PracTools (version 1.4.3)

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)