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Inference on Two Population DATA CARLSBAD; INPUT YEAR COUNT CARDS; 2009 397 2009 286 2009 2682009 254 2009 571 2009 6042009 384 2010 314 2010 257 2010.

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Presentation on theme: "Inference on Two Population DATA CARLSBAD; INPUT YEAR COUNT CARDS; 2009 397 2009 286 2009 2682009 254 2009 571 2009 6042009 384 2010 314 2010 257 2010."— Presentation transcript:

1 Inference on Two Population DATA CARLSBAD; INPUT YEAR COUNT @@; CARDS; 2009 397 2009 286 2009 2682009 254 2009 571 2009 6042009 384 2010 314 2010 257 2010 2782010 252 2010 613 2010 6462010 253 ods graphics on; PROC UNIVARIATE DATA=CARLSBAD NORMAL; VAR COUNT; BY YEAR; TITLE 'PROBLEM ASSUMING NORMALITY'; PROC TTEST DATA=CARLSBAD; CLASS YEAR; VAR COUNT; TITLE 'Problem Assuming Normality'; PROC RANK DATA=CARLSBAD OUT=RANKED; VAR COUNT; PROC TTEST DATA=RANKED; CLASS YEAR; VAR COUNT; TITLE 'Wilcoxon-Mann-Whitney test with PROC RANK'; PROC NPAR1WAY data=carlsbad wilcoxon; Class year; Var count; TITLE 'Wilcoxon-Mann-Whitney test with PROC NPAR1WAY'; RUN;ods graphics off; QUIT;

2 Inference on Two Population PROBLEM ASSUMING NORMALITY ------------------------------------------ YEAR=2009 ------------------------------------- UNIVARIATE 프로시저 변수 : COUNT 적률 N 7 가중합 7 평균 394.857143 관측치 합 2764 표준편차 142.987678 분산 20445.4762 왜도 0.67728241 첨도 -1.3040573 제곱합 1214058 수정 제곱합 122672.857 변동계수 36.212509 평균의 표준오차 54.0442625 위치모수 검정 : Mu0=0 검정 -- 통계량 --- -------p 값 ------- 스튜던트의 t t 7.306181 Pr > |t| 0.0003 부호 M 3.5 Pr >= |M| 0.0156 부호 순위 S 14 Pr >= |S| 0.0156 정규성 검정 검정 ---- 통계량 ---- -------p- 값 ------- Shapiro-Wilk W 0.864041 Pr < W 0.1645 Kolmogorov-Smirnov D 0.208307 Pr > D >0.1500 Cramer-von Mises W-Sq 0.069546 Pr > W-Sq 0.2470 Anderson-Darling A-Sq 0.44369 Pr > A-Sq 0.2043 PROBLEM ASSUMING NORMALITY ------------------------------------------ YEAR=2010 --------------------------- UNIVARIATE 프로시저 변수 : COUNT 적률 N 7 가중합 7 평균 373.285714 관측치 합 2613 표준편차 176.602864 분산 31188.5714 왜도 1.18136027 첨도 -0.8247496 제곱합 1162527 수정 제곱합 187131.429 변동계수 47.3103729 평균의 표준오차 66.7496083 위치모수 검정 : Mu0=0 검정 -- 통계량 --- -------p 값 ------- 스튜던트의 t t 5.592328 Pr > |t| 0.0014 부호 M 3.5 Pr >= |M| 0.0156 부호 순위 S 14 Pr >= |S| 0.0156 정규성 검정 검정 ---- 통계량 ---- -------p- 값 ------- Shapiro-Wilk W 0.70274 Pr < W 0.0040 Kolmogorov-Smirnov D 0.345737 Pr > D 0.0124 Cramer-von Mises W-Sq 0.187549 Pr > W-Sq 0.0050 Anderson-Darling A-Sq 1.012182 Pr > A-Sq <0.0050

3 Inference on Two Population The TTEST Procedure Variable: COUNT YEAR N Mean Std Dev Std Err Minimum Maximum 2009 7 394.9 143.0 54.0443 254.0 604.0 2010 7 373.3 176.6 66.7496 252.0 646.0 Diff (1-2) 21.5714 160.7 85.8853 YEAR Method Mean 95% CL Mean Std Dev 95% CL Std Dev 2009 394.9 262.6 527.1 143.0 92.1403 314.9 2010 373.3 210.0 536.6 176.6 113.8 388.9 Diff (1-2) Pooled 21.5714 -165.6 208.7 160.7 115.2 265.2 Diff (1-2) Satterthwaite 21.5714 -166.5 209.6 Method Variances DF t Value Pr > |t| Pooled Equal 12 0.25 0.8059 Satterthwaite Unequal 11.502 0.25 0.8061 Equality of Variances Method Num DF Den DF F Value Pr > F Folded F 6 6 1.53 0.6210 _____________________________________________________________________________________

4 Inference on Two Population

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6 Wilcoxon-Mann-Whitney test with PROC RANK 6 The TTEST Procedure Variable: COUNT (COUNT 값이 순위별로 교체됨 ) YEAR N Mean Std Dev Std Err Minimum Maximum 2009 7 8.1429 3.2878 1.2427 3.0000 12.0000 2010 7 6.8571 5.1130 1.9325 1.0000 14.0000 Diff (1-2) 1.2857 4.2984 2.2976 YEAR Method Mean 95% CL Mean Std Dev 95% CL Std Dev 2009 8.1429 5.1022 11.1836 3.2878 2.1186 7.2399 2010 6.8571 2.1284 11.5859 5.1130 3.2948 11.2592 Diff (1-2) Pooled 1.2857 -3.7203 6.2917 4.2984 3.0823 7.0955 Diff (1-2) Satterthwaite 1.2857 -3.8176 6.3890 Method Variances DF t Value Pr > |t| Pooled Equal 12 0.56 0.5861 Satterthwaite Unequal 10.237 0.56 0.5878 Equality of Variances Method Num DF Den DF F Value Pr > F Folded F 6 6 2.42 0.3067

7 Inference on Two Population

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9 Problem using Wilcoxon-Mann-Whitney test The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable COUNT Classified by Variable YEAR Sum of Expected Std Dev Mean YEAR N Scores Under H0 Under H0 Score 2009 7 57.0 52.50 7.826238 8.142857 2010 7 48.0 52.50 7.826238 6.857143 Wilcoxon Two-Sample Test Statistic 57.0000 Normal Approximation Z 0.5111 One-Sided Pr > Z 0.3046 Two-Sided Pr > |Z| 0.6093 t Approximation One-Sided Pr > Z 0.3089 Two-Sided Pr > |Z| 0.6178 Z includes a continuity correction of 0.5. Kruskal-Wallis Test Chi-Square 0.3306 DF 1 Pr > Chi-Square 0.5653

10 Inference on Two Population

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