Before revision:  Analytical characterizations of the distributions of p-values under the null of no p-hacking and the alternative where there is p-hacking allow us to both analyze the power of existing tests and provide new more powerful statistical tests for p-hacking . Results are extended to practical situations where there is publication bias and when reported p-values are rounded.
After revision:  Specifically, the shape of the power functions results in both complete monotonicity as well as bounds on the distribution of p-values under the null of no p-hacking and the alternative where there is p-hacking allow us to both analyze the power of existing tests and provide new more powerful statistical tests for p-hacking . Results are extended to practical situations where there is publication bias and when reported p-values are rounded.