On two-sided p-values for non-symmetric distributions

Two-sided statistical tests and p-values are well defined only when the test statistic in question has a symmetric distribution. A new two-sided p-value called conditional p-value $P_C$ is introduced here. It is closely related to the doubled p-value and has an intuitive appeal. Its use is advocated for both continuous and discrete distributions. An important advantage of this p-value is that equivalent 1-sided tests are transformed into $P_C$-equivalent 2-sided tests. It is compared to the widely used doubled and minimum likelihood p-values. Examples include the variance test, the binomial and the Fisher's exact test.