The fragility index is a clinically motivated metric designed to supplement the $p$ value during hypothesis testing. The measure relies on two pillars: selecting cases to have their outcome modified and modifying the outcomes. The measure is interesting but the case selection suffers from a drawback which can hamper its interpretation. This work presents the drawback and a method, the stochastic generalized fragility indices, designed to remedy it. Two examples concerning electoral outcomes and the causal effect of smoking cessation illustrate the method.

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