The Role of Exchangeability in Sequential Updating of Findings from Small Studies and The Challenges of Identifying Exchangeable Data sets

This chapter discusses the notion of exchangeability and how it relates to Bayesian analyses and sequential accumulation of scientific knowledge. We illustrate an example of two small exchangeable data sets that when synthesized yield a more precise interval for the effect of interest, and we demonstrate that establishing exchangeability is challenging, and that exchangeable data sets are rare in the social sciences. The chapter concludes with suggestions for calibrating nonexchangeable data sets in order to use them in the sequential updating of findings from related studies.