The normalized discrepancy for trees $T_1$ and $T_2$ is given by $\textrm{disc}(T_1, T_2) = \left| \frac{d_{\text{split}}(T_1, T_2)}{2n-6} - \frac{d_q(T_1, T_2)}{2q(n)} \right|$ where $d_{\text{split}}(T_1, T_2)$ is the split distance between $T_1$ and $T_2$ and $d_q(T_1, T_2)$ is the quartet distance between $T_1$ and $T_2$.