Pq220012380p

Failure to handle more than one internal
representation in visual detection tasks
Andrei Gorea*† and Dov Sagi‡
*Laboratoire de Psychologie Expe´rimentale, Centre National de la Recherche Scientifique & Rene´ Descartes University, 71 Ave. Edouard Vaillant, 92774Boulogne-Billancourt, France; and ‡Department of Neurobiology͞Brain Research, Weizmann Institute of Science, Rehovot, 76100 Israel Edited by Jacob Nachmias, University of Pennsylvania, Philadelphia, PA, and approved August 22, 2000 (received for review April 13, 2000) Perceptual studies make a clear distinction between sensitivity and
adjusting their decision criteria to the occurrence probability decision criterion. The former is taken to characterize the process-
of the signal was assessed for a number of different strength ing efficiency of the underlying sensory system and it increases
signals presented in isolation with one out of three occurrence with stimulus strength. The latter is regarded as the manifestation
probabilities. A second experimental condition was meant to of a subjective operation whereby individuals decide on (as op-
check whether the performance above (i.e., both sensitivities posed to react reflexively to) the occurrence of an event based on
and criteria) is maintained when two equal strength stimuli factors such as expectation and payoff, in addition to its strength.
with different occurrence probabilities are displayed simulta- To do so, individuals need to have some knowledge of the internal
neously. Potential context-related interactions between deci- response distributions evoked by this event or its absence. In a
sion criteria (and sensitivities) were further studied in a third natural, behaviorally relevant multistimulus environment, observ-
condition involving the simultaneous presentation of stimuli ers must handle many such independent distributions to optimize
differing in both strength and occurrence probability.
their decision criteria. Here we show that they cannot do so.
Instead, while leaving sensitivity unchanged, lower and higher
Experimental Design and Methods
visibility events tend to be reported respectively less and more
Fig. 1b illustrates the sequence of events within one trial. In each frequently than when they are presented in isolation. This behav-
block of trials and on each trial, observers were presented with, ior is in quantitative agreement with predictions based on the
in sequence (i) a fixation white circle present during the whole notion that observers represent a multistimulus environment as a
trial; (ii) one white and one black ‘‘precue’’ circles; (iii) two 3 unitary internal distribution to which each stimulus contributes
cycles͞deg vertical Gabor targets of contrasts C proportionally to its probability of occurrence. Perceptual phenom-
sented within the precue circles with probabilities, P ena such as blindsight, hemineglect, and extinction may be, at least
(iv) after their offset (‘‘delay’’ period), one of the precues in part, accounted for in such a way.
randomly disappeared. Observers had to respond whether or not a target was presented inside the persistent (postcue) circle only.
decision making ͉ psychophysics ͉ criteria drift ͉ unitary internal This experimental format combines partial report (4) and signal detection techniques. It requires that observers monitor both locations until the ‘‘appearance’’ of the postcue. The stimuli were It is well established (1, 2) and by now common knowledge presented on a 29 cd͞m2 gray background. The fixation circle
that humans (and nonhumans) can and do set the reference was 0.5° in diameter. The cue circles were displayed 1.6° to the strength of an internal response beyond which internal events left and to the right of fixation (on the dashed large circles absent will be assumed to represent external events in relation to the in the actual trials; Fig. 1b) with their locations randomized probability and͞or the payoff associated with the latter: equally energetic events will be reported more frequently if 1,P1 and C2,P2 were consistently asso- ciated with the cue polarities, and observers were informed of their occurrence is likely (or the payoff is high) than if it is not.
