The following is information from R. Simon regarding the Neuroscan Synamp2 Quik-caps set-up at CMU.
"The information contained in the Synamp2 manual regarding the referencing system is not accurate; there was a feature whose implementation was planned, but never fully executed.
Basically, the collection of any electrical signal needs some type of a baseline, "ground" electrode (more of a signal ground, and not a true earth ground). In order to measure voltage, we need a signal ground - thus, the need for a ground electrode in the cap. The amplitude of this ground is generally 0 (i.e. measured against itself is zero). However, in order for an electrophysiological signal to be considered as having relevance to the site of recording, it needs to be expressed as a differential between two sites indicating nonzero amplitudes. An electrical recording from anywhere on the body will show a signal, so in order to for relevance to be attributed to that signal, a nearby recording needs to be subtracted from that original recording. Therefore, you need an electrode devoted as your physiological reference. This signal is also collected against signal ground, so it is nonzero. Thus, the recording at Cz is equal to Cz-REF, with both signals having been collected against the signal ground (GND).
With the Synamp2 Quik-caps, there is a specific wire that is used as the carrier for the reference signal; this wire is input into the "active reference" input on the headbox, and this is the signal used as the REF in the differential measurements. The GND signal is used as signal ground, and is hard-wired to the electrode located just posterior to FPz. The REF electrode, however, is adaptable in the Synamp2 Quik-caps. You'll notice on that black wire labeled REF that it terminates in a safety socket connector BEFORE it gets to the electrode. This enables you to connect different electrodes into the REF wire. By default, when the caps are initially delivered to customers, the REF is connected to an electrode located between Cz and CPz. Many people prefer to use a non-cortical site as reference (e.g. mastoid, earlobe, nasion) so as to eliminate sacrificing a site of interest.
The Synamp2 64-channel caps also have a lead for each mastoid, and these are wired to active channels on the headbox. Thus if you used the cap "out of the box" the REF would be between Cz and CPz, and both M1 and M2 would be collected as active channels. It sounds like someone disconnected the M1 electrode from the M1 wire (the drop downs have an in-line touch-proof connection, like the REF), and plugged that into the REF wire. This means that M1 is no longer being collected as an active channel; by plugging it into REF, this makes the M1 electrode the reference electrode (since its signal is now carried along the REF wire to the "active reference" input in the headbox. The fact that the electrode plugged into REF is labeled M1 is actually immaterial; for example, if this electrode was attached to the nasion site, that would be the reference. NOTE: whatever channel is used as the "active reference" is NOT listed in the "channel assignment table."
So far, so good.
However, typically you want the reference site to be equidistant from all electrodes, in order to not establish a hemispheric bias. Thus, the reference is either along the midline, or is a combination of symmetrical sites in both hemispheres (usually either the mastoid behind each ear, or each earlobe). In the old days, it was common to fuse electrodes on both sites together into one connector, and this was plugged into the reference input. This is called a "linked ears/mastoid" reference scheme. However, recent research has shown this type of scheme is not optimal, as it can actually attenuate effects of laterality; plus, it inhibits proper inverse solutions for performing dipole analysis/source localization. Thus it has grown more common to use an "average mastoid/ears" reference: one ear/mastoid is used as reference, and the other is collected as an active channel. Then, offline, the electrodes are re-referenced to HALF the other mastoid site.
The reason it's HALF is that, if you simply re-reference to the other mastoid, you are essentially just reassigning the reference electrode from one site to the next. This is not what we want to accomplish; we want to ultimately set the reference as an average of BOTH mastoids/ears. Remember, each active electrode is essentially a differential, thus:
Cz = Cz - REF
Let's say that our REF is M1, and M2 is collected as an active channel. Sticking with Cz as the focal point in our example, we have:
Cz = Cz - M1
M2 = M2 - M1
If we re-reference all sites to M2, we are essentially subtracting M2 from Cz. So, we have:
Cz-M2 = (Cz-M1)-(M2-M1)
and you can see how the M1 terms cancel out, leaving Cz-M2. But this is NOT what we want; we eventually want:
Cz = Cz - [(M1+M2]/2]
note the latter term represents the average of the two mastoids. So, how do we re-reference, so we get from the original Cz (Cz-M1) to the above? By subtracting HALF of M2.
Note the equations below:
Cz - M2/2 = (Cz-M1)-[(M2-M1)/2]
removing all brackets leaves
which simplifies to
factoring out the -1/2 in the mastoids we have
The easiest way to accomplish this re-referencing (obtaining an AVERAGE mastoid reference, when a single mastoid is used as the original reference) is to initially set the bipolar channels (typically the EOGs, EMG and EKG) as "skipped operations" so they are NOT re-referenced; we want to leave those as-is. Then, go into the Transforms menu, and select GFP/Reference. In that dialog box, just select the other mastoid as the only channel AND then make sure "include implicit analog reference" is checked ON. This basically includes the original reference as part of the calculation for the new reference. Thus, it would calculate the average of the M2 channel, and the original reference, which is M1.
It is important to note that M1 essentially equals M1-M1 - any electrode referenced to itself is zero. Thus, the average of M1 and M2 essentially simplifies to...M2/2!"