Abstract:
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We scrutinize randomization tests, a hypothesis testing approach which draws conclusions about the presence of treatment effects instead of making inference in terms of population parameters. Its merits have not been fully recognized ever though the dawn of incorporating randomization in the design and analysis of experiments was pioneered by Sir R. A. Fisher in the 1920s. Today, the term randomization test is used in many places often interchangeably with permutation test. While permutation tests are described as "distribution-free", as we will reveal, the method has its basis in the population model, and thus are fundamentally different from randomization-based approaches. Also, we give a general model that incorporates both randomization tests and permutation tests as special cases. We conclude that the simple, intuitive randomization test mitigates the ethical issue in randomized clinical trials, conforms to the experimental context, and provides assessment beyond the constraints of the population model.
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