# CVcalc3: Coefficient of variation of an estimated total in a 3-stage... In PracTools: Tools for Designing and Weighting Survey Samples

## 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

 1 2 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) if PSUs are selected by simple random sampling; or, equal to S_{U1(pwr)}^2 divided by t_{U}^2 if PSUs are selected by ppswr 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

## 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.

## Value

Value of the coefficient of variation of an estimated total

## Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

## 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. (2013, sect. 9.2.4). Practical Tools for Designing and Weighting Survey Samples. New York: Springer.

CVcalc3
 1 2 3 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 )