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

In samplesize4surveys: Sample Size Calculations for Complex Surveys

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.

Details

We note that the coefficent of variation is defined as:

cve = \frac{√{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{α}{2}}√{Var((\bar{y}_1 - \bar{y}_2)-(\bar{y}_3 - \bar{y}_4))}

Value

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

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

ss4p

Examples

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)

Example output

Loading required package: TeachingSampling
Loading required package: timeDate
With the parameters of this function: N = 10000 n =  400 mu1 = 50 mu2 = 55 mu3 = 50 mu4 = 65 sigma1 = 10 sigma2 = 12 sigma3 = 10 sigma4 = 12 DEFF =  1 conf = 0.95 . 
             
The estimated coefficient of variation is  21.6444 . 
             
The margin of error is 2.121112 . 
 
$cve
[1] 21.6444

$Margin_of_error
[1] 2.121112

With the parameters of this function: N = 10000 n =  400 mu1 = 50 mu2 = 55 mu3 = 50 mu4 = 65 sigma1 = 10 sigma2 = 12 sigma3 = 10 sigma4 = 12 DEFF =  1 conf = 0.95 . 
             
The estimated coefficient of variation is  21.6444 . 
             
The margin of error is 2.121112 . 
 
$cve
[1] 21.6444

$Margin_of_error
[1] 2.121112

With the parameters of this function: 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 . 
             
The estimated coefficient of variation is  40.20269 . 
             
The margin of error is 5.177763 . 
 
$cve
[1] 40.20269

$Margin_of_error
[1] 5.177763

samplesize4surveys documentation built on Jan. 18, 2020, 1:11 a.m.