Package 'samplingbook' reference manual

Title:	Survey Sampling Procedures
Description:	Sampling procedures from the book 'Stichproben - Methoden und praktische Umsetzung mit R' by Goeran Kauermann and Helmut Kuechenhoff (2010).
Authors:	Juliane Manitz [aut,cre], Mark Hempelmann [ctb], Goeran Kauermann [ctb], Helmut Kuechenhoff [aut], Shuai Shao [ctb], Cornelia Oberhauser [ctb], Nina Westerheide [ctb], Manuel Wiesenfarth [ctb]
Maintainer:	Juliane Manitz <[email protected]>
License:	GPL (>= 2)
Version:	1.2.4
Built:	2024-11-11 06:16:20 UTC
Source:	https://github.com/jmanitz/samplingbook

Survey Sampling Procedures

Description

Sampling procedures from the book 'Stichproben - Methoden und praktische Umsetzung mit R' by Goeran Kauermann and Helmut Kuechenhoff (2010).

Details

Package:	Samplingbook
Type:	Package
Version:	1.2.1
Date:	2016-07-05
License:	GPL(>=2)
LazyLoad:	yes

Index:

election	German Parliament Election Data
htestimate	Horvitz-Thompson Estimator
influenza	Population and Cases of Influenza in Administrative Districts of Germany
mbes	Model Based Estimation
money	Money Data Frame
pop	Small Suppositious Sampling Example
pps.sampling	Sampling with Probabilities Proportional to Size
sample.size.mean	Sample Size Calculation for Mean Estimation
sample.size.prop	Sample Size Calculation for Proportion Estimation
Samplingbook-package	Survey Sampling Procedures
Smean	Sampling Mean Estimation
Sprop	Sampling Proportion Estimation
stratamean	Stratified Sample Mean Estimation
stratasamp	Sample Size Calculation for Stratified Sampling
tax	Hypothetical Tax Refund Data Frame

Author(s)

Author: Juliane Manitz <[email protected]>, contributions by
Mark Hempelmann <[email protected]>,
Goeran Kauermann <[email protected]>,
Helmut Kuechenhoff <[email protected]>,
Shuai Shao <[email protected]>,
Cornelia Oberhauser <[email protected]>,
Nina Westerheide <[email protected]>,
Manuel Wiesenfarth <[email protected]>

Maintainer: Juliane Manitz <[email protected]>

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

German Parliament Election Data

Description

Data frame with number of citizens eligible to vote and results of the elections in 2002 and 2005 for the German Bundestag, the first chamber of the German parliament.

Usage

data(election)data(election)

Format

A data frame with 299 observations (corresponding to constituencies) on the following 13 variables.

state: factor, the 16 German federal states
eligible_02: number of citizens eligible to vote in 2002
SPD_02: a numeric vector, percentage for the Social Democrats SPD in 2002
UNION_02: a numeric vector, percentage for the conservative Christian Democrats CDU/CSU in 2002
GREEN_02: a numeric vector, percentage for the Greens in 2002
FDP_02: a numeric vector, percentage for the Liberal Party FDP in 2002
LEFT_02: a numeric vector, percentage for the Left Party PDS in 2002
eligible_05: number of citizens eligible to vote in 2005
SPD_05: a numeric vector, percentage for the Social Democrats SPD in 2005
UNION_05: a numeric vector, percentage for the conservative Christian Democrats CDU/CSU in 2005
GREEN_05: a numeric vector, percentage for the Greens in 2005
FDP_05: a numeric vector, percentage for the Liberal Party FDP in 2005
LEFT_05: a numeric vector, percentage for the Left Party in 2005

Details

German Federal Elections

Half of the Members of the German Bundestag are elected directly from Germany's 299 constituencies, the other half one on the parties' land lists. Accordingly, each voter has two votes in the elections to the German Bundestag. The first vote, allowing voters to elect their local representatives to the Bundestag, decides which candidates are sent to Parliament from the constituencies. The second vote is cast for a party list. And it is this second vote that determines the relative strengths of the parties represented in the Bundestag. At least 598 Members of the German Bundestag are elected in this way. In addition to this, there are certain circumstances in which some candidates win what are known as 'overhang mandates' when the seats are being distributed.

The data set provides the percentage of second votes for each party, which determines the number of seats each party gets in parliament. These percentages are calculated by the number of votes for a party divided by number of valid votes.

Source

The data is provided by the R package flexclust.

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Homepage of the Bundestag: http://www.bundestag.de.

Friedrich Leisch. A Toolbox for K-Centroids Cluster Analysis. Computational Statistics and Data Analysis, 51 (2), 526-544, 2006.

Examples

data(election)
summary(election)

# 1) Draw a simple sample of size n=20
n <- 20
set.seed(67396)
index <- sample(1:nrow(election), size=n)
sample1 <- election[index,]
Smean(sample1$SPD_02, N=nrow(election))
# true mean
mean(election$SPD_02)

# 2) Estimate sample size to forecast proportion of SPD in election of 2005
sample.size.prop(e=0.01, P=mean(election$SPD_02), N=Inf)

# 3) Usage of previous knowledge by model based estimation
# draw sample of size n = 20
N <- nrow(election)
set.seed(67396)
sample <- election[sort(sample(1:N, size=20)),]
# secondary information SPD in 2002
X.mean <- mean(election$SPD_02)
# forecast proportion of SPD in election of 2005
mbes(SPD_05 ~ SPD_02, data=sample, aux=X.mean, N=N, method='all')
# true value
Y.mean <- mean(election$SPD_05)
Y.mean
# Use a second predictor variable
X.mean2 <- c(mean(election$SPD_02),mean(election$GREEN_02))
# forecast proportion of SPD in election of 2005 with two predictors
mbes(SPD_05 ~ SPD_02+GREEN_02, data=sample, aux=X.mean2, N=N, method= 'regr')
data(election)
summary(election)

# 1) Draw a simple sample of size n=20
n <- 20
set.seed(67396)
index <- sample(1:nrow(election), size=n)
sample1 <- election[index,]
Smean(sample1$SPD_02, N=nrow(election))
# true mean
mean(election$SPD_02)

# 2) Estimate sample size to forecast proportion of SPD in election of 2005
sample.size.prop(e=0.01, P=mean(election$SPD_02), N=Inf)

