NCGS DATA 15:37 Saturday, January 25, 2003 1 frequency distributions of age, a coarse distribution combined groups, one group example SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS The UNIVARIATE Procedure Variable: AGE Moments N 197 Sum Weights 197 Mean 54.9543147 Sum Observations 10826 Std Deviation 9.92178309 Variance 98.4417798 Skewness -0.2372462 Kurtosis 0.15586696 Uncorrected SS 614230 Corrected SS 19294.5888 Coeff Variation 18.0546025 Std Error Mean 0.70689778 Basic Statistical Measures Location Variability Mean 54.95431 Std Deviation 9.92178 Median 55.00000 Variance 98.44178 Mode 53.00000 Range 50.00000 Interquartile Range 13.00000 NOTE: The mode displayed is the smallest of 2 modes with a count of 13. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 77.74012 Pr > ІtІ <.0001 Sign M 98.5 Pr >= ІMІ <.0001 Signed Rank S 9751.5 Pr >= ІSІ <.0001 NCGS DATA 15:37 Saturday, January 25, 2003 2 frequency distributions of age, a coarse distribution combined groups, one group example SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS The UNIVARIATE Procedure Variable: AGE Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.987807 Pr < W 0.0893 Kolmogorov-Smirnov D 0.061013 Pr > D 0.0734 Cramer-von Mises W-Sq 0.092223 Pr > W-Sq 0.1444 Anderson-Darling A-Sq 0.620017 Pr > A-Sq 0.1061 Quantiles (Definition 5) Quantile Estimate 100% Max 77 99% 77 95% 71 90% 67 75% Q3 62 50% Median 55 25% Q1 49 10% 42 5% 37 1% 30 0% Min 27 NCGS DATA 15:37 Saturday, January 25, 2003 3 frequency distributions of age, a coarse distribution combined groups, one group example SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS The UNIVARIATE Procedure Variable: AGE Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 27 102 74 58 30 18 77 19 31 171 77 25 31 106 77 90 31 97 77 146 NCGS DATA 15:37 Saturday, January 25, 2003 4 frequency distributions of age, a coarse distribution combined groups, one group example SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS The UNIVARIATE Procedure Variable: AGE Stem Leaf # Boxplot Normal Probability Plot 76 0000 4 І 77+ **+** 74 000 3 І І ***+ 72 00 2 І І **+ 70 0000 4 І І **+ 68 00000 5 І І **+ 66 000000000000 12 І 67+ **** 64 0000 4 І І *+ 62 00000000000000000 17 +-----+ І *** 60 000000000000000 15 І І І ***+ 58 00000000000 11 І І І **+ 56 0000000000000 13 І І 57+ *** 54 0000000000000000000 19 *--+--* І *** 52 00000000000000000000000 23 І І І ***+ 50 00000000000000 14 І І І **++ 48 0000000000000 13 +-----+ І ***++ 46 00000000000 11 І 47+ ***+ 44 0000 4 І І **+ 42 0000 4 І І ** 40 0000 4 І І +** 38 000 3 І І ++* 36 0000 4 І 37+ ++** 34 0 1 І І ++ * 32 00 2 І І ++ ** 30 0000 4 І І+* * * 28 І 26 0 1 0 27+* ----+----+----+----+--- +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 NCGS DATA 15:37 Saturday, January 25, 2003 5 frequency distributions of age, a coarse distribution combined groups, one group example SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS Frequency щ ***** щ ***** щ ***** 40 ъ ***** щ ***** ***** ***** щ ***** ***** ***** щ ***** ***** ***** щ ***** ***** ***** 30 ъ ***** ***** ***** щ ***** ***** ***** щ ***** ***** ***** щ ***** ***** ***** щ ***** ***** ***** ***** 20 ъ ***** ***** ***** ***** щ ***** ***** ***** ***** ***** щ ***** ***** ***** ***** ***** щ ***** ***** ***** ***** ***** щ ***** ***** ***** ***** ***** 