ss4HHSm {samplesize4surveys}

Sample Sizes for Household Surveys in Two-Stages for Estimating Single Means

Description

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

Usage

ss4HHSm(N, M, rho, mu, sigma, delta, conf, m)

Arguments

N

The population size.

M

Number of clusters in the population.

rho

The Intraclass Correlation Coefficient.

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.

delta

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

conf

The statistical confidence. By default conf = 0.95.

m

(vector) Number of households selected within PSU.

Details

In two-stage (2S) sampling, the design effect is defined by

DEFF = 1 + (\bar{m}-1)\rho

Where \rho is defined as the intraclass correlation coefficient, \bar{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

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.

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

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

See Also

ICC

Examples

ss4HHSm(N = 50000000, M = 3000, rho = 0.034, 
        mu = 10, sigma = 2, delta = 0.03, conf = 0.95,
        m = c(5:15))

##################################
# Example with BigCity data      #
# Sample size for the estimation #
# of the unemployment rate       #
##################################

library(TeachingSampling)
data(BigCity)

BigCity1 <- BigCity %>% 
            group_by(HHID) %>%
            summarise(IncomeHH = sum(Income),
                      PSU = unique(PSU))
                      
summary(BigCity1$IncomeHH)
mean(BigCity1$IncomeHH)
sd(BigCity1$IncomeHH)

N <- nrow(BigCity)
M <- length(unique(BigCity$PSU))
rho <- ICC(BigCity1$IncomeHH, BigCity1$PSU)$ICC
mu <- mean(BigCity1$IncomeHH)
sigma <- sd(BigCity1$IncomeHH)
delta <- 0.05
conf <- 0.95
m <- c(5:15)
ss4HHSm(N, M, rho, mu, sigma, delta, conf, m)