Overview
What is a SecondGeneration pvalue?
The secondgeneration pvalue (SGPV) is an extension of the pvalue that formally accounts for scientific relevance. It turns out that verifying that a statistically significant result is scientifically meaningful is not only good scientific practice, but it is also a natural way to control the Type I error rate. As a result, the secondgeneration pvalue has nice frequency properties that are automatically controlled through the sample size.
The secondgeneration pvalue is essentially the proportion of datasupported hypotheses that are null, or practically null, hypotheses. This is an advance for datarich environments, where traditional pvalue adjustments are needlessly punitive.
About the SGPV
Interpretation and Properties
The secondgeneration pvalue, denoted by Pδ, depends on a interval null hypothesis. The subscript δ denotes this dependence and distinguishes it from the classical pvalue.
Interval null hypotheses are constructed by incorporating information about the scientific context – such as inherent limits on measurement precision, clinical significance, or scientific significance – into statistical hypotheses that are stated a priori. The interval null should contain, in addition to the precise point null hypothesis, all other point hypotheses that are practically null and would maintain the scientific null premise. While the point null may be numerically distinct, all the hypotheses in the interval null are considered scientifically equivalent to the null premise.
Given a interval null hypothesis, the secondgeneration pvalue, Pδ, has the following properties:

The secondgeneration pvalue, Pδ, is a number between 0 and 1.

Pδ is essentially the fraction of datasupported hypotheses that are null hypotheses.

When Pδ = 0, the data only support hypotheses that are scientifically or clinically meaningful, i.e., those that are meaningful alternative hypotheses.

When Pδ = 1, the data only support null, or practically null, hypotheses, i.e., those that are not scientifically or clinically meaningful.

When Pδ ≈ 1/2, the data are strictly inconclusive. The degree of inconclusiveness is represented by Pδ.

Pδ has improved error rate control.

Pδ, because it is not a probability, is not adjusted for multiple comparisons.
A distinguishing feature of secondgeneration pvalues is that they are intended as summary statistics that indicate when a study has met its a priori defined endpoint.
Links
Further reading and exploring

Papers on SGPVs: Plos ONE & The American Statistician & Shrinkage and SGPVs

Software: R package for SGPVs (CRAN) & STATA & Python

Talks with SPGV context: ASA SSI 2017 & Hollister ENAR 2019 & Welty ENAR 2019