# 3) Usage of previous knowledge by model based estimation
# draw sample of size n = 20
N <- nrow(election)
set.seed(67396)
sample <- election[sort(sample(1:N, size=20)),]
# secondary information SPD in 2002
X.mean <- mean(election$SPD_02)
# forecast proportion of SPD in election of 2005
mbes(SPD_05 ~ SPD_02, data=sample, aux=X.mean, N=N, method='all')
# true value
Y.mean <- mean(election$SPD_05)
Y.mean
# Use a second predictor variable
X.mean2 <- c(mean(election$SPD_02),mean(election$GREEN_02))
# forecast proportion of SPD in election of 2005 with two predictors
mbes(SPD_05 ~ SPD_02+GREEN_02, data=sample, aux=X.mean2, N=N, method= 'regr')

Horvitz-Thompson Estimator

Description

Calculates Horvitz-Thompson estimate with different methods for variance estimation such as Yates and Grundy, Hansen-Hurwitz and Hajek.

Usage

htestimate(y, N, PI, pk, pik, method = 'yg')
htestimate(y, N, PI, pk, pik, method = 'yg')

Arguments

`y`	vector of observations
`N`	integer for population size
`PI`	square matrix of second order inclusion probabilities with `n` rows and cols. It is necessary to be specified for variance estimation by methods `'ht'` and `'yg'`.
`pk`	vector of first order inclusion probabilities of length `n` for the sample elements. It is necessary to be specified for variance estimation by methods `'hh'` and `'ha'`.
`pik`	an optional vector of first order inclusion probabilities of length `N` for the population elements . It can be used for variance estimation by method `'ha'`.
`method`	method to be used for variance estimation. Options are `'yg'` (Yates and Grundy) and `'ht'` (Horvitz-Thompson), approximate options are `'hh'` (Hansen-Hurwitz) and `'ha'` (Hajek).

Details

For using methods 'yg' or 'ht' has to be provided matrix PI, and for 'hh' and 'ha' has to be specified vector pk of inclusion probabilities. Additionally, for Hajek method 'ha' can be specified pik. Unless, an approximate Hajek method is used.

Value

The function htestimate returns a value, which is a list consisting of the components

`call`	is a list of call components: `y` observations, `N` population size, `PI` inclusion probabilities, `pk` inclusion probabilities of sample, `pik` full inclusion probabilities and `method` method for variance estimation
`mean`	mean estimate
`se`	standard error of the mean estimate

Author(s)

Juliane Manitz

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

data(influenza)
summary(influenza)

# pps.sampling()
set.seed(108506)
pps <- pps.sampling(z=influenza$population,n=20,method='midzuno')
sample <- influenza[pps$sample,]
# htestimate()
N <- nrow(influenza)
# exact variance estimate
PI <- pps$PI
htestimate(sample$cases, N=N, PI=PI, method='yg')
htestimate(sample$cases, N=N, PI=PI, method='ht')
# approximate variance estimate
pk <- pps$pik[pps$sample]
htestimate(sample$cases, N=N, pk=pk, method='hh')
pik <- pps$pik
htestimate(sample$cases, N=N, pk=pk, pik=pik, method='ha')
# without pik just approximate calculation of Hajek method
htestimate(sample$cases, N=N, pk=pk, method='ha') 
# calculate confidence interval based on normal distribution for number of cases
est.ht <- htestimate(sample$cases, N=N, PI=PI, method='ht')
est.ht$mean*N  
lower <- est.ht$mean*N - qnorm(0.975)*N*est.ht$se
upper <- est.ht$mean*N + qnorm(0.975)*N*est.ht$se
c(lower,upper) 
# true number of influenza cases
sum(influenza$cases)
data(influenza)
summary(influenza)

# pps.sampling()
set.seed(108506)
pps <- pps.sampling(z=influenza$population,n=20,method='midzuno')
sample <- influenza[pps$sample,]
# htestimate()
N <- nrow(influenza)
# exact variance estimate
PI <- pps$PI
htestimate(sample$cases, N=N, PI=PI, method='yg')
htestimate(sample$cases, N=N, PI=PI, method='ht')
# approximate variance estimate
pk <- pps$pik[pps$sample]
htestimate(sample$cases, N=N, pk=pk, method='hh')
pik <- pps$pik
htestimate(sample$cases, N=N, pk=pk, pik=pik, method='ha')
# without pik just approximate calculation of Hajek method
htestimate(sample$cases, N=N, pk=pk, method='ha') 
# calculate confidence interval based on normal distribution for number of cases
est.ht <- htestimate(sample$cases, N=N, PI=PI, method='ht')
est.ht$mean*N  
lower <- est.ht$mean*N - qnorm(0.975)*N*est.ht$se
upper <- est.ht$mean*N + qnorm(0.975)*N*est.ht$se
c(lower,upper) 
# true number of influenza cases
sum(influenza$cases)

Population and Cases of Influenza for Administrative Districts of Germany

Description

The data frame influenza provides cases of influenza and inhabitants for administrative districts of Germany in 2007.

Usage

data(influenza)data(influenza)

Format

A data frame with 424 observations on the following 4 variables.

id: a numeric vector
district: a factor with levels LK Aachen, LK Ahrweiler, ..., SK Zweibruecken, names of administrative districts in Germany
population: a numeric vector specifying the number of inhabitants in the specific administrative district
cases: a numeric vector specifying the number of influenza cases in the specific administrative district

Details

Data of 2007. If you want to use the population numbers in the future, be aware of local governmental reorganizations, e.g. district unions.

Source

Database SurvStat of Robert Koch-Institute. Many thanks to Hermann Claus.

