I will conduct an EEG study and I have the choice between a 32 or 64 channel EEG system. Which system would you recommand for event-related potentials (ERPs)?
the optimal number of channels in an EEG study depends on multiple factors, the most important ones are:
1. Research question(s) and type(s) of data analysis: If you are planning to run a simple ERP study on relatively well-known ERP components (MMN, P300, N400, etc.) and are not expecting to do fine-grained analyses of scalp topography (for which ERPs/EEG would not be the best method anyway), then 32 or even fewer electrodes may be perfectly sufficient. Often researchers use 64 or even 128 electrodes and then have no idea of how to analyze the data, so they group them in 6-15 'regions of interest' (ROIs), which ultimately gives you similar data as if they had run the study with 6 or 15 electrodes. Moreover, they may lose some channels during the experiment and will have to exclude or replace the data (e.g., by data interpolation). Preparing fewer electrodes is much easier and makes more sense (see point #2). However, if you want to do complex data analyses including source localization, more electrodes are generally an advantage. If data preprocessing involves artefact correction (e.g., eyeblinks) based on ICA, then you should not use less then 32 electrodes, and 64 would be better.
2. Preparation time (injecting gel to establish contact and lowering the impedance at each electrode): preparing and monitoring 64 channels takes much more time (30-60 minutes, depending on skills, scalp condition, and EEG/cap system), so some populations (kids, older people, patients) are not unlikely to get impatient and a little frustrated, which will affect their co-operation during the experiment and thus the EEG (and performance) data.
3. Comparability to similar previous research: Again, depending on your specific research question and approach, there may be certain standards in your field that you might want to respect to maximize comparability between your data and previous studies. A good idea might be to carefully read those papers (especially recent ones, as standards tend to change) and to discuss their specific methods - and their relevance to the findings - with your supervisor or collaborators. Ask yourself how you want do analyze the data (both in terms of processing steps and in terms of statistical models, including scalp topography, e.g., with factors hemisphere, laterality within each hemisphere, and position along the anterior-posterior axis).
A last comment: in addition to the number of EEG channels (and potential extra channels such as EOG etc), you might also want to think about the choice of reference electrode(s) and sampling rate. The average of left and right mastoid electrodes is a frequent choice for references, but you should use only one of them as reference online (and calculate the average off-line), i.e., do NOT connect the mastoid electrodes during the recording session. In some research areas, the nose tip is the best reference (e.g., for MMN studies, to distinguish between MMN and N2b components), while others use the average of all electrodes as an offline reference. The respective choice can have major impact on your data, so check out previous studies in your field. For example, with mastoid references you might see an N400 all over the scalp, whereas with an average reference you will always see a local N400 and a compensatory positivity on the scalp (because here the average of all electrodes has to be zero by definition). As to sampling rates, 250 - 500 Hz are often sufficient. Good intro books to EEG/ERPs are the ones by Steve Luck and by Todd Handy, also regarding filter selection etc. During the recording session, it's generally good to filter as little as possible (it's better to filter off-line).
I hope this helps - and wish you good luck with your study !!!
perhaps one brief addition: all the above holds for the case where your 32 and 64 channel EEG systems and caps are the same. If they are not, this would obviously also have an impact. While the pros and cons of the various systems are relatively uncontroversial, researchers still differ in their preferences of which features are the most important ones. For example, some systems (such as EGI's geodesic sensor net) tend to dry out faster than others (not good for a long EEG session), while other systems vary in terms of how much a single problematic channel affects other channels. In short, even if you decide to use fewer electrodes, you may decide to use the 64-channel system (and configure it for fewer channels).
More channels most often means to have more accuracy when applying source localization methods. If accurate source localization is one of your first aims then it could be worth to think about switching from EEG to MEG as data aquisition method. Depending on the available MEG system you can use more then 100 channels, no electrodes have to be glued or fixed on the skalp and the magnetic signals are suffering a little less from physically based distortions.
this is an answer to your follow-up question re linked-mastoids.
Using linked mastoids as the reference during the EEG recording session is not recommended, because you virtually create a short-circuit between the two scalp areas, and you won't be able to find what was really going on at the left versus the right mastoid. To my knowledge, this can never be undone (not even by removing the linked mastoid data and re-estimating them by interpolating data from other electrodes), because even electrodes close to the mastoid will be somewhat influenced by the linking (plus they are usually likely to pick up more EEG activity). The proper procedure is to use only one of the mastoids as the online reference and to treat the other mastoid electrode like any other ('active') EEG channel. Only offline should you 'link' the left and right mastoid electrodes by re-referencing the EEG to their arithmetic average. This procedure also has the advantage that you can first check if each of the two mastoid channels are 'clean'. Thus, if one of them (say ML) is noisy while the other one (MR) is not, I would only use the clean one (rather than 'importing' the noise by mathematically 'linking' them). Obviously, if you started with a linked mastoid reference, this is not an option anymore (and you will never know if the noise came from the left or the right mastoid).
