E.2SI(NI, nI, Ni, ni, y, PSU)

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## Example 1
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# Uses Lucy data to draw a twostage simple random sample 
# accordind to a 2SI design. Zone is the clustering variable
data(Lucy)
attach(Lucy)
summary(Zone)
# The population of clusters or Primary Sampling Units
UI<-c("A","B","C","D","E")
NI <- length(UI)
# The sample size is nI=3
nI <- 3
# Selects the sample of PSUs
samI<-S.SI(NI,nI)
dataI<-UI[samI]
dataI   
# The sampling frame of Secondary Sampling Unit is saved in Lucy1 ... Lucy3
Lucy1<-Lucy[which(Zone==dataI[1]),]
Lucy2<-Lucy[which(Zone==dataI[2]),]
Lucy3<-Lucy[which(Zone==dataI[3]),]
# The size of every single PSU
N1<-dim(Lucy1)[1]
N2<-dim(Lucy2)[1]
N3<-dim(Lucy3)[1]
Ni<-c(N1,N2,N3)
# The sample size in every PSI is 135 Secondary Sampling Units
n1<-135
n2<-135
n3<-135
ni<-c(n1,n2,n3)
# Selects a sample of Secondary Sampling Units inside the PSUs
sam1<-S.SI(N1,n1)
sam2<-S.SI(N2,n2)
sam3<-S.SI(N3,n3)
# The information about each Secondary Sampling Unit in the PSUs
# is saved in data1 ... data3
data1<-Lucy1[sam1,]
data2<-Lucy2[sam2,]
data3<-Lucy3[sam3,]
# The information about each unit in the final selected sample is saved in data
data<-rbind(data1, data2, data3)
attach(data)
# The clustering variable is Zone
Cluster <- as.factor(as.integer(Zone))
# The variables of interest are: Income, Employees and Taxes
# This information is stored in a data frame called estima
estima <- data.frame(Income, Employees, Taxes)
# Estimation of the Population total
E.2SI(NI,nI,Ni,ni,estima,Cluster)

########################################################
## Example 2 Total Census to the entire population
########################################################
# Uses Lucy data to draw a cluster random sample
# accordind to a SI design ...
# Zone is the clustering variable
data(Lucy)
attach(Lucy)
summary(Zone)
# The population of clusters
UI<-c("A","B","C","D","E")
NI <- length(UI)
# The sample size equals to the population size of PSU
nI <- NI
# Selects every single PSU
samI<-S.SI(NI,nI)
dataI<-UI[samI]
dataI   
# The sampling frame of Secondary Sampling Unit is saved in Lucy1 ... Lucy5
Lucy1<-Lucy[which(Zone==dataI[1]),]
Lucy2<-Lucy[which(Zone==dataI[2]),]
Lucy3<-Lucy[which(Zone==dataI[3]),]
Lucy4<-Lucy[which(Zone==dataI[4]),]
Lucy5<-Lucy[which(Zone==dataI[5]),]
# The size of every single PSU
N1<-dim(Lucy1)[1]
N2<-dim(Lucy2)[1]
N3<-dim(Lucy3)[1]
N4<-dim(Lucy4)[1]
N5<-dim(Lucy5)[1]
Ni<-c(N1,N2,N3,N4,N5)
# The sample size of Secondary Sampling Units equals to the size of each PSU
n1<-N1
n2<-N2
n3<-N3
n4<-N4
n5<-N5
ni<-c(n1,n2,n3,n4,n5)
# Selects every single Secondary Sampling Unit inside the PSU
sam1<-S.SI(N1,n1)
sam2<-S.SI(N2,n2)
sam3<-S.SI(N3,n3)
sam4<-S.SI(N4,n4)
sam5<-S.SI(N5,n5)
# The information about each unit in the cluster is saved in Lucy1 ... Lucy5
data1<-Lucy1[sam1,]
data2<-Lucy2[sam2,]
data3<-Lucy3[sam3,]
data4<-Lucy4[sam4,]
data5<-Lucy5[sam5,]
# The information about each Secondary Sampling Unit
# in the sample (census) is saved in data
data<-rbind(data1, data2, data3, data4, data5)
attach(data)
# The clustering variable is Zone
Cluster <- as.factor(as.integer(Zone))
# The variables of interest are: Income, Employees and Taxes
# This information is stored in a data frame called estima
estima <- data.frame(Income, Employees, Taxes)
# Estimation of the Population total
E.2SI(NI,nI,Ni,ni,estima,Cluster)
# Sampling error is null