Some Aspects of the Statistical Analysis of “Split Plot” Experiments in Completely Randomized Layouts
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完全随机布局下裂区试验统计分析的若干方面
- 研究问题
- 在随机分配处理且每个受试者具有多个条件响应的裂区试验中，如何检验处理效应、条件效应及二者交互？
- 方法与思路
- 作者从多变量模型解释裂区设计，在不同联合分布假设下讨论假设表述，重点发展适用的非参数检验程序。
- 材料陈述的贡献
- 摘要称针对多种假设组合给出参数或非参数检验，并用可能不满足正态性和方差齐性的数值例子说明方法。
- 阅读关注点
- 应核对随机化单位、同一受试者响应之间的依赖结构，以及各非参数检验的假设、计算步骤和有效性范围。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；检验有效性条件及数值结果未完整提供，历史程序可用性和刊本变化均未知。
原文摘要
The statistical analysis of completely randomized “split-plot” experiments is discussed from the point of view of the underlying multivariate model. In doing this, first certain well-known aspects of the parametric case are reviewed; however, attention is primarily directed toward the development of appropriate non-parametric procedures. The general structure of “split-plot” experiments involves N randomly chosen subjects to whom treatments have been assigned according to a completely randomized design and from each of whom is obtained an observation vector, the components of which represent the responses of the subject to each one of several conditions. Hence, the data matrix has the appearance of a set of mixed models, each one of which corresponds to a particular treatment. The different conditions correspond to the “split plot” treatments in agricultural experiments while the different treatments correspond to the “whole plot” treatments. Alternatively, such designs may be interpreted simply as multivariate one-way layouts in which the components of the observation vector have been measured in the same units (or on the same scale) and hence are comparable. In such experiments, a number of hypotheses are of interest—the hypothesis of no treatment effects, the hypothesis of no condition effects, the hypothesis of no interaction between treatments and conditions. Various formulations of these hypotheses are discussed under several different combinations of assumptions concerning the joint distribution of the components of the observation vector. In each case considered, appropriate parametric or non-parametric test procedures are indicated. Some of the methods considered in the paper are illustrated in a numerical example. The example is representative of a situation in which some of the standard assumptions regarding normality and variance homogeneity may not hold. In this part of the paper, certain aspects of the efficient computation of the various test criteria are indicated. Corresponding algorithms are presented in Koch and Sen [16] and Koch [15]. Finally, computer programs based on these algorithms have been written and can be made available to interested persons.