第九章 非参数检验

1、第九章 非参数检验医学统计之星上次更新日期：非参数统计是统计分析的重要组成部分。可是与之很不相称的是它的理论发展远 远不及参数检验完善，因而比较完善的可供使用的方法也不多。在 SAS 中，非参数统计主要由UNIVARIATE过程、MEANS过程和NPAR1WAY过程来实现, 前两者在前面的章节中已经介绍，它们可以进行配对设计差值的符号秩和检验 （WILCOXON 配对法）；后者是一个单因素的非参数方差分析过程,可进行成组设计的两样本（WILCOXON法）或多样本比较（KRUSKAL-WALLIS法）的秩和检验。本章将主要介绍NPAR1WAY过程。站由于在理论上还有争议，作为权威性的统计软件，SAS不提供非参检验两 两比较的方法。据我所知，其余统计软件里也只有PEMS提供这一功能（因为 她是医统医百的配套软件，而非参两两比较是写入了该书的）。如果你需要这一结果，那么恐怕只有手算了。9.0.1 语法格式PROC NPAR1WAY DATA= FF 值p值5.474 0.0298Average Scores Were Used for Ties以下为 Wilcoxon 秩和检验的分析结果分组

2、变量名Wilcoxon Scores (Rank Sums) for Variable 应变量名N 样本量Classified by Variable 分组变量名Sum ofScores 各组的秩和ExpectedUnder H0 各组的期望秩和Std DevUnder H0秩和的标准差MeanScore 各组的平均秩次110170.0115.015.152900417.000000021283.0138.015.15290046.9166667Average Scores Were Used for TiesWilcoxon 2-Sample Test (Normal Approximation)(with Continuity Correction of .5)S = 170.000 Z = 3.59667 Prob |Z| = 0.0003如果按照正态近似法做秩和检验，则 Z=3.59667，p=0.0003。T-Test Approx. Significance = 0.0017做近似t检验则p=0.0017Kruskal-Wallis Test (Chi-Square App

3、roximation)CHISQ = 13.174DF = 1Prob CHISQ = 0.0003用 近似做 K-W 法秩和检验，则 =13.174，p=0.0003。以下为中位数检验的分析结果Median Scores (Number of Points Above Median)for Variable 应变量名Classified by Variable 分组变量名Sum ofExpectedStd DevMean分组变量名 N Scores Under H0 Under H0 Score 样本量 各组的中位秩次和 各组期望中位秩次和 中位秩次的标准差 各组平均中 位秩次1109.05.01.195228610.9000000002122.06.01.195228610.166666667Average SCores Were Used for TiesMedian2-Sample Test(Normal Approximation)S =9.00000Z =3.34664Prob |Z|= 0.0008用正态近似法做中位数检验，则 Z=3.34664，p=0.0008。Med

4、ian 1-Way Analysis (Chi-Square Approximation)CHISQ = 11.200 DF = 1 Prob CHISQ = 0.0008用C2近似法做中位数检验，则C2=11.200, p=0.0008。以下为 Van der Waerden 比分检验的结果Van der Waerden SCores (Normal) for Variable 应变量名Classified by Variable分组变量名Std DevMeanSum ofExpeCted分组变量名NSCoresUnder H0Under H0SCore比分样本量各组的比分和各组的期望比分和比分和的标准差 各组的平均1107.348697340.02.095896480.734869734212-7.348697340.02.09589648-.612391445Average SCores Were Used for TiesVan der Waerden 2-Sample Test (Normal Approximation)S = 7.34870 Z = 3.50623 Pro

5、b |Z| = 0.0005用正态近似法做 Van der Waerden 检验，则 Z=3.50623, p=0.0005。Van der Waerden 1-Way Analysis (Chi-Square Approximation)CHISQ = 12.294DF = 1Prob CHISQ = 0.0005用 C2近似法做 Van der Waerden 检验，则=12.294, p=0.0005。-以下为 Savage 比分检验的结果Savage SCores (Exponential) for Variable 应变量名Classified by Variable 分组变量名Sum ofExpeCtedStd DevMean分组变量名 N样本量SCoresUnder H0Under H0SCore1012各组的比分和7.14463489-7.14463489各组的期望比分和 比分和的标准差0.00.02.179659462.17965946各组的平均比0.714463489-.595386241Average SCores Were Used2-Sample Test (

6、Normal Approximation)Prob |Z| = 0.0010 用正态近似法做 Savage 检验，则 Z=3.27787， p=0.0010。Savage 1-Way Analysis (Chi-Square Approximation)for TiesSavageS = 7.14463Z = 3.27787CHISQ =10.744DF = 1Prob CHISQ = 0.0010用 C2近似法做 Savage 检验，则 C2=10.744, p=0.0010。以下为 Kolmogorov-Smirnov 检验的结果Kolmogorov-Smirnov Test for Variable 应变量名Classified by Variable 分组变量名EDFDeviation from Mean分组变量名Nat Maximumat Maximum1100.20000000-1.379902982121.000000001.25967331220.63636364Maximum Deviation OCCurred at Observation 22 Value of DAY at Maximum 13.0000000Kolmogorov-Smirnov 2-Sample Test (AsymptotiC)KS = 0.398344D = 0.800000KSa =1.86840Prob KSa = 0.0019Kolmogorov-Smirnov 检验的最后结果为统计量 Ksa=1.86840， p=0.0019。以下为 Cramer-von Mises 检验的结果Cramer-von Mises Test for Variable 应变量名Classified by Variable 分组变量名SummedDeviation分组变量名Nfrom Mean1100.7758076632120.646506386Cramer-von Mises StatistiC (AsymptotiC)CM = 0.064651CMa = 1.42231Cramer-von Mises 统计量 C

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