非参数统计：方法与应用

（全书例题R语言实现）

第二章

2.1

例2.1
a <- c(88,12)
b <- c(0.95,0.05)
chisq.test(a,p = b) $p.value p = 0.001318969
例2.2
a <- c(380,69,43,8)
b <- c(0.8,0.12,0.07,0.01)
chisq.test(a, p = b) $p.value p = 0.1127
例2.4(续2.2)
a <- c(380,69,51)
b <- c(0.8,0.12,0.08)
chisq.test(a, p = b) p.valuep=0.06805例2.4a<−c(3,8,10,7,2)b<−c(0.1174,0.2355,0.328,0.2437,0.0754)chisq.test(a,p=b)p.value p = 0.06805 例2.4 a <- c(3,8,10,7,2) b <- c(0.1174,0.2355,0.328,0.2437,0.0754) chisq.test(a, p = b)p.valuep=0.06805例2.4a<−c(3,8,10,7,2)b<−c(0.1174,0.2355,0.328,0.2437,0.0754)chisq.test(a,p=b)p.value p = 0.9929581

2.2

例题2.6 (1)
x = c(-5,-3,-1,0,1,2,4,7,8)
y = c(1,1,2,1,5,5,3,1,1)
mu = mean(rep(x,y))
z = (x-mu)/3
f0 = pnorm(z, 0, 1)
n = length(x)
sn = NULL
for(i in 1:n){
sn[i] <- sum(y[1:i])
}
Sn <- sn/20
D = max(abs(Sn-f0))

例题2.8
a <-c(11,11,8,9,7,9,12)
b=rep(1/7,7)
a=a/sum(a)
ks.test(jitter(a),jitter(b))

2.3

例题2.7
binom.test(9,10,alternative = ‘greater’,conf.level = 0.9)
例题2.8
binom.test(10,12,alternative = ‘greater’,conf.level = 0.9)
例题2.9
binom.test(12,14,alternative = ‘two.sided’,conf.level = 0.9)
例题2.10
binom.test(1,8,alternative = ‘two.sided’,conf.level = 0.95)
例题2.11
binom.test(5,6,alternative = ‘greater’,conf.level = 0.9)
例题2.12
binom.test(2,13,alternative = ‘less’,conf.level = 0.9)
例题2.14
binom.test(7,18,p=0.25,alternative = ‘greater’,conf.level = 0.9)
例题2.15
p1 <- pbinom(3,13,0.75,lower.tail = T)
p1
例题2.16
p2 <- pbinom(3,8,0.5,lower.tail = T)
p2
2.4
例题2.17
x1 <- c(24.3,25.8,25.4,24.8,25.2,25.1,25,25.5)
d <- abs(x1-25)
x2 <- x1[-which(d==0)]
wilcox.test(x2,alternative = ‘greater’,mu=25)
例题2.18
x1 <- c(42,51,31,61,44,55,48)
x2 <- c(38,53,36,52,33,49,36)
wilcox.test(x1-x2,alternative = ‘less’,mu=0)
例题2.21
y1 <- c(14,12,18,7,11,9,16,15,13,11,18,8,13,10,14,16,
15,12,17,7,11,9,16,15)
y2 <- c(10,4,14,6,9,6,12,12,10,5,15,6,9,6,11,12,11,6,
14,5,10,4,13,10)
wilcox.test(y1-y2,alternative = ‘two.sided’,exact = F,correct = T,mu=3)
2.5
例题2.19
library(tseries)
y1 <- c(1,1,0,1,0,0,1,1,1,0)
runs.test(factor(y1),alternative = ‘two.sided’)
例题2.20
y1 <- c(0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,1)

第三章

3.1

例题3.1
x1 <- c(2,2,2,2,3,3,3,3,3,3,2,3,3,2,3)
x2 <- c(3,4,2,3,2,3,4,4,2,4,4,3,4,4,4)
n1 <- sum(x1-x2>0)
n2 <- sum(x1-x2<0)
n=n1+n2
binom.test(n1,n,alternative = ‘less’)
例题3.2
x <- c(2,3,3,3,3,3,3,3,2,3,2,2,5,2,5,3,1)
y <- c(4,4,5,5,3,2,5,3,1,5,5,5,4,5,5,5,5)
n1 <- sum(x-y>0)
n2 <- sum(x-y<0)
n=n1+n2
binom.test(n1,n,alternative = ‘less’)

