ss4dm {samplesize4surveys}

The required sample size for estimating a single difference of proportions

Description

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

Usage

ss4dm(
  N,
  mu1,
  mu2,
  sigma1,
  sigma2,
  DEFF = 1,
  conf = 0.95,
  cve = 0.05,
  rme = 0.03,
  T = 0,
  R = 1,
  plot = FALSE
)

Arguments

N

The maximun population size between the groups (strata) that we want to compare.

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.

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.

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.

rme

The maximun relative margin of error that can be allowed for the estimation.

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

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

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

Where

n_0=\frac{z^2_{1-\frac{alpha}{2}}S^2}{\varepsilon^2 (\mu_1 - \mu_2)^2}

and S^2=(\sigma_1^2 + \sigma_2^2) * (1 - (T * R)) * DEFF Also note that the minimun sample size to achieve a coefficient of variation cve is defined by:

n = \frac{S^2}{|\bar{y}_1-\bar{y}_2|^2 cve^2 + \frac{S^2}{N}}

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

e4p

Examples

ss4dm(N=100000, mu1=50, mu2=55, sigma1 = 10, sigma2 = 12, cve=0.05, rme=0.03)
ss4dm(N=100000, mu1=50, mu2=55, sigma1 = 10, sigma2 = 12, cve=0.05, rme=0.03, plot=TRUE)
ss4dm(N=100000, mu1=50, mu2=55, sigma1 = 10, sigma2 = 12, DEFF=3.45, conf=0.99, cve=0.03, 
     rme=0.03, plot=TRUE)

#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)

N1 <- table(SPAM)[1]
N2 <- table(SPAM)[2]
N <- max(N1,N2)

BigLucy.yes <- subset(BigLucy, SPAM == 'yes')
BigLucy.no <- subset(BigLucy, SPAM == 'no')
mu1 <- mean(BigLucy.yes$Income)
mu2 <- mean(BigLucy.no$Income)
sigma1 <- sd(BigLucy.yes$Income)
sigma2 <- sd(BigLucy.no$Income)

# The minimum sample size for simple random sampling
ss4dm(N, mu1, mu2, sigma1, sigma2, DEFF=1, conf=0.99, cve=0.03, rme=0.03, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4dm(N, mu1, mu2, sigma1, sigma2, DEFF=3.45, conf=0.99, cve=0.03, rme=0.03, plot=TRUE)