The accuracy of EEG forward models partially depends on the conductivity values of the head tissues. Yet the influence of the conductivity parameters on the model output is still not well understood. In this paper, we apply a variance-based sensitivity analysis method to the EEG forward model. This method has the advantage to be a global sensitivity analysis, meaning that the influence of each parameter is quantified with all the parameters varying at the same time. This gives much more information than one-at-a-time sensitivity analysis and local analysis using derivatives or perturbations. In particular, it helps to understand the interaction between parameters, which can be very important in non-linear models, and can not be taken into account with other sensitivity analysis. By performing a variance-based sensitivity analysis of the scalp potential topographies on a three-layer EEG forward model (brain, skull, scalp), we found out several results. For a superficial dipolar source, the influence of the brain conductivity is negligible and the influence of skull and scalp conductivities appears mainly via their interaction. This means that for such a model, almost all the variance of the scalp topographies is driven by one parameter, which is a function of skull and scalp conductivities. Results are also presented in the case of skull anisotropy and with a scalp current injection (EIT). This global sensitivity analysis gives new information about EEG forward models : it identifies the main input factors among conductivities which need further modelization refinment, and gives directions on how to calibrate these parameters.