10 ъ ***** ***** ***** ***** ***** ***** щ ***** ***** ***** ***** ***** ***** ***** ***** ***** щ ***** ***** ***** ***** ***** ***** ***** ***** ***** щ ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** щ ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** ***** шттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттттт 25 30 35 40 45 50 55 60 65 70 75 AGE Midpoint NCGS DATA 15:37 Saturday, January 25, 2003 6 frequency distributions of age, a coarse distribution combined groups, one group example SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS The FREQ Procedure Cumulative Cumulative AGE Frequency Percent Frequency Percent тттттттттттттттттттттттттттттттттттттттттттттттттттттттт 27 1 0.51 1 0.51 30 1 0.51 2 1.02 31 3 1.52 5 2.54 33 2 1.02 7 3.55 35 1 0.51 8 4.06 37 4 2.03 12 6.09 38 1 0.51 13 6.60 39 2 1.02 15 7.61 40 2 1.02 17 8.63 41 2 1.02 19 9.64 42 1 0.51 20 10.15 43 3 1.52 23 11.68 44 1 0.51 24 12.18 45 3 1.52 27 13.71 46 7 3.55 34 17.26 47 4 2.03 38 19.29 48 4 2.03 42 21.32 49 9 4.57 51 25.89 50 9 4.57 60 30.46 51 5 2.54 65 32.99 52 10 5.08 75 38.07 53 13 6.60 88 44.67 54 6 3.05 94 47.72 55 13 6.60 107 54.31 56 7 3.55 114 57.87 57 6 3.05 120 60.91 58 3 1.52 123 62.44 59 8 4.06 131 66.50 60 7 3.55 138 70.05 61 8 4.06 146 74.11 62 11 5.58 157 79.70 63 6 3.05 163 82.74 NCGS DATA 15:37 Saturday, January 25, 2003 7 frequency distributions of age, a coarse distribution combined groups, one group example SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS The FREQ Procedure Cumulative Cumulative AGE Frequency Percent Frequency Percent тттттттттттттттттттттттттттттттттттттттттттттттттттттттт 64 4 2.03 167 84.77 66 5 2.54 172 87.31 67 7 3.55 179 90.86 68 3 1.52 182 92.39 69 2 1.02 184 93.40 70 1 0.51 185 93.91 71 3 1.52 188 95.43 72 1 0.51 189 95.94 73 1 0.51 190 96.45 74 3 1.52 193 97.97 77 4 2.03 197 100.00 NCGS DATA 15:37 Saturday, January 25, 2003 8 frequency distributions of age, a coarse distribution combined groups, one group example SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS Plot of PERCENT*AGE. Symbol used is '*'. щ P щ e 6.5990 ъ * * r щ c 6.0914 ъ e щ n 5.5838 ъ * t щ 5.0761 ъ * o щ f 4.5685 ъ * * щ T 4.0609 ъ * * o щ t 3.5533 ъ * * * * a щ l 3.0457 ъ * * * щ F 2.5381 ъ * * r щ e 2.0305 ъ * * * * * q щ u 1.5228 ъ * * * * * * * e щ n 1.0152 ъ * * * * * c щ y 0.5076 ъ * * * * * * * * * щ шттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътт 25 30 35 40 45 50 55 60 65 70 75 80 AGE NCGS DATA 15:37 Saturday, January 25, 2003 9 frequency distributions of age, a coarse distribution combined groups, one group example kernel smoothed density estimates The KDE Procedure Inputs Data Set WORK.ONE Number of Observations Used 197 Variable AGE Bandwidth Method Sheather-Jones Plug In Controls AGE Grid Points 401 Lower Grid Limit 27 Upper Grid Limit 77 Bandwidth Multiplier 0.75 Statistics AGE Mean 54.95 Variance 97.94 Standard Deviation 9.90 Range 50.00 Interquartile Range 13.00 Bandwidth 2.40 NCGS DATA 15:37 Saturday, January 25, 2003 10 frequency distributions of age, a coarse distribution combined groups, one group example kernel smoothed density estimates The KDE Procedure Percentiles AGE 0.5 27.00 1.0 30.00 2.5 31.00 5.0 37.00 10.0 42.00 25.0 49.00 50.0 55.00 75.0 62.00 90.0 67.00 95.0 71.00 97.5 74.00 99.0 77.00 99.5 77.00 Levels Percent