ANALYSIS OF RANDOMIZED EXPERIMENTS WITH ORTHOGONAL BLOCK STRUCTURE .2. TREATMENT STRUCTURE AND GENERAL ANALYSIS OF VARIANCE
ANALYSIS OF RANDOMIZED EXPERIMENTS WITH ORTHOGONAL BLOCK STRUCTURE .2. TREATMENT STRUCTURE AND GENERAL ANALYSIS OF VARIANCE
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DOI：
10.1098/rspa.1965.0013
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发表时间：
1965-01-01
影响因子：
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通讯作者：
NELDER, JA
中科院分区：
文献类型：
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作者：
NELDER, JA
先前已经证明，用于一组实验单元的任何正交块结构都可以由一组相互正交的幂等矩阵Ci来表示。当对单元应用不同处理时，处理效果的任何线性模型都可以由另一组相互正交的幂等矩阵Tj来表示。对具有正交块结构的单元具有以任何模式施加的任何处理的任何试验的分析可以用矩阵Ci、Tj和列出应用于每个单元的处理的设计矩阵N来表示。单位处理的可加性假设和有效的随机化对于分析的有效性至关重要。针对这一一般情况，建立了相应的估计方程，给出了平衡的一般定义，并用几个实例加以说明。给出了用正交区组结构和线性处理模型处理所有试验分析的通用计算机程序的概要。
Any orthogonal block structure for a set of experimental units has been previously shown to be expressible by a set of mutually orthogonal, idempotent matrices Ci. When differential treatments are applied to the units, any linear model of treatment effects is expressible by another set of mutually orthogonal idempotent matrices Tj. The analysis of any experiment having any set of treatments applied in any pattern whatever to units with an orthogonal block structure, is expressible in terms of the matrices Ci, Tjand the design matrix N, which lists the treatments applied to each unit. A unit-treatment additivity assumption and a valid randomization are essential to the validity of the analysis. The relevant estimation equations are developed for this general situation, and the idea of balance is given a generalized definition, which is illustrated by several examples. An outline is sketched for a general computer program to deal with the analysis of all experiments with an orthogonal block structure and linear treatment model.