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

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

`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.

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 β and confidence 1-α, is defined by:

n = \frac{S2^2}{\frac{D^2}{(z_{1-α} + z_{β})^2}\frac{(N-1)^3}{N^2(N*K+2N+2)}+\frac{S2^2}{N}}

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

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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)