Density Lower Upper 1 0.004474 30.00 77.00 5 0.005540 33.00 76.50 10 0.007988 37.00 73.00 50 0.03435 49.00 61.63 90 0.04363 52.00 54.50 95 0.04476 53.00 53.50 99 0.04476 53.00 53.50 100 0.04480 53.25 53.25 NCGS DATA 15:37 Saturday, January 25, 2003 11 frequency distributions of age, a coarse distribution combined groups, one group example kernel smoothed density estimates Plot of density*AGE. Legend: A = 1 obs, B = 2 obs, etc. щ щ 0.05 ъ щ щ щ DDDDDDA щ BD CC 0.04 ъ CB ADA щ DA CD щ D DDDDDDDC щ D ADC D щ D ADA e 0.03 ъ D CA n щ D CB s щ D BC i щ D AD t щ D DB y 0.02 ъ AD BDB щ AC BDA щ CC CD щ ADA DC щ CDC ADC 0.01 ъ ADDDDDDA ADDB щ BDDDDC BDDDDA щ CDDDDDDDDDB CDDDDB щ CDDDDA A щ BDDA 0.00 ъ щ шттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътт 25 30 35 40 45 50 55 60 65 70 75 80 AGE NCGS DATA 15:37 Saturday, January 25, 2003 12 frequency distributions of trigl, a fine distribution two group example: 3= drug group, 5= placebo group --------------------------------------------------------- TRETGRP=3 ---------------------------------------------------------- The UNIVARIATE Procedure Variable: TRIGL Moments N 102 Sum Weights 102 Mean 141.470588 Sum Observations 14430 Std Deviation 89.4595108 Variance 8003.00408 Skewness 3.19302058 Kurtosis 17.1248113 Uncorrected SS 2849724 Corrected SS 808303.412 Coeff Variation 63.2354131 Std Error Mean 8.85781148 Basic Statistical Measures Location Variability Mean 141.4706 Std Deviation 89.45951 Median 120.0000 Variance 8003 Mode 82.0000 Range 685.00000 Interquartile Range 81.00000 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 15.97128 Pr > ІtІ <.0001 Sign M 51 Pr >= ІMІ <.0001 Signed Rank S 2626.5 Pr >= ІSІ <.0001 NCGS DATA 15:37 Saturday, January 25, 2003 13 frequency distributions of trigl, a fine distribution two group example: 3= drug group, 5= placebo group --------------------------------------------------------- TRETGRP=3 ---------------------------------------------------------- The UNIVARIATE Procedure Variable: TRIGL Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.744587 Pr < W <0.0001 Kolmogorov-Smirnov D 0.161632 Pr > D <0.0100 Cramer-von Mises W-Sq 0.867028 Pr > W-Sq <0.0050 Anderson-Darling A-Sq 4.959887 Pr > A-Sq <0.0050 Quantiles (Definition 5) Quantile Estimate 100% Max 725 99% 331 95% 294 90% 249 75% Q3 168 50% Median 120 25% Q1 87 10% 68 5% 59 1% 44 0% Min 40 NCGS DATA 15:37 Saturday, January 25, 2003 14 frequency distributions of trigl, a fine distribution two group example: 3= drug group, 5= placebo group --------------------------------------------------------- TRETGRP=3 ---------------------------------------------------------- The UNIVARIATE Procedure Variable: TRIGL Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 40 49 314 93 44 9 324 66 49 28 326 98 50 23 331 58 53 20 725 53 Stem Leaf # Boxplot Normal Probability Plot 7 2 1 * 725+ * 6 І 6 І 5 І 5 І 4 І 4 І 3 375+ ++ 3 1233 4 0 І ***+*++ 2 5556779 7 0 І ****+ 2 011224 6 І І +++**** 1 55556667777777889 17 +-----+ І ++++***** 1 0000000001111112222233333333444444 34 *--+--* І +******** 0 5556666777777788888888899999999 31 +-----+ І *************** 0 44 2 І 25+* * * +++++ ----+----+----+----+----+----+---- +----+----+----+----+----+----+----+----+----+----+ Multiply Stem.Leaf by 10**+2 -2 -1 0 +1 +2 NCGS DATA 15:37 Saturday, January 25, 2003 15 frequency