Abstract:
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Sample size is a necessary feature of quantitative studies. Typically determined by available funding, sample size defines the level of precision of the resulting statistical inference. In contrast to most sample surveys, respondent-driven sampling (RDS) studies do not start with a sample of a fixed size drawn from a sampling frame; rather, they depend on recruitment chains branching from a small number of "seeds" with whom RDS recruitment begins. Although researchers may have a target sample size when they start the study, the peer recruitment of RDS brings uncertainty to the resulting sample size, essentially making it a random variable over which researchers have little control. This study aims to calculate distributions of sample sizes by modeling individual recruitment through a Bernoulli distribution and decomposing the size recursively, resulting in an exhaustive enumeration of all possible scenarios of peer recruitment. To expedite the computational process, we propose an approximation algorithm which estimates the sample size distribution by trimming off unlikely scenarios with negligibly small probabilities of occurrence.
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