3.2

例题3.3
x <- c(78,70,67,81,76,72,85,83)
y <- c(62,58,63,77,80,73,82,78)
wilcox.test(x,y,paired = T,alternative = ‘two.sided’,
exact = T,correct = F)
x <- c(78,70,67,81,76,72,85,83)
y <- c(62,58,63,77,80,73,82,78)
wilcox.test(x,y,paired = T,alternative = ‘greater’,
exact = T,correct = F)

第四章

4.1

例题4.1
x = c(0.94,1.56,1.15)
y = c(1.20,1.63,2.26,1.87,2.20,1.30)
wilcox.test(x,y,paired = F,alternative = ‘less’)
例题4.2
x <- c(83,82,84,96,90,64,91,71,75,72)
y <- c(42,61,52,78,69,81,75,78,78,65)
wilcox.test(x,y,paired = F,alternative = ‘greater’)

4.2

例题4.3
library(tseries)
y <- c(0,0,0,1,0,0,1,1,1,0,
0,0,0,0,1,1,1,1,1,1)
y <- as.factor(y)
runs.test(y)

4.3

例题4.4
f1 <- c(60,21,11,4,4)
f2 <- c(130,50,10,6,4)
f <- f1+f2
n1 <- sum(f1);n2 <- sum(f2);n <- sum(f)
e1 <- f*(n1/n);e2 <- f-e1
Q <- sum((f1-e1)^{2/e1)+sum((f2-e2)}2/e2)
qchisq(0.05,df=4,lower.tail = F)
pchisq(Q,df=4,lower.tail = F)

4.4

例题4.5
f1 <- c(58,51,47,44,22,14)
f2 <- c(31,46,53,73,51,20)
s1 <- cumsum(f1)/sum(f1)
s2 <- cumsum(f2)/sum(f2)
D <- max(abs(s1-s2));D
K-S检验
ks.test(f1,f2,exact = F)
由于数据不是连续变量，所以采用卡方检验
f <- f1+f2
n1 <- sum(f1);n2 <- sum(f2);n <- sum(f)
e1 <- f*(n1/n);e2 <- f-e1
Q <- sum((f1-e1)^{2/e1)+sum((f2-e2)}2/e2)
pchisq(Q,df=5,lower.tail = F)
例题4.6
x1 <- c(3.1,2.1,8.2,2.7,3.4,7.9,3.2)
x2 <- c(5.3,3.7,5.8,3.5,4.8,5.6,6.8,9.3,10.3)
ks.test(x1,x2,alternative = ‘greater’)
例题4.7
x1 <- c(160,138,137)#美国产
x2 <- c(179,167,148,145,144,139,138)#进口
ks.test(x1,x2,alternative = ‘two.sided’)

第五章

5.1

例题5.1
c1=c(1,0,0,1,1,0,0,0,0,1,0,0,1,1,1,0,1,0)
c2=c(0,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0)
c3=c(0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0,0)
c4=c(1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,1,1)
d1 <- data.frame(c1,c2,c3,c4)
CochranQ <- function(data){
y <- apply(data,1,sum)
x <- apply(data,2,sum)
k <- ncol(data)
Q <- (k-1)(ksum(x^2)-(sum(x))2)/(k*sum(y)-sum(y^2))
return(list(Q.value = Q,p.value = pchisq(Q,k-1,lower.tail = F)))}
CochranQ(d1)
例题5.2
c1 <- c(0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0)
c2 <- c(0,1,1,0,0,1,1,1,0,0,1,1,1,1,1,1,0,1)
c3 <- c(0,1,0,0,1,1,1,0,1,0,1,1,1,1,1,1,1,1)
d2 <- data.frame(c1,c2,c3)
CochranQ(d2)
例题5.3
c1=c(1,1,0,0,0,0,1,0,0,0,1,0,0,1,1,0,0,1,1,1)
c2=c(0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1)
c3=c(0,0,1,1,1,1,0,0,0,0,1,0,1,1,1,1,1,0,1,0)
d3 <- data.frame(c1,c2,c3)
CochranQ(d3)

