A wave of recent many-analysts studies struggle to explain the “hidden uncertainty” in their results. We propose global sensitivity analysis (GSA) as a method to better see and understand this uncertainty. By comprehensively exploring the space of all possible model options and pinpointing how much uncertainty in the results is due to single or to high-order model specifications, GSA will improve current many-analysts study methods. In particular, it allows for an explained-variance feasibility calculation to determine if it is worth running a costly many-analysts study in the first place. We demonstrate the effectiveness of GSA by replicating the many-analysts study by Breznau, Rinke and Wuttke et al., which hoped to shed light on how immigration impacts public preferences for social policy but left 95% of the variance in the results unexplained.