distributions of trigl, a fine distribution two group example: 3= drug group, 5= placebo group --------------------------------------------------------- TRETGRP=5 ---------------------------------------------------------- The UNIVARIATE Procedure Variable: TRIGL Moments N 95 Sum Weights 95 Mean 145.715789 Sum Observations 13843 Std Deviation 69.2133094 Variance 4790.48219 Skewness 0.79952077 Kurtosis 0.09755578 Uncorrected SS 2467449 Corrected SS 450305.326 Coeff Variation 47.4988398 Std Error Mean 7.10113571 Basic Statistical Measures Location Variability Mean 145.7158 Std Deviation 69.21331 Median 135.0000 Variance 4790 Mode 51.0000 Range 300.00000 Interquartile Range 96.00000 NOTE: The mode displayed is the smallest of 15 modes with a count of 2. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 20.52007 Pr > ІtІ <.0001 Sign M 47.5 Pr >= ІMІ <.0001 Signed Rank S 2280 Pr >= ІSІ <.0001 NCGS DATA 15:37 Saturday, January 25, 2003 16 frequency distributions of trigl, a fine distribution two group example: 3= drug group, 5= placebo group --------------------------------------------------------- TRETGRP=5 ---------------------------------------------------------- The UNIVARIATE Procedure Variable: TRIGL Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.939516 Pr < W 0.0003 Kolmogorov-Smirnov D 0.10213 Pr > D 0.0159 Cramer-von Mises W-Sq 0.232171 Pr > W-Sq <0.0050 Anderson-Darling A-Sq 1.551589 Pr > A-Sq <0.0050 Quantiles (Definition 5) Quantile Estimate 100% Max 348 99% 348 95% 292 90% 251 75% Q3 188 50% Median 135 25% Q1 92 10% 65 5% 55 1% 48 0% Min 48 NCGS DATA 15:37 Saturday, January 25, 2003 17 frequency distributions of trigl, a fine distribution two group example: 3= drug group, 5= placebo group --------------------------------------------------------- TRETGRP=5 ---------------------------------------------------------- The UNIVARIATE Procedure Variable: TRIGL Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 48 27 292 47 49 36 298 94 51 68 299 76 51 43 305 71 55 15 348 20 Stem Leaf # Boxplot Normal Probability Plot 34 8 1 0 350+ * 32 І 30 5 1 І І * +++ 28 15289 5 І 290+ *****+++ 26 2 1 І І * +++ 24 1317 4 І І **+++ 22 268 3 І 230+ **++ 20 43 2 І І +** 18 1478002559 10 +-----+ І +**** 16 12453 5 І І 170+ +*** 14 01688993369 11 І + І І +**** 12 445669123455788 15 *-----* І ***** 10 156893447 9 І І 110+ +*** 8 00456824679 11 +-----+ І **** 6 02257723367 11 І І ******* 4 891157 6 І 50+* * * **+++ ----+----+----+----+ +----+----+----+----+----+----+----+----+----+----+ Multiply Stem.Leaf by 10**+1 -2 -1 0 +1 +2 NCGS DATA 15:37 Saturday, January 25, 2003 18 frequency distributions of trigl, a fine distribution two group example: 3= drug group, 5= placebo group The UNIVARIATE Procedure Variable: TRIGL Schematic Plots 800 + І І І * 700 + І І І 600 + І І І 500 + І І І 400 + І І 0 І 0 300 + 0 І І І І І І І І І І 200 + І +-----+ І +-----+ І І І І + І І + І І *-----* *-----* 100 + І І +-----+ І +-----+ І І І І І 0 + NCGS DATA 15:37 Saturday, January 25, 2003 19 frequency distributions of trigl, a fine distribution two group example: 3= drug group, 5= placebo group The UNIVARIATE Procedure Variable: TRIGL Schematic Plots ------------+-----------+----------- TRETGRP 3 5 NCGS DATA 15:37 Saturday, January 25, 2003 20 frequency distributions of trigl, a fine distribution two group example: 