ss4ddmH: The required sample size for testing a null hyphotesis for a...

In samplesize4surveys: Sample Size Calculations for Complex Surveys

Description

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

Usage

ss4ddmH(
  N,
  mu1,
  mu2,
  mu3,
  mu4,
  sigma1,
  sigma2,
  sigma3,
  sigma4,
  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.
mu3	The value of the estimated mean of the variable of interes for the third population.
mu4	The value of the estimated mean of the variable of interes for the fourth 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.
sigma3	The value of the estimated variance of the variable of interes for the third population.
sigma4	The value of the estimated mean of a variable of interes for the fourth population.
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: (mu_1 - mu_2) - (mu_3 - mu_4) = 0 \ \ \ \ vs. \ \ \ \ H_a: (mu_1 - mu_2) - (mu_3 - mu_4) = D \neq 0

Note that the minimun sample size, restricted to the predefined power β and confidence 1-α, is defined by:

n = \frac{S^2}{\frac{D^2}{(z_{1-α} + z_{β})^2}+\frac{S^2}{N}}

where S^2=(σ_1^2 + σ_2^2 + σ_3^2 + σ_4^2) * (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

ss4pH

Examples

ss4ddmH(N = 100000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, D=3)
ss4ddmH(N = 100000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, D=1, plot=TRUE)
ss4ddmH(N = 100000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, D=0.5, DEFF = 2, plot=TRUE)
ss4ddmH(N = 100000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, D=0.5, DEFF = 2, conf = 0.99, 
       power = 0.9, plot=TRUE)

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

BigLucyT0 <- BigLucyT0T1[Time == 0,]
BigLucyT1 <- BigLucyT0T1[Time == 1,]
N1 <- table(BigLucyT0$ISO)[1]
N2 <- table(BigLucyT0$ISO)[2]
N <- max(N1,N2)

BigLucyT0.yes <- subset(BigLucyT0, ISO == 'yes')
BigLucyT0.no <- subset(BigLucyT0, ISO == 'no')
BigLucyT1.yes <- subset(BigLucyT1, ISO == 'yes')
BigLucyT1.no <- subset(BigLucyT1, ISO == 'no')
mu1 <- mean(BigLucyT0.yes$Income)
mu2 <- mean(BigLucyT0.no$Income)
mu3 <- mean(BigLucyT1.yes$Income)
mu4 <- mean(BigLucyT1.no$Income)
sigma1 <- sd(BigLucyT0.yes$Income)
sigma2 <- sd(BigLucyT0.no$Income)
sigma3 <- sd(BigLucyT1.yes$Income)
sigma4 <- sd(BigLucyT1.no$Income)

# The minimum sample size for testing 
# H_0: (mu_1 - mu_2) - (mu_3 - mu_4) = 0   vs.   
# H_a: (mu_1 - mu_2) - (mu_3 - mu_4) = D = 3

ss4ddmH(N, mu1, mu2, mu3, mu4, sigma1, sigma2, sigma3, sigma4,
 D = 3, conf = 0.99, power = 0.9, DEFF = 3.45, plot=TRUE)

samplesize4surveys documentation built on Jan. 18, 2020, 1:11 a.m.