Practicing safe statistics with the mid‐p

Abstract The mid‐p‐value is the standard p‐value for a test minus half the difference between it and the nearest lower possible value. Its smaller size lends it an obvious appeal to users — it provides a more significant‐looking summary of the evidence against the null hypothesis. This paper examines the possibility that the user might overstate the significance of the evidence by using the smaller mid‐ p in place of the standard p ‐value. Routine use of the mid‐ p is shown to control a quantity related to the Type I error rate. This related quantity is appropriate to consider when the decision to accept or reject the null hypothesis is not always firm. The natural, subjective interpretation of a p ‐value as the probability that the null hypothesis is true is also examined. The usual asymptotic correspondence between these two probabilities for one‐sided hypotheses is shown to be strengthened when the standard p ‐value is replaced by the mid‐ p .