Approximations to b* in the prediction of design effects due to clustering

Kish's well-known expression for the design effect due to clustering is often used to inform sample design, using an approximation such as b_bar in place of b. If the design involves either weighting or variation in cluster sample sizes, this can be a poor approximation. In this article we discuss the sensitivity of the approximation to departures from the implicit assumptions and propose an alternative approximation.