The combined effects of multiple predators often cannot be predicted from their independent effects. Emergent multiple predator effects (MPEs) include risk enhancement, where combined predators kill more prey than predicted by their individual effects, and risk reduction, where fewer prey are killed than predicted. Current methods for detecting MPEs are biased because they assume linear functional responses and/or no prey depletion. As a result, past studies overestimated the occurrence of risk enhancement for additive designs, and tended to overestimate the occurrence of risk reduction for substitutive designs. Characterising the predators' functional responses and accounting for prey depletion reduces biases in detection, estimation, interpretation and generalisation of the emergent effects of predator diversity on prey survival. These findings have implications beyond MPE's and should be considered in all studies aimed at understanding how multiple factors combine when demographic rates are density dependent.