Tunneling spectroscopy is often used to study electronic properties of metal and semiconductor surfaces. The normalized differential conductivity of tunneling was considered to be an invariant quantity showing the surface density of states (DOS). This understanding is critically examined in this paper using known tunneling theory. We assume a number of possible surface DOS distributions to simulate the I-V characteristics and the normalized differential conductivity. The obtained results show that this conductivity does provide quite a good invariant quantity and it indicates some features of the surface state distributions. In particular, it shows empty state features of samples more strikingly than occupied ones. A sign reversion of the conductivity may occur in the positive sample-voltage range related to a decrease in DOS. An explanation is given in terms of electron tunneling probability depending on electron energy.