Earlier in this chapter, we defined the absolute voltage as the potential between a given electrode and the average of the entire surface of the head. This is a strictly theoretical concept, because we can’t record from the entire surface of the head. How would you get an electrode on the bottom side of someone’s skull?
However, many researchers try to approximate the absolute voltage by using the average across all the electrode sites in their recording as the reference. Although this has been shown to be a good approximation for one particular generator site when an extremely broad array of electrodes is used (Dien, 1998), it often provides a very poor approximation of the absolute voltage (see Chapter 7 in Luck, 2014). Nonetheless, the average reference can still be useful under some conditions. For example, it is commonly used for studies of face-elicited N170 activity (Rossion & Jacques, 2012), and we used it for the N170 paradigm in the ERP CORE (Kappenman et al., 2021).
In this exercise, we’ll re-reference the data in Grand_N400_diff.erp to the average of all the EEG electrodes. To accomplish this, load Grand_N400_diff.erp into ERPLAB if it’s not already loaded, and make sure that the original ERPset is active (rather than the ERPsets that you created with Cz or Oz as the reference). Select EEGLAB > ERPLAB > ERP Operations > ERP Channel Operations, clear out any equations that remain in the text box from the last time you used this routine, and make sure that the Mode is set to Create new ERPset.
Now click the Reference assistant button. In the text box labeled Ch_REF near the top of the window, type avgchan( 1:28 ). This indicates that you want to use the average of channels 1–28 as the reference. We’re excluding channels 29 and 30, which are the EOG channels. As before, select Exclude these channels with 29 30 in the text box. Then click OK. You’ll see that the list of equations subtracts avgchan( 1:28) from each individual channel, except for the EOG channels. If you go through the algebra of this subtraction, you’ll see that this will create EEG channels that are equal to the active electrode minus the average of all the electrodes. Now click RUN, and then name the new ERPset Grand_N400_diff_AvgRef.
Now plot the data. Just as you saw with the Oz reference, you’ll see that the difference between related and unrelated targets with the average reference is positive at some sites and negative at others. This is an inevitable consequence of using the average of all sites as the reference. That is, at every moment in time, the average-referenced voltages across the different electrode sites must sum to zero, so the voltage will be negative at some electrode sites and positive at others. This is true both for parent waveforms (e.g., the waveforms for the related and unrelated target words) and for difference waveforms. So, when you use the average reference, don’t think you’ve discovered something interesting when you find that your experimental effect is positive in some channels and negative in others. It’s just a necessary consequence of the algebra. Some components and experimental effects will exhibit such polarity inversions with other references, but it is inevitable with the average reference.
I’d like to point out using the average across sites as the reference in order to approximate the absolute voltage assumes that the surface of the head sums to zero, but this is only true for spheres. I have yet to meet someone with a spherical head. And no neck. Fortunately, there is a way to estimate the true zero, called the Reference Electrode Standardization Technique (REST), and there is an EEGLAB plugin that implements it (Dong et al., 2017). I haven’t tried it myself or looked at the math, so I don’t have an opinion about whether it’s useful and robust. But if you really want to get an estimate of the absolute voltage, REST seems like the best current approach.
