广义正交表正交性的等价条件  

The Equivalent Conditions of the Orthogonality of Generalized Orthogonal Arrays

作　　者：吴亚桢[1] 张建军[1] 张应山[2] 田萍[1] 廖靖宇[1] 

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》2014年第11期230-240,共11页Mathematics in Practice and Theory

基　　金：河南省基础研究计划项目(132300410322);河南省教育厅科学技术研究重点资助项目(13A110753);许昌学院科研项目(2013100)

摘　　要：广义正交表是一种类似于正交表的新设计.正交平衡性是广义正交表必须满足的基本要求之一,它是正交表正交性的推广,它能够使得试验因子在方差分析中保持柯赫伦定理成立,因而可以像正交表一样进行试验设计和方差分析,从而不但保证其数据分析模型符合"不自生"逻辑,而且也可以保证试验因子的各种关系比较的数据分析结论具有客观一致性和可重复再现性,但试验次数大幅减少.利用矩阵象技术,提出并证明了广义正交表的组合正交性不但等价于其矩阵象的正交性,而且也等价于其广义关联矩阵的正交性.借助于SAS软件可以方便快速的验证某些区组设计相应的行列设计是否为广义正交表.Generalized orthogonal arraysarrays. Orthogonal balanced is one of theare new ones which are similar to the orthogonalbasic requirements of the generalized orthogonalarrays, which is a generalization of the orthogonality Of orthogonal arrays, it can make theexperimental factors to keep KeHeLun theorem established in the analysis of variance, thusthe experiment design and variance analysis can be dealt as orthogonal arrays, which not onlyensure the data analysis model according with non-authigenic logic, but also can guaranteethe data analysis conclusion among experimental factors of all kinds of relative comparisonsis objective consistent and repeatable reproducibility, but the run size is small By using thematrix image methods, the paper proposes and proves that the combination orthogonality ofgeneralized orthogonal arrays is not only equivalent to the orthogonality of its matrix image,but also the orthogonality of its generalized incidence matrix. By using SAS software canfacilitate rapid to test whether the row-column design corresponding to some block designs isa generalized orthogonal array.

关 键 词：广义正交表 正交平衡 再现性 矩阵象 区组设计 

分 类 号：O212.6[理学—概率论与数理统计]