非参数统计（第二版）习题R程序(2)

shuju3.var=var(shuju3);shuju3.var shuju3.sd=sd(shuju3);shuju3.sd e0=pnorm(30,shuju3.mean,shuju3.sd) e1=pnorm(40,shuju3.mean,shuju3.sd)-pnorm(30,shuju3.mean,shuju3.sd) e2=pnorm(50,shuju3.mean,shuju3.sd)-pnorm(40,shuju3.mean,shuju3.sd) e3=pnorm(60,shuju3.mean,shuju3.sd)-pnorm(50,shuju3.mean,shuju3.sd) e4=pnorm(70,shuju3.mean,shuju3.sd)-pnorm(60,shuju3.mean,shuju3.sd) e5=pnorm(80,shuju3.mean,shuju3.sd)-pnorm(70,shuju3.mean,shuju3.sd) e6=1-pnorm(80,shuju3.mean,shuju3.sd) e=c(e0,e1,e2,e3,e4,e5,e6);e ee=n*c(e0,e1,e2,e3,e4,e5,e6);ee x.squ=sum((nn^2)/(ee))-n;x.squ #方法一

value<-qchisq(1-0.05,length(ee)-1);value #方法二

pvalue<-1-pchisq(x.squ,length(ee)-1);pvalue 例2.22

healthy<-c(87,77,92,68,80,78,84,77,81,80,80,77,92,86, 76,80,81,75,77,72,81,90,84,86,80,68,77,87,76,77,78,92,

75,80,78);healthy

ks.test(healthy,pnorm,80,6) 第三章

#Brown_Mood中位数 #Brown-Mood中位数检验程序 BM.test<-function(x,y,alt){ xy<-c(x,y)

md.xy<-median(xy) #利用中位数的检验

#md.xy<-quantile(xy,0.25) #利用p分位数的检验

t<-sum(xy>md.xy) lx<-length(x) ly<-length(y) lxy<-lx+ly

A<-sum(x>md.xy) if (alt==\ {w<-1-phyper(A,lx,ly,t)} else if (alt==\ {w<-phyper(A,lx,ly,t)}

conting.table=matrix(c(A,lx-A,lx,t-A,ly-(t-A),ly,t,lxy-t,lxy),3,3)

col.name<-c(\

row.name<-c(\

dimnames(conting.table)<-list(row.name, col.name) list(contingency.table=conting.table,p.vlue=w) } 例3.2

X<-c(698,688,675,656,655,648,640,639,620) Y<-c(780,754,740,712,693,680,621) #方法一： BM.test(X,Y,\#方法二： XY<-c(X,Y) md.xy<-median(XY) t<-sum(XY>md.xy) lx<-length(X) ly<-length(Y) lxy<-lx+ly A<-sum(X>md.xy) #没有修正时的情形

pvalue1<-pnorm(A,lx*t/(lx+ly),

sqrt(lx*ly*t*(lx+ly-t)/(lx+ly)^3));pvalue1 #修正时的情形

pvalue2<-pnorm(A,lx*t/(lx+ly)-0.5, sqrt(lx*ly*t*(lx+ly-t)/(lx+ly)^3));pvalue2 3.2、Wilcoxon-Mann-Whitney秩和检验 #求两样本分别的秩和的程序. Qiuzhi<-function(x,y){ n1<-length(y) yy<-c(x,y) wm=0 for(i in 1:n1){

wm=wm+sum(y[i]>yy,1) } wm } 例3.3

weight.low=c(134,146,104,119,124,161, 107,83,113,129,97,123) m=length(weight.low)

weight.high=c(70,118,101,85,112,132,94) n=length(weight.high) #方法一：

wy<-Qiuzhi(weight.low,weight.high)##wy=50 wxy<-wy-n*(n+1)/2;wxy#=22 mean<-m*n/2

var<-m*n*(m+n+1)/12

pvalue<-1-2*pnorm(wxy,mean-0.5,var);pvalue #方法二

wilcox.test(weight.high,weight.low) 例3.4

Mx-My的R参考程序：

x1<-c(140,147,153,160,165,170,171,193) x2<-c(130,135,138,144,148,155,168) n1<-length(x1) n2<-length(x2)

th.hat<-median(x2)-median(x1) B=10000

Tboot=c(rep(0,1000)) #vector of length Bootstrap for (i in 1:B) {

xx1=sample(x1,5,T) #sample of size n1 with replacement from x1

xx2=sample(x2,5,T) #sample of size n2 with replacement from x2

Tboot[i]=median(xx2)-median(xx1) }

th<-median(Tboot);th se=sd(Tboot)

Normal.conf=c(th+qnorm(0.025,0,1)*se,th-qnorm(0.025,0,1)*se);Normal.conf

Percentile.conf=c(2*th-quantile(Tboot,0.975),2*th-quantile

(Tboot,0.025));Percentile.conf

Provotal.conf=c(quantile(Tboot,0.025),quantile(Tboot,0.975));Provotal.conf th.hat

