PracTools (version 1.2.5)

CVcalc3: Coefficient of variation of an estimated total in a 3-stage sample

Description

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

Usage

CVcalc3(V=NULL, m=NULL , nbar=NULL, qbar=NULL, k1=1, k2=1, delta1=NULL, delta2=NULL,
            Bsq=NULL, Wsq=NULL, W2sq=NULL, W3sq=NULL)

Arguments

V

unit relvariance of analysis variable in the population

m

number of sample PSUs

nbar

number of sample secondary units per PSU

qbar

number of sample elements per SSU

k1

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

k2

ratio of \(W_{2}^{2} + W_{3}^{2}\) to \(V\). Default value is 1.

delta1

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

delta2

measure of homogeneity between SSUs within PSUs, equal to \(W_{2}^{2}/(W_{2}^{2} + W_{3}^{2})\)

Bsq

unit relvariance of PSU totals, equal to population variance of totals divided by \(\bar{t}_{U}^2\)

Wsq

within PSU relvariance of elements

W2sq

unit SSU relvariance

W3sq

unit element relvariance

Value

Value of the coefficient of variation of an estimated total

Details

CVcalc3 computes the coefficient of variation of an estimated total for a three-stage sample. PSUs can be selected either with varying probabilities and with replacement or with equal probabilities and with replacement. SSUs and elements within SSUs 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 SSUs is selected in each PSU and the same number of elements is selected within each sample SSU. See Sect. 9.2.4 of Valliant, Dever, and Kreuter (2018) 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. 9.2.4). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

CVcalc3

Examples

# NOT RUN {
CVcalc3(V=1, m=20 , nbar=5, qbar=10, delta1=0.02, delta2=0.10)
CVcalc3(V=1, m=20 , nbar=5, qbar=10, delta1=0.02, delta2=0.09)
CVcalc3(V=2, m=20 , nbar=5, qbar=10, k1=5, k2=10, Bsq=1, Wsq=9, W2sq=2 , W3sq=18 )
# }