# 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

 1 2 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 <hugogutierrez at usantotomas.edu.co>

## References

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

ss4pH
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 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)