samplesize4surveys (version 4.1.1)

ss4ddpH: The required sample size for testing a null hyphotesis for a double difference of proportions

Description

This function returns the minimum sample size required for testing a null hyphotesis regarding a double difference of proportion.

Usage

ss4ddpH(
  N,
  P1,
  P2,
  P3,
  P4,
  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.

P3

The value of the thrid estimated proportion.

P4

The value of the fourth 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: $$H_0: (P_1 - P_2) - (P_3 - P_4) = 0 \ \ \ \ vs. \ \ \ \ H_a: (P_1 - P_2) - (P_3 - P_4) = D \neq 0 $$ 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 \(S^2 = (P1 * Q1 + P2 * Q2 + P3 * Q3 + P4 * Q4) * (1 - (T * R)) * DEFF\) and \(Q_i=1-P_i\) for \(i=1,2, 3, 4\).

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 {
ss4ddpH(N = 100000, P1 = 0.5, P2 = 0.5, P3 = 0.5, P4 = 0.5, D=0.03)
ss4ddpH(N = 100000, P1 = 0.5, P2 = 0.5, P3 = 0.5, P4 = 0.5, D=0.03, plot=TRUE)
ss4ddpH(N = 100000, P1 = 0.5, P2 = 0.5, P3 = 0.5, P4 = 0.5, D=0.03, DEFF = 2, plot=TRUE)
ss4ddpH(N = 100000, P1 = 0.5, P2 = 0.5, P3 = 0.5, P4 = 0.5, 
D=0.03, conf = 0.99, power = 0.9, DEFF = 2, plot=TRUE)

#################################
# Example with BigLucyT0T1 data #
#################################
data(BigLucyT0T1)
attach(BigLucyT0T1)

BigLucyT0 <- BigLucyT0T1[Time == 0,]
BigLucyT1 <- BigLucyT0T1[Time == 1,]
N1 <- table(BigLucyT0$SPAM)[1]
N2 <- table(BigLucyT1$SPAM)[1]
N <- max(N1,N2)
P1 <- prop.table(table(BigLucyT0$ISO))[1]
P2 <- prop.table(table(BigLucyT1$ISO))[1]
P3 <- prop.table(table(BigLucyT0$ISO))[2]
P4 <- prop.table(table(BigLucyT1$ISO))[2]
# The minimum sample size for simple random sampling
ss4ddpH(N, P1, P2, P3, P4, D = 0.05, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4ddpH(N, P1, P2, P3, P4, D = 0.05, DEFF = 2, T = 0.5, R = 0.5, conf=0.95, plot=TRUE)
# }