The random utility model (RUM, McFadden and Richter (1990)) has been the standard tool to describe the behavior of a population of decision makers. RUM assumes that decision makers behave as if they maximize a rational preference over a choice set. This assumption may fail when consideration of all alternatives is costly. We provide a theoretical and statistical framework that unifies well‐known models of random (limited) consideration and generalizes them to allow for preference heterogeneity. We apply this methodology in a novel stochastic choice data set that we collected in a large‐scale online experiment. Our data set is unique since it exhibits both choice set and (attention) frame variation. We run a statistical survival race between competing models of random consideration and RUM. We find that RUM cannot explain the population behavior. In contrast, we cannot reject the hypothesis that decision makers behave according to the logit attention model (Brady and Rehbeck (2016)).