samplesize4surveys (version 4.1.1)

e4dp: Statistical errors for the estimation of a difference of proportions

Description

This function computes the cofficient of variation and the standard error when estimating a difference of proportions under a complex sample design.

Usage

e4dp(N, n, P1, P2, DEFF = 1, T = 0, R = 1, conf = 0.95, plot = FALSE)

Arguments

N

The population size.

n

The sample size.

P1

The value of the first estimated proportion.

P2

The value of the second estimated proportion.

DEFF

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

T

The overlap between waves. By default T = 0.

R

The correlation between waves. By default R = 1.

conf

The statistical confidence. By default conf = 0.95.

plot

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

Value

The coefficient of variation and the margin of error for a predefined sample size.

Details

We note that the margin of error is defined as: $$cve = \frac{\sqrt{Var(\hat{P}_1 - \hat{P}_2) }}{\hat{P}_1 - \hat{P}_2}$$ Also, note that the magin of error is defined as: $$\varepsilon = z_{1-\frac{\alpha}{2}}\sqrt{Var(\hat{P}_1 - \hat{P}_2)}$$

References

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

See Also

ss4p

Examples

# NOT RUN {
e4dp(N=10000, n=400, P1=0.5, P2=0.6)
e4dp(N=10000, n=400, P1=0.5, P2=0.6, plot=TRUE)
e4dp(N=10000, n=400, P1=0.5, P2=0.6, DEFF=3.45, conf=0.99, plot=TRUE)
e4dp(N=10000, n=400, P1=0.5, P2=0.6, T=0.5, R=0.5, DEFF=3.45, conf=0.99, plot=TRUE)
# }