samplesize4surveys (version 4.1.1)

ss4S2H: The required sample size for testing a null hyphotesis for a single variance

Description

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

Usage

ss4S2H(N, S2, S20, K = 0, DEFF = 1, conf = 0.95, power = 0.8, plot = FALSE)

Arguments

N

The population size.

S2

The value of the estimated variance

S20

The value to test for the single variance

K

The excess kurtosis of the variable in the 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.

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: $$H_0: P - P_0 = 0 \ \ \ \ vs. \ \ \ \ H_a: P - P_0 = D > 0 $$ Note that the minimun sample size, restricted to the predefined power \(\beta\) and confidence \(1-\alpha\), is defined by: $$n = \frac{S2^2}{\frac{D^2}{(z_{1-\alpha} + z_{\beta})^2}\frac{(N-1)^3}{N^2(N*K+2N+2)}+\frac{S2^2}{N}}$$

References

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

See Also

e4p

Examples

# NOT RUN {
ss4S2H(N = 10000, S2 = 120, S20 = 110, K = 0)
ss4S2H(N = 10000, S2 = 120, S20 = 110, K = 2, DEFF = 2, power = 0.9)
ss4S2H(N = 10000, S2 = 120, S20 = 110, K = 2, DEFF = 2, power = 0.8, plot = TRUE)

#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)
N <- nrow(BigLucy)
S2 <- var(BigLucy$Income)

# The minimum sample size for testing 
# H_0: S2 - S2_0 = 0   vs.   H_a: S2 - S2_0 = D = 8000
D = 8000 
S20 = S2 - D 
K <- kurtosis(BigLucy$Income)
ss4S2H(N, S2, S20, K, DEFF=1, conf = 0.99, power = 0.8, plot=TRUE)
# }