A recruitment method to obtain community samples of children for survey research in Switzerland

Appendix

The Bernese Sampling Plan

Let N be the size of the population (e.g. the number of children of ages 10–15 in the Canton of Zurich) and n be the target sample size (the number of children to be sampled). Assuming that a list of municipalities is available and for each municipality j the number of population members N _j is known. The goal of the Bernese Sampling Plan is to draw a sample such that the number of municipalities in the sample is limited or, more specifically, that a minimum number of at least k sample members is allotted to each municipality in the sample. In a simple random sample (SRS) the number of expected sample members in municipality j is equal to P × N _j, with p = n/N, which may reach the critical k in large municipalities. Hence, the Bernese Sampling Plan starts off by dividing the municipalities into two groups, large municipalities for which p × N _j ≥ k and small municipalities with p × N _j < k. Let N ^small denote the total size of the population living in the small municipalities. Then, in each of the large municipalities, an SRS of n _j = p × N _j subjects (with random rounding for non-integer n _j) can be drawn. Among the small municipalities, however, p/k × N ^small clusters of size k are selected by sampling municipalities proportional to size PPS and, within each sampled municipality, drawing an SRS of k subjects. As shown by Jann (2007), the depicted procedure is an EPSEM with an a priori sampling probability of p = n/N for each population member.