We already have multiple threads tagged as p-values that reveal lots of misunderstandings about them. Ten months ago we had a thread about psychological journal that "banned" $p$-values, now American Statistical Association (2016) says that with our analysis we "should not end with the calculation of a $p$-value".
American Statistical Association (ASA) believes that the scientific community could benefit from a formal statement clarifying several widely agreed upon principles underlying the proper use and interpretation of the $p$-value.
The committee lists other approaches as possible alternatives or supplements to $p$-values:
In view of the prevalent misuses of and misconceptions concerning $p$-values, some statisticians prefer to supplement or even replace $p$-values with other approaches. These include methods that emphasize estimation over testing, such as confidence, credibility, or prediction intervals; Bayesian methods; alternative measures of evidence, such as likelihood ratios or Bayes Factors; and other approaches such as decision-theoretic modeling and false discovery rates. All these measures and approaches rely on further assumptions, but they may more directly address the size of an effect (and its associated uncertainty) or whether the hypothesis is correct.
So let's imagine post-$p$-values reality. ASA lists some methods that can be used in place of $p$-values, but why are they better? Which of them can be real-life replacement for a researcher that used $p$-values for all his life? I imagine that this kind of questions will appear in post-$p$-values reality, so maybe let's try to be one step ahead of them. What is the reasonable alternative that can be applied out-of-the-box? Why this approach should convince your lead researcher, editor, or readers?
As this follow-up blog entry suggests, $p$-values are unbeatable in their simplicity:
The p-value requires only a statistical model for the behavior of a statistic under the null hypothesis to hold. Even if a model of an alternative hypothesis is used for choosing a “good” statistic (which would be used for constructing the p-value), this alternative model does not have to be correct in order for the p-value to be valid and useful (i.e.: control type I error at the desired level while offering some power to detect a real effect). In contrast, other (wonderful and useful) statistical methods such as Likelihood ratios, effect size estimation, confidence intervals, or Bayesian methods all need the assumed models to hold over a wider range of situations, not merely under the tested null.
Are they, or maybe it is not true and we can easily replace them?
I know, this is broad, but the main question is simple: what is the best (and why), real-life alternative to $p$-values that can be used as a replacement?
ASA (2016). ASA Statement on Statistical Significance and $P$-values. The American Statistician. (in press)