  All scientific interpretations of statistical outputs depend on background
(auxiliary) assumptions that are rarely delineated or explicitly interrogated.
These include not only the usual modeling assumptions, but also deeper
assumptions about the data-generating mechanism that are implicit in
conventional statistical interpretations yet are unrealistic in most health,
medical and social research. We provide arguments and methods for
reinterpreting statistics such as P-values and interval estimates in
unconditional terms, which describe compatibility of observations with an
entire set of underlying assumptions, rather than with a narrow target
hypothesis conditional on the assumptions. Emphasizing unconditional
interpretations helps avoid overconfident and misleading inferences in light of
uncertainties about the assumptions used to arrive at the statistical results.
These include not only mathematical assumptions, but also those about absence
of systematic errors, protocol violations, and data corruption. Unconditional
descriptions introduce assumption uncertainty directly into the primary
statistical interpretations of results, rather than leaving it for the
discussion of limitations after presentation of conditional interpretations.
The unconditional approach does not entail different methods or calculations,
only different interpretation of the usual results. We view use of
unconditional description as a vital component of effective statistical
training and presentation. By interpreting statistical outputs in unconditional
terms, researchers can avoid making overconfident statements based on
statistical outputs. Instead, reports should emphasize the compatibility of
results with a range of plausible explanations, including assumption
violations.
