e4S2: Statistical errors for the estimation of a single variance
In samplesize4surveys: Sample Size Calculations for Complex Surveys

Description Usage Arguments Details Value Author(s) References See Also Examples

This function computes the cofficient of variation and the margin of error when estimating a single variance under a sample design.

1	e4S2(N, n, K = 0, DEFF = 1, conf = 0.95, plot = FALSE)

`N`	The population size.
`n`	The sample size.
`K`	The 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`.
`plot`	Optionally plot the errors (cve and margin of error) against the sample size.

We note that the coefficient of variation is defined as:

cve = \frac{√{Var(\hat{S^2})}}{\hat{S^2}}

Also, note that the magin of error is defined as:

\varepsilon = z_{1-\frac{α}{2}}√{Var(\hat{S^2})}

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

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

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

ss4p

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e4S2(N=10000, n=400, K = 0)
e4S2(N=10000, n=400, K = 1, DEFF = 2, conf = 0.99)
e4S2(N=10000, n=400, K = 2, DEFF = 2, conf = 0.99, plot=TRUE)

Loading required package: TeachingSampling
Loading required package: dplyr

Attaching package: ‘dplyr’

The following objects are masked from ‘package:stats’:

    filter, lag

The following objects are masked from ‘package:base’:

    intersect, setdiff, setequal, union

Loading required package: magrittr
Loading required package: timeDate
With the parameters of this function: N = 10000 n =  400 Kurtosis =  0 DEFF =  1 conf = 0.95 . 
The estimated coefficient of variation is  6.929589 . 
The margin of error is 13.58174 . 
 
$cve
[1] 6.929589

$Margin_of_error
[1] 13.58174

With the parameters of this function: N = 10000 n =  400 Kurtosis =  1 DEFF =  2 conf = 0.99 . 
The estimated coefficient of variation is  12.0022 . 
The margin of error is 30.91562 . 
 
$cve
[1] 12.0022

$Margin_of_error
[1] 30.91562

With the parameters of this function: N = 10000 n =  400 Kurtosis =  2 DEFF =  2 conf = 0.99 . 
The estimated coefficient of variation is  13.85883 . 
The margin of error is 35.69798 . 
 
$cve
[1] 13.85883

$Margin_of_error
[1] 35.69798