Ideally, our real-world behavior is strongly determined by our context, for the simple reason that some behaviors are only appropriate in some situations (e.g., eating during an internal context of hunger, or using slang during an external context of casual interaction).
Context-inappropriate behavior is often seen as a failure of cognitive control (e.g., continuing to eat when no longer hungry, or using a common slang phrase in a formal setting).
This perspective is called "context processing," based on work pioneered by Todd Braver, Dianna Barch, Jon Cohen, and others. This framework is useful for understanding prefrontal cortex function and disorders like schizophrenia and Parkinson's, largely through the use of a particular version of a task known as the "AX Continuous Performance task" or AX-CPT. In the AX-CPT, certain stimuli ("A" and "X", usually) are used to establish a "default" context, and infrequent stimuli (collectively referred to as "B" and "Y") are presented to examine whether, and how quickly, subjects can engage controlled processing of infrequent contexts.
The expectancy AX-CPT is unique because it can reveal poorer performance among those who are highly controlled in their processing of context. This is particularly useful for cognitive science, because it rules out pesky "pure smarts" interpretations of results (along the lines of "population X is better at task Y because they're better at all tasks.") Instead, with the AX-CPT, we can say that "population X is better at task Y because they are better at context processing, as exemplified by their worse performance on AX-CPT."
Unfortunately, AX-CPT is very confusing. It requires some complicated analyses: while the requisite statistics are simple, the task structure and the meaning of those analyses can be difficult for nonexperts to grasp. So perhaps foolishly, I'm going to attempt to describe a paper which exemplifies this problem, and contains some interesting manipulations whose consequences are not acknowledged in the paper.
This 2003 study by Dias, Foxe & Javitt uses variations on the expectancy AX-CPT to examine differences in event-related potentials to contextually infrequent responses. If the AX-CPT were ever complicated, Dias et al. have compounded that problem, by running three variants on it, all with different probabilities for each stimulus context.
Some background about the task is necessary. In the AX-CPT, four types of stimuli are presented serially. A response is required to the letter "A" when it is followed by the letter "X"; other stimuli, collectively referred to as "B" and "Y", stipulate that no response should be provided. In the expectancy version, the "AX" sequence occurs 70% of the time: thus, "AY" trials can be difficult for those who are anticipating or maintaining the "A" stimulus (and it's associated highly-probable response, if followed by an "X"), whereas "BX" trials can be difficult for those who failed to maintain the "B" stimulus and are tempted to give a response to the "X" stimulus (which is of course associated with a target-response).
The point of the paper was to change which stimulus pair was most frequent, in order to examine differences between the cognitive processes engaged in providing an infrequent response and those involved in inhibiting an infrequent response.
In the standard expectancy AX-CPT, which Dias et al call AX-70, the AX pair occurs 70% of the time. In Dias et al's AY-70 condition, the AY pair occurs 70% of the time, and similarly BX-70 was associated with 70% frequency of the BX pair.
Note that the AY-70 and BX-70 conditions in this study are taxing on vigilance, since responses are provided on only 12.5% of the trials. Accordingly, any effects noted in those conditions may be due to the different response probabilities in that task, OR to the tendency for subjects to start "day-dreaming" during the task.
Similarly, note that the difference between (for example) BX-70 and AX-70 is not solely in terms of stimulus type and response probabilities (70% no-responding in the former and 70% responding in the latter) but also in terms of the probability of particular stimuli: in the AX-70 task, the letter "A" and the letter "X" each occur on 87.5% of the trials, whereas all other letters of the alphabet will occur 30% of the time (a little less than 1% probability for each other letter). However, in the BX-70 task, only the letter "X" occurs on 87.5% of the trials, all other letters occur with about 1% frequency. Again, we see that the conditions differ not only in response probabilities but also in the distribution of stimulus probabilities. Thus any differences observed between conditions might be due either to stimulus probability differences OR to differing response probabilities.
The primary finding is that going in a predominantly "nogo" context (cue "A" in BX-70 minus cue "A" in AY-70) has a more posterior scalp distribution than not going in a predominantly "go" context (cue "B" in AX-70 minus cue "B" in AY-70).