References

Database of Robert Koch-Institute http://www3.rki.de/SurvStat/

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

data(influenza)
summary(influenza)

# 1) Usage of pps.sampling
set.seed(108506)
pps <- pps.sampling(z=influenza$population,n=20,method='midzuno')
pps
sample <- influenza[pps$sample,]
sample

# 2) Usage of htestimate
set.seed(108506)
pps <- pps.sampling(z=influenza$population,n=20,method='midzuno')
sample <- influenza[pps$sample,]
# htestimate()
N <- nrow(influenza)
# exact variance estimate
PI <- pps$PI
htestimate(sample$cases, N=N, PI=PI, method='ht')
htestimate(sample$cases, N=N, PI=PI, method='yg')
# approximate variance estimate
pk <- pps$pik[pps$sample]
htestimate(sample$cases, N=N, pk=pk, method='hh')
pik <- pps$pik
htestimate(sample$cases, N=N, pk=pk, pik=pik, method='ha')
# without pik just approximative calculation of Hajek method
htestimate(sample$cases, N=N, pk=pk, method='ha') 
# calculate confidence interval based on normal distribution for number of cases
est.ht <- htestimate(sample$cases, N=N, PI=PI, method='ht')
est.ht$mean*N  
lower <- est.ht$mean*N - qnorm(0.975)*N*est.ht$se
upper <- est.ht$mean*N + qnorm(0.975)*N*est.ht$se
c(lower,upper) 
# true number of influenza cases
sum(influenza$cases)
data(influenza)
summary(influenza)

# 1) Usage of pps.sampling
set.seed(108506)
pps <- pps.sampling(z=influenza$population,n=20,method='midzuno')
pps
sample <- influenza[pps$sample,]
sample

# 2) Usage of htestimate
set.seed(108506)
pps <- pps.sampling(z=influenza$population,n=20,method='midzuno')
sample <- influenza[pps$sample,]
# htestimate()
N <- nrow(influenza)
# exact variance estimate
PI <- pps$PI
htestimate(sample$cases, N=N, PI=PI, method='ht')
htestimate(sample$cases, N=N, PI=PI, method='yg')
# approximate variance estimate
pk <- pps$pik[pps$sample]
htestimate(sample$cases, N=N, pk=pk, method='hh')
pik <- pps$pik
htestimate(sample$cases, N=N, pk=pk, pik=pik, method='ha')
# without pik just approximative calculation of Hajek method
htestimate(sample$cases, N=N, pk=pk, method='ha') 
# calculate confidence interval based on normal distribution for number of cases
est.ht <- htestimate(sample$cases, N=N, PI=PI, method='ht')
est.ht$mean*N  
lower <- est.ht$mean*N - qnorm(0.975)*N*est.ht$se
upper <- est.ht$mean*N + qnorm(0.975)*N*est.ht$se
c(lower,upper) 
# true number of influenza cases
sum(influenza$cases)

Model Based Estimation

Description

mbes is used for model based estimation of population means using auxiliary variables. Difference, ratio and regression estimates are available.

Usage

mbes(formula, data, aux, N = Inf, method = 'all', level = 0.95, ...)
mbes(formula, data, aux, N = Inf, method = 'all', level = 0.95, ...)

Arguments

`formula`	object of class `formula` (or one that can be coerced to that class): symbolic description for connection between primary and secondary information
`data`	data frame containing variables in the model
`aux`	known mean of auxiliary variable, which provides secondary information
`N`	positive integer for population size. Default is `N=Inf`, which means that calculations are carried out without finite population correction.
`method`	estimation method. Options are `'simple','diff','ratio','regr','all'`. Default is `method='all'`.
`level`	coverage probability for confidence intervals. Default is `level=0.95`.
`...`	further options for linear regression model

Details

The option method='simple' calculates the simple sample estimation without using the auxiliary variable. The option method='diff' calculates the difference estimate, method='ratio' the ratio estimate, and method='regr' the regression estimate which is based on the selected model. The option method='all' calculates the simple and all model based estimates. For methods 'diff', 'ratio' and 'all' the formula has to be y~x with y primary and x secondary information. For method 'regr', it is the symbolic description of the linear regression model. In this case, it can be used more than one auxiliary variable. Thus, aux has to be a vector of the same length as the number of auxiliary variables in order as specified in the formula.

Value

The function mbes returns an object, which is a list consisting of the components

`call`	is a list of call components: `formula` formula, `data` data frame, `aux` given value for mean of auxiliary variable, `N` population size, `type` type of model based estimation and `level` coverage probability for confidence intervals
`info`	is a list of further information components: `N` population size, `n` sample size, `p` number of auxiliary variables, `aux` true mean of auxiliary variables in population and `x.mean` sample means of auxiliary variables
`simple`	is a list of result components, if `method='simple'` or `method='all'` is selected: `mean` mean estimate of population mean for primary information, `se` standard error of the mean estimate, and `ci` vector of confidence interval boundaries
`diff`	is a list of result components, if `method='diff'` or `method='all'` is selected: `mean` mean estimate of population mean for primary information, `se` standard error of the mean estimate, and `ci` vector of confidence interval boundaries
`ratio`	is a list of result components, if `method='ratio'` or `method='all'` is selected: `mean` mean estimate of population mean for primary information, `se` standard error of the mean estimate, and `ci` vector of confidence interval boundaries
`regr`	is a list of result components, if `type='regr'` or `type='all'` is selected: `mean` mean estimate of population mean for primary information, `se` standard error of mean estimate, `ci` vector of confidence interval boundaries, and `model` underlying linear regression model

Author(s)

Juliane Manitz

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

## 1) simple suppositious example
data(pop)
# Draw a random sample of size=3
set.seed(802016)
data <- pop[sample(1:5, size=3),]
names(data) <- c('id','x','y')
# difference estimator
mbes(formula=y~x, data=data, aux=15, N=5, method='diff', level=0.95)
# ratio estimator
mbes(formula=y~x, data=data, aux=15, N=5, method='ratio', level=0.95)
# regression estimator
mbes(formula=y~x, data=data, aux=15, N=5, method='regr', level=0.95)

## 2) Bundestag election
data(election)
# draw sample of size n = 20
N <- nrow(election)
set.seed(67396)
sample <- election[sort(sample(1:N, size=20)),]
# secondary information SPD in 2002
X.mean <- mean(election$SPD_02)
# forecast proportion of SPD in election of 2005
mbes(SPD_05 ~ SPD_02, data=sample, aux=X.mean, N=N, method='all')
# true value
Y.mean <- mean(election$SPD_05)
Y.mean
# Use a second predictor variable
X.mean2 <- c(mean(election$SPD_02),mean(election$GREEN_02))
# forecast proportion of SPD in election of 2005 with two predictors
mbes(SPD_05 ~ SPD_02+GREEN_02, data=sample, aux=X.mean2, N=N, method= 'regr')

