dub {PracTools}

Sample sizes for a double sampling design

Description

Compute samples sizes at each phase of a two-phase design where strata are created using the first phase.

Usage

dub(c1, c2, Ctot, Nh, Sh, Yh.bar)

Arguments

c1

cost per unit in phase-1

c2

cost per unit in phase-2

Ctot

Total variable cost

Nh

Vector of stratum population counts or proportions

Sh

Vector of stratum population standard deviations

Yh.bar

Vector of stratum population means

Details

Compute the first and second phase sample sizes for a double sampling design. A first phase sample is selected by simple random sampling (srs). Strata are formed based on information collected in the first phase. The Neyman allocation to strata of the second phase sample is computed ignoring costs. Optimal total sample sizes are computed for the first and second phases, given per-unit costs for the first and second phases and a fixed total budget for both phases combined.

Value

A list object with elements:

V1

Variance component associated with phase-1

V2

Variance component associated with phase-2

n1

Phase-1 sample size

n2

Total phase-2 sample across all strata

"n2/n1"

Fraction that phase-2 is of phase-1

ney.alloc

Vector of stratum sample sizes for phase-2 sample

Vopt

Variance of mean with the calculated phase-1 and phase-2 sample sizes

nsrs

Size of an srs that has cost Ctot, assuming each unit costs c2

Vsrs

Variance of mean in an srs of cost Ctot, assuming each unit costs c2

Vratio

Ratio of Vopt to Vsrs

Ctot

Input value of total cost

cost.chk

Computed value of phase-1 plus phase-2 sample with optimal sample sizes; should agree with Ctot

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Cochran W (1977, sect. 12.3) Sampling Techniques. New York: John Wiley & Sons, Inc.

Neyman J (1938) Contribution to the theory of sampling human populations. Journal of the American Statistical Association, 33(201), 101-116.

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 17.5.2). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

Examples

Wh <- rep(0.25,4)
Ph <- c(0.02,0.12,0.37,0.54)
Sh <- sqrt(Ph*(1-Ph))
c1 <- 10
c2 <- 50
Ctot <- 20000
dub(c1, c2, Ctot, Nh=Wh, Sh, Yh.bar=Ph)