this mapping before each block. A few blocks also were run with Signal detection experiments also have established that, for a horizontal targets and͞or with cues and targets displayed above unique stimulus strength and occurrence probability, observ- and below fixation. Incorrect responses were signaled by a short ers can simultaneously entertain a number of response criteria that translate into different levels of confidence as to the For each experimental block, the contrasts of the two targets occurrence of that stimulus (1, 2). The literature remains silent, however, on the issue of whether or not humans can 1 and C2) and their probabilities (P1 and P2) were fixed and systematically mapped on each of the two cue polarities with entertain multiple criteria based on different probabilities observers having full knowledge of this cue-color͞stimulus- associated with a number of simultaneous, spatially distinct mapping at the start of each experimental block. C events. Common sense admits the proposition according to in the range of 0.02 to 0.05. The specific values for each observer which the (yes͞no) report of the occurrence of any among N were chosen based on preliminary experiments with no other distinct events can be biased by the a priori likelihood of that event (Fig. 1a). But is this still the case in an environment Јs between 0.5 and 3.5 (i.e., most of the characterized by a variety of stimulus intensities? A multi- Ј range) and dЈ differences between 0.7 and 2 (see stimulus environment where different events differ in their below). Probabilities of the targets could be 0, 0.25, 0.50, or 0.75.
likelihood is the typical milieu of most organisms. Character- Stimulus characteristics were manipulated to yield three exper- izing decision making within such an ambience is, then, of critical significance for understanding how humans regulate The ‘‘single’’ condition involved the presentation of one single (or adapt) the point on their sensory continuum they use as a target in each trial (obtained by setting one of the two proba- reference for judging ‘‘reality’’ given the actual magnitudes and probabilities of the ongoing physical events (3). In the This paper was submitted directly (Track II) to the PNAS office.
present study, this broad issue is scaled down to its most †To whom reprint requests should be addressed. E-mail: [email protected].
elementary form, whereby decision criteria are studied for only two stimuli at a time that may or may not differ in their The publication costs of this article were defrayed in part by page charge payment. Thisarticle must therefore be hereby marked “advertisement” in accordance with 18 U.S.C.
strength. In one ‘‘baseline’’ condition, observers’ capacity of §1734 solely to indicate this fact.
12380 –12384 ͉ PNAS ͉ October 24, 2000 ͉ vol. 97 ͉ no. 22
Under the ‘‘dual’’ conditions, two stimuli͞signals were pre- sented in each trial with their probabilities paired so as to yield a constant average signal probability of 0.5 (i.e., 0.25–0.75, 0.50–0.50, and 0.75–0.25). Thus, here again three dЈ and cA values were assessed for each contrast in a pair. There were two sorts of dual conditions. Under the ‘‘dual-same’’ condition, the two stimuli in a pair were of identical contrasts (C1 ϭ C2). Under the ‘‘dual-different’’ condition, the two contrasts were different (C1 Ͻ C2) and paired so as to yield dЈ differences between 0.7 and 2. Fig. 1c displays the 12 stimulus pairings defined by the probabilities and contrasts of the stimuli. C-P pairings were The most extensive data sets (three contrast pairs) were obtained from two naive, well-trained observers. An additional naive observer VR and the first author were run with only one contrast pair. Some critical points in the main experiment also were confirmed with the second author. Observer AG and additional naive observer VR also were run in a second exper- iment equivalent in all respects to the dual-different condition with the exception that one of the two stimuli never had to be reported and the observers were told so from the start. In all cases, one datum point was estimated from at least 312 trials but more typically from 416–832 trials.
Results
Operationally, the question raised here is whether or not the
criteria for the paired stimuli remain unchanged when assessed under single and dual conditions. Fig. 2a shows that the absolute PSYCHOLOGY
criteria (cA ϭ ϪzFA, i.e., the standard z-score of false alarms; Fig. 1a) for single and dual-same conditions are scattered about the identity (slope 1, dotted) line for both the low (C1, solid symbols; paired t test ϭ 0.3, df ϭ 40, P ϭ 0.38, not significant) and the high (C2, open symbols; paired t test ϭ Ϫ1.05, df ϭ 40, P ϭ 0.15, not significant) contrasts used with each observer. The linear regression lines with errors in both coordinates (5) fit to each data subset (solid and dashed lines, respectively) are also close to this identity line. For both single and dual-same con- ditions, the average likelihood ratio criterion (␤; Fig. 1a) for signal probabilities 0.25, 0.5, and 0.75 was (in agreement with the (a) The Signal Detection Theory (1) framework for the dual-criterion known conservative behavior of humans; ref. 1) 1.35, 1.05, and experiment. Gaussian functions describe the probability density, P(z), of theinternal response distributions (in standard z-scores; abscissa) for the noise [N: 0.75 and did not depend on dЈ. This is evidence that, for spatially PN(z)] alone (dashed curve) and for the signal ϩ noise [S: PS(z)]. Thin vertical distinct, equal strength stimuli, observers can and do entertain lines show their means with sensitivity (dЈ ϭ zHit Ϫ zFA, with zHit and zFA the independent criteria in relation to the specified stimulus z scores for the observed correct target detection and false alarm rates) being the distance between these means (dЈ ϭ 1 in this case) measured in units of the In contrast with the above, cAs assessed under the dual- noise standard deviation, ␴N, and assuming that N and S are normally distrib- different condition are systematically different from the corre- uted with ␴ ϭ ␴N ϭ ␴S. We define an ‘‘absolute’’ criterion as cA ϭ ϪzFA.
