Two Thurstonian theories, designed to account for the adverse effect of increased signal range on absolute identification, were contrasted and tested. The range theory of Braida and Durlach partitions the variance underlying the d′ performance measure into a sensory term, which is assumed to be unaffected by signal range, and a criterial term, which is affected by it. The attention-band theory of Green and Luce assumes that the signal representation arises from a distribution with either a small or a large variance depending upon whether or not it happens to fall within the band. It attributes the effect of range to changes in the probability that signals fall in the band. In addition, they suggested that the band location is affected by two tendencies: to be at the ends of the signal range, which accounts for edge effects in the data, and to track the previous signal, which accounts for sequential effects. They placed no emphasis on criterion effects.
Examination of data from a number of experiments leads to several conclusions about these theories. An analysis in terms of the Braida-Durlach framework of a multiple-observation AI experiment showed range to affect both sensory and criterion variance. This suggests that both theories are incorrect, the one for assuming range does not affect the sensory component and the other for assuming that it does not affect the criterion component. Detailed sequential analyses make clear that the major component of the one-trial sequential effects is systematic shifts in response criteria, not changes in sensitivity as had been postulated in the original version of the attention-band model. The band does not track signals on a trial-by-trial basis. Nonetheless, a number of experiments all based upon some form of clustering of signals to attract attention make clear that sizable changes in sensitivity can be produced. It appears that attention is drawn in a somewhat sluggish fashion to the region where "the action is," but it is not drawn there in a single trial. Among these studies were ones in which the range, spacing, and distribution of signals were the same as in the usual random design, and the clustering was effected by means of sequential dependencies in the presentation schedule. Pronounced changes in d′ were in accord with the attention idea, but inconsistent with the range theory since range was not changed.
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