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Question answering (QA) models are shown to be insensitive to large perturbations to inputs; that is, they make correct and confident predictions even when given largely perturbed inputs from which humans can not correctly derive answers. In addition, QA models fail to generalize to other domains and adversarial test sets, while humans maintain high accuracy. Based on these observations, we assume that QA models do not use intended features necessary for human reading but rely on spurious features, causing the lack of generalization ability. Therefore, we attempt to answer the question: If the overconfident predictions of QA models for various types of perturbations are penalized, will the out-of-distribution (OOD) generalization be improved? To prevent models from making confident predictions on perturbed inputs, we first follow existing studies and maximize the entropy of the output probability for perturbed inputs. However, we find that QA models trained to be sensitive to a certain perturbation type are often insensitive to unseen types of perturbations. Thus, we simultaneously maximize the entropy for the four perturbation types (i.e., word- and sentence-level shuffling and deletion) to further close the gap between models and humans. Contrary to our expectations, although models become sensitive to the four types of perturbations, we find that the OOD generalization is not improved. Moreover, the OOD generalization is sometimes degraded after entropy maximization. Making unconfident predictions on largely perturbed inputs per se may be beneficial to gaining human trust. However, our negative results suggest that researchers should pay attention to the side effect of entropy maximization.