Efficacy of Sign Test

Definition

Let $T$ be a test statistic and $\mu ({\theta }_n):=E_{{\theta }_n}(T)$, then the efficacy of $T$ is defined as $c_T:={\lim }_{n\to \infty }\frac{{\mu }^{\prime }(0)}{[n\mathrm{Var}(T){]}^{1/2}}$ where ${\mu }^{\prime }(0)$ can be interpreted as the rate of change of the mean of $T$