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

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

`N`	The population size.
`mu`	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.

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 β and confidence 1-α, is defined by:

n = \frac{S^2}{\frac{D^2}{(z_{1-α} + z_{β})^2}+\frac{S^2}{N}}

Where S^2=σ^2 * DEFF and σ^2 is the population variance of the varible of interest.

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

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)