  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.
