拉丁方设计的统计量分布证明过程教学设计

Teaching Design of Proving of StatisticsDistribution for Latin Design

摘要: 拉丁方设计是《试验设计》析因试验部分实施的重要方法，也包含了方差分析内容，以往的关于 拉丁方设计检验统计量的证明较为繁杂，大多教材只给出其结论。 本文基于自定义的水平均值索 引矩阵及其性质，证明拉丁方设计的检验统计量的分布，通俗易懂，并且容易推广到其他的方差 分析模型。

Abstract: Latin square design is an important method for analysis of variance (ANOVA) in the course of experimental design. The previous proof of test statistics for Latin design is difficult for most students to understand, therefore many textbooks only give some conclusions about Latin design. In this paper, based on the defined horizontal mean index matrix and its properties, the proving process about test statistics for Latin design is easy to understand, and can be easily extended to other models for analysis of variance.