samplesize4surveys (version 4.1.1)

b4ddm: Statistical power for a hyphotesis testing on a double difference of means.

Description

This function computes the power for a (right tail) test of double difference of means

Usage

b4ddm(
  N,
  n,
  mu1,
  mu2,
  mu3,
  mu4,
  sigma1,
  sigma2,
  sigma3,
  sigma4,
  D,
  DEFF = 1,
  conf = 0.95,
  T = 0,
  R = 1,
  plot = FALSE
)

Arguments

N

The population size.

n

The sample size.

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 value of the null effect.

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.

T

The overlap between waves. By default T = 0.

R

The correlation between waves. By default R = 1.

plot

Optionally plot the power achieved for an specific sample size.

Value

The power of the test.

Details

We note that the power is defined as: $$1-\Phi(Z_{1-\alpha} - \frac{(D - [(\mu_1 - \mu_2) - (\mu_3 - \mu_4)])}{\sqrt{\frac{1}{n}(1-\frac{n}{N})S^2}})$$ where $$S^2 = DEFF (\sigma_1^2 + \sigma_2^2 + \sigma_3^2 + \sigma_4^2$$

References

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

See Also

ss4p

Examples

# NOT RUN {
b4ddm(N = 100000, n = 400, mu1=50, mu2=55, mu3=50, mu4=55, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, D = 7)
b4ddm(N = 100000, n = 400, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, D = 12, plot = TRUE)
b4ddm(N = 100000, n = 4000, mu1=50, mu2=55, mu3=50, mu4=65, 
sigma1 = 10, sigma2 = 12, sigma3 = 10, sigma4 = 12, D = 11, DEFF = 2, conf = 0.99, plot = TRUE)
# }