3= drug group, 5= placebo group kernel smoothed density estimates --------------------------------------------------------- TRETGRP=3 ---------------------------------------------------------- The KDE Procedure Inputs Data Set WORK.ONE Number of Observations Used 102 Variable TRIGL Bandwidth Method Sheather-Jones Plug In Controls TRIGL Grid Points 401 Lower Grid Limit 40 Upper Grid Limit 725 Bandwidth Multiplier 0.75 Statistics TRIGL Mean 141 Variance 7925 Standard Deviation 89.02 Range 685 Interquartile Range 81.00 Bandwidth 15.55 NCGS DATA 15:37 Saturday, January 25, 2003 21 frequency distributions of trigl, a fine distribution two group example: 3= drug group, 5= placebo group kernel smoothed density estimates --------------------------------------------------------- TRETGRP=3 ---------------------------------------------------------- The KDE Procedure Percentiles TRIGL 0.5 40.00 1.0 44.00 2.5 49.00 5.0 59.00 10.0 68.00 25.0 87.00 50.0 120 75.0 168 90.0 249 95.0 294 97.5 326 99.0 331 99.5 725 Levels Percent Density Lower Upper 1 0.000601 40.00 341 5 0.000968 40.00 324 10 0.001383 40.00 263 50 0.005749 67.40 138 90 0.007711 86.24 98.23 95 0.007813 87.95 93.09 99 0.007826 91.38 91.38 100 0.007826 91.38 91.38 NCGS DATA 15:37 Saturday, January 25, 2003 22 frequency distributions of trigl, a fine distribution two group example: 3= drug group, 5= placebo group kernel smoothed density estimates --------------------------------------------------------- TRETGRP=5 ---------------------------------------------------------- The KDE Procedure Inputs Data Set WORK.ONE Number of Observations Used 95 Variable TRIGL Bandwidth Method Sheather-Jones Plug In Controls TRIGL Grid Points 401 Lower Grid Limit 48 Upper Grid Limit 348 Bandwidth Multiplier 0.75 Statistics TRIGL Mean 146 Variance 4740 Standard Deviation 68.85 Range 300 Interquartile Range 96.00 Bandwidth 18.74 NCGS DATA 15:37 Saturday, January 25, 2003 23 frequency distributions of trigl, a fine distribution two group example: 3= drug group, 5= placebo group kernel smoothed density estimates --------------------------------------------------------- TRETGRP=5 ---------------------------------------------------------- The KDE Procedure Percentiles TRIGL 0.5 48.00 1.0 48.00 2.5 51.00 5.0 55.00 10.0 65.00 25.0 92.00 50.0 135 75.0 188 90.0 251 95.0 292 97.5 299 99.0 348 99.5 348 Levels Percent Density Lower Upper 1 0.000258 48.00 348 5 0.001366 48.00 292 10 0.001628 48.00 251 50 0.005033 72.75 159 90 0.006301 128 138 95 0.006349 131 135 99 0.006356 133 134 100 0.006356 134 134 NCGS DATA 15:37 Saturday, January 25, 2003 24 frequency distributions of trigl, a fine distribution two group example: 3= drug group, 5= placebo group kernel smoothed density estimates D=DRUG GROUP, P=PLACEBO GROUP Plot of density3*TRIGL. Symbol used is 'D'. Plot of density5*TRIGL. Symbol used is 'P'. density3 щ 0.008 ъ щ DDDD щ D DD щ D D щ D D щ D DDPP 0.006 ъ DD PPDDPP щ D PPP DDP щ DPPPPP DPP щ DDP DPP щ DP DDP щ D DDP 0.004 ъ PD DPP щ D DPP щ PD DDPP щ DD D PP щ D D PP щ D DD PP 0.002 ъ D DD PPP щ D DD PPPPDP щ DDDDDD DDPPPPP щ DD PPDDDD щ DDDDDDP DD щ PPDDD DDD 0.000 ъ DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD щ шттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътт 40.0 108.5 177.0 245.5 314.0 382.5 451.0 519.5 588.0 656.5 725.0 TRIGL NOTE: 802 obs had missing values. 