The p-value has been debated exorbitantly in the last decades, experiencing fierce critique, but also finding some advocates. I share the point of view that null hypothesis testing needs to be expanded to answer the question whether an effect is relevant rather than whether it is zero. The fundamental issue with its misleading interpretation stems from its common use for testing the unrealistic null hypothesis of an effect that is precisely zero. A meaningful question asks instead whether the effect is relevant.
It is then unavoidable that a threshold for relevance is chosen. Considerations that can lead to agreeable conventions for this choice are presented for the standard}{several commonly used statistical situations. Based on the threshold, a simple quantitative measure of relevance emerges naturally. Statistical inference for the effect should be based on the confidence interval for the relevance measure. A classification of results that goes beyond a simple distinction like ``significant / non-significant'' is proposed. On the other hand, if desired, a single number called the ``secured relevance'' may summarize the result, like the p-value does it, but with a scientifically meaningful interpretation.
This is the abstract of a paper that is under revision with PLOS-One.