Fig. 2.

Orthogonal components of visual spatial attention can be defined using signal detection theory. (A) Signal detection theory supposes that when an observer is engaged in a detection task, each stimulus is transformed into an internal representation of evidence for whether a signal has occurred. However, the value of this evidence variable will vary from trial to trial due to noise. The distribution associated with the stimulus that contains a signal (“Signal + noise”) has a larger mean (i.e., stronger evidence) than the distribution associated with the stimulus containing only noise “Noise only”). In its simplest form (i.e., assuming the distributions are well- approximated by Gaussians and have equal SD), the signal detection model is fully specified by 2 parameters. Sensitivity, or d′, is the difference between the means of the 2 distributions normalized by their SD. Intuitively, one can see that as the 2 distributions (“Noise only” vs. “Signal + noise”) overlap less (larger d′), behavioral performance will improve. Criterion, or c, is the fixed value used by the observer to categorize a stimulus as either signal or noise. A stimulus that triggers an evidence value greater than the criterion is reported as signal and otherwise is reported as noise. (B) Parameters c and d′ of a signal detection model can be inferred based on the relative frequencies of different responses to stimuli: hits, misses, false alarms (FA), and correct rejections (CR). The relative frequency of each of these 4 responses corresponds to a separate area of the 2 distributions and fully specifies the model, and therefore c and d′. Since there are only 2 degrees of freedom (i.e., when expressed as probabilities, each column must sum to 1), the model is completely specified with a single number from each column (traditionally, “hit rate” and “false alarm rate”). (C) If one considers only the hit rate, any change between different cueing conditions might be due to a change in only criterion, only sensitivity, or both. It is thus crucial to also consider changes in the false alarm rate. (Left) If only the criterion has changed, an improvement in the hit rate can only come at the expense of an increased false alarm rate. (Right) If only sensitivity has improved, an increase in hit rate can be achieved with a decrease in false alarms.