value Obs Value Obs 0.666 75 3.286 22 0.800 74 3.444 82 0.950 9 3.689 84 0.999 2 3.818 60 1.000 98 4.000 37 Stem Leaf # Boxplot 40 0 1 | 38 2 1 | 36 9 1 | 34 4 1 | 32 9 1 | 30 000000700245 12 | 28 01295 5 | 26 04441137 8 +-----+ 24 40044 5 | | 22 0022573668889 13 | | 20 007789179 9 *--+--* 18 13122446 8 | | 16 0147995 7 | | 14 44663667 8 +-----+ 12 020 3 | 10 000000068978 12 | 8 05 2 | 6 7 1 | ----+----+----+----+ Multiply Stem.Leaf by 10**-1 The SAS System The UNIVARIATE Procedure Variable: sleep Normal Probability Plot 4.1+ * | *+++ | *++ | +*+ | ++* | ******* | **++ | ***+ | **+ | ***** | *** | *** | +*** | **** | ++** | ******** | * **++ 0.7+* +++ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 The SAS System The UNIVARIATE Procedure Variable: eat Moments N 98 Sum Weights 98 Mean 2.209 Sum Observations 216.482 Std Deviation 0.33227861 Variance 0.11040907 Skewness 0.33505111 Kurtosis -0.2267817 Uncorrected SS 488.918418 Corrected SS 10.70968 Coeff Variation 15.0420374 Std Error Mean 0.03356521 Basic Statistical Measures Location Variability Mean 2.209000 Std Deviation 0.33228 Median 2.139500 Variance 0.11041 Mode 2.000000 Range 1.65100 Interquartile Range 0.44400 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 65.81219 Pr > |t| <.0001 Sign M 49 Pr >= |M| <.0001 Signed Rank S 2425.5 Pr >= |S| <.0001 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.961713 Pr < W 0.0060 Kolmogorov-Smirnov D 0.143486 Pr > D <0.0100 Cramer-von Mises W-Sq 0.268118 Pr > W-Sq <0.0050 Anderson-Darling A-Sq 1.548556 Pr > A-Sq <0.0050 Quantiles (Definition 5) Quantile Estimate 100% Max 2.9370 99% 2.9370 95% 2.8180 90% 2.7270 75% Q3 2.4440 50% Median 2.1395 25% Q1 2.0000 10% 1.8460 5% 1.7860 1% 1.2860 The SAS System The UNIVARIATE Procedure Variable: eat Quantiles (Definition 5) Quantile Estimate 0% Min 1.2860 Extreme Observations -----Lowest---- ----Highest---- Value Obs Value Obs 1.286 13 2.818 55 1.611 87 2.846 38 1.667 75 2.889 47 1.750 52 2.929 78 1.786 40 2.937 6 Stem Leaf # Boxplot 29 34 2 | 28 01259 5 | 27 388 3 | 26 47779 5 | 25 004677 6 | 24 34466 5 +-----+ 23 11368889 8 | | 22 00235777779 11 | + | 21 1122225578 10 *-----* 20 00000000000000000000477 23 +-----+ 19 123346 6 | 18 000355888 9 | 17 59 2 | 16 17 2 | 15 14 13 12 9 1 0 ----+----+----+----+--- Multiply Stem.Leaf by 10**-1 The SAS System The UNIVARIATE Procedure Variable: eat Normal Probability Plot 2.95+ *++ * | *****+ | **+++ | ***++ | ***+ | **+ | +*** | +**** | ++*** | ******* | ***+ | ******+ | ** +++ | * *+++ | +++ | +++ |+ 1.25+* +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 The SAS System The UNIVARIATE Procedure Variable: app Moments N 98 Sum Weights 98 Mean 2.57482653 Sum Observations 252.333 Std Deviation 0.92853238 Variance 0.86217237 Skewness 0.25251242 Kurtosis -0.5467517 Uncorrected SS 733.344423 Corrected SS 83.6307201 Coeff Variation 36.0619391 Std Error Mean 0.09379593 Basic Statistical Measures Location Variability Mean 2.574827 Std Deviation 0.92853 Median 2.500000 Variance 0.86217 Mode 1.000000 Range 4.00000 Interquartile Range 1.35500 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 