samplesize4surveys (version 4.1.1)

ss4S2: The required sample size for estimating a single variance

Description

This function returns the minimum sample size required for estimating a single variance subjecto to predefined errors.

Usage

ss4S2(N, K = 0, DEFF = 1, conf = 0.95, cve = 0.05, me = 0.03, plot = FALSE)

Arguments

N

The population size.

K

The population excess kurtosis of the variable in the population.

DEFF

The design effect of the sample design. By default DEFF = 1, which corresponds to a simple random sampling design.

conf

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

cve

The maximun coeficient of variation that can be allowed for the estimation.

me

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

plot

Optionally plot the errors (cve and margin of error) against the sample size.

Details

Note that the minimun sample size to achieve a particular relative margin of error \(\varepsilon\) is defined by: $$n = \frac{n_0}{\frac{(N-1)^3}{N^2(N*K+2N+2)}+\frac{n_0}{N}}$$ Where $$n_0=\frac{z^2_{1-\frac{\alpha}{2}}*DEFF}{\varepsilon^2}$$ Also note that the minimun sample size to achieve a particular coefficient of variation \(cve\) is defined by: $$n = \frac{N^2(N*K+2N+2)*DEFF}{cve^2*(N-1)^3+N(N*K+2N+2)*DEFF}$$

References

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

See Also

e4p

Examples

# NOT RUN {
ss4S2(N = 10000, K = 0, cve = 0.05, me = 0.03)
ss4S2(N = 10000, K = 1, cve = 0.05, me = 0.03)
ss4S2(N = 10000, K = 1, cve = 0.05, me = 0.05, DEFF = 2)
ss4S2(N = 10000, K = 1, cve = 0.05, me = 0.03, plot = TRUE)

#############################
# Example with BigLucy data #
#############################

data(BigLucy)
attach(BigLucy)
N <- nrow(BigLucy)
K <- kurtosis(BigLucy$Income)
# The minimum sample size for simple random sampling
ss4S2(N, K, DEFF=1, conf=0.99, cve=0.03, me=0.1, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4S2(N, K, DEFF=3.45, conf=0.99, cve=0.03, me=0.1, plot=TRUE)
# }