  This paper derives a new powerful test for mediation that is easy to use.
Testing for mediation is empirically very important in psychology, sociology,
medicine, economics and business, generating over 100,000 citations to a single
key paper. The no-mediation hypothesis $H_{0}:\theta_{1}\theta _{2}=0$ also
poses a theoretically interesting statistical problem since it defines a
manifold that is non-regular in the origin where rejection probabilities of
standard tests are extremely low. We prove that a similar test for mediation
only exists if the size is the reciprocal of an integer. It is unique, but has
objectionable properties. We propose a new test that is nearly similar with
power close to the envelope without these abject properties and is easy to use
in practice. Construction uses the general varying $g$-method that we propose.
We illustrate the results in an educational setting with gender role beliefs
and in a trade union sentiment application.
