组间平衡区组设计的性质及应用  

Properties and Application of Block Designs with Balanced Between Blocks

作　　者：杨林[1] 吴亚桢[1] 廖靖宇[1] 张应山[2] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000 [2]华东师范大学金融与统计学院,上海200241

出　　处：《数学的实践与认识》2017年第24期139-148,共10页Mathematics in Practice and Theory

基　　金：教育部高等学校博士学科点专项基金资助项目(44k550500);国家自然科学基金(11101381);许昌市科技计划项目(1505008)

摘　　要：区组设计的平衡性是对区组设计研究的重要概念,而组间平衡是其中基于重复次数概念的一种平衡性.探讨了组间平衡性的相关哲学概念和数学性质,并且从理论上证明了组间平衡区组设计的数学判定条件,并给出了计算机验证组间平衡性的方法.作为应用,在一般象数学的试验设计模型的基础上,证明了具有组间平衡性质的广义正交表,不但使得试验因子效应的估计无偏和方差最小,而且可以使得对试验中心值或者总体均值的估计无偏和方差最小,并且在区组试验数据较大时,其估计和区组大小的分解式基本无关,保证试验的数据分析结论具有再现性.Balance block design is an important concept of block design research, and the balanced between blocks is based on the concept of repetitions of a kind of balanced. This article discusses the balanced between blocks of related philosophical concepts and mathematical properties, and theoretically proves the balanced block design mathematical decision condition between blocks, and gives the method of balanced between blocks by computer validation.As application, in general, on the basis of experiment design model about image mathematics, the generalized orthogonal arrays with the balanced between blocks can make not only the estimator of the experimental center value being both unbiased and minimum variance,but also the overall mean value being both unbiased and minimum variance, having nothing to do with the decomposition of the block size type when the size of block is large, hence the data analysis conclusion possesses numerous advantages of reproducibility and makes the experimental center value is stable.

关 键 词：区组设计 组间平衡 关联矩阵 试验中心值 再现性 

分 类 号：O212.6[理学—概率论与数理统计]