Most models of ambiguity aversion satisfy the Anscombe-Aumann monotonicity axiom. Monotonicity implies a weak form of separability of preferences across events that occur with unknown probability. We construct a test of weak separability by modifying the Allais paradox, adapting it to the Anscombe-Aumann framework. Three experimental studies are conducted. Study 1 finds frequent, systematic violations of weak separability in the lab. These findings replicate in study 2, where we employ a subject pool of online workers and use a natural rather than an artificial source of uncertainty. Investigating a potential explanation of the violations, study 3 suggests that the certainty effect plays a major role.