Chapter 6. Sampling#

Figure 6.1: Sampling and Inference#

suppressPackageStartupMessages(library(spatstat))
suppressPackageStartupMessages(library(diagram))
plot.new()
plot.window(c(-8.5,5),c(-5,5))
W1 <- ellipse(a=2.5,b=2,centre=c(-6,0),phi=0,npoly=1024)
plot(W1,add=TRUE)
W2 <- ellipse(a=2.5,b=2,centre=c(3,0),phi=0,npoly=1024)
plot(W2,add=TRUE)
text(-6.5,-1,"a",cex=.6)
text(-7,1.1,"b",cex=.6)
text(-5,1.2,"c",cex=.6)
text(-4,0,"d",cex=.6)
text(-6,-1.5,"e",cex=.6)
text(-6.5,0.5,"f",cex=.6)
text(-8.2,.5,"g",cex=.6)
text(-5,0.6,"h",cex=.6)
text(-6.2,1.2,"i",cex=.6)
text(-7,1.5,"j",cex=.6)
text(-8,-.5,"k",cex=.6)
text(-5.8,0.8,"l",cex=.6)
text(-7,-1.1,"m",cex=.6)
text(-7.5,1,"n",cex=.6)
text(-5,-1,"o",cex=.6)
text(-6.8,-.3,"p",cex=.6)
text(-5.5,-.2,"q",cex=.6)
text(-4.7,-.8,"r",cex=.6)
text(-6.2,1.8,"s",cex=.6)
text(-7.5,.2,"t",cex=.6)
text(-4.3,.5,"u",cex=.6)
text(-4.5,-.2,"v",cex=.6)
text(-4.3,-.7,"w",cex=.6)
text(-5.3,1.5,"x",cex=.6)
text(-6.3,-.1,"y",cex=.6)
text(-6.1,-.6,"z",cex=.6)
text(2,1.1,"b",cex=.6)
text(3,-1.5,"e",cex=.6)
text(4,0.6,"h",cex=.6)
text(2,-1.1,"m",cex=.6)
text(5.7,.5,"u",cex=.6)
text(3.7,1.5,"x",cex=.6)
arrows(-3.5,1,0.5,1,angle=20,length=.1)
arrows(0.5,-1,-3.5,-1,angle=20,length=.1)
text(-6,3,"Population",cex=.75)
text(3,3,"Sample",cex=.75)
text(-1.6,1.3,"Sampling",cex=.75)
text(-1.4,-1.3,"Inference",cex=.75)

Table 6.1 Table 6.1: Observations From CPS Data Set#

dat <- read.table("cps09mar.txt")
experience <- dat[,1]-dat[,4]-6
mbf <- (dat[,11]==2)&(dat[,12]<=2)&(dat[,2]==1)&(experience==12)
dat1 <- dat[mbf,]
wage <- as.matrix(dat1[,5]/(dat1[,6]*dat1[,7]))
lwage <- log(wage)
education <- dat1[,4]
n <- length(wage)
df <- data.frame(wage, education)
print(df)
       wage education
1  37.92735        18
2  40.86538        18
3  14.18269        13
4  16.82692        16
5  33.17308        16
6  29.80769        18
7  54.61538        16
8  43.07692        18
9  14.42308        12
10 14.90385        16
11 21.63462        18
12 11.09467        16
13 10.00000        13
14 31.73077        14
15 11.05769        12
16 18.75000        16
17 27.35043        14
18 24.03846        16
19 36.05769        18
20 23.07692        16

Other Empirical Illustrations in Chapter 6#

mwage <- mean(wage)
mlwage <- mean(lwage)
meducation <- mean(education)
vwage <- mean((wage-mwage)^2)
vlwage <- mean((lwage-mlwage)^2)
veducation <- mean((education-meducation)^2)
swage <- sqrt(vwage)
slwage <- sqrt(vlwage)
seducation <- sqrt(veducation)
uswage <- sd(wage)
uslwage <- sd(lwage)
useducation <- sd(education)
sewage <- uswage/sqrt(n)
seeducation <- useducation/sqrt(n)
c <- cov(wage,education)
corr <- c/uswage/useducation
gmean <- exp(mlwage)
medwage <- median(wage)
cat("Sample size, mean wage, mean log(wage), mean education \n")
print(n)
print(mwage)
print(mlwage)
print(meducation)
Sample size, mean wage, mean log(wage), mean education 
[1] 20
[1] 25.72968
[1] 3.131925
[1] 15.7
cat("Standard deviation: wage, log(wage), education \n")
print(swage)
print(slwage)
print(seducation)
Standard deviation: wage, log(wage), education 
[1] 12.1252
[1] 0.4901793
[1] 2.002498
cat("Geometric mean, median\n")
print(gmean)
print(medwage)
Geometric mean, median
[1] 22.91806
[1] 23.55769
cat("Unbiased Standard deviation: wage, log(wage), education \n")
print(uswage)
print(uslwage)
print(useducation)
Unbiased Standard deviation: wage, log(wage), education 
[1] 12.4402
[1] 0.5029133
[1] 2.05452
cat("s.e. of mean estimator: wage, education \n")
print(sewage)
print(seeducation)
s.e. of mean estimator: wage, education 
[1] 2.781713
[1] 0.4594046
cat("covariance,correlation \n")
print(c)
print(corr)
covariance,correlation 
         [,1]
[1,] 14.76231
          [,1]
[1,] 0.5775859