关于假设检验的误解：客观概率与统计检验力

Misconceptions about Hypothesis Testing: Objective Probability and Statistical Power

摘要: 文章主要是揭示目前假设检验常见误解，以提供正确使用方法。首先简单回顾假设检验的哲学基础，揭示证伪法对于假设检验的重要性。以两样本t检验为例，测查心理与教育统计学习者对假设检验的理解。结果发现超过六成的学习者没能正确理解客观概率，超过八成的学习者没能正确理解统计检验力。假设检验使用客观概率解释概率，客观概率是相对于事件集合而言，零假设和备择假设都是属于单个事件并没有概率，不应错误使用p值。统计软件算出的p值也没有说明统计检验力，实验设计必须事先计算统计检验力。

Abstract: The main purpose of this article is to reveal the common misconceptions about hypothesis testing and provide the correct way to use it. First, the philosophical basis of hypothesis testing is briefly reviewed, and the importance of falsificationism for hypothesis testing is revealed. The two-sample t-test is used as an example to test the understanding of hypothesis testing among learners in psychological and educational statistics. The results show that more than 60% of the learners failed to correctly understand the objective probability, and more than 80% of the learners failed to correctly understand the power of the test. Hypothesis testing uses objective probabilities to explain probability, which is relative to the set of events, and both the null hypothesis and the alternative hypothesis belong to a single event and have no probability, and the p-value should not be used incorrectly. The p-value calculated by the statistical software also does not indicate the statistical power, and the experimental design must calculate the statistical power in advance.