The Language of Betting as a Strategy for Statistical and Scientific Communication

Abstract: The established language for statistical testing --- significance levels, power, and p-values --- is overly complicated and deceptively conclusive. Even teachers of statistics and scientists who use statistics misinterpret the results of statistical tests, tending to misstate their meaning and exaggerate their certainty. We can communicate the meaning and limitations of statistical evidence more clearly using the language of betting. This paper calls attention to a simple betting interpretation of likelihood ratios. This interpretation leads to methods that lend themselves to meta-analysis and accounting for multiple testing. It is closely related to the interpretation of probability as frequency, but it does not encourage the fallacy that probabilistic models imply the existence of unseen alternative worlds. For more on the betting interpretation of probability, see \cite{Shafer/Vovk:2019} and the other working papers at www.probabilityandfinance.com.