操作理论测试理论中的投影可靠性:条件期望,希尔伯特空间几何,以及对心理测量实践的含义
1The University of British Columbia, Vancouver, Canada.
Educational and psychological measurement
|November 17, 2025
概括
这项研究使用希尔伯特空间几何学重新定义了可靠性,将其视为定理,而不是假设. 这一新框架将心理测量可靠性与回归和统计模型联系起来,以提高测量理解.
科学领域:
- 心理测量 心理测量 心理测量
- 数学统计学数学统计学
- 几何分析 几何分析
背景情况:
- 经典测试理论依赖于可靠性的假设.
- 现有的框架缺乏可靠性的统一数学基础.
研究的目的:
- 用希尔伯特空间投影几何学重新构想可靠性.
- 为了提供一个严格的,基于定理的可靠性定义.
- 将可靠性与相关的统计概念统一起来.
主要方法:
- 定义的真分作为有条件的预期 (直角投影).
- 可靠性表达为预测的真分数的方差除以观察到的分数方差.
- 使用了操作者理论视角和测量理论证明.
主要成果:
- 可靠性是从投影几何学中作为定理得出的.
- 可靠性量化了投影效率 (二次共因数).
- 统一的可靠性与回归R平方,共同性和预测准确性.
结论:
- 希尔伯特空间框架为可靠性提供了一个严格的数学基础.
- 这种方法将心理测量理论与现代统计和几何分析联系起来.
- 测量误差是投影的直角补充;可靠性测量得分对齐.
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