# clusOpt3: Compute optimal sample sizes for a three-stage sample In PracTools: Tools for Designing and Weighting Survey Samples

## Description

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

## Usage

 1 clusOpt3(unit.cost, delta1, delta2, unit.rv, k1=1, k2=1, CV0=NULL, tot.cost=NULL, cal.sw) 

## Arguments

 unit.cost vector with three components for unit costs: C1 = unit cost per primary sampling unit (PSU); C2 = unit cost per secondary sampling unit (SSU); C3 = unit cost per element delta1 homogeneity measure among elements within PSUs delta2 homogeneity measure among elements within SSUs unit.rv population unit relvariance k1 ratio of B^2 + W^2 to the population unit relvariance k2 ratio of W_{2}^2 + W_{3}^2 to the population 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

clusOpt3 will compute m_{opt}, \bar{n}_{opt}, and \bar{\bar{q}}_{opt} for a three-stage sample which uses simple random sampling at each stage or ppswr at the first stage and srs at the second and third stages.

## Value

List with values:

 C1 unit cost per PSU C2 unit cost per SSU C3 unit cost per element delta1 homogeneity measure among elements within PSUs delta2 homogeneity measure among elements within SSUs unit relvar unit relvariance k1 ratio of B^2 + W^2 to the population unit relvariance k2 ratio of W_{2}^2 + W_{3}^2 to the population unit relvariance cost total budget for variable costs if cal.sw=1; or computed cost if cal.sw=2 m.opt optimum number of sample PSUs n.opt optimum number of sample SSUs per PSU q.opt optimum number of sample elements per SSU CV achieved 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, p. 225). Sample Survey Methods and Theory, Vol.II. John Wiley & Sons.

Valliant, R., Dever, J., Kreuter, F. (2013, sect. 9.3.2). Practical Tools for Designing and Weighting Survey Samples. New York: Springer.

clusOpt2, clusOpt2fixedPSU, clusOpt3fixedPSU
 1 2 3 4 5 6  # optima for a fixed total budget clusOpt3(unit.cost=c(500, 100, 120), delta1=0.01, delta2=0.10, unit.rv=1, k1=1, k2=1, tot.cost=100000,cal.sw=1) # optima for a target CV clusOpt3(unit.cost=c(500, 100, 120), delta1=0.01, delta2=0.10, unit.rv=1, k1=1, k2=1, CV0=0.01,cal.sw=2)