Measures of information and surprise, such as the Shannon information value (S value), quantify the signal present in a stream of noisy data. We illustrate the use of such information measures in the context of interpreting P values as compatibility indices. S values help communicate the limited information supplied by conventional statistics and cast a critical light on cutoffs used to judge and construct those statistics. Misinterpretations of statistics may be reduced by interpreting P values and interval estimates using compatibility concepts and S values instead of "significance" and "confidence."
Keywords: P value; S value; compatibility; confidence intervals; information; random error; significance tests; statistical inference.
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