A New Measure of Overlap: An Alternative to the p--value

In this paper we present a new measure for the overlap of two density functions which provides motivation and interpretation currently lacking with benchmark measures based on the proportion of similar response, also known as the overlap coefficient. We use this new measure to present an alternative to the $p$--value as a guide to the choice of treatment in a comparative trial; where a current treatment and a new treatment are undergoing investigation. We show that it is possible to reject the null hypothesis; i.e. the new treatment is significantly different in response to the old treatment, while the proposed new summary for the same experiment indicates that as low as one in ten individuals subject to the new treatment behave differently to individuals on the old one.