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单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,秩和检验（非参数检验）,实习十二,目的要求,掌握利用,univariate,过程完成,配对设计,资料的非参数检验；,掌握利用,npar1way,过程,及选择项,Wilcoxon,的使用完成完全随机设计两组、多组资料的秩和检验；,熟悉利用,freq,过程,完成,随机区组设计,资料的秩和检验且能对结果作分析。,非参数统计的适用情况,（1）等级资料；,（2）偏态分布；,（3）分布不明；,（4）个别数据偏离过大；,（5）各组方差明显不齐。,非参数统计的优缺点,优点：不受总体分布的限制，适用范围广。,缺点：没有充分利用资料提供的信息。检验,效能低于参数检验。,适用参数检验条件的资料，应首选参数检验。,例1,某研究者欲研究保健食品对小鼠抗疲劳作用，将同种属的小鼠按性别和年龄相同、体重相近配成对子，共10对，并将每对中的两只小鼠随机分到保健食品两个不同的剂量组，过一定时期将小鼠杀死，测得其肝糖原含量（mg/100g），结果见下表，问不同剂量组的小鼠肝糖原含量有无差别？,配对资料的秩和检验,data,SAS1;,input,x1 x2;,d=x1-x2,;,Cards,;,620.16 958.47 866.50 838.42 641.22 788.90,812.91 815.20 738.96 783.17 899.38 910.92,760.78 758.49 694.95 870.80 749.92 862.26 793.94 805.48,;,proc,univariate,normal,;,var,d;,run,;,Tests for Location:Mu0=0,Test -Statistic-p Value-,Students t t -2.25916 Pr|t|0.0502,Sign M -3 Pr=|M|0.1094,Signed Rank S -21 Pr=|S|0.0313,Tests for Normality,Test -Statistic-p Value-,Shapiro-Wilk W 0.843269 Pr D 0.1362,Cramer-von Mises W-Sq 0.106441 Pr W-Sq 0.0824 Anderson-Darling A-Sq 0.657567 Pr A-Sq 0.0625,符号秩和,单样本秩和检验,data,a;,input,nf;,cards,;,2.15 2.10 2.20 2.12 2.42 2.52,2.62 2.72 2.99 3.19 3.37 4.57,;,proc,univariate,normal,mu0=2.15,;,var,nf;,run,;,Tests for Location:Mu0=2.15,Test -Statistic-p Value-,Students t t 2.898449 Pr|t|0.0145,Sign M 3.5 Pr=|M|0.0654,Signed Rank S 29.5 Pr=|S|0.0059,Tests for Normality,Test -Statistic-p Value-,Shapiro-Wilk W 0.837966 Pr D 0.1500,Cramer-von Mises W-Sq 0.092826 Pr W-Sq 0.1281,Anderson-Darling A-Sq 0.651796 Pr A-Sq 0.0704,例,2,为比较两种刺激物的对人的影响力的持续时间，现随机抽取,13,个试验对象接受第一种刺激物，,6,个试验对象接受第二种刺激物。持续时间如下表,，问,二种刺激物的持续时间是否有差异？,两独立样本秩和检验,持续时间表,(minutes),刺激物1组 1.94 1.94 2.92 2.92 2.92 2.92,3.27 3.27 3.27 3.27 3.70 3.70 3.74,刺激物2组 3.27 3.27 3.27 3.70 3.70 3.74,PROC NPAR1WAY过程格式,PROC NPAR,1,WAY,Wilcoxon,；,CLASS,变量；,VAR,变量表；,RUN；,data sas1；,do a=1 to 2；,input n；,do j=1 to n；,input x；,output；end；end；,cards；,13,1.94 1.94 2.92 2.92 2.92 2.92 3.27,3.27 3.27 3.27 3.70 3.70 3.74,6,3.27 3.27 3.27 3.70 3.70 3.74,；,proc sort；排序过程,by a；,run；,proc univariate,normal,；考虑各组的正态性,var x；by a；,run；,proc npar,1,way,wilcoxon,；,class a；,var x；,exact,；输出精确的概率,run,；,结果,The NPAR1WAY Procedure,Wilcoxon Scores(Rank Sums)for Variable x,Classified by Variable a,Sum of Expected Std Dev Mean,a N Scores Under H0 Under H0 Score,-,1 13 110.50 130.0 11.004784 8.500,2 6 79.50 60.0 11.004784 13.250,每组得分和 H0成立时的得分和 H0成立时的标准差 平均得分,Average scores were used for ties.,Wilcoxon Two-Sample Test,Statistic(S)79.5000,Normal Approximation,Z 1.7265,One-Sided Pr Z 0.0421,Two-Sided Pr|Z|0.0843,t Approximation,One-Sided Pr Z 0.0507,Two-Sided Pr|Z|0.1014,T统,计量,正态近似法,结果（超出,表范围时使,用）,近似t检验结果,Exact Test,One-Sided Pr=S 0.0527,Two-Sided Pr=|S-Mean|0.1054,小样本时可通过加exact选项要求输出精确的概率。,大样本时可直接采用正态近似的结果。,例3 多组独立样本资料的秩和检验,data sasbook；,do a=1 to 4；,do j=1 to 10；,input x；,output；end；end；,cards；,1.23 1.14 1.63 1.00 1.35 2.01 1.64 1.13 1.01 1.70,2.59 0.96 3.96 0.23 1.61 2.94 1.96 3.68 0.54 2.59,2.50 3.92 3.33 0.23 2.07 3.90 2.84 2.42 3.72 3.00,0.40 0.51 2.49 0.74 2.59 2.36 3.00 3.31 3.21 3.12,；,proc sort；,by a；,run,；,proc univariate,normal,；,by a；,var x；,run；,proc npar,1,way,wilcoxon,；,class a；,var x；,run,；,Wilcoxon Scores(Rank Sums)for Variable x,Classified by Variable a,Sum of Expected Std Dev Mean,a N Scores Under H0 Under H0 Score,1 10 130.00 205.0 32.006610 13.000,2 10 202.50 205.0 32.006610 20.250,3 10 275.00 205.0 32.006610 27.500,4 10 212.50 205.0 32.006610 21.250,Average scores were used for ties.,Kruskal-Wallis Test,Chi-Square 7.7513,DF 3,Pr Chi-Square 0.0514,k3,且每组例数均大于5，则此时不能查表，,且H值近似服从自由度为k-1的卡方分布。,例4：随机区组设计的秩和检验,data,ex107;,do,b=,1,to,8,;,do,a=,1,to,4,;,input,x;,output,;,end,;,end,;,cards,;,8.4 9.6 9.8 11.7,11.6 12.7 11.8 12.0,9.4 9.1 10.4 9.8,9.8 8.7 9.9 12.0,8.3 8.0 8.6 8.6,8.6 9.8 9.6 10.6,8.9 9.0 10.6 11.4,8.3 8.2 8.5 10.8,;,proc,freq,;,tables,b*a*x/,scores,=,rank,cmh2,;/,*得到FRIEDMAN统计量*/,run,;,Summary Statistics for a by x,Controlling for b,Cochran-Mantel-Haenszel Statistics(Based on Rank Scores),Statistic Alternative Hypothesis DF Value Prob,1 Nonzero Correlation 1 14.1304 0.0002,2 Row Mean Scores Differ 3 14.5443 0.0023,Total Sample Size=32,作业：,page204，第4、6、7题,
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