ss4dpH {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 proportion.
Usage
ss4dpH(
N,
P1,
P2,
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. |
P1 |
The value of the first estimated proportion. |
P2 |
The value of the second estimated proportion. |
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: P_1 - P_2 = 0 \ \ \ \ vs. \ \ \ \ H_a: P_1 - P_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 = (P1 * Q1 + P2 * Q2) * (1 - (T * R)) * DEFF
and Q_i=1-P_i
for i=1,2
.
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
ss4dpH(N = 100000, P1 = 0.5, P2 = 0.55, D=0.03)
ss4dpH(N = 100000, P1 = 0.5, P2 = 0.55, D=0.03, plot=TRUE)
ss4dpH(N = 100000, P1 = 0.5, P2 = 0.55, D=0.03, DEFF = 2, plot=TRUE)
ss4dpH(N = 100000, P1 = 0.5, P2 = 0.55, D=0.03, conf = 0.99, power = 0.9, DEFF = 2, plot=TRUE)
#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)
N1 <- table(SPAM)[1]
N2 <- table(SPAM)[2]
N <- max(N1,N2)
P1 <- prop.table(table(SPAM))[1]
P2 <- prop.table(table(SPAM))[2]
# The minimum sample size for testing
# H_0: P_1 - P_2 = 0 vs. H_a: P_1 - P_2 = D = 0.05
D = 0.05
ss4dpH(N, P1, P2, D, DEFF = 2, plot=TRUE)
# The minimum sample size for testing
# H_0: P - P_0 = 0 vs. H_a: P - P_0 = D = 0.02
D = 0.01
ss4dpH(N, P1, P2, D, conf = 0.99, power = 0.9, DEFF = 3.45, plot=TRUE)