5.2

例题5.4
a1 <- c(1,1,2,3,2,1,1,2,2,2,1,1,1,1,1,1,1,1)
a2 <- c(3,2,3,2,1,3,2,3,1,1,3,3,2,3,2.5,2,2,2)
a3 <- c(2,3,1,1,3,2,3,1,3,3,2,2,3,2,2.5,3,3,3)
d1 <- data.frame(a1,a2,a3)
friedman.test(as.matrix(d1))
例题5.5
c1 <- c(10,2,4,6,3,5,7,6,10,8,5,2,4,6)
c2 <- c(3,5,10,3,4,4,10,10,5,9,4,5,5,5)
c3 <- c(6,9,3,10,10,6,6,3,7,7,2,4,10,8)
c4 <- c(8,4,8,4,6,7,5,5,6,6,6,7,9,10)
d2 <- data.frame(c1,c2,c3,c4)
friedman.test(as.matrix(d2))

第六章

6.1

例题6.1
c1 <- c(22,19,29,24,37,27,28,25,23,26)
c2 <- c(2,6,16,11,7,18,14,21,10,17)
c3 <- c(5,1,4,8,9,15,12,20,13,3)
c4 <- c(30,32,34,36,39,35,40,31,33,38)
d1 <- list(c1,c2,c3,c4)
kruskal.test(d1)

例题6.2
b1 <- c(60,75,62,76,73,98,86)
b2 <- c(72,52,68,82,74,64,87)
b3 <- c(61,85,78,66,70,59,69,79)
b4 <- c(63,58,65,71,84,77,80,89)
d2 <- list(b1,b2,b3,b4)
kruskal.test(d2)
例题6.3
c1 <- c(62,56,62,84,90,48,49,64,69,72,
73,79,89,98,92,52,54,84,82,69,
56,48,64,72,78,84,86,92,98,62)
c2 <- c(73,78,92,86,84,69,73,92,98,81)
c3 <- c(84,86,98,72,69,79,86,84,70,90)
d3 <- list(c1,c2,c3)
kruskal.test(d3)

6.2

例题6.4
d4 <- matrix(c(111,18,19,17,644,218,105,119,290,204,113,108,57,49,32,58),nrow = 4)
chisq.test(d4)
例题6.4(1)
d5 <- matrix(c(40,25,20),nrow = 1)
chisq.test(d5)

第七章

7.1

例题7.1
u <- c(1,2,5,9,4,6,3,7,10,8)
v <- c(5,3,9,6,8,4,2,1,7,10)
RC <- function(u,v){
D = sum((u-v)^2)
n <- length(u)
R <- 1-6D/(n(n^2-1))
return ®
}
RC(u,v)
例题7.2
c1 <- c(82,87,60,98,75,89,84,78,80,94,85,68)
c2 <- c(86,78,65,88,64,90,80,77,76,96,85,70)
u <- rank(c1)
v <- rank(c2)
RC(u,v)
例题7.3
c1 <- c(92,90,90,87,81,80,79,77,68,67,65,64,
61,60,59,55,76,76,74,68,46,42,39,38)
c2 <- c(56,70,71,76,69,68,62,70,55,66,59,58,
50,54,43,45,64,63,54,65,34,32,30,31)
u <- rank(c1)
v <- rank(c2)
RC(u,v)
例题7.4
c1 <- c(92,90,90,87,81,80,79,77,68,67,65,64,
61,60,59,55,76,76,74,68,46,42,39,38)
c2 <- c(56,70,71,76,69,68,62,70,55,66,59,58,
50,54,43,45,64,63,54,65,34,32,30,31)
cor.test(c1,c2,method = ‘spearman’)
例题7.5
c1 <- c(82,87,60,98,75,89,84,78,80,94,85,68)
c2 <- c(86,78,65,88,64,90,80,77,76,96,85,70)
cor.test(c1,c2,method = ‘spearman’)
例题7.6
c1 <- c(49,36,127,91,72,34,155,11)
c2 <- c(39,42,10,25,22,35,15,48)
cor.test(c1,c2,method = ‘spearman’)
7.2
例题7.6(1)
x <- c(82,87,60,98,75,89,84,78,80,94,85,68)
y <- c(86,78,65,88,64,90,80,77,76,96,85,70)
n <- length(c1);u=0;v=0
for(i in 1:(n-1)){
for(j in (i+1):n){
u=u+((x[j]-x[i])(y[j]-y[i])>0)
v=v+((x[j]-x[i])(y[j]-y[i])<0)
}
}
tau <- (u-v)/choose(n,2)
tau