## 3) money sample
data(money)
mu.X <-  mean(money$X)
x <- money$X[which(!is.na(money$y))]
y <- na.omit(money$y)
# estimation
mbes(y~x, aux=mu.X, N=13, method='all')

## 4) model based two-phase sampling with mbes() 
id <- 1:1000
x <- rep(c(1,0,1,0),times=c(10,90,70,830))
y <- rep(c(1,0,NA),times=c(15,85,900))
phase <- rep(c(2,1), times=c(100,900))
data <- data.frame(id,x,y,phase)
# mean of x out of first phase
mean.x <- mean(data$x)
mean.x
N1 <- length(data$x) 
# calculation of estimation for y 
est.y <- mbes(y~x, data=data, aux=mean.x, N=N1, method='ratio')
est.y
# correction of standard error with uncertaincy in first phase
v.y <- var(data$y, na.rm=TRUE)
se.y <- sqrt(est.y$ratio$se^2 + v.y/N1)
se.y
# corrected confidence interval
lower <- est.y$ratio$mean - qnorm(0.975)*se.y
upper <- est.y$ratio$mean + qnorm(0.975)*se.y
c(lower, upper)
## 1) simple suppositious example
data(pop)
# Draw a random sample of size=3
set.seed(802016)
data <- pop[sample(1:5, size=3),]
names(data) <- c('id','x','y')
# difference estimator
mbes(formula=y~x, data=data, aux=15, N=5, method='diff', level=0.95)
# ratio estimator
mbes(formula=y~x, data=data, aux=15, N=5, method='ratio', level=0.95)
# regression estimator
mbes(formula=y~x, data=data, aux=15, N=5, method='regr', level=0.95)

## 2) Bundestag election
data(election)
# draw sample of size n = 20
N <- nrow(election)
set.seed(67396)
sample <- election[sort(sample(1:N, size=20)),]
# secondary information SPD in 2002
X.mean <- mean(election$SPD_02)
# forecast proportion of SPD in election of 2005
mbes(SPD_05 ~ SPD_02, data=sample, aux=X.mean, N=N, method='all')
# true value
Y.mean <- mean(election$SPD_05)
Y.mean
# Use a second predictor variable
X.mean2 <- c(mean(election$SPD_02),mean(election$GREEN_02))
# forecast proportion of SPD in election of 2005 with two predictors
mbes(SPD_05 ~ SPD_02+GREEN_02, data=sample, aux=X.mean2, N=N, method= 'regr')

## 3) money sample
data(money)
mu.X <-  mean(money$X)
x <- money$X[which(!is.na(money$y))]
y <- na.omit(money$y)
# estimation
mbes(y~x, aux=mu.X, N=13, method='all')

## 4) model based two-phase sampling with mbes() 
id <- 1:1000
x <- rep(c(1,0,1,0),times=c(10,90,70,830))
y <- rep(c(1,0,NA),times=c(15,85,900))
phase <- rep(c(2,1), times=c(100,900))
data <- data.frame(id,x,y,phase)
# mean of x out of first phase
mean.x <- mean(data$x)
mean.x
N1 <- length(data$x) 
# calculation of estimation for y 
est.y <- mbes(y~x, data=data, aux=mean.x, N=N1, method='ratio')
est.y
# correction of standard error with uncertaincy in first phase
v.y <- var(data$y, na.rm=TRUE)
se.y <- sqrt(est.y$ratio$se^2 + v.y/N1)
se.y
# corrected confidence interval
lower <- est.y$ratio$mean - qnorm(0.975)*se.y
upper <- est.y$ratio$mean + qnorm(0.975)*se.y
c(lower, upper)

Money Data Frame

Description

Data provides guesses and true values for students wallet money.

Usage

data(money)data(money)

Format

A data frame with 13 observations (corresponding to the students) on the following 3 variables.

id: a numeric vector of identification number
X: a numeric vector of secondary information, guesses of money in the wallet
y: a numeric vector of primary information, counted money in the wallet. NA means subject was not included into the sample.

Details

In a lesson an experiment was made, in which the students were asked to guess the current amount of money in their wallet. A simple sample of these students was drawn, who counted the money in their wallet exactly. Using this secondary information, model based estimation of the population mean is possible.

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

data(money)
print(money)

# Usage of mbes()
mu.X <-  mean(money$X)
x <- money$X[which(!is.na(money$y))]
y <- na.omit(money$y)
# estimation
mbes(y~x, aux=mu.X, N=13, method='all')
data(money)
print(money)

# Usage of mbes()
mu.X <-  mean(money$X)
x <- money$X[which(!is.na(money$y))]
y <- na.omit(money$y)
# estimation
mbes(y~x, aux=mu.X, N=13, method='all')

Small Suppositious Sampling Example

Description

pop is a suppositious data frame for a small population with 5 elements. It is used for simple illustration of survey sampling estimators.

Usage

data(pop)data(pop)

Format

A data frame with 5 observations on the following 3 variables.

id: a numeric vector of individual identification values
X: a numeric vector of first characteristic
Y: a numeric vector of second characteristic

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

data(pop)
print(pop)

## 1) Usage of Smean()
data(pop)
Y <- pop$Y
Y
# Draw a random sample pop size=3
set.seed(93456)
y <- sample(x = Y, size = 3)
sort(y)
# Estimation with infiniteness correction
est <- Smean(y = y, N = length(pop$Y))
est

## 2) Usage of mbes()
data(pop)
# Draw a random sample of size=3
set.seed(802016)
data <- pop[sample(1:5, size=3),]
names(data) <- c('id','x','y')
# difference estimator
mbes(formula=y~x, data=data, aux=15, N=5, method='diff', level=0.95)
# ratio estimator
mbes(formula=y~x, data=data, aux=15, N=5, method='ratio', level=0.95)
# regression estimator
mbes(formula=y~x, data=data, aux=15, N=5, method='regr', level=0.95)
data(pop)
print(pop)

## 1) Usage of Smean()
data(pop)
Y <- pop$Y
Y
# Draw a random sample pop size=3
set.seed(93456)
y <- sample(x = Y, size = 3)
sort(y)
# Estimation with infiniteness correction
est <- Smean(y = y, N = length(pop$Y))
est

## 2) Usage of mbes()
data(pop)
# Draw a random sample of size=3
set.seed(802016)
data <- pop[sample(1:5, size=3),]
names(data) <- c('id','x','y')
# difference estimator
mbes(formula=y~x, data=data, aux=15, N=5, method='diff', level=0.95)
# ratio estimator
mbes(formula=y~x, data=data, aux=15, N=5, method='ratio', level=0.95)
# regression estimator
mbes(formula=y~x, data=data, aux=15, N=5, method='regr', level=0.95)

Sampling with Probabilities Proportional to Size

Description

The function provides sample techniques with sampling probabilities which are proportional to the size of a quantity z.