3.3、Mood方差检验 qiuzhi<-function(x,y){ xy<-c(x,y) zhi<-NULL

for (i in 1:length(x)){ zhi<-c(zhi,sum(x[i]>=xy)) } zhi }

引例：

x1<-c(48,56,59,61,84,87,91,95) x2<-c(2,22,49,78,85,89,93,97) zhi_x1=qiuzhi(x1,x2);zhi_x1 #zhi_x2=qiuzhi(x2,x1);zhi_x2 #var_x1=var(x1);var_x1 #var_x2=var(x2);var_x2 m=length(x1);m n=length(x2);n

mean_R=(m+n+1)/2;mean_R

mean1=m*(m+n+1)*(m+n-1)/12;mean1

var1=m*n*(m+n+1)*(m+n+2)*(m+n-2)/180;var1 M1=sum((zhi_x1-mean_R)^2);M1

p_value=2*pnorm(M1,mean1-0.5,sqrt(var1)) p_value 例3.5

X<-c(4.5,6.5,7,10,12) Y<-c(6,7.2,8,9,9.8) zhi_X=qiuzhi(X,Y);zhi_X m=length(X);m n=length(Y);n

mean_R=(m+n+1)/2;mean_R

mean2=m*(m+n+1)*(m+n-1)/12;mean2

var2=m*n*(m+n+1)*(m+n+2)*(m+n-2)/180;var2 M2=sum((zhi_X-mean_R)^2);M2 #方法一：查附表9 #方法二：

p_value=2*(1-pnorm(M2,mean2-0.5,sqrt(var2))) p_value #方法三

Z=1/(sqrt(var2))*(M2-mean2+0.5);Z

3.4、Moses方差检验 qiuzhi<-function(x,y){ xy<-c(x,y) zhi<-NULL

for (i in 1:length(x)){ zhi<-c(zhi,sum(x[i]>=xy)) } zhi } 例3.6

x1<-c(8.2,10.7,7.5,14.6,6.3,9.2,11.9, 5.6,12.8,5.2,4.9,13.5) m1=length(x1);m1

x2<-c(4.7,6.3,5.2,6.8,5.6,4.2, 6.0,7.4,8.1,6.5) m2=length(x2);m2

A<-matrix(x1,ncol=3);A#随机分组 a1=sample(x1,3,F) xx2=NULL for(i in 1:m1){

if(sum(a1==x1[i])==0) xx2=c(xx2,x1[i]) }

a2=sample(xx2,3,F)

xx3=NULL for(i in 1:(m1-3)){

if(sum(a2==xx2[i])==0) xx3=c(xx3,x1[i]) }

a3=sample(xx3,3,F)

x11=sum((A[1,]-mean(x1))^2);x11 x12=sum((A[2,]-mean(x1))^2);x12 x13=sum((A[3,]-mean(x1))^2);x13 x14=sum((A[4,]-mean(x1))^2);x14

SSA<-c(x11,x12,x13,x14);SSA B<-matrix(x2[1:9],ncol=3);B y11=sum((B[1,]-mean(x2))^2);y11 y12=sum((B[2,]-mean(x2))^2);y12 y13=sum((B[3,]-mean(x2))^2);y13 SSB<-c(y11,y12,y13);SSB zhi_SSA=qiuzhi(SSA,SSB);zhi_SSA zhi_SSB=qiuzhi(SSB,SSA);zhi_SSB S=sum(zhi_SSA);S TM=S-4*(4+1)/2;TM #方法一(查附表4)

拒绝域C=(TMW(0.975,m1,m2))

其中W(0.975,m1,m2)=m1*m2-W(0.025,m1,m2). #方法二（Wilcoxon秩和检验） wilcox.test(SSA,SSB)

#方法二（Mann-Whitney秩和检验） m=length(SSA);m n=length(SSB);n

mean_AB=m*n/2;mean_AB var_AB=m*n*(m+n+1)/12;var_AB p_value=1-pnorm(S,mean_AB,sqrt(var_AB));p_value 第四章

4.1、试验设计和方差分析的基本概念回顾 #R软件中单因素方差分析的函数 例4.1 #方法一：

****Analysis of Variance Model ****

y<-c(2.0,1.4,2.0,2.8,2.4,1.9,1.8,2.5,2.0,1.5,2.1,2.2);y lever<-c(\

x<-factor(lever);x xy<-data.frame(y,x) attach(xy)

aov(formula=y~x,data=xy) aov.xy<-aov(formula=y~x,data=xy) summary(aov.xy)

#方法二：

x1<-c(1.4,1.9,2.0,1.5) x2<-c(2.0,2.4,1.8,2.2) x3<-c(2.6,2.8,2.5,2.1) y<-c(x1,x2,x3);y