A Theory of Statistical Inference for Ensuring the Robustness of Scientific Results

Journal Article (Journal Article)

Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting uncertainty. Any one theory of inference is neither right nor wrong but merely an axiom that may or may not be useful. Each of the many diverse theories of inference can be valuable for certain applications. However, no existing theory of inference addresses the tendency to choose, from the range of plausible data analysis specifications consistent with prior evidence, those that inadvertently favor one’s own hypotheses. Because the biases from these choices are a growing concern across scientific fields, and in a sense the reason the scientific community was invented in the first place, we introduce a new theory of inference designed to address this critical problem. We introduce hacking intervals, which are the range of a summary statistic one may obtain given a class of possible endogenous manipulations of the data. Hacking intervals require no appeal to hypothetical data sets drawn from imaginary superpopulations. A scientific result with a small hacking interval is more robust to researcher manipulation than one with a larger interval and is often easier to interpret than a classical confidence interval. Some versions of hacking intervals turn out to be equivalent to classical confidence intervals, which means they may also provide a more intuitive and potentially more useful interpretation of classical confidence intervals.

Full Text

Duke Authors

Cited Authors

  • Coker, B; Rudin, C; King, G

Published Date

  • October 1, 2021

Published In

Volume / Issue

  • 67 / 10

Start / End Page

  • 6174 - 6197

Electronic International Standard Serial Number (EISSN)

  • 1526-5501

International Standard Serial Number (ISSN)

  • 0025-1909

Digital Object Identifier (DOI)

  • 10.1287/mnsc.2020.3818

Citation Source

  • Scopus