Usage

pps.sampling(z, n, id = 1:N, method = 'sampford', return.PI = FALSE)
pps.sampling(z, n, id = 1:N, method = 'sampford', return.PI = FALSE)

Arguments

`z`	vector of quantities which determine the sampling probabilities in the population
`n`	positive integer for sample size
`id`	an optional vector with identification values for population elements. Default is `'id = 1:N'`, where `'N'` is length of `'z'`.
`method`	the sampling method to be used. Options are `'sampford'`, `'tille'`, `'midzuno'` or `'madow'`.
`return.PI`	logical. If `TRUE` the pairwise inclusion probabilities for all individuals in the population are returned.

Details

The different methods vary in their run time. Therefore, method='sampford' is stopped if N > 200 or if n/N < 0.3. method='tille' is stopped if N > 500. In case of large populations use method='midzuno' or method='madow'.

Value

The function pps.sampling returns a value, which is a list consisting of the components

`call`	is a list of call components: `z` vector of quantity data, `n` sample size, `id` identification values, and `method` sampling method
`sample`	resulted sample
`pik`	inclusion probabilities
`PI`	sample second order inclusion probabilities
`PI.full`	full second order inclusion probabilities

Author(s)

Juliane Manitz

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

## 1) simple suppositious example
data <- data.frame(id = 1:7, z = c(1.8, 2 ,3.2 ,2.9 ,1.5 ,2.0 ,2.2))
# Usage of pps.sampling for Sampford method
set.seed(178209)
pps.sample_sampford <- pps.sampling(z=data$z, n=2, method='sampford', return.PI=FALSE)
pps.sample_sampford
# sampling elements
id.sample <- pps.sample_sampford$sample
id.sample
# other methods
set.seed(178209)
pps.sample_tille <- pps.sampling(z=data$z, n=2, method='tille')
pps.sample_tille
set.seed(178209)
pps.sample_midzuno <- pps.sampling(z=data$z, n=2, method='midzuno')
pps.sample_midzuno
set.seed(178209)
pps.sample_madow <- pps.sampling(z=data$z, n=2, method='madow')
pps.sample_madow

## 2) influenza
data(influenza)
summary(influenza)

set.seed(108506)
pps <- pps.sampling(z=influenza$population,n=20,method='midzuno')
pps
sample <- influenza[pps$sample,]
sample
## 1) simple suppositious example
data <- data.frame(id = 1:7, z = c(1.8, 2 ,3.2 ,2.9 ,1.5 ,2.0 ,2.2))
# Usage of pps.sampling for Sampford method
set.seed(178209)
pps.sample_sampford <- pps.sampling(z=data$z, n=2, method='sampford', return.PI=FALSE)
pps.sample_sampford
# sampling elements
id.sample <- pps.sample_sampford$sample
id.sample
# other methods
set.seed(178209)
pps.sample_tille <- pps.sampling(z=data$z, n=2, method='tille')
pps.sample_tille
set.seed(178209)
pps.sample_midzuno <- pps.sampling(z=data$z, n=2, method='midzuno')
pps.sample_midzuno
set.seed(178209)
pps.sample_madow <- pps.sampling(z=data$z, n=2, method='madow')
pps.sample_madow

## 2) influenza
data(influenza)
summary(influenza)

set.seed(108506)
pps <- pps.sampling(z=influenza$population,n=20,method='midzuno')
pps
sample <- influenza[pps$sample,]
sample

Sample Size Calculation for Mean Estimation

Description

The function sample.size.mean returns the sample size needed for mean estimations either with or without consideration of finite population correction.

Usage

sample.size.mean(e, S, N = Inf, level = 0.95)
sample.size.mean(e, S, N = Inf, level = 0.95)

Arguments

`e`	positive number specifying the precision which is half width of confidence interval
`S`	standard deviation in population
`N`	positive integer for population size. Default is `N=Inf`, which means that calculations are carried out without finite population correction.
`level`	coverage probability for confidence intervals. Default is `level=0.95`.

Value

The function sample.size.mean returns a value, which is a list consisting of the components

`call`	is a list of call components: `e` precision, `S` standard deviation in population, and `N` integer for population size
`n`	estimate of sample size

Author(s)

Juliane Manitz

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

# sample size for precision e=4
sample.size.mean(e=4,S=10,N=300)
# sample size for precision e=1
sample.size.mean(e=1,S=10,N=300)
# sample size for precision e=4
sample.size.mean(e=4,S=10,N=300)
# sample size for precision e=1
sample.size.mean(e=1,S=10,N=300)

Sample Size Calculation for Proportion Estimation

Description

The function sample.size.prop returns the sample size needed for proportion estimation either with or without consideration of finite population correction.

Usage

sample.size.prop(e, P = 0.5, N = Inf, level = 0.95)
sample.size.prop(e, P = 0.5, N = Inf, level = 0.95)

Arguments

`e`	positive number specifying the precision which is half width of confidence interval
`P`	expected proportion of events with domain between values 0 and 1. Default is `P=0.5`.
`N`	positive integer for population size. Default is `N=Inf`, which means that calculations are carried out without finite population correction.
`level`	coverage probability for confidence intervals. Default is `level=0.95`.

Details

For meaningful calculation, precision e should be chosen smaller than 0.5, because the domain of P is between values 0 and 1. Furthermore, precision e should be smaller than proportion P, respectively (1-P).

