P values are often taken to be something they are not, a probability measure regarding the truth of the null hypothesis. P values work well if we interpret them as an index of compatibility between the data and a spectrum of parameter values, as graphed in the P value function. But the proclivity to degrade P values into dichotomous bins corresponding to statistical significance, coupled with widespread misinterpretation of what a P value measures, is reason to seek an alternative that provides clearer, more intuitive interpretations. The S-value, or surprise index, is a possible alternative. It measures the degree to which the observed data are unusual, given the null hypothesis or other test hypothesis, by translating the data into the surprise equivalent of consecutive coin flips that all come up heads. S-values may help to avoid the worst practices regarding P values-the tendency to dichotomize them into significance tests and to interpret them as probability statements about the null hypothesis. If adopting the S-value could move us away from significance testing, it is worth a try.
