F检验和信度系数α

F-Test and Reliability Coefficient Alpha

一次测验之后，可以把检验分数表为关于因子Ａ（代表人）和因子Ｂ（代表题目）的两向分类模型．对这个模型，我们感兴趣的一个问题是：因子Ａ效应之间的差异是否显著，用Ｆ－检验可以对此进行检验．在测验理论中考虑的另一个问题是；测验分数是否反映出考生的真实水平，通常用信度系数α作为可靠性的一种度量．对同一个考生样本来说，因子Ａ的Ｆ－检验与α系数之间存在函数关系．根据这一关系可以进一步认识这两个不同统计量的作用．

After a test, the test scores can be represented as two--way classification model about factor A (representing person) and factor B(representing item). For this model, a problem which is interested is that difference among effects of factor A is whether significant or not, and it is can be examined by F-statistic. But significance of score difference is not the same as true levels of examinees are whether reflected by test scores. In test theory, degree of examinee's true levels reflected by test scores is usually measured by reliability coefficient, as yet statistic of estimate that most used is coefficient alpha. In this paper, the relation between two statistics come from test scores for same examinee's sample is obtained, and some results are deduced based on this relation.