Value

The function sample.size.prop returns a value, which is a list consisting of the components

`call`	is a list of call components `e` precision, `P` expected proportion, `N` population size, and `level` coverage probability for confidence intervals
`n`	estimate of sample size

Author(s)

Juliane Manitz

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

## 1) examples with different precisions
# precision 1% for election forecast of SPD in 2005
sample.size.prop(e=0.01, P=0.5, N=Inf)
data(election)
sample.size.prop(e=0.01, P=mean(election$SPD_02), N=Inf)
# precision 5% for questionnaire
sample.size.prop(e=0.05, P=0.5, N=300)
sample.size.prop(e=0.05, P=0.5, N=Inf)
# precision 10%
sample.size.prop(e=0.1, P=0.5, N=300)
sample.size.prop(e=0.1, P=0.5, N=1000)

## 2) tables in the book
# table 2.2
P_vector <- c(0.2, 0.3, 0.4, 0.5)
N_vector <- c(10, 100, 1000, 10000)
results <- matrix(NA, ncol=4, nrow=4)
for (i in 1:length(P_vector)){
  for (j in 1:length(N_vector)){
    x <- try(sample.size.prop(e=0.1, P=P_vector[i], N=N_vector[j]))
    if (class(x)=='try-error') {results[i,j] <- NA}
    else {results[i,j] <- x$n}
  }
}
dimnames(results) <- list(paste('P=',P_vector, sep=''), paste('N=',N_vector, sep=''))
results
# table 2.3
P_vector <- c(0.5, 0.1)
e_vector <- c(0.1, 0.05, 0.03, 0.02, 0.01)
results <- matrix(NA, ncol=2, nrow=5)
for (i in 1:length(e_vector)){
  for (j in 1:length(P_vector)){
    x <- try(sample.size.prop(e=e_vector[i], P=P_vector[j], N=Inf))
    if (class(x)=='try-error') {results[i,j] <- NA}
    else {results[i,j] <- x$n}
  }
}
dimnames(results) <- list(paste('e=',e_vector, sep=''), paste('P=',P_vector, sep=''))
results

## 1) examples with different precisions
# precision 1% for election forecast of SPD in 2005
sample.size.prop(e=0.01, P=0.5, N=Inf)
data(election)
sample.size.prop(e=0.01, P=mean(election$SPD_02), N=Inf)
# precision 5% for questionnaire
sample.size.prop(e=0.05, P=0.5, N=300)
sample.size.prop(e=0.05, P=0.5, N=Inf)
# precision 10%
sample.size.prop(e=0.1, P=0.5, N=300)
sample.size.prop(e=0.1, P=0.5, N=1000)

## 2) tables in the book
# table 2.2
P_vector <- c(0.2, 0.3, 0.4, 0.5)
N_vector <- c(10, 100, 1000, 10000)
results <- matrix(NA, ncol=4, nrow=4)
for (i in 1:length(P_vector)){
  for (j in 1:length(N_vector)){
    x <- try(sample.size.prop(e=0.1, P=P_vector[i], N=N_vector[j]))
    if (class(x)=='try-error') {results[i,j] <- NA}
    else {results[i,j] <- x$n}
  }
}
dimnames(results) <- list(paste('P=',P_vector, sep=''), paste('N=',N_vector, sep=''))
results
# table 2.3
P_vector <- c(0.5, 0.1)
e_vector <- c(0.1, 0.05, 0.03, 0.02, 0.01)
results <- matrix(NA, ncol=2, nrow=5)
for (i in 1:length(e_vector)){
  for (j in 1:length(P_vector)){
    x <- try(sample.size.prop(e=e_vector[i], P=P_vector[j], N=Inf))
    if (class(x)=='try-error') {results[i,j] <- NA}
    else {results[i,j] <- x$n}
  }
}
dimnames(results) <- list(paste('e=',e_vector, sep=''), paste('P=',P_vector, sep=''))
results

Sampling Mean Estimation

Description

The function Smean estimates the population mean out of simple samples either with or without consideration of finite population correction.

Usage

Smean(y, N = Inf, level = 0.95)
Smean(y, N = Inf, level = 0.95)

Arguments

`y`	vector of sample data
`N`	positive integer specifying population size. Default is `N=Inf`, which means that calculations are carried out without finite population correction.
`level`	coverage probability for confidence intervals. Default is `level=0.95`.

Value

The function Smean returns a value, which is a list consisting of the components

`call`	is a list of call components: `y` vector with sample data, `n` sample size, `N` population size, `level` coverage probability for confidence intervals
`mean`	mean estimate
`se`	standard error of the mean estimate
`ci`	vector of confidence interval boundaries

Author(s)

Juliane Manitz

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

data(pop)
Y <- pop$Y
Y
# Draw a random sample of size=3
set.seed(93456)
y <- sample(x = Y, size = 3)
sort(y)
# Estimation with infiniteness correction
est <- Smean(y = y, N = length(pop$Y))
est
data(pop)
Y <- pop$Y
Y
# Draw a random sample of size=3
set.seed(93456)
y <- sample(x = Y, size = 3)
sort(y)
# Estimation with infiniteness correction
est <- Smean(y = y, N = length(pop$Y))
est

Sampling Proportion Estimation

Description

The function Sprop estimates the proportion out of samples either with or without consideration of finite population correction. Different methods for calculating confidence intervals for example based on binomial distribution (Agresti and Coull or Clopper-Pearson) or based on hypergeometric distribution are used.

Usage

Sprop(y, m, n = length(y), N = Inf, level = 0.95)
Sprop(y, m, n = length(y), N = Inf, level = 0.95)

Arguments

`y`	vector of sample data containing values 0 and 1
`m`	an optional non-negative integer for number of positive events
`n`	an optional positive integer for sample size. Default is `n=length(y)`.
`N`	positive integer for population size. Default is `N=Inf`, which means calculations are carried out without finite population correction.
`level`	coverage probability for confidence intervals. Default is `level=0.95`.

Details

Sprop can be called by usage of a data vector y with the observations 1 for event and 0 for failure. Moreover, it can be called by specifying the number of events m and trials n.

Value

The function Sprop returns a value, which is a list consisting of the components

`call`	is a list of call components: `y` sample data, `m` number of positive events in the sample, `n` sample size, `N` population size, `level` coverage probability for confidence intervals
`p`	proportion estimate
`se`	standard error of the proportion estimate
`ci`	is a list of confidence interval boundaries for proportion. In case of a finite population of size `N`, it is given `approx`, the hypergeometric confidence interval with normal distribution approximation, and `exact`, the exact hypergeometric confidence interval. If the population is very large `N=Inf`, it is calculated `bin`, the binomial confidence interval, which is asymptotic, `cp` the exact confidence interval based on binomial distribution (Clopper-Pearson), and `ac`, the asymptotic confidence interval based on binomial distribution by Wilson (Agresti and Coull (1998)).
`nr`	In case of finite population of size `N`, it is given a list of confidence interval boundaries for number in population with `approx`, the hypergeometric confidence interval with normal distribution approximation, and `exact`, the exact hypergeometric confidence interval.

