Motivation p-values and standard null hypothesis testing have come under intense scrutiny in recent years (Wasserstein et al., 2016, Benjamin et al., 2018); s-values and safe tests offer several advantages. Most importantly, in contrast top-values, s-values behave excellently under optional continuation, the highly common practice in which the decision to perform additional tests partly depends on the outcome of previous tests. A second reason is their enhanced interpretability, and a third is their flexibility: s-values based on Fisherian, Neyman-Pearsonian and Bayes-Jeffreys’ testing philosophies all can be accommodated for. These three types of s-values can be freely combined, while preserving Type I error guarantees; at the same time, they keep a clear (monetary) interpretation even if one dismisses ‘significance’ altogether, as recently advocated by Amrhein et al. (2019).

Here come S-values! https://arxiv.org/abs/1906.07801

It looks interesting - I will give it a read and comment further.

That's more or less how I understand this work.