# clusOpt2: Compute optimal sample sizes for a two-stage sample In PracTools: Tools for Designing and Weighting Survey Samples

 clusOpt2 R Documentation

## 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

clusOpt2(C1, C2, delta, unit.rv, k=1, CV0=NULL, tot.cost=NULL, cal.sw)


### Arguments

 C1 unit cost per primary sampling unit (PSU) C2 unit cost per element delta homogeneity measure δ unit.rv unit relvariance k ratio of B^2 + W^2 to unit relvariance CV0 target CV tot.cost total budget for variable costs cal.sw specify type of optimum: 1 = find optimal m.opt for fixed total budget; 2 = find optimal m.opt for target CV0

### 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 B^2 + W^2 to unit relvariance cost total budget for variable costs, C-C_{0} if cal.sw=1; or computed cost if cal.sw=2 m.opt optimum number of sample PSUs n.opt optimum number of sample elements per PSU CV computed CV if cal.sw=1; or target CV if cal.sw=2

### 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. (2018, sect. 9.3.1). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

clusOpt2fixedPSU, clusOpt3, clusOpt3fixedPSU

### Examples

    # optimum for a fixed total budget
clusOpt2(C1=750, C2=100, delta=0.05, unit.rv=1, k=1, tot.cost=100000, cal.sw=1)
# optimum for a target CV
clusOpt2(C1=750, C2=100, delta=0.01, unit.rv=1, k=1, CV0=0.05, cal.sw=2)


PracTools documentation built on Aug. 17, 2022, 5:06 p.m.