区组设计的矩阵象的计算及其应用  

Calculation and Application of Matrix Image for Block Design

作　　者：张明珠[1] 张应山[2] 廖靖宇[3] 杨林[3] 吴亚桢[3] 

机构地区：[1]三峡大学理学院,湖北宜昌443002 [2]华东师范大学金融与统计学院,上海200241 [3]许昌学院数学与统计学院,河南许昌461000

出　　处：《数学的实践与认识》2015年第13期123-132,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);河南省教育厅科学技术研究重点项目(12A110022);河南省科技厅资助项目(122300410269)

摘　　要：平衡区组设计是对传统平衡不完全区组设计(BIBD)、部分平衡不完全区组设计(PBIBD)和拉丁矩阵(或拉丁方)设计等区组设计的一种推广,这种区组设计比传统区组设计的多种平衡条件更弱,满足新平衡条件的平衡区组设计更多,也更容易构造,并且新构造出的区组设计仍然保持着原有各种形式的区组设计的各种平衡性,因而保持着在统计分析中的优良性质,从而可以和原来各种形式平衡区组设计一样用于试验设计和统计分析.研究新的一般区组设计的性质的一个重要工具是它们的矩阵象性质.首先对一般区组设计的矩阵象的定义和计算进行研究,这些矩阵象的运算性质和正交表的矩阵象运算性质基本类似,可以和正交表的矩阵象一样进行应用.正交表矩阵象的主要应用有两方面:正交表构造和数据分析研究.先把平衡区组设计的矩阵象应用于简单构造平衡区组设计.Balanced block design is an extension of conventional balanced incomplete block design （BIBD）, partial balanced incomplete block design （PBIBD） and Latin matrix （or Latin square） design. This block design has weaker balanced conditions than conventional block design. Hence, more balanced block design can satisfy the new balanced conditions which make the construction of balanced block design easier. The constructed block design still has the excellent properties in statistical analysis of conventional block designs. Hence, it can also be used for experiment design and statistical analysis. One important tool for studding the properties of new general block design is the matrix image property. The calculation of matrix image of general block design is studied firstly in this paper. The operation property of the matrix image is basic similar with that of matrix image of orthogonal array. Hence, it can be used as same as matrix image of orthogonal array. The main application of matrix image of orthogonal array includes construction of orthogonal array and analytical approach of data. The matrix image is used for construction of balanced block design in this paper.

关 键 词：区组设计 平衡 试验设计 矩阵象 替换构造 

分 类 号：O212.6[理学—概率论与数理统计]