The Death of the Statistical Tests of Hypotheses

Some foundations of statistical science have been questioned recently, especially the use and abuse of p-values. See also this article published in FiveThirtyEight.com. Statistical tests of hypotheses rely on p-values and other mysterious parameters and concepts that only the initiated can understand: power, type I error, type II error, or UMP tests, just to name a few. Pretty much all of us have had to learn this old stuff (pre-dating the existence of computers) in some college classes. Sometimes results from a statistical test will be published in a mainstream journal - for instance about whether or not global warming is accelerating - using the same jargon that few understand, and accompanied by misinterpretations and flaws in the use of the test itself.