ss4dmH {samplesize4surveys} | R Documentation |
The required sample size for testing a null hyphotesis for a single difference of proportions
Description
This function returns the minimum sample size required for testing a null hyphotesis regarding a single difference of proportions.
Usage
ss4dmH(
N,
mu1,
mu2,
sigma1,
sigma2,
D,
DEFF = 1,
conf = 0.95,
power = 0.8,
T = 0,
R = 1,
plot = FALSE
)
Arguments
N |
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. |
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. |
D |
The minimun effect to test. |
DEFF |
The design effect of the sample design. By default |
conf |
The statistical confidence. By default |
power |
The statistical power. By default |
T |
The overlap between waves. By default |
R |
The correlation between waves. By default |
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_1 - mu_2 = 0 \ \ \ \ vs. \ \ \ \ H_a: mu_1 - mu_2 = 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_1^2 + \sigma_2^2) * (1 - (T * R)) * DEFF
Author(s)
Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>
References
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas
See Also
Examples
ss4dmH(N = 100000, mu1=50, mu2=55, sigma1 = 10, sigma2 = 12, D=3)
ss4dmH(N = 100000, mu1=50, mu2=55, sigma1 = 10, sigma2 = 12, D=1, plot=TRUE)
ss4dmH(N = 100000, mu1=50, mu2=55, sigma1 = 10, sigma2 = 12, D=0.5, DEFF = 2, plot=TRUE)
ss4dmH(N = 100000, mu1=50, mu2=55, sigma1 = 10, sigma2 = 12, D=0.5, DEFF = 2, conf = 0.99,
power = 0.9, plot=TRUE)
#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)
N1 <- table(SPAM)[1]
N2 <- table(SPAM)[2]
N <- max(N1,N2)
BigLucy.yes <- subset(BigLucy, SPAM == 'yes')
BigLucy.no <- subset(BigLucy, SPAM == 'no')
mu1 <- mean(BigLucy.yes$Income)
mu2 <- mean(BigLucy.no$Income)
sigma1 <- sd(BigLucy.yes$Income)
sigma2 <- sd(BigLucy.no$Income)
# The minimum sample size for testing
# H_0: mu_1 - mu_2 = 0 vs. H_a: mu_1 - mu_2 = D = 3
D = 3
ss4dmH(N, mu1, mu2, sigma1, sigma2, D, DEFF = 2, plot=TRUE)
# The minimum sample size for testing
# H_0: mu_1 - mu_2 = 0 vs. H_a: mu_1 - mu_2 = D = 3
D = 3
ss4dmH(N, mu1, mu2, sigma1, sigma2, D, conf = 0.99, power = 0.9, DEFF = 3.45, plot=TRUE)