How the brain processes sensory input to produce goal-oriented behavior is not well-understood. Advanced data acquisition technology in conjunction with novel statistical methods holds the key to future progress in this area. Recent studies have applied Granger causality to multivariate population recordings such as local field potential (LFP) or electroencephalography (EEG) in event-related paradigms. The aim is to reveal the detailed time course of stimulus-elicited information transaction among various sensory and motor cortices. Presently, interdependency measures like coherence and Granger causality are calculated on ongoing brain activity obtained by removing the average event-related potential (AERP) from each trial. In this paper we point out the pitfalls of this approach in light of the inevitable occurrence of trial-to-trial variability of event-related potentials in both amplitudes and latencies. Numerical simulations and experimental examples are used to illustrate the ideas. Special emphasis is placed on the important role played by single trial analysis of event-related potentials in experimentally establishing the main conclusion.