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

TL;DR

This paper introduces hacking intervals, a new inference framework that quantifies the robustness of scientific results against researcher manipulation, addressing bias issues in data analysis.

Contribution

The paper proposes hacking intervals, a novel approach to measure how results withstand endogenous data manipulations, enhancing robustness and interpretability over traditional confidence intervals.

Findings

Hacking intervals quantify robustness to researcher bias.

Small hacking intervals indicate more manipulation-resistant results.

Some hacking intervals align with classical confidence intervals.

Abstract

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. Since 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.