To Aid Statistical Inference, Emphasize Unconditional Descriptions of Statistics
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We have elsewhere reviewed proposals to reform terminology and improve interpretations of conventional statistics by emphasizing logical and information concepts over probability concepts. We here give detailed reasons and methods for reinterpreting statistics (including but not limited to) P-values and interval estimates in unconditional terms, which describe compatibility of observations with an entire set of analysis assumptions, rather than just a narrow target hypothesis. Such reinterpretations help avoid overconfident inferences whenever there is uncertainty about the assumptions used to derive and compute the statistical results. Examples of such assumptions include not only standard statistical modeling assumptions, but also assumptions about absence of systematic errors, protocol violations, and data corruption. Unconditional descriptions introduce uncertainty about such assumptions directly into statistical presentations of results, rather than leaving that only to the informal discussion that ensues. We thus view unconditional description as a vital component of good statistical training and presentation.
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