samplesize4surveys (version 4.1.1)

e4ddp: Statistical errors for the estimation of a double difference of proportions

Description

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

Usage

e4ddp(N, n, P1, P2, P3, P4, DEFF = 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.

P3

The value of the third estimated proportion.

P4

The value of the fouth estimated proportion.

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.

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: $$cve = \frac{\sqrt{Var((\hat{P}_1 - \hat{P}_2) - (\hat{P}_3 - \hat{P}_4) ) }}{(\hat{P}_1 - \hat{P}_2) - (\hat{P}_3 - \hat{P}_4)}$$ Also, note that the magin of error is defined as: $$\varepsilon = z_{1-\frac{\alpha}{2}}\sqrt{Var((\hat{P}_1 - \hat{P}_2) - (\hat{P}_3 - \hat{P}_4) )}$$

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 {
e4ddp(N=10000, n=400, P1=0.5, P2=0.6, P3=0.5, P4=0.7)
e4ddp(N=10000, n=400, P1=0.5, P2=0.6, P3=0.5, P4=0.7, plot=TRUE)
e4ddp(N=10000, n=400, P1=0.5, P2=0.6, P3=0.5, P4=0.7, DEFF=3.45, conf=0.99, plot=TRUE)
# }