ss4ddm: The required sample size for estimating a double difference of means

Description

This function returns the minimum sample size required for estimating a double difference of means subjecto to predefined errors.

Usage

ss4ddm(
  N,
  mu1,
  mu2,
  mu3,
  mu4,
  sigma1,
  sigma2,
  sigma3,
  sigma4,
  DEFF = 1,
  conf = 0.95,
  cve = 0.05,
  rme = 0.03,
  T = 0,
  R = 1,
  plot = FALSE
)

Arguments

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.

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. 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.

The overlap between waves. By default T = 0.

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 $$n_0=\frac{z^2_{1-\frac{alpha}{2}}S^2}{\varepsilon^2 \mu^2}$$ and $S^2=(\sigma_1^2 + \sigma_2^2 + \sigma_3^2 + \sigma_4^2) * (1 - (T * R)) * DEFF$ Also note that the minimun sample size to achieve a coefficient of variation $cve$ is defined by: $$n = \frac{S^2}{|(\bar{y}_1-\bar{y}_2) - (\bar{y}_3-\bar{y}_4) |^2 cve^2 + \frac{S^2}{N}}$$

References

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

Examples

Run this code

# NOT RUN {
ss4ddm(N=100000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, cve=0.05, rme=0.03)
ss4ddm(N=100000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, cve=0.05, rme=0.03, plot=TRUE)
ss4ddm(N=100000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, DEFF=3.45, conf=0.99, cve=0.03, 
     rme=0.03, plot=TRUE)

#############################
# Example with BigLucy data #
#############################
data(BigLucyT0T1)
attach(BigLucyT0T1)

BigLucyT0 <- BigLucyT0T1[Time == 0,]
BigLucyT1 <- BigLucyT0T1[Time == 1,]
N1 <- table(BigLucyT0$ISO)[1]
N2 <- table(BigLucyT0$ISO)[2]
N <- max(N1,N2)

BigLucyT0.yes <- subset(BigLucyT0, ISO == "yes")
BigLucyT0.no <- subset(BigLucyT0, ISO == "no")
BigLucyT1.yes <- subset(BigLucyT1, ISO == "yes")
BigLucyT1.no <- subset(BigLucyT1, ISO == "no")
mu1 <- mean(BigLucyT0.yes$Income)
mu2 <- mean(BigLucyT0.no$Income)
mu3 <- mean(BigLucyT1.yes$Income)
mu4 <- mean(BigLucyT1.no$Income)
sigma1 <- sd(BigLucyT0.yes$Income)
sigma2 <- sd(BigLucyT0.no$Income)
sigma3 <- sd(BigLucyT1.yes$Income)
sigma4 <- sd(BigLucyT1.no$Income)

# The minimum sample size for simple random sampling
ss4ddm(N, mu1, mu2, mu3, mu4, sigma1, sigma2, sigma3, sigma4, 
DEFF=1, conf=0.95, cve=0.001, rme=0.001, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4ddm(N, mu1, mu2, mu3, mu4, sigma1, sigma2, sigma3, sigma4, 
DEFF=3.45, conf=0.99, cve=0.03, rme=0.03, plot=TRUE)
# }