Semantic and Cognitive Tools to Aid Statistical Inference: Replace Confidence and Significance by Compatibility and Surprise
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Researchers often misinterpret and misrepresent statistical outputs. This abuse has led to a large literature on modification or replacement of testing thresholds and P-values with confidence intervals, Bayes factors, and other devices. Because the core problems appear cognitive rather than statistical, we review some simple proposals to aid researchers in interpreting statistical outputs. These proposals emphasize logical and information concepts over probability, and thus may be more robust to common misinterpretations than are traditional descriptions. The latter treat statistics as referring to targeted hypotheses conditional on background assumptions. In contrast, we advise reinterpretation of P-values and interval estimates in unconditional terms, in which they describe compatibility of data with the entire set of analysis assumptions. We use the Shannon transform of the P-value p, also known as the surprisal or S-value s=-log(p), to provide a measure of the information supplied by the testing procedure against these assumptions, and to help calibrate intuitions against simple physical experiments like coin tossing. We also advise tabulating or graphing test statistics for alternative hypotheses, and interval estimates for different percentile levels, to thwart fallacies arising from arbitrary dichotomies. We believe these simple reforms are well worth the minor effort they require.
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