A simple explanation for this effect is that motor activity in primary motor and parietal cortices could have shifted the distribution more posteriorly in the case where a response is provided (the Go in a No-Go context).
A less simple explanation is that the actual cues indicating NoGo in a predominant Go context (any letter other than "A" and "X", each occurring with ~1% frequency, and perfectly predicting a nogo response) are far less frequent than the actual cues presented to indicate Go in a predominant NoGo context ("A", occuring 20% of the time, and predicting a response 50% of the time). Thus NoGo in a Go context is indicated by more infrequent and more predictive (task-relevant) stimuli than Go in a NoGo context. This confound in the comparisons would be expected to lead to the observed anterior shift, given that the central assumption of the AX-CPT is that frontal regions are involved in processing task relevance and context!
Below, I've summarized some other results from the paper, but these are not likely to be interest to anyone outside of the probability effect literature (thus the blocked text)..
For stimulus & response probability freaks:
1) First, subjects were slower in the AY-70 than the AX-70. The authors ascribe this to the low probability of responding. Critically, this argument should also apply in the BX-70 condition - but no slowing was observed there. Arguably, this asymmetry is actually due to the differences in stimulus probability I mention above: in the BX-70 condition, the presentation of an "A" predicts that a response will be required with 50% probability - giving subjects time and motivation to prepare a response ahead of time. In contrast, the presentation of an "A" in the AY-70 case predicts a response with only 12.5% probability, which apparently gives subjects little motivation to prepare a response.
2) False alarms were greatest in the AX-70, consistent with intuition (false alarms will be greater when there's a greater probability of responding in the first place) and with myriad previous work from the AX-CPT.
3) Errors of ommission were not reported, but such errors would be expected if some subjects began "daydreaming" in the AY-70 and BX-70 conditions. This complicates the interpretation of subsequent results, since ommission errors are not covaried in those other analyses: any observed differences could be due to construct of interest OR to general differences in vigilance and arousal between conditions.
4) Dias et al. recorded scalp electrical potentials (in the form of ERPs) in every condition. As one would expect based on the different probabilities between conditions (both of responding and of the appearance of particular stimuli), the ERPs showed robust differences in the epoch of 300-600ms, roughly in line with the p3 "oddball" response, which is known to be sensitive to frequency.
5) All conditions differed in this p3 oddball response to the "A" cue, and the topographic location of this difference in the BX-70 condition was consistent with the p3b (i.e., the difference was largest over centro-parietal electrodes). After subtracting the ERP to the "A" cue in the AX-70 condition from that in the BX-70 condition, dipole source modeling indicated that over 90% of the variance in the ERP was accounted for by a source located in parietal cortex (BA 40, the inferior parietal lobe, in the vicinity of the temporoparietal junction). Nonetheless, frontal (ACC & dlPFC) dipoles were able to account for over 74% of this ERP, which indicates that some frontal source could have contributed to this oddball response. In fact, the best predictor of the ERP was a combination of frontal (dlPFC) and parietal (BA 40) dipoles, indicating that this p3-like response could arise jointly from two discrete generators. The implication is that the "A" cue-related ERPs specific to the BX-70 condition reflects the preparation of a infrequent Go response in a context where withholding responses is more frequent. However, this difference is confounded with the fact that the "A" cue is far more salient in the BX-70 condition than in the AY-70 condition (with 20% versus 70% probability), and so the subtraction employed by Dias et al might identify stimulus-frequency sensitive regions, rather than those which are specific response-frequency (i.e., to the need to Go in a situation where not-responding is more frequent).
6) Conversely, the authors propose to have found the opposite effect as well: an index of "withholding a response in a prepotent Go context" based on the the fact that the "B" cue (really, cues) elicited both a frontal negativity (270ms) and a subsequent positivity (450ms) only in the AX-70 task, perhaps analogous to the N2-P3 complex often observed in other studies of stimulus probability (e.g., oddball studies). The authors note that this should not (and does not) occur in the BX-70 and AY-70, in which presentation of a B specifies no change in the anticipated response. Once again, however, in this case the "B" cues are far, far more infrequent (about 1% for each non-A and non-X letter of the alphabet), suggesting that this might index not only response-probability differences but also those of stimulus-probability.