# Compute optimal sample sizes for a two-stage sample

### Description

Compute the sample sizes that minimize the variance of the *pwr*-estimator of a total in a two-stage sample.

### Usage

1 |

### Arguments

`C1` |
unit cost per primary sampling unit (PSU) |

`C2` |
unit cost per element |

`delta` |
homogeneity measure |

`unit.rv` |
unit relvariance |

`k` |
ratio of |

`CV0` |
target CV |

`tot.cost` |
total budget for variable costs |

`cal.sw` |
specify type of optimum:
1 = find optimal |

### Details

`clusOpt2`

will compute *m_{opt}* and *\bar{n}_{opt}* for a two-stage sample
which uses simple random sampling at each stage or *ppswr* at the first stage and *srs* at the second.

### Value

List with values:

`C1` |
unit cost per PSU |

`C2` |
unit cost per element |

`delta` |
homogeneity measure |

`unit relvar` |
unit relvariance |

`k` |
ratio of |

`cost` |
total budget for variable costs, |

`m.opt` |
optimum number of sample PSUs |

`n.opt` |
optimum number of sample elements per PSU |

`CV` |
computed CV if |

### Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

### References

Hansen,M.H., Hurwitz,W.N., and Madow,W.G. (1953, chap. 6, sect. 16). *Sample Survey Methods and Theory*, Vol.I. John Wiley & Sons.

Valliant, R., Dever, J., Kreuter, F. (2013, sect. 9.3.1). *Practical Tools for Designing and Weighting Survey Samples*. New York: Springer.

### See Also

`clusOpt2fixedPSU`

, `clusOpt3`

, `clusOpt3fixedPSU`

### Examples

1 2 3 4 |