Author(s)

Juliane Manitz

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Agresti, Alan/Coull, Brent A. (1998): Approximate Is Better than 'Exact' for Interval Estimation of Binomial Proportions. The American Statistician, Vol. 52, No. 2 , pp. 119-126.

Examples

# 1) Survey in company to upgrade office climate
Sprop(m=45, n=100, N=300)
Sprop(m=2, n=100, N=300)

# 2) German opinion poll for 03/07/09 with 
# (http://www.wahlrecht.de/umfragen/politbarometer.htm)
# a) 302 of 1206 respondents who would elect SPD.
# b) 133 of 1206 respondents who would elect the Greens.
Sprop(m=302, n=1206, N=Inf)
Sprop(m=133, n=1206, N=Inf)

# 3) Rare disease of animals (sample size n=500 of N=10.000 animals, one infection)
# for 95% one sided confidence level use level=0.9
Sprop(m=1, n=500, N=10000, level=0.9)

# 4) call with data vector y
y <- c(0,0,1,0,1,0,0,0,1,1,0,0,1)
Sprop(y=y, N=200)
# is the same as
Sprop(m=5, n=13, N=200)
# 1) Survey in company to upgrade office climate
Sprop(m=45, n=100, N=300)
Sprop(m=2, n=100, N=300)

# 2) German opinion poll for 03/07/09 with 
# (http://www.wahlrecht.de/umfragen/politbarometer.htm)
# a) 302 of 1206 respondents who would elect SPD.
# b) 133 of 1206 respondents who would elect the Greens.
Sprop(m=302, n=1206, N=Inf)
Sprop(m=133, n=1206, N=Inf)

# 3) Rare disease of animals (sample size n=500 of N=10.000 animals, one infection)
# for 95% one sided confidence level use level=0.9
Sprop(m=1, n=500, N=10000, level=0.9)

# 4) call with data vector y
y <- c(0,0,1,0,1,0,0,0,1,1,0,0,1)
Sprop(y=y, N=200)
# is the same as
Sprop(m=5, n=13, N=200)

Stratified Sample Mean Estimation

Description

The function stratamean estimates the population mean out of stratified samples either with or without consideration of finite population correction.

Usage

stratamean(y, h, Nh, wh, level = 0.95, eae = FALSE)
stratamean(y, h, Nh, wh, level = 0.95, eae = FALSE)

Arguments

`y`	vector of target variable.
`h`	vector of stratifying variable.
`Nh`	vector of sizes of every stratum, which has to be supplied in alphabetical or numerical order of the categories of h.
`wh`	vector of weights of every stratum, which has to be supplied in alphabetical or numerical order of the categories of h.
`level`	coverage probability for confidence intervals. Default is `level=0.95`.
`eae`	`TRUE` for extensive output with the result in each and every stratum. Default is `eae=FALSE`.

Details

If the absolute stratum sizes Nh are given, the variances are calculated with finite population correction. Otherwise, if the stratum weights wh are given, the variances are calculated without finite population correction.

Value

The function stratamean returns a value, which is a list consisting of the components

`call`	is a list of call components: `y` target variable in sample data, `h` stratifying variable in sample data, `Nh` sizes of every stratum, `wh` weights of every stratum, `fpc` finite population correction, `level` coverage probability for confidence intervals
`mean`	mean estimate for population
`se`	standard error of the mean estimate for population
`ci`	vector of confidence interval boundaries for population

Author(s)

Shuai Shao and Juliane Manitz

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

# random data
testy <- rnorm(100)
testh <- c(rep("male",40), rep("female",60))
stratamean(testy, testh, wh=c(0.5, 0.5))
stratamean(testy, testh, wh=c(0.5, 0.5), eae=TRUE)

# tax data
data(tax)
summary(tax)

nh <- as.vector(table(tax$Class))
wh <- nh/sum(nh)
stratamean(y=tax$diff, h=as.vector(tax$Class), wh=wh, eae=TRUE)
# random data
testy <- rnorm(100)
testh <- c(rep("male",40), rep("female",60))
stratamean(testy, testh, wh=c(0.5, 0.5))
stratamean(testy, testh, wh=c(0.5, 0.5), eae=TRUE)

# tax data
data(tax)
summary(tax)

nh <- as.vector(table(tax$Class))
wh <- nh/sum(nh)
stratamean(y=tax$diff, h=as.vector(tax$Class), wh=wh, eae=TRUE)

Sample Size Calculation for Stratified Sampling

Description

The function stratasamp calculates the sample size for each stratum depending on type of allocation.

Usage

stratasamp(n, Nh, Sh = NULL, Ch = NULL, type = 'prop')
stratasamp(n, Nh, Sh = NULL, Ch = NULL, type = 'prop')

Arguments

`n`	positive integer specifying sampling size.
`Nh`	vector of population sizes of each stratum.
`Sh`	vector of standard deviation in each stratum.
`Ch`	vector of cost for a sample in each stratum.
`type`	type of allocation. Default is `type='prop'` for proportional, alternatives are `type='opt'` for optimal and `type='costopt'` for cost-optimal.

Value

The function stratasamp returns a matrix, which lists the strata and the sizes of observation depending on type of allocation.

Author(s)

Shuai Shao and Juliane Manitz

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

#random proportional stratified sample
stratasamp(n=500, Nh=c(5234,2586,649,157))
stratasamp(n=500, Nh=c(5234,2586,649,157), Sh=c(251,1165,8035,24725), type='opt')
#random proportional stratified sample
stratasamp(n=500, Nh=c(5234,2586,649,157))
stratasamp(n=500, Nh=c(5234,2586,649,157), Sh=c(251,1165,8035,24725), type='opt')

Sample Size Determination for Stratified Sampling

Description

The function stratasize determinates the total size of stratified samples depending on type of allocation and determinated by specified precision.

