  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.