612 obs hidden. NCGS DATA 15:37 Saturday, January 25, 2003 25 frequency distributions of log trigl two group example: 3= drug group, 5= placebo group SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS --------------------------------------------------------- TRETGRP=3 ---------------------------------------------------------- The UNIVARIATE Procedure Variable: ltrigl Moments N 102 Sum Weights 102 Mean 4.81331862 Sum Observations 490.9585 Std Deviation 0.5086421 Variance 0.25871678 Skewness 0.43147887 Kurtosis 0.54920648 Uncorrected SS 2389.27008 Corrected SS 26.1303952 Coeff Variation 10.5673889 Std Error Mean 0.05036307 Basic Statistical Measures Location Variability Mean 4.813319 Std Deviation 0.50864 Median 4.787457 Variance 0.25872 Mode 4.406719 Range 2.89729 Interquartile Range 0.65806 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 95.57238 Pr > ІtІ <.0001 Sign M 51 Pr >= ІMІ <.0001 Signed Rank S 2626.5 Pr >= ІSІ <.0001 NCGS DATA 15:37 Saturday, January 25, 2003 26 frequency distributions of log trigl two group example: 3= drug group, 5= placebo group SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS --------------------------------------------------------- TRETGRP=3 ---------------------------------------------------------- The UNIVARIATE Procedure Variable: ltrigl Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.985193 Pr < W 0.3146 Kolmogorov-Smirnov D 0.056182 Pr > D >0.1500 Cramer-von Mises W-Sq 0.049478 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.317262 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 6.58617 99% 5.80212 95% 5.68358 90% 5.51745 75% Q3 5.12396 50% Median 4.78746 25% Q1 4.46591 10% 4.21951 5% 4.07754 1% 3.78419 0% Min 3.68888 NCGS DATA 15:37 Saturday, January 25, 2003 27 frequency distributions of log trigl two group example: 3= drug group, 5= placebo group SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS --------------------------------------------------------- TRETGRP=3 ---------------------------------------------------------- The UNIVARIATE Procedure Variable: ltrigl Extreme Observations ------Lowest----- -----Highest----- Value Obs Value Obs 3.68888 49 5.74939 93 3.78419 9 5.78074 66 3.89182 28 5.78690 98 3.91202 23 5.80212 58 3.97029 20 6.58617 53 Stem Leaf # Boxplot Normal Probability Plot 64 9 1 0 6.5+ * 62 І 60 І ++ 58 0 1 І І +*++ 56 8589 4 І І **** 54 08124699 8 І І ***** 52 2247359 7 І І **** 50 24991123455 11 +-----+ 5.1+ +**** 48 0345667790333447899 19 І + І І ***** 46 11222890023788 14 *-----* І +**** 44 1112233790022335678 19 +-----+ І ****** 42 023568877 9 І І ****+ 40 8917 4 І І ***+ 38 917 3 І І ***+ 36 98 2 І 3.7+* ++*+ ----+----+----+----+ +----+----+----+----+----+----+----+----+----+----+ Multiply Stem.Leaf by 10**-1 -2 -1 0 +1 +2 NCGS DATA 15:37 Saturday, January 25, 2003 28 frequency distributions of log trigl two group example: 3= drug group, 5= placebo group SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS --------------------------------------------------------- TRETGRP=5 ---------------------------------------------------------- The UNIVARIATE Procedure Variable: ltrigl Moments N 95 Sum Weights 95 Mean 4.86887307 Sum Observations 462.542941 Std Deviation 0.48608714 Variance 0.23628071 Skewness -0.147943 Kurtosis -0.6571685 Uncorrected SS 2274.27326 Corrected SS 22.2103868 Coeff Variation 9.98356574 Std Error Mean 0.04987149 Basic Statistical Measures Location Variability Mean 4.868873 Std Deviation 0.48609 Median 4.905275 Variance 0.23628 Mode 3.931826 Range 1.98100 Interquartile Range 0.71465 NOTE: The mode displayed is the smallest of 15 modes with a count of 2. