Nested generalized cyclic row-column designs
Nested generalized cyclic row-column designs
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嵌套广义循环行列设计
DOI：
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发表时间：
1985
期刊：
影响因子：
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通讯作者：
J. John
中科院分区：
文献类型：
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作者：
R. Ipinyomi;J. John
嵌套行-列设计具有布置在B区组中的v个处理，每个区组包括分组为p行和q列的pq个单元。一类设计的基础上的一个周期性的施工方法的定义。研究了这种嵌套广义循环行列设计的典型效率因子。将5 < v < 15，p < 3，q < 7和r < v的有效设计制成表格，其中r = bpq/v是每个处理的重复数。行-列设计用于消除两个方向的异质性。更一般地说，一个实验可能有几个区块，每个区块包含排列在p行和q列中的pq图，其中区块可以代表另一个区块因子或提供基本行列设计的复制。这些设计称为嵌套行-列设计，因为行和列嵌套在区组中。由耶茨（1940）引入的格子正方形设计就是这种设计的例子。Singh和Dey（1979）已经考虑了一般分析和平衡的概念。Singh & Dey（1979），Street（1981）和Agrawal & Prasad（1982 a）给出了几个系列的平衡嵌套行列设计。Preece（1967）提供了一个嵌套平衡不完全区组设计表，其中一些设计也可用作平衡嵌套行列设计。Street（1981）和Agrawal & Prasad（1982 b）给出了基于部分平衡设计的其他系列。Jarrett和Hall（1982）给出了一些基于循环和广义循环构造方法的小型设计的例子，他们认为这些设计可以提供最近邻设计和方法的有用替代方案。作为平衡嵌套行-列设计的一个例子，考虑以下由Singh & Dey（1979）给出的设计，五个处理0，1，2，3，4排列在五个两行两列的区组中：
SUMMARY A nested row-column design has v treatments arranged in b blocks each comprising pq units grouped into p rows and q columns. A class of designs based on a cyclical method of construction is defined. The canonical efficiency factors of such nested generalized cyclic row-column designs are examined. Efficient designs are tabulated for 5 < v < 15, p < 3, q < 7 and r < v, where r = bpq/v is the number of replications of each treatment. Row-column designs are used to eliminate heterogeneity in two directions. More generally, an experiment may have several blocks each containing pq plots arranged in p rows and q columns, where the blocks may represent a further blocking factor or provide replications of the basic row-column design. These designs are called nested row-column designs, since rows and columns are nested within blocks. The lattice square designs, introduced by Yates (1940), are examples of such designs. A general analysis and the concept of balance have been considered by Singh & Dey (1979). Several series of balanced nested row-column designs have been given by Singh & Dey (1979), Street (1981) and Agrawal & Prasad (1982a). Preece (1967) provides a table of nested balanced incomplete block designs and a number of these designs can also be used as balanced nested row-column designs. Other series based on partially balanced designs have been given by Street (1981) and Agrawal & Prasad (1982b). Jarrett & Hall (1982) gave some examples of small designs based on cyclic and generalized cyclic methods of con- struction, which they suggested could provide useful alternatives to nearest neighbour designs and methods. As an example of a balanced nested row-column design, consider the following design, given by Singh & Dey (1979), for five treatments 0, 1, 2, 3, 4 arranged in five blocks of two rows and two columns: