samplesize4surveys (version 4.1.1)

e4ddm: Statistical errors for the estimation of a double difference of means

Description

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

Usage

e4ddm(
  N,
  n,
  mu1,
  mu2,
  mu3,
  mu4,
  sigma1,
  sigma2,
  sigma3,
  sigma4,
  DEFF = 1,
  conf = 0.95,
  T = 0,
  R = 1,
  plot = FALSE
)

Arguments

N

The population size.

n

The sample size.

mu1

The value of the estimated mean of the variable of interes for the first population.

mu2

The value of the estimated mean of the variable of interes for the second population.

mu3

The value of the estimated mean of the variable of interes for the third population.

mu4

The value of the estimated mean of the variable of interes for the fourth population.

sigma1

The value of the estimated variance of the variable of interes for the first population.

sigma2

The value of the estimated mean of a variable of interes for the second population.

sigma3

The value of the estimated variance of the variable of interes for the third population.

sigma4

The value of the estimated mean of a variable of interes for the fourth 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.

T

The overlap between waves. By default T = 0.

R

The correlation between waves. By default R = 1.

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

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 {
e4ddm(N=10000, n=400, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12)
e4ddm(N=10000, n=400, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, plot=TRUE)
e4ddm(N=10000, n=400, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, DEFF=3.45, conf=0.99, plot=TRUE)
# }