Symmetry and Asymmetry in Experimental Design

实验设计中的对称性和不对称性

• 批准号: 0604997
• 负责人: John Morgan
• 金额: $ 14.43万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604997&HistoricalAwards=false
• 关键词: Symmetry; Asymmetry; Experimental; Design

Blocking of experimental material is a fundamental device for variance reduction in the design of comparative experiments. The investigator is exploring efficient applications of this principle from three distinct perspectives based on symmetry/asymmetry notions in the treatments to be compared, in the available experimental material, and in external restrictions on the set of permissible designs. Conventional design optimality theory rests strongly on the assumption of equality of treatment interest, expressed through summary measures of experimental information that are invariant to treatment permutation. The first goal is to develop a coherent optimality theory for evaluating designs when permutability is not tenable, that is, when experimenters are faced with asymmetry in treatment interest. Equality of treatment replications is another conventional symmetry that, depending on the number of blocks available and their sizes, can result in underutilization of resources and consequent reduction of information. The second goal is to develop theory for dealing with asymmetry of treatment replication in a comprehensive fashion. In some experiments it is demanded that blocks be partitioned into subsets so that each treatment occurs exactly once in each subset; a design for this situation is said to be resolvable. Resolvability is an added symmetry in treatment assignment, over that ordinarily required of a block design. The third goal is to extend theory for optimal resolvable designs to cover numbers of treatments, replicates and block sizes for which there are currently no available results.Collectively, the investigator is pursuing an approach to the design of comparative experiments that, by virtue of wider applicability, can compile significantly expanded design catalogs as resources for experimenters in a wide range of disciplines. A component of each of the problems described above, as the optimality theory evolves, is the building and compiling of designs for many combinations of blocks and treatments, and cataloging these online for free access by researchers, experimenters, and statistical practitioners. Making good designs easily available provides a basic tool for more efficient experimentation, aiding progress in scientific advancement and industrial innovation by increasing the quality of information that experiments can produce.

在比较实验设计中，实验材料的区组化是减少方差的基本手段。研究人员正在从三个不同的角度探索这一原则的有效应用，这些角度基于待比较的治疗中、可用实验材料中以及对允许设计集的外部限制中的对称/不对称概念。传统的设计最优性理论强烈依赖于治疗利益平等的假设，通过对治疗排列不变的实验信息的汇总测量来表达。第一个目标是发展一个连贯的最优性理论，用于评估当置换是站不住脚的设计，也就是说，当实验者面临着不对称的治疗利益。治疗重复的平等性是另一种传统的对称性，根据可用的块的数量及其大小，可能导致资源利用不足和随之而来的信息减少。第二个目标是发展理论，以全面的方式处理不对称的治疗复制。在某些实验中，要求将块划分为子集，以便每个子集中的每个处理只发生一次;这种情况下的设计被称为可解析的。可分辨性是在处理分配中增加的对称性，超过了通常要求的区组设计。 第三个目标是扩展最佳可解析设计的理论，以涵盖目前尚无可用结果的处理次数、重复次数和区组大小。总的来说，研究人员正在寻求一种比较实验设计方法，凭借更广泛的适用性，可以编制显着扩展的设计目录，作为广泛学科实验者的资源。随着最优性理论的发展，上述每个问题的一个组成部分是构建和编译许多块和处理组合的设计，并将其在线编目，供研究人员，实验者和统计从业者免费访问。使好的设计容易获得，为更有效的实验提供了一个基本工具，通过提高实验产生的信息质量，帮助科学进步和工业创新。