# 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

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

### 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, equal to population variance of totals divided by \bar{t}_{U}^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 Wsq within PSU relvariance, equal to average element population variance divided by \bar{y}_{U}^2

### 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.

### 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. 9.2.1). Practical Tools for Designing and Weighting Survey Samples. New York: Springer.

CVcalc3
 1 2 3 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)