Surprise!

Measures of information and surprise, such as the Shannon information (the $S$ 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".