PracTools (version 1.6)

CVcalc2: Coefficient of variation of an estimated total in a 2-stage sample

Description

Compute the coefficient of variation of an estimated total in a two-stage design. Primary sampling units (PSUs) can be selected either with probability proportional to size (pps) or with equal probability. Elements are selected via simple random sampling (srs).

Usage

CVcalc2(V=NULL, m=NULL , nbar=NULL, k=1, delta=NULL, Bsq=NULL, Wsq=NULL)

Value

Value of the coefficient of variation of an estimated total

Arguments

V

unit relvariance of analysis variable in the population

m

number of sample PSUs

nbar

number of sample elements per PSU

k

ratio of \(B^2 + W^2\) to \(V\). Default value is 1.

delta

measure of homogeneity equal to \(B^2/(B^2 + W^2)\)

Bsq

unit relvariance of PSU totals

Wsq

within PSU relvariance

Author

Richard Valliant, Jill A. Dever, Frauke Kreuter

Details

CVcalc2 computes the coefficient of variation of an estimated total for a two-stage sample. PSUs can be selected either with varying probabilities and with replacement or with equal probabilities and with replacement. Elements within PSUs are selected by simple random sampling. The \(CV\) formula is appropriate for approximating the relvariance of the probability-with-replacement (pwr)-estimator of a total when the same number of elements is selected within each sample PSU. See Sections 9.2.1--9.2.3 of Valliant, Dever, and Kreuter (2013) for details of formulas.

References

Cochran, W.G. (1977, pp.308-310). Sampling Techniques. New York: John Wiley & Sons.

Saerndal, C.E., Swensson, B., and Wretman, J. (1992). Model Assisted Survey Sampling. New York: Springer.

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 9.2.1). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

CVcalc3

Examples

CVcalc2(V=1, m=20 , nbar=5, k=1, delta=0.05)
CVcalc2(V=10, m=20 , nbar=5, k=1, delta=0.5)
CVcalc2(V=2.5, m=20 , nbar=5, k=2, Bsq=1, Wsq=4)