  We revisit the work of Chang and Ran on bounding the slopes of
$\overline{\mathscr{M}_{15}}$ and $\overline{\mathscr{M}_{16}}$, correct one of
the formulas used at the conclusion of the argument, and recompute the lower
bounds on the slopes, yielding $s(\overline{\mathscr{M}_{15}})>6.5$ but not for
$\overline{\mathscr{M}_{16}}$. Our contribution only involves plugging in
formulas.
