Conductors and minimal discriminants are two measures of degeneracy of the singular fiber in a family of hyperelliptic curves. In the case of elliptic curves, the Tate-Ogg-Saito formula shows that (the negative of) the Artin conductor equals the minimal discriminant. In the case of genus two curves, Qing Liu showed that equality no longer holds in general, but the two invariants are related by an inequality. We extend Liu’s inequality to hyperelliptic curves of arbitrary genus assuming that the residue characteristic is large compared to the genus.