Why are p-values controversial?

While it is often argued that a p-value is a probability; see Wasserstein & Lazar (2016), we argue that a p-value is not defined as a probability. A p-value is a bijection of the sufficient statistic for a given test which maps to the same scale as the type I error probability. As such, the use of p-values in a test should be no more a source of controversy than the use of a sufficient statistic. It is demonstrated that there is, in fact, no ambiguity about what a p-value is, contrary to what has been claimed in recent public debates in the applied statistics community. We give a simple example to illustrate that rejecting the use of p-values in testing for a normal mean parameter is conceptually no different from rejecting the use of a sample mean. The p-value is innocent; the problem arises from its misuse and misinterpretation. The way that pvalues have been informally defined and interpreted appears to have led to tremendous confusion and controversy regarding their place in statistical analysis.