  Multiterminal measurements have typically been employed to examine electronic
properties of strongly correlated electronic materials such as transition metal
oxides without the influence of contact effects. In contrast, in this work we
investigate the interface properties of Fe$_3$O$_4$ with different metals, with
the contact effects providing a window on the physics at work in the correlated
oxide. Contact resistances are determined by means of four-terminal electrical
measurements as a function of source voltage and temperature. Contact
resistances vary systematically with the work function of the electrode metal,
$\phi(M)$, $M=$Cu, Au and Pt, with higher work function yielding lower contact
resistance. This trend and the observation that contact resistances are
directly proportional to the Fe$_3$O$_4$ resistivity are consistent with
modeling the oxide as an effective $p$-type semiconductor with hopping
transport. The jumps in contact resistance values at the bias-driven
insulator-metal transition have a similar trend with $\phi$($M$), consistent
with the transition mechanism of charge gap closure by electric field.
