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How can we draw trustworthy scientific conclusions? One criterion is that astudy can be replicated by independent teams. While replication is criticallyimportant, it is arguably insufficient. If a study is biased for some reasonand other studies recapitulate the approach then findings might be consistentlyincorrect. It has been argued that trustworthy scientific conclusions requiredisparate sources of evidence. However, different methods might have sharedbiases, making it difficult to judge the trustworthiness of a result. Weformalize this issue by introducing a "distributional uncertainty model", whichcaptures biases in the data collection process. Distributional uncertainty isrelated to other concepts in statistics, ranging from correlated data toselection bias and confounding. We show that a stability analysis on a singledata set allows to construct confidence intervals that account for bothsampling uncertainty and distributional uncertainty.

Calibrated inference: statistical inference that accounts for both sampling uncertainty and distributional uncertainty