sponding ones observed under the single and dual-same condi- Defined in this way, criteria are independent of the univariance assumption tions (Fig. 2b). With very few exceptions, they lie above (solid (i.e., ␴S ϭ ␴N), because they depend on the N distribution only. The corre- sponding values of the likelihood ratio criterion, ϭ Ϫ5.03, df ϭ 46, P Ͻ 0.00002) and below ␤ ϭ Ps(z ϭ cA)͞PN(z ϭ cA), characterize observers’ response bias independently of dЈ. Error rate is mini- (open symbols; paired t test ϭ 4.37, df ϭ 46, P Ͻ 0.0001) the mized when ␤ ϭ PN͞PS, (with PN and PS the a priori N and S probabilities) but identity (slope 1, dotted) line for the low (C1) and high (C2) experimental results show that observers adopt a more conservative behavior contrasts, respectively. This is to say that the cAs associated with with ␤s closer to one (1). The vertical dashed and continuous heavy lines show the low and high contrasts in a dual-different pair ‘‘drift’’ as if optimal criteria for PS ϭ 0.5 and PS ϭ 0.25, respectively. The shaded area ‘‘attracted’’ by the mean of the internal response distribution denotes the False Alarm (FA) rate for the latter case. (b) One trial sequence as associated with the high and low contrast stimuli, respectively.
detailed in the text. (c) The 12 experimental conditions as characterized by the This is so despite the fact that observers have full knowledge of combination of two distinct stimuli of contrast C1 and C2 and of four stimulus the properties of the signals, that is, of their contrasts and Fig. 2 c and d shows that, unlike cAs, dЈs remain insensitive to bilities, or equivalently, one of the two contrasts in a pair to zero).
the experimental condition. They lie close to the slope 1 Stimulus characteristics (C and P) were fixed and announced at diagonal, whether assessed in single vs. the average of the the beginning of each experimental block. The target was dual-same and dual-different conditions (open and solid sym- presented randomly across trials within a white or a black cue bols, respectively, in Fig. 2c) or under dual-same vs. dual- circle so that cue polarity yielded no meaning in this condition.
different conditions (Fig. 2d).
For a given C, the probability of the signal (0.25, 0.50, or 0.75) The cA shifts observed under the dual-different condition are was randomized across blocks so that three sensitivity (dЈ) and not entailed by the mere presence of two targets of different criterion (cA, ␤; Fig. 1a) values were assessed for each C. Signal contrasts, but rather by the decisions taken on their occurrence.
contrasts also were randomized across blocks.
The dual-different condition was rerun with two observers (AG PNAS ͉ October 24, 2000 ͉ vol. 97 ͉ no. 22 ͉ 12381
Correspondence between criteria (a and b) and dЈs (c and d) assessed under single, dual-same, and dual-different conditions. Different symbols are for different observers. Data points represented by identical symbols are for different stimulus probabilities and͞or contrasts. (a and b) Solid and open symbols showthe absolute criteria obtained for the low (C1) and high (C2) contrasts, respectively, in a stimulus pair. (a) cA[single] vs. cA[dual-same] comparison. The identitylocus is shown as the dotted (slope 1) line. Solid and dashed regression lines are fits with errors in both coordinates (5) through the solid (C1 stimuli) and open(C2 stimuli) symbols, respectively. (b) As in a but for the cA[mean (single ϩ dual-same)] vs. cA[dual-different] comparison. Note the upward and downward shiftsof the dual-different criteria associated with low (solid symbols) and high (open symbols) contrasts, respectively, in a stimulus pair. (c) dЈ[single] vs. dЈ[dual]comparison with closed (solid regression line) and open (dashed regression line) symbols showing dual-different and dual-same data, respectively. The identityline is dotted. (d) dЈ[dual-same] vs. dЈ[dual-different] comparison. The identity and the regression line through all experimental points are dotted and solid,respectively.
