Pairwise and variance balanced incomplete block designs
Pairwise and variance balanced incomplete block designs
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成对和方差平衡的不完全区组设计
DOI：
10.1007/bf02479828
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发表时间：
1974
影响因子：
1
通讯作者：
W. Federer
中科院分区：
文献类型：
--
作者：
A. Hedayat;W. Federer
本文的目的有三个方面。第一个目的是汇编和系统化关于不完全区组设计平衡的两个方面的已发表和分散的结果，即，两两平衡和方差平衡。这样做是为了建立这两个概念的平衡在出版的文献中的地位，并把它们放在一个形式，这是有用的，在这一领域的进一步工作。本文的第二个目的是提出一种构造不等重复和/或不等区组大小试验设计的方法，使之具有方差平衡性质。构造方法涉及来自两个或多个区组设计的区组的联合，以及用附加处理对某些区组进行扩充;该方法被表示为非联合区组设计。该方法的直接扩展将产生具有不等重复和/或不等区组设计的部分平衡区组设计。扩大方差平衡区组设计的概念和可用性，以适应不平等的复制和/或不平等的区组大小是很重要的研究人员，教师和实验需要这样的设计。比如说，动物营养学家或心理学家不再要求区组具有恒定的窝数或家系大小，对于材料不足的处理，可以在处理上进行不等重复，并且在所有标准化处理契约上仍能达到方差相等的目标.本文的第三个目的是应用联合区组设计方法构造一个不等重复不等区组的家系大小方差平衡设计。对推广不化区组设计方法构造其它方差平衡或部分平衡区组设计族给出了一些评论。
SummaryThe purpose of this paper is three-fold. The first purpose is to compile and to systematize published and dispersed results on two aspects of balancing in incomplete block designs, i.e., pairwise balance and variance balance. This was done in order to establish the status of these two concepts of balance in published literature and to put them in a form which is useful for further work in this area. Also, the results in this form are necessary for the development of the remainder of the paper.The second purpose of this paper is to present a method of constructing unequal replicate and/or unequal block size experiment designs for which the variance balance property is achieved. The method of construction involves the union of blocks from two or more block designs and the augmentation of some of the blocks with additional treatments; the method is denoted asunionizing block designs. A straight-forward extension of the method would produce a partially balanced block design with unequal replicate and/or unequal block designs. The enlargement of the concept and availability of variance blanced block designs to accommodate unequal replication and/or unequal block sizes is important to the researcher, the teacher, and the experimenter needing such designs. For example, an animal nutritionist or a psychologist is no longer required to have constant litter or family sizes for the blocks and may have unequal replication on the treatments for those treatments with insufficient material and still attain the goal of equal variances on all normalized treatment contracts.The third purpose of the paper is to apply the unionizing block designs method to construct a family of unequal replicate and unequal block size variance balanced designs. Some comments are given on the extension of the unionizing block designs method to construct other families of variance balanced or partially balanced block designs.