One last point: there has been some debate as to how important it is to average the two mastoid electrodes (or earlobe electrodes) in the first place in order to get a 'proper' reference. Proponents of this view claim that using just one mastoid (or earlobe) electrode would result in lateralized ERP effects (increasing or decreasing the true degree of left- or right-lateralization of these effects). In my own experience, this is usually NOT the case. Whenever I compared left versus right versus averaged mastoid electrodes, the ERPs looked virtually the same (both within subjects and in the group average), and statistical analyses never led to any different effects. In contrast, problems did occur if we used a noisy mastoid channel as a reference (either just that one, or in an average with the clean one). Therefore, in my experience, if one of the mastoid channels looks noisy, it's usually better to use just the other one (even if that means that you end up with different references for different subject data sets). However, before opting for this unusual procedure, you first have to convince yourself (and the reviewers and editors) that this is appropriate and does, in fact, not affect your data. You would do that by demonstrating that in subjects with two clean mastoid channels, it does not matter if you reference to (i) left mastoid, (ii) right mastoid, or (iii) average of both mastoids. Even then, some reviewers may not like (or believe) it. If possible at all, it may be better to simply run more participants and exclude data sets with noisy channels.
a decision of how to select ROIs partly depends on the standards in your field (so checking out previous articles related to or relevant to your own study is a good idea). Apart from that, below is my subjective rationale for (almost always) using (i) anteriority for midline electrodes [Fz,Cz,Pz,Oz] (in a separate analysis) and (ii) anteriority (3-4 levels), hemisphere (left vs right), and laterality (medial vs lateral) for lateral electrodes [e.g., F7/8, F3/4, C3/4, T3/4, T5/6, P3/4]. The array above (roughly corresponding to the 10-20 system) only uses 16 electrodes (4 midline + 16 lateral ones), where each single electrode corresponds to one ROI, but of course you can include more electrodes in any given ROI (either by averaging across multiple electrodes: e.g., Left anterior = F7+F5/2) or by adding more levels of (e.g.) laterality. Some studies use just 4 ROIs (left-right X anterior-posterior) or 6 ROIs (left-right X anterior-central-posterior), thereby collapsing over quite a number of electrodes, which leads to significant data loss. (Why use 30 electrodes if you only analyze 4 ROIs? But of course, if all you want to say is that there is an ERP effect over one quadrant - say left-anterior - and not others, a 2x2 array of ROIs is fine.)
Here is the justification for my own approach: 1. Analyzing the midline electrodes separately from the other (lateral) electrodes often gives you (a) a good idea of condition main effects as well as (b) a first idea of their distribution along the ant-post axis (many ERP components of interest to me such as N400 and P600 happen to be close to the midline). Follow-up analyses (either at individual midline electrodes such as CZ or with pair-wise comparisons such as CZ vs PZ are easy to do, and then you are done). For the N400, very often analyses at lateral electrodes only confirm what you already find at the midline, so in your Methods section you can say that you'll report effects at lateral electrodes only if they go beyond what you've already found at the midline (e.g., a right-lateralization of your P600), simplifying your Results section and allowing you to focus on the important stuff (and avoiding redundant information that doesn't add anything). A second potential advantage of separating the analysis for midline electrodes is that this leads to an even number of levels for the left-to-right dimensions (hemisphere and laterality), as explained next. However, in some studies analyzing the midline electrodes along with the lateral ones may make sense (I'm not elaborating on this here). 2. For lateral electrodes, our model of Anteriority (3-4 levels) x Hemisphere (2) x Laterality (2) gives you two laterality dimensions with exactly 2 levels (instead of, say, 3 levels such as left_hemisphere--midline--right_hemisphere). The advantage of having only 2 levels is that this simplifies your follow-up analyses, which are typically run to ultimately nail down effects in more detail. Thus, if your ANOVA (or mixed model analysis) gives you an interaction of Condition x Hemisphere, this can only mean either of 2 things: the condition effect (say a larger negativity in one condition) is either larger over the left or larger over the right hemisphere. In principle, you don't even have to do any follow-up analysis: all you have to do is look at the voltage map, which will show (and convince your readers/reviewers/editors) which one it is. In contrast, if you use 3 levels (LH-midline-RH) and find a condition x hemisphere(or laterality) interaction, this interaction can mean lots of things (e.g., LH>mid=RH, or LHRH, and so on). This means, you would need to run 3 follow-up analyses (LH vs mid, mid vs RH, and LH vs RH) to figure out what's really going on. If you have a condition x anteriority x hemisphere 3-way interaction, it gets even more complicated, and you have to consider Bonferroni corrections for the many possible follow-up analyses. The same logic holds for factor Laterality (medial vs lateral). If you get a condition x laterality interaction, it usually means that the ERP effect is more prominent near the midline (i.e., at medial electrodes) than at lateral site (or, in rare cases: lateral > medial), and once again just checking your voltage maps would tell you which one it is (not requiring any additional follow-up statistics).
Which leads me to my last point: There is a common misunderstanding of what a significant interaction of, say, Condition x Hemisphere means. Many researchers believe this means that the Condition effect is more significant over one hemisphere than the other, which - in principle - is the wrong interpretation (even though it's often the actual data pattern). Thus what you often see is that researchers follow up the interaction to show that the condition main effect has a smaller p-value in one hemisphere than the other. In rare cases, the p-values will be very similar for both hemispheres, and then some researchers are very confused as this seems to contradict their initial interaction. However, what this interaction really means is: the amplitude difference between conditions (e.g., our N400 difference wave) is significantly larger over one hemisphere than the other. This is why simply looking at voltage maps (illustrating difference waves) is - in principle - sufficient to clarify if the N400 difference is LH>RH or RH>LH. If an N400 amplitude is LARGER over one Hemisphere, this does not necessarily mean it is also more significant (even though this is often true). As even reviewers tend to confuse the magnitude of effects (amplitude difference in microvolts) and the significance of the difference (p-value), I tend to include the follow-up analyses in my own papers too. But strictly speaking, just showing the voltage maps should usually do the job (i.e., whenever the color coding shows clear differences between LH and RH).
Seeing that you're working in neurolingustics, these suggestions may be applicable to your data. As an illustration of my points above, I'm attaching a recent ERP paper with Kristina Kasparian on L1 attrition; I have highlighted relevant text in the Methods section.