Frank Harrell doesn’t like p-values:
In my [Frank’s] opinion, null hypothesis testing and p-values have done significant harm to science. The purpose of this note is to catalog the many problems caused by p-values. As readers post new problems in their comments, more will be incorporated into the list, so this is a work in progress.
His attitudes are similar to mine:
I [Andrew] agree with most of the ASA’s statement on p-values but I feel that the problems are deeper, and that the solution is not to reform p-values or to replace them with some other statistical summary or threshold, but rather to move toward a greater acceptance of uncertainty and embracing of variation.
I also agree with Harrell not to take the so-called Fisher exact test seriously (see Section 3.3 of this paper from 2003).