例题7.7
x <- c(82,87,60,98,75,89,84,78,80,94,85,68)
y <- c(86,78,65,88,64,90,80,77,76,96,85,70)
cor.test(x,y,method = ‘kendall’)
例题7.8
c1 <- c(1,2.5,2.5,4.5,4.5)
c2 <- c(2,3.5,3.5,1,5)
cor.test(c1,c2,method = ‘kendall’)
例题7.8(1)
c1 <- c(9,16.6,16.2,11.3,16.2,7.1,7.8,4.0,11.2,1.3)
c2 <- c(7.8,19.3,20.1,7.1,13,4.8,8.9,7.4,10,1.5)
cor.test(c1,c2,method = ‘kendall’)
cor.test(c1,c2,method = ‘spearman’)
例题7.9
c1 <- c(40,35,30,36,41,45,48)
c2 <- c(18,0,6,15,24,30,45)
c3 <- c(2.5,2,1.5,2.4,3,2.8,2.9)
txy <- cor.test(c2,c3,method = ‘kendall’)$ estimate
txz <- cor.test(c2,c1,method = ‘kendall’)$ estimate
tyz <- cor.test(c3,c1,method = ‘kendall’)$ estimate
T1 <- (txy-txz*tyz)/sqrt((1-txz^2)*(1-tyz2))
T1

第八章

8.1

例题8.1
c1 <- c(1,2,5,9,4,6,3,7,10,8)
c2 <- c(1,3,4,7,5,6,2,10,8,9)
c3 <- c(1,7,6,5,3,4,9,10,2,8)
c4 <- c(1,5,2,4,6,7,10,3,9,8)
c5 <- c(1,8,6,10,5,7,2,4,9,3)
c6 <- c(5,3,9,6,8,2,4,1,7,10)
data <- data.frame(c1,c2,c3,c4,c5,c6)
R <- apply(data,1,sum)
k <- ncol(data)
n <- nrow(data)
S <- sum((R-k*(n+1)/2)^2)
W <- 12S/((k^2)*(n3-n));W
例题8.2
c1 <- c(5.5,2.5,5.5,4,7,8,1,9,2.5,10)
c2 <- c(1,3,7.5,7.5,5,2,10,9,4,6)
c3 <- c(1,4,2.5,2.5,6,8.5,8.5,6,6,10)
c4 <- c(1,2,3.5,3.5,9,6,8,5,10,7)
c5 <- c(1,8,6,10,5,7,2,4,9,3)
c6 <- c(1.5,1.5,7.5,9.5,3.5,6,9.5,3.5,5,7.5)
data <- data.frame(c1,c2,c3,c4,c5,c6)
k <- ncol(data)
n <- nrow(data)
t <- matrix(nrow = 1,ncol = k)
for(i in 1:k){
t[,i] <- sum((table(data[,i]))^3-table(data[,i]))
}
sum(t)
data_r <- apply(data,2,rank)
R <- apply(data_r,1,sum)
S <- sum((R-k(n+1)/2)^2)
W <- 12S/((k^2)*(n3-n)-ksum(t))
W
例题8.3
pchisq(k*(n-1)*W,n-1,lower.tail = F)

