假设检验两类错误的动态可视化教学研究

Research on Dynamic Visualization Teaching of Hypothesis Testing for Two Types of Errors

摘要: 假设检验中的两类错误是概率论与数理统计教学的难点。针对学生普遍存在的概念混淆、计算障碍及关系理解困难等问题，文章基于正态分布构建动态可视化模型，系统解析了样本量固定时两类错误概率此消彼长的动态平衡关系，并量化展示了第一类错误概率、第二类错误概率与样本量的内在联系。通过理论机制分析、数值模拟与几何解释三位一体的研究方法，有效化解了知识抽象带来的认知障碍，助力学生深入理解核心内容。

Abstract: The two types of errors in hypothesis testing represent a challenging topic in the teaching of probability theory and mathematical statistics. To address students’ widespread difficulties, such as conceptual confusion, computational barriers, and struggles in understanding relationships, this paper constructs a dynamic visualization model based on the normal distribution. This model systematically analyzes the dynamic balance relationship where the probabilities of the two types of errors vary inversely when the sample size is fixed. It further quantifies the intrinsic connections among the probability of Type I error (α), the probability of Type II error (β), and the sample size (n). Through a tripartite research approach integrating theoretical mechanism analysis, numerical simulation, and geometric interpretation, the study effectively overcomes cognitive obstacles arising from the abstract nature of the topic, thereby helping students gain a deeper understanding of the core concepts.