For historical reasons, many ERP studies use the mastoid process (the thick bone behind the ear) as the reference electrode. This is why the data shown in Figure 5.1D use the left mastoid as the reference. However, it seems a little odd to use a reference that is lateralized to one side of the head. Might this lead to some kind of hemispheric bias in the data? In reality, this isn’t usually a significant problem. However, just to be safe, many researchers use the average of the left and right mastoids (Lm and Rm) as the reference. In this exercise, we’re going to look at two ways of transforming the data to reference the simulation data to the average of Lm and Rm. This exercise exemplifies an important principle, namely that data recorded using one electrode site as the reference can easily be re-referenced offline, in software, to one of the other electrode sites (or some combination of electrode sites).
Open up the spreadsheet from the previous exercise and make sure everything is back to the way it was originally (or download the spreadsheet again). Make 3 new columns just to the right of the columns for the referenced data, and label them Fz-Avg, Cz-Avg, and Pz-Avg. If you look at how the referencing is done for the Fz channel at the first time point (cell O4 of the spreadsheet), you’ll see that the referenced value is the single-ended value for Fz (cell J4) at this time point minus the single-ended value for Lm (cell M4, but with a “$” symbol before the letter so that it remains column M even if we paste it somewhere else). This is the subtraction that I used to reference the data in Figure 5.1.
We want to change this so that we subtract the average of Lm and Rm from Fz. That average is simply (Lm+Rm)/2, which would be ($M4+$N4)/2 given that Lm is in column M and Rm is in column N of our spreadsheet. So, to create a value for Fz using the average of Lm and Rm as the reference, we need the equation for the first time point to be =J4-($M4+$N4)/2. Go ahead and put this equation into cell S4, which should be in the new column that you labeled Fz-Avg. If you then copy and paste this equation into cells T4 and U4, the J4 should update to K4 and L4, respectively. If you then copy and paste these three cells to all the remaining time points, the row numbers should update, and you’ll have the appropriate values for all the cells.
Now compare the new values you created to the original referenced values (with Lm as the reference). They should be pretty similar. This is because the single-ended signal at Rm is nearly identical to the single-ended signal at Lm, so the average of Lm and Rm is nearly identical to the Lm signal. In turn, this is because the weights for Lm and Rm are pretty similar. However, there may be situations in which the Lm and Rm signals are not so similar (e.g., if the generator dipole happened to be near Lm without a generator near Rm). This is why it’s a good idea to use the average of Lm and Rm rather than just using one side.
In most systems, you don’t have access to the single-ended signals, so you wouldn’t be able to use this approach for referencing the data to the average of the two mastoids. For example, the original data might all be referenced to Lm. However, if you have a recording of Rm (also referenced to Lm), there is a trick you can use to re-reference the data to the average of Lm and Rm. The trick was described by Paul Nunez in his classic book on the biophysics of EEG (Nunez, 1981), and the algebra is spelled out in Chapter 5 of Luck (2014). Specifically, if you subtract 50% of the Rm signal from each channel that was already referenced to Lm, this is equivalent to taking the single-ended data from the active electrode and subtracting the average of the single-ended Lm and Rm signals. For example, to re-reference Fz to the average of Lm and Rm, you would take the already-referenced Fz channel (which is really Fz – Lm) and subtract 0.5 of the Rm channel (which is really Rm – Lm).
Create three new columns labeled Fz-Avg2, Cz-Avg2, and Pz-Avg2. Put equations into these columns that use this different approach to re-referencing. That is, take the values that were already referenced (Columns O-R) and subtract 0.5 times the Rm channel from the Fz, Cz, and Pz channels. Once you’ve created these three new channels, compare them with the previous set you created. You should see that these two ways of referencing to the average of Lm create exactly identical results. However, the first method can’t be used in most systems, because it requires access to the single-ended signals, so you may need to use the second method. When you’re working with real data instead of simulated data, you’ll do the referencing in ERPLAB using Channel Operations rather than in a spreadsheet. However, Channel Operations uses equations that are much like the spreadsheet equations. I hope that the experience you’ve now gotten with the spreadsheet will give you a better understanding of how the equations work in Channel Operations.
