Connecting simple and precise P‐values to complex and ambiguous realities (includes rejoinder to comments on “Divergence vs. decision P‐values”)

Mathematics is a limited component of solutions to real‐world problems, as it expresses only what is expected to be true if all our assumptions are correct, including implicit assumptions that are omnipresent and often incorrect. Statistical methods are rife with implicit assumptions whose violation can be life‐threatening when results from them are used to set policy. Among them are that there is human equipoise or unbiasedness in data generation, management, analysis, and reporting. These assumptions correspond to levels of cooperation, competence, neutrality, and integrity that are absent more often than we would like to believe. Given this harsh reality, we should ask what meaning, if any, we can assign to the P‐values, “statistical significance” declarations, “confidence” intervals, and posterior probabilities that are used to decide what and how to present (or spin) discussions of analyzed data. By themselves, P‐values and CI do not test any hypothesis, nor do they measure the significance of results or the confidence we should have in them. The sense otherwise is an ongoing cultural error perpetuated by large segments of the statistical and research community via misleading terminology. So‐called inferential statistics can only become contextually interpretable when derived explicitly from causal stories about the real data generator (such as randomization), and can only become reliable when those stories are based on valid and public documentation of the physical mechanisms that generated the data. Absent these assurances, traditional interpretations of statistical results become pernicious fictions that need to be replaced by far more circumspect descriptions of data and model relations.