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 97.62839 Pr > ІtІ <.0001 Sign M 47.5 Pr >= ІMІ <.0001 Signed Rank S 2280 Pr >= ІSІ <.0001 NCGS DATA 15:37 Saturday, January 25, 2003 29 frequency distributions of log trigl two group example: 3= drug group, 5= placebo group SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS --------------------------------------------------------- TRETGRP=5 ---------------------------------------------------------- The UNIVARIATE Procedure Variable: ltrigl Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.981064 Pr < W 0.1857 Kolmogorov-Smirnov D 0.070713 Pr > D >0.1500 Cramer-von Mises W-Sq 0.051776 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.371111 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 5.85220 99% 5.85220 95% 5.67675 90% 5.52545 75% Q3 5.23644 50% Median 4.90527 25% Q1 4.52179 10% 4.17439 5% 4.00733 1% 3.87120 0% Min 3.87120 NCGS DATA 15:37 Saturday, January 25, 2003 30 frequency distributions of log trigl two group example: 3= drug group, 5= placebo group SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS --------------------------------------------------------- TRETGRP=5 ---------------------------------------------------------- The UNIVARIATE Procedure Variable: ltrigl Extreme Observations ------Lowest----- -----Highest----- Value Obs Value Obs 3.87120 27 5.67675 47 3.89182 36 5.69709 94 3.93183 68 5.70044 76 3.93183 43 5.72031 71 4.00733 15 5.85220 20 NCGS DATA 15:37 Saturday, January 25, 2003 31 frequency distributions of log trigl two group example: 3= drug group, 5= placebo group SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS --------------------------------------------------------- TRETGRP=5 ---------------------------------------------------------- The UNIVARIATE Procedure Variable: ltrigl Stem Leaf # Boxplot Normal Probability Plot 58 5 1 І 5.85+ ++ * 57 002 3 І І +* * 56 458 3 І 5.65+ **** 55 357 3 І І **+ 54 06789 5 І 5.45+ *** 53 26 2 І І ** 52 0134556779 10 +-----+ 5.25+ **** 51 015 3 І І І ** 50 0000335789 10 І І 5.05+ *** 49 011233458 9 *-----* І *** 48 223446889 9 І + І 4.85+ **** 47 3446 4 І І І **+ 46 025689 6 І І 4.65+ ** 45 2467 4 +-----+ І ** 44 3458 4 І 4.45+ +** 43 3488 4 І І +** 42 00899 5 І 4.25+ +** 41 337 3 І І +** 40 149 3 І 4.05+ *** 39 33 2 І І ** 38 79 2 І 3.85+* *+ ----+----+----+----+ +----+----+----+----+----+----+----+----+----+----+ Multiply Stem.Leaf by 10**-1 -2 -1 0 +1 +2 NCGS DATA 15:37 Saturday, January 25, 2003 32 frequency distributions of log trigl two group example: 3= drug group, 5= placebo group SIMPLE UNIVARIATE DISTRIBUTIONS AND HISTOGRAMS The UNIVARIATE Procedure Variable: ltrigl Schematic Plots І 7 + І І І 0 6.5 + І І І 6 + І І І І І І І І 5.5 + І І І І І І І +-----+ І +-----+ І І 5 + І І І І І І + І *--+--* І *-----* І І І І І І І 4.5 + +-----+ +-----+ І І І І І І І І І 4 + І І І І І І І І 3.5 + ------------+-----------+----------- TRETGRP 3 5 NCGS DATA 15:37 Saturday, January 25, 2003 33 frequency distributions of log trigl two group example: 3= drug