How These Estimates Were Obtained
Two separate sampling strategies were used in the study to determine the number of jazz musicians in each community. The first involved taking a sample of musicians belonging to the American Federation of Musicians (AFM) and determining what percentage of union musicians were jazz artists. The second employed an innovative sampling strategy called Respondent-Driven Sampling (RDS), which used the musicians themselves as "recruiters" of additional participants for the study, and then determining what percentage of the recruited study participants were union members.
With those two pieces of information -- the percentage of union members in the AFM sample who are jazz musicians and the percentage of musicians in the RDS sample who are union members -- it is possible to estimate the total population of jazz musicians in a particular community. This method of estimating the size of hard-to-reach populations, such as jazz musicians, is called "capture-recapture," based on the fact that two complementary sampling strategies are being used to identify (or "capture") union musicians, one a sample of union members and the other a sample of jazz musicians.
The population estimates were further refined by taking into account differences in the sizes of the "networks" to which union and non-union musicians belong. In New York, for example, union musicians are likely to belong to larger networks of jazz musicians than are non-union musicians. That is, they tend to have more ties to other jazz musicians than do non-union musicians. The larger the size of a particular musician's network, the more likely that person is to be recruited to the study, which introduces a bias into the population estimate if it is not controlled for by proportionately weighting the data. Sufficient information on network sizes was gathered in both New York and San Francisco to allow such weights to be assigned to the data. The relatively smaller size of the New Orleans RDS sample, however, was insufficient to allow reliable weights to be calculated, so the population estimate for New Orleans is not quite as precise as the other two