CAREER: A Modern Philosophy for Classical Statistical Testing and Estimation

基于Fisher、Neyman和Pearson思想的经典统计检验和估计在科学中无处不在。它们仍然是心理学、医学、流行病学、药理学、农业和环境科学等领域的核心。因此，它们在这些科学的经验成功中发挥着重要作用。然而，它们往往达不到科学家的雄心壮志，即量化数据如何积极支持假设，并表达估计的可变置信度。为了解决这些缺点，该项目为统计测试和估计提供了新的概念基础，并具有定量影响。它修改，扩展，并通过适应20世纪和21世纪的认识论思想，证据和知识的性质和条件的哲学研究加强这些基础。在此过程中，它展示了如何从数据中得出更细致入微的科学结论。这项研究还结合了两个教育目标的支持活动。首先，这个项目促进了统计概念和方法融入大学哲学课程，特别是批判性推理，认识论和科学哲学课程。它通过两个大学教师暑期研究所来实现这一目标。第二，该项目开始通过两个早期研究生暑期学校，建立一个从事统计哲学研究的早期职业学者网络。教育和研究目标之间的主要协同作用来自教学和新的研究方向之间的自然反馈。本研究从当代认识论中改编的思想包括证据和知识的模态条件，即坚持、敏感性和安全性。从概率化可靠性认识论的角度来看，费舍尔p值是一个概率的遵守措施，而两个新的定量后数据的证据措施对应的敏感性和安全性。这些包括与马约严重程度概念相关的统计功效的独特的后数据模拟。根据这些措施，数据在一定程度上是假设的证据，它们具有足够的粘附性，敏感性和安全性。相比之下，传统的Fisherian显著性检验仅测量数据对假设的粘附程度，这对于该假设的积极证据支持是必要的，但不是充分的。Neyman-Pearson检验并不量化数据为假设提供的证据，而是提供了一个决定程序，用于接受和拒绝长期具有特定错误率的假设。本项目的第一部分在一般统计测试和估计的背景下为这些想法奠定了理论基础。然后，第二部分通过修改R编程语言中的标准测试和评估包，在计算上实现这些想法。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Classical statistical testing and estimation, based on the ideas of Fisher, Neyman, and Pearson, are ubiquitous in science. They continue to be central in psychology, medicine, epidemiology, pharmacology, agriculture, and environmental science, among others. Thus, they play an important role in those sciences' empirical successes. Yet they often fall short of scientists' ambitions to quantify how data positively support hypotheses and to express the variable confidence of estimates. To address such shortcomings, this project develops new conceptual foundations for statistical testing and estimation with quantitative implications. It modifies, extends, and strengthens those foundations by adapting ideas from 20th- and 21st-century epistemology, the philosophical study of the nature and conditions for evidence and knowledge. In doing so, it shows how to draw more nuanced scientific conclusions from data. This research also integrates with supported activities towards two educational objectives. First, this project promotes the integration of statistical concepts and methods into college philosophy curricula, especially critical reasoning, epistemology, and philosophy of science courses. It does so through two faculty summer institutes for college instructors. Second, this project begins to build a network of early-career scholars engaged in graduate-level research in the philosophy of statistics through two summer schools for early-stage graduate students. The main synergy between the educational and research objectives arises from the natural feedback between teaching and new research directions.The ideas that this research adapts from contemporary epistemology include the modal conditions for evidence and knowledge of adherence, sensitivity, and safety. From the viewpoint of probabilized reliabilist epistemology, Fisherian p-values are a probabilistic measure of adherence, while two novel quantitative post-data measures of evidence correspond to sensitivity and safety. These include a distinct post-data analogue of statistical power related to Mayo's severity concept. Data are evidence for a hypothesis to the extent they are sufficiently adherent, sensitive, and safe according to these measures. By contrast, traditional Fisherian significance testing only measures how adherent data are for a hypothesis, which is necessary but not sufficient for positive evidential support of that hypothesis. And Neyman-Pearson testing does not quantify the evidence that data provide for a hypothesis at all, but rather provides a decision procedure for accepting and rejecting hypotheses with specified rates error in the long run. The first part of this project develops the theoretical foundation for these ideas in the context of general statistical testing and estimation. The second part then implements these ideas computationally by modifying standard testing and estimation packages in the R programming language. This paves the way for the seamless adoption and application of these new nuanced measures of evidence in sciences that continue to use classical statistical testing and estimation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.