Calculation
ERPs can be reliably measured using electroencephalography (EEG), a procedure that measures electrical activity of the brain over time using electrodes placed on the scalp. The EEG reflects thousands of simultaneously ongoing brain processes. This means that the brain response to a single stimulus or event of interest is not usually visible in the EEG recording of a single trial. To see the brain's response to a stimulus, the experimenter must conduct many trials (100 or more) and average the results together, causing random brain activity to be averaged out and the relevant waveform to remain, called the ERP.
The random (background) brain activity together with other bio-signals (e.g., EOG, EMG, EKG) and electromagnetic interference (e.g., line noise, fluorescent lamps) constitute the noise contribution to the recorded ERP. This noise obscures the signal of interest, which is the sequence of underlying ERPs under study. From an engineering point of view it is possible to define the signal-to-noise ratio (SNR) of the recorded ERPs. The reason that averaging increases the SNR of the recorded ERPs (making them discernible and allowing for their interpretation) has a simple mathematical explanation provided that some simplifying assumptions are made. These assumptions are:
- The signal of interest is made of a sequence of event-locked ERPs with invariable latency and shape
- The noise can be approximated by a zero-mean Gaussian random process of variance which is uncorrelated between trials and not time-locked to the event (this assumption can be easily violated, for example in the case of a subject doing little tongue movements while mentally counting the targets in an oddball paradigm).
Having defined, the trial number, and, the time elapsed after the th event, each recorded trial can be written as where is the signal and is the noise (Note that, under the assumptions above, the signal does not depend on the specific trial while the noise does).
The average of trials is
- .
The expected value of is (as hoped) the signal itself, .
Its variance is
- .
For this reason the noise amplitude of the average of trials is times that of a single trial.
Wide amplitude noise (such as eye blinks or movement artifacts) are often several orders of magnitude larger than the underlying ERPs. Therefore, trials containing such artifacts should be removed before averaging. Artifact rejection can be performed manually by visual inspection or using an automated procedure based on predefined fixed thresholds (limiting the maximum EEG amplitude or slope) or on time-varying thresholds derived from the statistics of the set of trials.
Read more about this topic: Event-related Potential
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