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Conducting a randomization test is a common method for testing causal null hypotheses in randomized experiments. The popularity of randomization tests is largely because their statistical validity only depends on the randomization design, and no distributional or modeling assumption on the outcome variable is needed. However, randomization tests may still suffer from other sources of bias, among which outcome misclassification is a significant one. We propose a model-free and finite-population sensitivity analysis approach for binary outcome misclassification in randomization tests. A central quantity in our framework is ``warning accuracy," defined as the threshold such that a randomization test result based on the measured outcomes may differ from that based on the true outcomes if the outcome measurement accuracy did not surpass that threshold. We show how learning the warning accuracy and related concepts can amplify analyses of randomization tests subject to outcome misclassification without adding additional assumptions. We show that the warning accuracy can be computed efficiently for large data sets by adaptively reformulating a large-scale integer program with respect to the randomization design. We apply the proposed approach to the Prostate Cancer Prevention Trial (PCPT). We also developed an open-source R package for implementation of our approach.