ss4mH: The required sample size for testing a null hyphotesis for a single mean

Description

This function returns the minimum sample size required for testing a null hyphotesis regarding a single mean

Usage

ss4mH(N, mu, mu0, sigma, DEFF = 1, conf = 0.95, power = 0.8, plot = FALSE)

Arguments

The population size.

The population mean of the variable of interest.

mu0

The value to test for the single mean.

sigma

The population variance of the variable of interest.

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.

power

The statistical power. By default power = 0.80.

plot

Optionally plot the effect against the sample size.

Details

We assume that it is of interest to test the following set of hyphotesis: $$H_0: mu - mu_0 = 0 \ \ \ \ vs. \ \ \ \ H_a: mu - mu_0 = D \neq 0 $$ Note that the minimun sample size, restricted to the predefined power $\beta$ and confidence $1-\alpha$, is defined by: $$n = \frac{S^2}{\frac{D^2}{(z_{1-\alpha} + z_{\beta})^2}+\frac{S^2}{N}}$$ Where $S^2=\sigma^2 * DEFF$ and $\sigma^2$ is the population variance of the varible of interest.

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 {
ss4mH(N = 10000, mu = 500, mu0 = 505, sigma = 100)
ss4mH(N = 10000, mu = 500, mu0 = 505, sigma = 100, plot=TRUE)
ss4mH(N = 10000, mu = 500, mu0 = 505, sigma = 100, DEFF = 2, plot=TRUE)
ss4mH(N = 10000, mu = 500, mu0 = 505, sigma = 100, conf = 0.99, power = 0.9, DEFF = 2, plot=TRUE)

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

N <- nrow(BigLucy)
mu <- mean(Income)
sigma <- sd(Income)

# The minimum sample size for testing 
# H_0: mu - mu_0 = 0   vs.   H_a: mu - mu_0 = D = 15
D = 15 
mu0 = mu - D 
ss4mH(N, mu, mu0, sigma, conf = 0.99, power = 0.9, DEFF = 2, plot=TRUE)

# The minimum sample size for testing 
# H_0: mu - mu_0 = 0   vs.   H_a: mu - mu_0 = D = 32
D = 32
mu0 = mu - D 
ss4mH(N, mu, mu0, sigma, conf = 0.99, power = 0.9, DEFF = 3.45, plot=TRUE)
# }