ss4p: The required sample size for estimating a single proportion
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 proportion subjecto to predefined errors.

1	ss4p(N, P, DEFF = 1, conf = 0.95, error = "cve", delta = 0.03, plot = FALSE)

`N`	The population size.
`P`	The value of the 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. By default `conf = 0.95`.
`error`	The type of error you want to minimize.
`delta`	The magnitude of the error you want to minimize.
`plot`	Optionally plot the errors (cve and margin of error) against the sample size.

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

n = \frac{n_0}{1+\frac{n_0}{N}}

Where

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

and

S^2=P(1-P)DEFF

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

n = \frac{S^2}{P^2cve^2+\frac{S^2}{N}}

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

ss4p(N=10000, P=0.05, error = "cve", delta=0.05, DEFF = 1, conf = 0.95, plot=TRUE)
ss4p(N=10000, P=0.05, error = "me", delta=0.05, DEFF = 1, conf = 0.95, plot=TRUE)
ss4p(N=10000, P=0.5, error = "rme", delta=0.05, DEFF = 1, conf = 0.95, plot=TRUE)

##########################
# Example with Lucy data #
##########################

data(Lucy)
attach(Lucy)
N <- nrow(Lucy)
P <- prop.table(table(SPAM))[1]
# The minimum sample size for simple random sampling
ss4p(N, P, DEFF=3.45, conf=0.95, error = "cve", delta = 0.03, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4p(N, P, DEFF=3.45, conf=0.95, error = "rme", delta = 0.03, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4p(N, P, DEFF=3.45, conf=0.95, error = "me", delta = 0.03, plot=TRUE)