Investigations in Robust Analysis of Variance

在社会和行为科学(以及其他领域)中设计的实验通常通过与方差分析(ANOVA)相关的技术来处理。当数据可能表现不佳时，应用统计学家和其他从业人员应该能够获得对个别影响的可靠估计，并伴随着适当的摘要和变异性的综合衡量。通过大幅增加适用于稳健方差分析所需的摘要和汇总的有限数量的可用小样本结果，该项目旨在为单向和双向布局的统一基本推理技术提供基础(包括关键表格)。对于不满足标准假设的数据(例如，通过包含一些异常观测或具有重尾)，需要在广泛的基础分布范围内表现良好的类似于ANOVA的过程。对于包括回归在内的更一般类型的线性模型，一些拟议的稳健程序可应用于ANOVA情况，但关于其在小样本中的性能的证据仍然太有限，无法选择首选技术或作出必要的分量(包括对效应及其标准误差的估计、对假设的相应检验、和详细的临界表)，以供统计应用。这项研究将探讨几种稳健方差分析的方法，主要基于M-估计，使用大样本结果和蒙特卡罗方法来建立小样本下的性质。这项工作将首先强调最广泛使用的设计：双向和单向布局。比克尔、德雷珀、费尔纳、汉佩尔、赫特曼斯佩格、霍格林、胡伯、约翰逊、卡法达尔、莱曼、莫斯特勒、洛克、朗切蒂、罗瑟乌、施拉德、斯塔赫尔、图基、约海和扎马尔之前的工作将提供主要的起点。莫斯特勒和他的同事们提出的这项研究将继续一系列长期得到社会科学和经济科学部支持的工作，该部门多年来在理解社会科学数据的统计方法方面取得了许多最具创新性的发展。首席调查员在社会科学家和统计学家中享有盛誉，因为他出色地编写了描述和说明继续发展的方法的技术性和更容易获得的教科书材料。

Designed experiments in the social and behavioral sciences (and other fields as well) customarily are handled by techniques associated with the analysis of variance (ANOVA). When the data may not be well behaved, applied statisticians and other practitioners should be able to obtain robust estimates of individual effects, accompanied by suitable summaries and aggregate measures of variability. By adding substantially to the limited number of available small-sample results that apply to the summaries and aggregates required for robust ANOVA, this project aims to provide the basis (including critical tables) for a unified body of basic inferential techniques for one-way and two-way layouts. For data that fail to satisfy the standard assumptions (for example, by containing some anomalous observations or by having heavy tails), ANOVA-like procedures are needed that perform well across a broad range of underlying distributions. A number of proposed robust procedures for the more general class of linear models, which also includes regression, may be applied in ANOVA situations, but evidence on their performance in small samples is still too limited to permit choice of a preferred technique or to make the necessary components (including estimates of effects and their standard errors, corresponding tests of hypotheses, and detailed critical tables) available for statistical applications. The proposed research will investigate several procedures for robust ANOVA, mainly based on M-estimation, using large-sample results and Monte Carlo to establish their properties in small samples. The work will at first emphasize the most widely used designs: two-way and one-way layouts. Previous work by Bickel, Draper, Fellner, Hampel, Hettmansperger, Hoaglin, Huber, Johnson, Kafadar, Lehmann, Mosteller, Rocke, Ronchetti, Rousseeuw, Schrader, Stahel, Tukey, Yohai, and Zamar will provide the main starting points. The research proposed by Mosteller and his associates will continue a line of work long supported by the Division of Social and Economic Science that has over the years produced many of the most innovative developments in statistical methods for making sense of social science data. The Principal Investigator has a most distinguished reputation among both social scientists and statisticians because of remarkable production of both technical and more accessible textbook materials describing and illustrating methods that continue to be developed.