samplesize4surveys (version 4.1.1)

ss4dpH: 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 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.

T

The overlap between waves. By default T = 0.

R

The correlation between waves. By default R = 1.

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 \(i=1,2\).

References

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

See Also

ss4pH

Examples

# NOT RUN {
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)
# }