In this study we deal with the problem of normal contact between rough surfaces. A power spectral density of the asperity heights which obeys a power-law within a given range of wavelengths has been considered. Hence, the resolution dependence of the statistical parameters computed according to the random process theory, of the plasticity index and of the contact predictions provided by stochastic and fractal contact models is discussed and emphasized. It is demonstrated that the plasticity index diverges to infinity when the lower cut-off length of the system vanishes, whereas the slope of the real contact area versus normal load curve tends to zero. In this limit case stochastic and fractal approaches predict either a vanishing real contact area or an infinite normal pressure, regardless of the asperity deformation assumptions. On the other hand, when a non-zero lower cut-off length exists, finite contact predictions can be obtained by applying the contact models at that scale length. This possibility is numerically investigated and, comparing contact results of several models, it is shown that the plasticity index plays an important role for the characterization of the interface mechanical response.