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The accuracy of forward models for EEG partly depends on the conductivity values of the head tissues. Yet, the influence of the conductivities on the model output is still not well understood. In this paper, we apply a variance-based sensitivity analysis method to the most common EEG forward models (three or four layers). This method is global because it quantifies the influence of each parameter with all the parameters varying at the same time. With nonlinear models, it helps to understand the interaction between parameters, which is not possible with simple sensitivity analyses (one-at-a-time variations, derivatives, and perturbations). By analyzing the potential topographies at the electrodes, we obtained several results. For a shallow dipole, the EEG topographies are mainly sensitive to the interaction between skull and scalp conductivities. It means that the variability of the EEG topographies is driven mostly by a function of skull and scalp conductivities. Similar results are presented for skull anisotropy and a current injection as performed in electrical impedance tomography. This global sensitivity analysis gives new information about EEG forward models-it identifies the main input parameters that need model refinement-and directions on how to calibrate these models.