8.2

例题8.4
c1 <- c(1,2,0,3,0,0,0)
c2 <- c(0,1,3,0,2,0,0)
c3 <- c(0,0,3,2,0,1,0)
c4 <- c(0,0,0,2,3,0,1)
c5 <- c(1,0,0,0,3,2,0)
c6 <- c(0,2,0,0,0,1,3)
c7 <- c(1,0,3,0,0,0,2)
data <- data.frame(c1,c2,c3,c4,c5,c6,c7)
data <- t(data)
m=3;k=7;n=7;l=1
R <- apply(data,2,sum)
S <- sum((R-km(m+1)/(2n))^2)
W <- 12S/((l^2)*n*(n2-1));W
例题8.5
Q <- l*(n^2-1)W/(m+1)
pchisq(Q,n-1,lower.tail = F)
例题8.6
P <- n(n-1)/2
alpha <- 0.3
Z <- qnorm(0.5alpha/P,0.1,lower.tail = F)
Z1 <- Zsqrt(km(m^2-1)/(6*(n-1)))
R=t(as.data.frame®)
colnames®=c(‘A’,‘B’,‘C’,‘D’,‘E’,‘F’,‘G’)
R

第九章

9.2

例题9.1
c1 <- c(14,67,30)
c2 <- c(30,105,13)
c3 <- c(4,60,14)
data <- data.frame(c1,c2,c3)
chisq.test(data)
例题9.2
Q=23.072;n=sum(data);r=c=3
phi=sqrt(Q/n)
C=sqrt(Q/(Q+n))
V=sqrt(Q/(n*min(r-1,c-1)))

