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Inference is the process of using facts we know to learn about facts we donot know. A theory of inference gives assumptions necessary to get from theformer to the latter, along with a definition for and summary of the resultinguncertainty. Any one theory of inference is neither right nor wrong, but merelyan axiom that may or may not be useful. Each of the many diverse theories ofinference can be valuable for certain applications. However, no existing theoryof inference addresses the tendency to choose, from the range of plausible dataanalysis specifications consistent with prior evidence, those thatinadvertently favor one's own hypotheses. Since the biases from these choicesare a growing concern across scientific fields, and in a sense the reason thescientific community was invented in the first place, we introduce a new theoryof inference designed to address this critical problem. We introduce hackingintervals, which are the range of a summary statistic one may obtain given aclass of possible endogenous manipulations of the data. Hacking intervalsrequire no appeal to hypothetical data sets drawn from imaginarysuperpopulations. A scientific result with a small hacking interval is morerobust to researcher manipulation than one with a larger interval, and is ofteneasier to interpret than a classical confidence interval. Some versions ofhacking intervals turn out to be equivalent to classical confidence intervals,which means they may also provide a more intuitive and potentially more usefulinterpretation of classical confidence intervals.

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