b4ddm: Statistical power for a hyphotesis testing on a double...

In samplesize4surveys: Sample Size Calculations for Complex Surveys

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.

Details

We note that the power is defined as:

1-Φ(Z_{1-α} - \frac{(D - [(μ_1 - μ_2) - (μ_3 - μ_4)])}{√{\frac{1}{n}(1-\frac{n}{N})S^2}})

where

S^2 = DEFF (σ_1^2 + σ_2^2 + σ_3^2 + σ_4^2

Value

The power of the test.

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

ss4p

Examples

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)

Example output

Loading required package: TeachingSampling
Loading required package: timeDate
With the parameters of this function: N = 1e+05 n =  400 mu1 = mu1 = 50 mu2 = 55 mu3 = 50 mu4 = 55 sigma1 = 10 sigma2 = 12 sigma3 = 10 sigma4 = D = 7 DEFF =  1 conf = 0.95 . 
The estimated power of the test is  99.99987 . 
 
$Power
[1] 99.99987

With the parameters of this function: N = 1e+05 n =  400 mu1 = mu1 = 50 mu2 = 55 mu3 = 50 mu4 = 65 sigma1 = 10 sigma2 = 12 sigma3 = 10 sigma4 = D = 12 DEFF =  1 conf = 0.95 . 
The estimated power of the test is  56.72958 . 
 
$Power
[1] 56.72958

With the parameters of this function: N = 1e+05 n =  4000 mu1 = mu1 = 50 mu2 = 55 mu3 = 50 mu4 = 65 sigma1 = 10 sigma2 = 12 sigma3 = 10 sigma4 = D = 11 DEFF =  2 conf = 0.99 . 
The estimated power of the test is  39.73696 . 
 
$Power
[1] 39.73696

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