区组大小不等的主效应设计  

Main-effect plans with blocks of natural size

作　　者：陈雪平[1] 林金官[2] 黄性芳[2] 汪红霞[2] 

机构地区：[1]江苏理工学院数理学院,常州213001 [2]南京审计大学统计科学与大数据研究院,南京211815

出　　处：《中国科学：数学》2017年第6期765-778,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11571073,11601195和11471172);教育部高等学校博士点基金(批准号:20120092110021);江苏省自然科学基金(批准号:BK20141326和BK20160289);江苏高校“青蓝工程”和江苏省高校自然科学基金(批准号:16KJB110005)资助项目

摘　　要：区组设计被广泛应用在人类的各种探索试验中.以往的研究中,区组大小通常被假定是相等的,但时常与实际情形相悖.本文讨论了区组大小不等时的正交主效应设计,该类设计的处理主效应可以通过区组因子达到正交;同时讨论了相关的设计性质.最后,本文给出了若干构造方法,包括如何添加新的区组,以及如何叠加不同区组大小的设计.结果表明相应设计具有较为灵活的区组数、区组大小和因子数.Block designs have been widely used in almost all areas of human investigations. It is comlnonly assumed that all blocks have the same size which may not, however, always be available because of practical restrictions. In this paper, the problem of main-effect plans with blocks of unequal sizes is addressed. The sufficient condition for each pair of factors to be orthogonal through the block factor is indicated. Useful properties on ANOVA （analysis of variance） of such designs are discussed. Construction procedures via augmenting new blocks and combining main-effect plans with unequal block sizes are also provided. The resulting designs have flexible sizes of blocks and factors.

关 键 词：关联矩阵 正交 等比例频数条件 加权相遇数 

分 类 号：O212.6[理学—概率论与数理统计]