Description Usage Arguments Details Author(s) References See Also Examples

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

1 2 |

`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 |

`conf` |
The statistical confidence. By default |

`power` |
The statistical power. By default |

`T` |
The overlap between waves. By default |

`R` |
The correlation between waves. By default |

`plot` |
Optionally plot the effect against the sample size. |

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*

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

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

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)
``` |

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