The meaning of randomization tests has become obscure in statistics education and practice over the last century. This article makes a fresh attempt at rectifying this core concept of statistics. A new term -- "quasi-randomization test" -- is introduced to define significance tests based on theoretical models and distinguish these tests from the "randomization tests" based on the physical act of randomization. The practical importance of this distinction is illustrated through a real stepped-wedge cluster-randomized trial. Building on the recent literature of randomization inference, a general framework of conditional randomization tests is developed and some practical methods to construct conditioning events are given. The proposed terminology and framework are then applied to understand several widely used (quasi-)randomization tests, including Fisher's exact test, permutation tests for treatment effect, quasi-randomization tests for independence and conditional independence, adaptive randomization, and conformal prediction.
翻译:随着统计教育和实践的发展,随机化检验的含义已经变得模糊。本文对统计学的这个核心概念进行了重新诠释。引入了一个新术语——“准随机化检验”,用于定义基于理论模型的显著性检验,并将这些检验与基于物理随机化的“随机化检验”区分开来。通过一个真实的分段楔形簇随机试验,说明了这种区分的实际重要性。在近期随机化推断的文献基础上,建立了一个条件随机化检验的通用框架,并提供了一些构建条件事件的实用方法。然后,将所提出的术语和框架应用于理解几个广泛使用的(准)随机化检验,包括 Fisher 精确检验、治疗效应的排列检验、独立性和条件独立性的准随机化检验、自适应随机化和符合性预测。