group, 5= placebo group kernel smoothed density estimates --------------------------------------------------------- TRETGRP=3 ---------------------------------------------------------- The KDE Procedure Inputs Data Set WORK.ONE Number of Observations Used 102 Variable ltrigl Bandwidth Method Sheather-Jones Plug In Controls ltrigl Grid Points 401 Lower Grid Limit 3.6889 Upper Grid Limit 6.5862 Bandwidth Multiplier 0.75 Statistics ltrigl Mean 4.81 Variance 0.26 Standard Deviation 0.51 Range 2.90 Interquartile Range 0.66 Bandwidth 0.16 NCGS DATA 15:37 Saturday, January 25, 2003 34 frequency distributions of log trigl two group example: 3= drug group, 5= placebo group kernel smoothed density estimates --------------------------------------------------------- TRETGRP=3 ---------------------------------------------------------- The KDE Procedure Percentiles ltrigl 0.5 3.69 1.0 3.78 2.5 3.89 5.0 4.08 10.0 4.22 25.0 4.47 50.0 4.79 75.0 5.12 90.0 5.52 95.0 5.68 97.5 5.79 99.0 5.80 99.5 6.59 Levels Percent Density Lower Upper 1 0.07412 3.69 5.95 5 0.1673 3.91 5.80 10 0.2372 4.02 5.68 50 0.6558 4.41 5.05 90 0.7522 4.62 4.83 95 0.7525 4.62 4.82 99 0.7526 4.62 4.81 100 0.7529 4.65 4.65 NCGS DATA 15:37 Saturday, January 25, 2003 35 frequency distributions of log trigl two group example: 3= drug group, 5= placebo group kernel smoothed density estimates --------------------------------------------------------- TRETGRP=5 ---------------------------------------------------------- The KDE Procedure Inputs Data Set WORK.ONE Number of Observations Used 95 Variable ltrigl Bandwidth Method Sheather-Jones Plug In Controls ltrigl Grid Points 401 Lower Grid Limit 3.8712 Upper Grid Limit 5.8522 Bandwidth Multiplier 0.75 Statistics ltrigl Mean 4.87 Variance 0.23 Standard Deviation 0.48 Range 1.98 Interquartile Range 0.71 Bandwidth 0.15 NCGS DATA 15:37 Saturday, January 25, 2003 36 frequency distributions of log trigl two group example: 3= drug group, 5= placebo group kernel smoothed density estimates --------------------------------------------------------- TRETGRP=5 ---------------------------------------------------------- The KDE Procedure Percentiles ltrigl 0.5 3.87 1.0 3.87 2.5 3.93 5.0 4.01 10.0 4.17 25.0 4.52 50.0 4.91 75.0 5.24 90.0 5.53 95.0 5.68 97.5 5.70 99.0 5.85 99.5 5.85 Levels Percent Density Lower Upper 1 0.1331 3.87 5.85 5 0.2191 3.93 5.77 10 0.2927 4.04 5.69 50 0.5631 4.63 5.27 90 0.8294 4.89 4.99 95 0.8394 4.92 4.96 99 0.8408 4.93 4.94 100 0.8409 4.94 4.94 NCGS DATA 15:37 Saturday, January 25, 2003 37 frequency distributions of log trigl two group example: 3= drug group, 5= placebo group kernel smoothed density estimates D=DRUG GROUP, P=PLACEBO GROUP Plot of density3*ltrigl. Symbol used is 'D'. Plot of density5*ltrigl. Symbol used is 'P'. density3 щ 1.0 ъ щ щ щ щ PPPPP 0.8 ъ PPP PPP щ DDDDDDDDDDDDD PPP щ DDDD PP DDDD PP щ DDD PP DDD PP щ DD PP DD PP 0.6 ъ DD PP DD PP щ DD PP DD PPP щ DD PPP DD PP щ DD PPPP DD PPP щ DD PPPPP DDD PPP 0.4 ъ DDPPP DD PPP щ PDDP DDD PPPP щ PDDD DDDDD PPP щ PPDD DDDD PP щ PPDDD DDDDP 0.2 ъ PPDDD DDDP щ DDDD DDD щ DDDD DDD щ DDD DDD щ DDDDD DDDD 0.0 ъ DDDDDDDDDDDDDDD шттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътттттттттътт 3.6889 3.9786 4.2683 4.5581 4.8478 5.1375 5.4273 5.7170 6.0067 6.2964 6.5862 ltrigl NOTE: 802 obs had missing values. 589 obs hidden.