9.3

例题9.3
y1 <- c(18,29,18,12)
y2 <- c(20,13,16,20)
d5 <- t(data.frame(y1,y2))
lie <- function(data){
n <- sum(data)
y <- apply(data,1,sum)
E1 <- n - max(y)
x <- apply(data,2,max)
E2 <- n-sum(x)
return(list(la.value = (E1-E2)/E1, My.value = max(y),
v1 = n - max(y)))
}
lie(d5)
例题9.4
y1 <- c(40,182,204,200)
y2 <- c(42,176,208,148)
d6 <- data.frame(y1,y2)
n=sum(d6)
My=max(apply(d6,1,sum))
Mx=max(apply(d6,2,sum))
my=sum(apply(d6,1,max))
mx=sum(apply(d6,2,max))
lambda <- (mx+my-Mx-My)/(2n-Mx-My)
lambda
例题9.5
chisq.test(d5)
d51 <- d5[,-1]
d52 <- d51[,-2]
chisq.test(d52)
例题9.6
chisq.test(d6)
例题9.7
tauy <- function(x){
n <- sum(x)
fy <- apply(x,1,sum)#y边际频数
fx <- apply(x,2,sum)#x边际频数
E1 <- sum(fy(1-fy/n))#自己预测自己的误差
r <- nrow(x);c <- ncol(x)
E <- matrix(nrow = r,ncol = c)
for(j in 1:r){
for(i in 1:c){
E[j,i]=x[j,i](1-x[j,i]/fx[i])
}
}
E2 <- sum(E)#考虑x的预测误差
return ((E1-E2)/E2)
}
a1 <- c(3191,2370,1286,935)
a2 <- c(1120,1183,528,187)
data <- data.frame(a1,a2)
tauy(data)
例题9.8
taux <- function(x){
n <- sum(x)
fy <- apply(x,1,sum)#y边际频数
fx <- apply(x,2,sum)#x边际频数
E1 <- sum(fx(1-fx/n))#自己预测自己的误差
r <- nrow(x);c <- ncol(x)
E <- matrix(nrow = r,ncol = c)
for(i in 1:c){
for(j in 1:r){
E[j,i]=x[j,i](1-x[j,i]/fy[j])
}
}
E2 <- sum(E)#考虑y的预测误差
return ((E1-E2)/E2)
}
a1 <- c(3191,2370,1286,935)
a2 <- c(1120,1183,528,187)
data <- data.frame(a1,a2)
taux(data)
例题9.9
tauy(d6)
例题9.10
c1 <- c(14,18,8)
c2 <- c(13,2,15)
c3 <- c(13,15,2)
d7 <- data.frame(c1,c2,c3)
chisq.test(d7)
tauy(d7)
例题9.11
c1 <- c(2,32,10)
c2 <- c(44,10,2)
d8 <- data.frame(c1,c2)
chisq.test(d8)
tauy(d8)
taux(d8)
例题9.12
gamma <- function(x){
r <- nrow(x);c <- ncol(x)
n1 <- matrix(nrow = r-1,ncol = c-1)
for(i in 1:(r-1)){
for(j in 1:(c-1)){
n1[i,j] <- x[i,j]sum(x[(i+1):r,(j+1):c])
}
}
ns <- sum(n1)
n2 <- matrix(nrow = r-1,ncol = c-1)
for(i in 1:(r-1)){
for(j in c:2){
n2[i,j-1] <- x[i,j]sum(x[(i+1):r,1:(j-1)])
}
}
nd <- sum(n2)
G <- (ns-nd)/(ns+nd)
return (list(G=G,ns=ns,nd=nd))
}
gamma(t(d8))
例题9.13
c1 <- c(60,0)
c2 <- c(48,12)
d9 <- data.frame(c1,c2)
gamma(d9)
例题9.14
n <- sum(t(d8))
G <- gamma(t(d8))G;ns<−gamma(t(d8))G;ns <- gamma(t(d8))G;ns<−gamma(t(d8))ns;nd <- gamma(t(d8))$nd
Z <- Gsqrt((ns+nd)/(n(1-G^2)));Z
pnorm(Z,lower.tail = T)
例题9.15
y1 <- c(38,5,4)
y2 <- c(18,16,6)
y3 <- c(4,4,5)
data <- t(data.frame(y1,y2,y3))
Sod <- function(data){
r <- nrow(data);c <- ncol(data)
n1 <- matrix(nrow = r-1,ncol = c-1)
for(i in 1:(r-1)){
for(j in 1:(c-1)){
n1[i,j] <- data[i,j]sum(data[(i+1):r,(j+1):c])
}}
ns <- sum(n1)
n2 <- matrix(nrow = r-1,ncol = c-1)
for(i in 1:(r-1)){
for(j in c:2){
n2[i,j-1] <- data[i,j]sum(data[(i+1):r,1:(j-1)])
}}
nd <- sum(n2)
n3 <- matrix(nrow = r,ncol = c-1)
for(i in 1:r){
for(j in 1:(c-1)){
n3[i,j] <- data[i,j]sum(data[i,(j+1):c])
}}
Ty = sum(n3)
dyx <- (ns-nd)/(ns+nd+Ty)
return (dyx)
}
Sod(data)
例题9.16
x <- apply(data,2,sum);y <- apply(data,1,sum)
A2 <- (sum(x%%t(x))-t(x)%%x)0.5
B2 <- (sum(y%%t(y))-t(y)%%y)0.5
A3 <- prod(x);B3 <- prod(y);n <- sum(data)
s1 <- abs(ns-nd)-n/(2(r-1)(c-1))
se <- sqrt((A2B2)/(n-1)-(A2B3+A3B2)/(n(n-1))+(A3B3)/(n(n-1)*(n-2)))
s1/se
pnorm(abs(s1/se),lower.tail = F)
例题9.17
x1 <- c(4.2,3,2.9,3.2,2.7,3.1,2.3)
x2 <- c(3.2,2.9,2.7,2.1,1.9,3.1,2.8)
x3 <- c(3.1,2.8,2.2,1.1,2,2.5)
y <- c(x1,x2,x3)
E1 <- sum((y-mean(y))^2)
E2 <- sum((x1-mean(x1))^2) + sum((x2-mean(x2))^2) + sum((x3-mean(x3))^2)
eta2 <- (E1-E2)/E1
eta2
例题9.18
k <- 3;n <- length(y)
f <- (eta2/(k-1))/((1-eta2)/(n-k));f
pf((eta2/(k-1))/((1-eta2)/(n-k)),k-1,n-k,ncp=0,lower.tail = F)

