samplesize4surveys (version 4.1.1)

ss2s4m: Sample Sizes in Two-Stage sampling Designs for Estimating Signle Means

Description

This function computes a grid of possible sample sizes for estimating single means under two-stage sampling designs.

Usage

ss2s4m(N, mu, sigma, conf = 0.95, delta = 0.03, M, to = 20, rho)

Arguments

N

The population size.

mu

The value of the estimated mean of a variable of interest.

sigma

The value of the estimated standard deviation of a variable of interest.

conf

The statistical confidence. By default conf = 0.95. By default conf = 0.95.

delta

The maximun relative margin of error that can be allowed for the estimation.

M

Number of clusters in the population.

to

(integer) maximum number of final units to be selected per cluster. By default to = 20.

rho

The Intraclass Correlation Coefficient.

Value

This function returns a grid of possible sample sizes. The first column represent the design effect, the second column is the number of clusters to be selected, the third column is the number of units to be selected inside the clusters, and finally, the last column indicates the full sample size induced by this particular strategy.

Details

In two-stage (2S) sampling, the design effect is defined by $$DEFF = 1 + (m-1)\rho$$ Where \(\rho\) is defined as the intraclass correlation coefficient, m is the average sample size of units selected inside each cluster. The relationship of the full sample size of the two stage design (2S) with the simple random sample (SI) design is given by $$ n_{2S} = n_{SI}*DEFF$$

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ICC

Examples

# NOT RUN {
ss2s4m(N=100000, mu=10, sigma=2, conf=0.95, delta=0.03, M=50, rho=0.01)
ss2s4m(N=100000, mu=10, sigma=2, conf=0.95, delta=0.03, M=50, to=40, rho=0.1)
ss2s4m(N=100000, mu=10, sigma=2, conf=0.95, delta=0.03, M=50, to=40, rho=0.2)
ss2s4m(N=100000, mu=10, sigma=2, conf=0.95, delta=0.05, M=50, to=40, rho=0.3)

##########################################
# Almost same mean in each cluster       #
#                                        #
# - Heterogeneity within clusters        #
# - Homogeinity between clusters         #
#                                        #
#  Decision rule:                        #
#    * Select a lot of units per cluster #
#    * Select a few of clusters          #
##########################################

# Population size
N <- 1000000
# Number of clusters in the population
M <- 1000
# Number of elements per cluster
N/M

# The variable of interest
y <- c(1:N)
# The clustering factor
cl <- rep(1:M, length.out=N)

rho = ICC(y,cl)$ICC
rho

ss2s4m(N, mu=mean(y), sigma=sd(y), conf=0.95, delta=0.03, M=M, rho=rho)


##########################################
# Very different means per cluster       #
#                                        #
# - Heterogeneity between clusters       #
# - Homogeinity within clusters          #
#                                        #
#  Decision rule:                        #
#    * Select a few of units per cluster #
#    * Select a lot of clusters          #
##########################################

# Population size
N <- 1000000
# Number of clusters in the population
M <- 1000
# Number of elements per cluster
N/M

# The variable of interest
y <- c(1:N)
# The clustering factor
cl <- kronecker(c(1:M),rep(1,N/M))

rho = ICC(y,cl)$ICC
rho

ss2s4m(N, mu=mean(y), sigma=sd(y), conf=0.95, delta=0.03, M=M, rho=rho)

##########################
# Example with Lucy data #
##########################

data(BigLucy)
attach(BigLucy)
N <- nrow(BigLucy)
P <- prop.table(table(SPAM))[1]
y <- Income
cl <- Segments

rho <- ICC(y,cl)$ICC
M <- length(levels(Segments))

ss2s4m(N, mu=mean(y), sigma=sd(y), conf=0.95, delta=0.03, M=M, rho=rho)

##########################
# Example with Lucy data #
##########################

data(BigLucy)
attach(BigLucy)
N <- nrow(BigLucy)
P <- prop.table(table(SPAM))[1]
y <- Years
cl <- Segments

rho <- ICC(y,cl)$ICC
M <- length(levels(Segments))

ss2s4m(N, mu=mean(y), sigma=sd(y), conf=0.95, delta=0.03, M=M, rho=rho)
# }