# b4dm: Statistical power for a hyphotesis testing on a difference of... In samplesize4surveys: Sample Size Calculations for Complex Surveys

## Description

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

## Usage

 1 2 b4dm(N, n, mu1, mu2, sigma1, sigma2, D, DEFF = 1, conf = 0.95, 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. 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. 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. 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))}{√{\frac{1}{n}(1-\frac{n}{N})S^2}})

where

S^2 = DEFF (σ_1^2 + σ_2^2

## Value

The power of the test.

## Author(s)

Hugo Andres Gutierrez Rojas <hugogutierrez at usantotomas.edu.co>

## References

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

ss4p
 1 2 3 4 b4dm(N = 100000, n = 400, mu1 = 5, mu2 = 5, sigma1 = 10, sigma2 = 15, D = 5) b4dm(N = 100000, n = 400, mu1 = 5, mu2 = 5, sigma1 = 10, sigma2 = 15, D = 0.03, plot = TRUE) b4dm(N = 100000, n = 4000, mu1 = 5, mu2 = 5, sigma1 = 10, sigma2 = 15, D = 0.05, DEFF = 2, conf = 0.99, plot = TRUE)