第十章

10.1

例题10.1
data <- c(18,25,16,28,15,30,14,28,8,12,6,15)
data <- array(data,dim = c(2,2,3),dimnames = list(c(‘台式’,‘台地式’),c(‘两代’,‘三代以上’),c(‘热带’,‘温带’,‘寒带’)))
loglin(data,list(1,2,3))pearson例题10.2data<−c(16,7,1,1,15,34,3,8,5,3,1,3)data<−array(data,dim=c(2,2,3),dimnames=list(c(′不吸烟′,′吸烟′),c(′<40′,′>=40′),c(′正常′,′尚可′,′异常′)))df1<−loglin(data,list(1,2,3))pearson 例题10.2 data <- c(16,7,1,1,15,34,3,8,5,3,1,3) data <- array(data,dim = c(2,2,3),dimnames = list(c('不吸烟','吸烟'),c('<40','>=40'),c('正常','尚可','异常'))) df1 <- loglin(data,list(1,2,3))pearson例题10.2data<−c(16,7,1,1,15,34,3,8,5,3,1,3)data<−array(data,dim=c(2,2,3),dimnames=list(c(′不吸烟′,′吸烟′),c(′<40′,′>=40′),c(′正常′,′尚可′,′异常′)))df1<−loglin(data,list(1,2,3))df
chi1 <- loglin(data,list(1,2,3))pearsonpchisq(chi1,df=df1,lower.tail=F)例题10.3df2<−loglin(data,list(2,c(1,3)))pearson pchisq(chi1,df=df1,lower.tail = F) 例题10.3 df2 <- loglin(data,list(2,c(1,3)))pearsonpchisq(chi1,df=df1,lower.tail=F)例题10.3df2<−loglin(data,list(2,c(1,3)))df
chi2 <- loglin(data,list(2,c(1,3)))$pearson
pchisq(chi2,df=df2,lower.tail = F)
例题10.4
c1 <- c(14,67,30)
c2 <- c(30,105,13)
c3 <- c(4,60,14)
data <- data.frame(c1,c2,c3)
data1 <- log(data)
meanx <- apply(data1,1,mean)
meany <- apply(data1,2,mean)
la <- mean(meanx);la
la1 <- meanx-la;la1
la2 <- meany-la;la2
la12 <- matrix(nrow = 3,ncol = 3)
for(i in 1:3){
for(j in 1:3){
la12[i,j] <- data1[i,j]-meanx[i]-meany[j]+la
}
};la12
例题10.5
data <- c(16,1,7,1,15,3,34,8,5,1,3,3)
data <- array(data,dim = c(2,2,3),dimnames = list(c(’<40’,’>=40’),c(‘不吸烟’,‘吸烟’),c(‘正常’,‘尚可’,‘异常’)))
data2 <- log(data)
la <- mean(data2);la
meanx <- apply(data2,1,mean);meanx
meany <- apply(data2,2,mean);meany
meanz <- apply(data2,3,mean);meanz
la1 <- meanx-la;la1
la2 <- meany-la;la2
la23 <- matrix(nrow = 2,ncol = 3)
for(j in 1:2){
for(k in 1:3){
la23[j,k] <- (data2[1,j,k]+data2[2,j,k])/2-meany[j]-meanz[k]+la
}
};la23
例题10.6
data <- c(3,17,4,2,176,197,293,23)
data <- array(data,dim = c(2,2,2),dimnames = list(c(‘A’,‘B’),c(‘少’,‘多’),c(‘死’,‘活’)))
chisq.test(data[1,])#A医院，独立
chisq.test(data[2,])#B医院，独立
c1 <- c(20,6)
c2 <- c(373,316)
data6 <- data.frame(c1,c2)
chisq.test(data6)#拒绝原假设，故相关