The size-dependent electrical resistivity of single-layer graphene ribbons has been studied experimentally for ribbon widths from 16 nm to 320 nm. The experimental findings are that the resistivity follows a more dramatic trend than that seen for metallic nanowires of similar dimensions, due to a combination of surface scattering from the edges, band-gap related effects and shifts in the Fermi level that show a strong width dependence. We show that the Charge Neutrality point switches polarity below a ribbon width of around 50 nm, and that at this point, the thermal coefficient of resistance is a maximum. The majority doping type therefore can be controlled by altering ribbon width. We also demonstrate that an alumina passivation layer has a significant effect on the mean free path of the charge carriers within the graphene, which can be probed directly via measurements of the width-dependent resistivity. We propose a model for conduction that takes edge and confinement effects into account.