Using a traditional Ellsberg urn, we measure ambiguity attitudes in a large representative survey and investigate their effects on households' portfolio decisions, in particular the decision to participate in the stock market. Tractably measuring ambiguity attitudes of the general public is made possible by a simplification of the recently introduced source method. Besides the widely studied ambiguity aversion, we find a(mbiguity generated likelihood) insensitivity, a new component of ambiguity attitudes recently found in laboratory studies, and now confirmed in a representative sample. A-insensitivity means that people do not sufficiently discriminate between different levels of likelihood. Contrary to prior expectation, ambiguity aversion is not associated with stock market participation, posing a challenge to modern ambiguity theories. A-insensitivity is negatively associated with stock market participation and with private business ownership. Using prospect theory and simulations, we explain our findings by loss aversion and reference dependence in ambiguity, factors that cannot be measured using traditional Ellsberg urns. Our study shows the importance of these factors for studying stock market participation and, more generally, for studying decisions that involve possible losses.