Geometries for the Behavioral Sciences

行为科学几何

• 批准号: 8911339
• 负责人: Jean-Claude Falmagne
• 金额: $ 12.5万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-08-01 至 1992-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8911339&HistoricalAwards=false
• 关键词: Geometries; Behavioral; Sciences

Researchers in many of the social and behavioral sciences often need to analyze the data of a complex experiment into a few essential features or trends, in order to ascertain the essential dimensions of variations in the phenomenon under investigation. Methods involving the mathematics of geometry can be very helpful in this regard, because they can provide the experimenter with potentially enlightening graphic representations of the data. There has been relatively little development of truly geometrical methods tailored to those fields. Useful techniques have been developed (e.g., factor analysis, multidimensional scaling) which are sometimes labeled `geometrical'. However, these techniques are based on extremely strong models (i.e., based on very restrictive assumptions), in which the geometry of the representing structure plays only a minor role. Moreover, the fundamental assumptions of these models are not easily testable, so that it is never quite clear how much of the results of the analysis have been forced upon the experimenter by the method itself. This research will remedy this situation and provide a collection of purely geometrical models suitable for a very general experimental setting in use by social and behavioral scientists. The experimental method is a variant of the so- called `method of triads', but the interpretation of the data differs drastically from traditional ones. The mathematical developments are largely based on the methods and concepts of modern geometry. One of the advantages of this approach is that the models tend to be weaker than traditional ones (i.e., to involve less restrictive assumptions) while being easily testable.

许多社会和行为科学的研究人员经常 我需要把一个复杂实验的数据分析成几个 基本特征或趋势，以确定基本的 在调查中的现象的变化的尺寸。 涉及几何数学的方法可能非常有帮助 在这方面，因为它们可以为实验者提供 潜在地启发数据的图形表示。 相对来说，真正的几何学 为这些领域量身定制的方法。 有用的技术已经 开发的（例如，因素分析，多维尺度）， 有时被称为“几何”。 然而，这些技术 基于非常强大的模型（即，基于非常 限制性假设），其中， 表示结构只起次要作用。 而且 这些模型的基本假设不容易检验， 因此，人们永远不清楚， 这种方法迫使实验者进行分析， 本身 这项研究将纠正这种情况，并提供一个 一组纯粹的几何模型， 社会和行为研究所使用的一般实验环境 科学家 实验方法是一个变种，所以- 称为“三元组方法”，但数据的解释 与传统的大不相同。 数学 发展在很大程度上是基于方法和概念， 现代几何学 这种方法的优点之一是， 该模型往往比传统模型弱（即，到 涉及较少的限制性假设）， 可测试的