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

This function returns the minimum sample size required for estimating a single mean subjec to predefined errors.

1 2 |

`N` |
The population size. |

`mu` |
The value of the estimated mean of a variable of interest. |

`sigma` |
The value of the estimated standard deviation of a variable of interest. |

`DEFF` |
The design effect of the sample design. By default |

`conf` |
The statistical confidence. By default conf = 0.95. By default |

`cve` |
The maximun coeficient of variation that can be allowed for the estimation. |

`rme` |
The maximun relative margin of error that can be allowed for the estimation. |

`plot` |
Optionally plot the errors (cve and margin of error) against the sample size. |

Note that the minimun sample size to achieve a relative margin of error *\varepsilon* is defined by:

*n = \frac{n_0}{1+\frac{n_0}{N}}*

Where

*n_0=\frac{z^2_{1-\frac{alpha}{2}}S^2}{\varepsilon^2 μ^2}*

and

*S^2=σ^2 DEFF*

Also note that the minimun sample size to achieve a coefficient of variation *cve* is defined by:

*n = \frac{S^2}{\bar{y}_U^2 cve^2 + \frac{S^2}{N}}*

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 | ```
ss4m(N=10000, mu=10, sigma=2, cve=0.05, rme=0.05)
ss4m(N=10000, mu=10, sigma=2, cve=0.05, rme=0.03, plot=TRUE)
ss4m(N=10000, mu=10, sigma=2, DEFF=3.45, cve=0.05, rme=0.03, plot=TRUE)
##########################
# Example with Lucy data #
##########################
data(Lucy)
attach(Lucy)
N <- nrow(Lucy)
mu <- mean(Income)
sigma <- sd(Income)
# The minimum sample size for simple random sampling
ss4m(N, mu, sigma, DEFF=1, conf=0.95, cve=0.03, rme=0.03, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4m(N, mu, sigma, DEFF=3.45, conf=0.95, cve=0.03, rme=0.03, plot=TRUE)
``` |

```
Loading required package: TeachingSampling
Loading required package: timeDate
With the parameters of this function: N = 10000 mu = 10 sigma = 2 DEFF = 1 conf = 0.95 .
The estimated sample size to obatin a maximun coefficient of variation of 5 % is n= 16 .
The estimated sample size to obatin a maximun margin of error of 5 % is n= 62 .
$n.cve
[1] 16
$n.rme
[1] 62
With the parameters of this function: N = 10000 mu = 10 sigma = 2 DEFF = 1 conf = 0.95 .
The estimated sample size to obatin a maximun coefficient of variation of 5 % is n= 16 .
The estimated sample size to obatin a maximun margin of error of 3 % is n= 168 .
$n.cve
[1] 16
$n.rme
[1] 168
With the parameters of this function: N = 10000 mu = 10 sigma = 2 DEFF = 3.45 conf = 0.95 .
The estimated sample size to obatin a maximun coefficient of variation of 5 % is n= 55 .
The estimated sample size to obatin a maximun margin of error of 3 % is n= 557 .
$n.cve
[1] 55
$n.rme
[1] 557
With the parameters of this function: N = 2396 mu = 432.0605 sigma = 266.9792 DEFF = 1 conf = 0.95 .
The estimated sample size to obatin a maximun coefficient of variation of 3 % is n= 361 .
The estimated sample size to obatin a maximun margin of error of 3 % is n= 970 .
$n.cve
[1] 361
$n.rme
[1] 970
With the parameters of this function: N = 2396 mu = 432.0605 sigma = 266.9792 DEFF = 3.45 conf = 0.95 .
The estimated sample size to obatin a maximun coefficient of variation of 3 % is n= 909 .
The estimated sample size to obatin a maximun margin of error of 3 % is n= 1681 .
$n.cve
[1] 909
$n.rme
[1] 1681
```

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