S-values and Surprisal intervals to Replace P-values and Confidence Intervals

Accepted - January 2024

Abstract

Misuse of statistical significance continues to be prevalent in science. The absence of intuitive explanations of this concept often leads researchers to incorrect conclusions. For this reason, some statisticians suggest adopting S-values (surprisals) instead of P-values, as they relate the statistical relevance of an event to the number of consecutive heads when flipping an unbiased coin. This paper introduces the concept of surprisal intervals (S-intervals) as extensions of confidence/compatibility intervals. The proposed approach imposes the assessment of outcomes in terms of more and less surprising than some values, instead of statistically significant and statistically non-significant. Moreover, a novel methodology for presenting multiple consecutive S-intervals (or compatibility intervals as well) in order to evaluate the variation in surprise (or compatibility) with various target hypotheses is discussed.