In neurophysiology, it is important to determine the causal relationships between neuronal sites. The major problem with existing methods for quantifying the causality in the brain, e.g. Granger causality, is that they assume an multi-variate autoregressive signal model for the multi-channel EEG signals and do not take the nonlinear dependencies between neuronal oscillations into account. In this paper, we propose to quantify the causality of the interactions based on the directed information (DI) criterion, which measures the information flow between two signals over time. The proposed measure is applied to real EEG data from control and schizophrenic subject groups. The significance of the computed DI values are verified by Fourier bootstrapping technique.