ss4S2: The required sample size for estimating a single variance
In psirusteam/samplesize4surveys: Sample Size Calculations for Complex Surveys

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

This function returns the minimum sample size required for estimating a single variance subjecto to predefined errors.

1	ss4S2(N, K = 0, DEFF = 1, conf = 0.95, cve = 0.05, me = 0.03, plot = FALSE)

`N`	The population size.
`K`	The population 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. By default `conf = 0.95`.
`cve`	The maximun coeficient of variation that can be allowed for the estimation.
`me`	The maximun margin of error that can be allowed for the estimation.
`plot`	Optionally plot the errors (cve and margin of error) against the sample size.

Note that the minimun sample size to achieve a particular relative margin of error \varepsilon is defined by:

n = \frac{n_0}{\frac{(N-1)^3}{N^2(N*K+2N+2)}+\frac{n_0}{N}}

Where

n_0=\frac{z^2_{1-\frac{α}{2}}*DEFF}{\varepsilon^2}

Also note that the minimun sample size to achieve a particular coefficient of variation cve is defined by:

n = \frac{N^2(N*K+2N+2)*DEFF}{cve^2*(N-1)^3+N(N*K+2N+2)*DEFF}

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

e4p

ss4S2(N = 10000, K = 0, cve = 0.05, me = 0.03)
ss4S2(N = 10000, K = 1, cve = 0.05, me = 0.03)
ss4S2(N = 10000, K = 1, cve = 0.05, me = 0.05, DEFF = 2)
ss4S2(N = 10000, K = 1, cve = 0.05, me = 0.03, plot = TRUE)

#############################
# Example with BigLucy data #
#############################

data(BigLucy)
attach(BigLucy)
N <- nrow(BigLucy)
K <- kurtosis(BigLucy$Income)
# The minimum sample size for simple random sampling
ss4S2(N, K, DEFF=1, conf=0.99, cve=0.03, me=0.1, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4S2(N, K, DEFF=3.45, conf=0.99, cve=0.03, me=0.1, plot=TRUE)