Usage

stratasize(e, Nh, Sh, level = 0.95, type = 'prop')
stratasize(e, Nh, Sh, level = 0.95, type = 'prop')

Arguments

`e`	positive number specifying sampling precision.
`Nh`	vector of population sizes in each stratum.
`Sh`	vector of standard deviation in each stratum.
`level`	coverage probability for confidence intervals. Default is `level=0.95`.
`type`	type of allocation. Default is `type='prop'` for proportional, alternative is `type='opt'` for optimal.

Value

The function stratasize returns a value, which is a list consisting of the components

`call`	is a list of call components: `e` specified precision, `Nh` population sizes of every stratum, `Sh` standard diviation of every stratum, `method` type of allocation, `level` coverage probability for confidence intervals.
`n`	determinated total sample size.

Author(s)

Shuai Shao

References

Kauermann, Goeran/Kuechenhoff, Helmut (2011): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

#random proportional stratified sample
stratasize(e=0.1, Nh=c(100000,300000,600000), Sh=c(1,2,3))

#random optimal stratified sample
stratasize(e=0.1, Nh=c(100000,300000,600000), Sh=c(1,2,3), type="opt")
#random proportional stratified sample
stratasize(e=0.1, Nh=c(100000,300000,600000), Sh=c(1,2,3))

#random optimal stratified sample
stratasize(e=0.1, Nh=c(100000,300000,600000), Sh=c(1,2,3), type="opt")

Sub-sample Mean Estimation

Description

The function submean estimates the population mean out of sub-samples (two-stage samples) either with or without consideration of finite population correction in both stages.

Usage

submean(y, PSU, N, M, Nl, m.weight, n.weight, method = 'simple', level = 0.95)
submean(y, PSU, N, M, Nl, m.weight, n.weight, method = 'simple', level = 0.95)

Arguments

`y`	vector of target variable.
`PSU`	vector of grouping variable which indicates the primary unit for each sample element.
`N`	positive integer specifying population size
`M`	positive integer specifying the number of primary units in the population.
`Nl`	vector of sample sizes in each primary unit, which has to be specified in alphabetical or numerical order of the categories of l.
`m.weight`	vector of primary sample unit weights, which has to be specified in alphabetical or numerical order of the categories of l.
`n.weight`	vector of secondary sample unit weights in each primary sample unit, which has to be specified in alphabetical or numerical order of the categories of l.
`method`	estimation method. Default is "simple", alternative is "ratio".
`level`	coverage probability for confidence intervals. Default is `level=0.95`.

Details

If the absolute sizes M and Nl are given, the variances are calculated with finite population correction. Otherwise, if the weights m.weight and n.weight are given, the variances are calculated without finite population correction.

Value

The function submean returns a value, which is a list consisting of the components

`call`	is a list of call components: `y` target variable in sample data, `PSU` gouping variable in sample data, `N` population size, `M` number of primary population units, `fpc` finite population correction, `method` estimation method, `level` coverage probability for confidence intervals
`mean`	mean estimate for population
`se`	standard error of the mean estimate for population
`ci`	vector of confidence interval boundaries for population

Author(s)

Shuai Shao and Juliane Manitz

References

Kauermann, Goeran/Kuechenhoff, Helmut (2011): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

y <- c(23,33,24,25,72,74,71,37,42)
psu <- as.factor(c(1,1,1,1,2,2,2,3,3))
# with finite population correction
submean(y, PSU=psu, N=700, M=23, Nl=c(100,50,75), method='ratio')
# without finite population correction
submean(y, PSU=psu, N=700, m.weight=3/23, n.weight=c(4/100,3/50,2/75), method='ratio')

# Chinese wage data
data(wage)
summary(wage)
submean(wage$Wage,PSU=wage$Region, N=990, M=33, Nl=rep(30,14))
y <- c(23,33,24,25,72,74,71,37,42)
psu <- as.factor(c(1,1,1,1,2,2,2,3,3))
# with finite population correction
submean(y, PSU=psu, N=700, M=23, Nl=c(100,50,75), method='ratio')
# without finite population correction
submean(y, PSU=psu, N=700, m.weight=3/23, n.weight=c(4/100,3/50,2/75), method='ratio')

# Chinese wage data
data(wage)
summary(wage)
submean(wage$Wage,PSU=wage$Region, N=990, M=33, Nl=rep(30,14))

Hypothetical Tax Refund Data Frame

Description

Simulated tax refund data frame including the estimated and actual refund value

Usage

data(tax)data(tax)

Format

A data frame with 9083 observations on the following 5 variables.

id: a numeric vector indicating the tax payer
estRefund: a numeric vector representing the estimated value of tax refund by the tax payer
actRefund: a numeric vector representing the actual tax refund calculated by the financial authority
diff: difference between estimated and acture tax refund
Class: a factor with levels 1, 2, 3, and 4 indicating the strata

Source

Due to data protection this is a simulated data set reflecting the real data.

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

data(tax)
summary(tax)

# illustration of stratamean
nh <- as.vector(table(tax$Class))
wh <- nh/sum(nh)
stratamean(y=tax$diff, h=as.vector(tax$Class), wh=wh, eae=TRUE)
data(tax)
summary(tax)

# illustration of stratamean
nh <- as.vector(table(tax$Class))
wh <- nh/sum(nh)
stratamean(y=tax$diff, h=as.vector(tax$Class), wh=wh, eae=TRUE)

Chinese wage data

Description

A data frame with hypothetical Chinese wages differenciated by region and industrial sector.

Usage

data(wage)data(wage)

Format

A data frame with 231 observations on the following 3 variables.

Region: factor, Chinese regions with 14 levels.
Sector: factor, industrial sector with 30 levels.
Wage: a numeric vector, average wage in the region and sector measured in Chinese yuan.

Details

The dataset is hypothetical. Its structure imitates the data in the Chinese Statistical Yearbook. The values are simulated corresponding to the distribution of the real data which are not publicly accessible.

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Examples

# Chinese wage data
data(wage)
summary(wage)
submean(wage$Wage,PSU=wage$Region, N=990, M=33, Nl=rep(30,14))
# Chinese wage data
data(wage)
summary(wage)
submean(wage$Wage,PSU=wage$Region, N=990, M=33, Nl=rep(30,14))

Package 'samplingbook'

Help Index

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Sample Size Calculation for Proportion Estimation

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