27.45137 Pr > |t| <.0001 Sign M 49 Pr >= |M| <.0001 Signed Rank S 2425.5 Pr >= |S| <.0001 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.978264 Pr < W 0.1041 Kolmogorov-Smirnov D 0.074582 Pr > D >0.1500 Cramer-von Mises W-Sq 0.072076 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.478325 Pr > A-Sq 0.2367 Quantiles (Definition 5) Quantile Estimate 100% Max 5.000 99% 5.000 95% 4.200 90% 4.000 75% Q3 3.272 50% Median 2.500 25% Q1 1.917 10% 1.333 5% 1.000 1% 1.000 The SAS System The UNIVARIATE Procedure Variable: app Quantiles (Definition 5) Quantile Estimate 0% Min 1.000 Extreme Observations ----Lowest---- ----Highest---- Value Obs Value Obs 1 98 4.200 43 1 52 4.200 72 1 35 4.384 85 1 34 4.428 78 1 18 5.000 68 Stem Leaf # Boxplot 50 0 1 | 48 | 46 | 44 3 1 | 42 008 3 | 40 00009 5 | 38 3 1 | 36 7958 4 | 34 04567 5 | 32 778368 6 +-----+ 30 00000048 8 | | 28 7712 4 | | 26 000275 6 | | 24 446670004456 12 *--+--* 22 7991 4 | | 20 00000669277 11 | | 18 05582244 8 +-----+ 16 7758 4 | 14 0467 4 | 12 5838 4 | 10 0000000 7 | ----+----+----+----+ Multiply Stem.Leaf by 10**-1 The SAS System The UNIVARIATE Procedure Variable: app Normal Probability Plot 5.1+ * | ++ 4.7+ ++ | +* 4.3+ *** | ****+ 3.9+ * ++ | ***+ 3.5+ ***+ | *** 3.1+ *** | ** 2.7+ *** | **** 2.3+ +** | **** 1.9+ *** | ** 1.5+ *** | *** 1.1+* * ***** +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 The SAS System The UNIVARIATE Procedure Variable: skin Moments N 98 Sum Weights 98 Mean 1.2755102 Sum Observations 125 Std Deviation 0.9281465 Variance 0.86145592 Skewness 0.44600146 Kurtosis -0.567415 Uncorrected SS 243 Corrected SS 83.5612245 Coeff Variation 72.7666855 Std Error Mean 0.09375695 Basic Statistical Measures Location Variability Mean 1.275510 Std Deviation 0.92815 Median 1.000000 Variance 0.86146 Mode 1.000000 Range 3.00000 Interquartile Range 1.00000 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 13.60443 Pr > |t| <.0001 Sign M 39.5 Pr >= |M| <.0001 Signed Rank S 1580 Pr >= |S| <.0001 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.855695 Pr < W <0.0001 Kolmogorov-Smirnov D 0.279971 Pr > D <0.0100 Cramer-von Mises W-Sq 1.111312 Pr > W-Sq <0.0050 Anderson-Darling A-Sq 5.918894 Pr > A-Sq <0.0050 Quantiles (Definition 5) Quantile Estimate 100% Max 3 99% 3 95% 3 90% 3 75% Q3 2 50% Median 1 25% Q1 1 10% 0 5% 0 1% 0 The SAS System The UNIVARIATE Procedure Variable: skin Quantiles (Definition 5) Quantile Estimate 0% Min 0 Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 0 95 3 54 0 93 3 60 0 92 3 66 0 77 3 78 0 75 3 91 Stem Leaf # Boxplot 30 0000000000000 13 | 28 | 26 | 24 | 22 | 20 00000000000000000000 20 +-----+ 18 | | 16 | | 14 | | 12 | + | 10 0000000000000000000000000000000000000000000000 46 *-----* 8 | 6 | 4 | 2 | 0 0000000000000000000 19 | ----+----+----+----+----+----+----+----+----+- Multiply Stem.Leaf by 10**-1 The SAS System The UNIVARIATE Procedure Variable: skin Normal Probability Plot 3.1+ *********+* * | ++ | ++ 2.5+ ++ | +++ | ******** 1.9+ ++ | ++ | ++ 1.3+ ++ | ************* | +++ 0.7+ ++ | ++ | ++ 0.1+* * *********** +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2