and VR) under conditions where one of the two stimuli (the representation of the internal response distributions associated ‘‘companion’’) was never reported. The postcue was never with each external event is of critical importance for the effi- presented for this stimulus, whereas the two cue polarities were ciency of these decision processes. Decision criteria should be set randomized over the two stimulus contrasts. For a target stim- so as to minimize some cost function, for example, the number ulus of 4%, observer VR showed a slight but consistent criterion of response errors (1). A failure to correctly represent the drop when the probability of either a 6% or 60% contrast distinct distributions associated with the different targets would companion (used in different blocks of trials) increased from translate into criteria shifts. The presently observed criteria zero to one. This is an effect opposite to the one observed in the drifts may be regarded as the consequence of such a failure.
main experiment. Observer AG showed no interaction whatso- More specifically, the present data are well fit by a model with ever for either a 4% or 6% target in the presence of either a 5% no free parameters posing that observers have access to only one or 60% companion (with each contrast pair run in different internal response distribution generated by the incoming stimuli.
blocks). Thus, when one internal response distribution needs not This unitary distribution is the weighted sum of the internal to be estimated (because no related report is requested), the distributions evoked by each of these stimuli with weights equal criteria used for the target stimuli do not drift toward the mean to their respective occurrence probabilities. Observers decide on of that distribution (as in the main experiment). This observation the occurrence of a signal in the standard way, that is, by goes against an interpretation of the main results reported here reference to a given likelihood ratio criterion (␤), a number that in terms of some sort of sensory adaptation (6).
depends only on the signal probability as denoted by the associated precues, and for that matter, postcues. However, the Modeling the Data and Discussion
likelihood ratios observers use for the comparison with this In a multistimulus environment where, potentially, decisions are number are computed from the merged distribution. For equal to be made on the occurrence of any external event, the reliable strength stimuli, the unitary distribution will be identical to each 12382 ͉ www.pnas.org
PSYCHOLOGY
Correspondence between data and predictions by a dual and unitary internal distribution model. (a) cA differences (⌬cA) measured in the dual-different condition (abscissa) are compared with the corresponding ⌬cAs averaged over the single and dual-same conditions (open symbols and dashed line; two-distribution model) and with the predictions of the unitary distribution model (closed symbols). ⌬cAs were computed as cA(C2,P) Ϫ cA(C1,1 Ϫ P), that is betweenthe criteria associated with the high contrast (C2) signal of probability P and the low contrast (C1) signal of probability 1 Ϫ P. Circles: cA(C2,0.25) Ϫ cA(C1,0.75);squares: cA(C2,0.50) Ϫ cA(C1,0.50); triangles cA(C2,0.75) Ϫ cA(C1,0.25); note that in the dual-different condition, the above predicted (unitary distribution) andmeasured ⌬cAs are, in order, small and negative, close to zero, and large and positive. Symbols lying along the diagonal of slope 1 passing through the originshow perfect correspondence between data and predictions. The main assumption of the unitary model (b–d) is that, in a multistimulus environment, observersset, for a given stimulus probability, the same (nonoptimal) likelihood ratio criterion (␤) as in a single-stimulus (or uniform) environment whereas the likelihoodratios they use for the comparison with this number are computed from the unitary internal response distribution (heavy continuous curves) generated by theensemble of stimuli on which they have to decide. The unitary distribution is the weighted sum of the internal distributions evoked by each of these stimuli withweights equal to their respective occurrence probabilities (thin Gaussian curves). (b–d) The three contrast-probability pairings used in the experiments. Theweaker and stronger signals in a pair are presented with probabilities 0.25, 0.75 (a), 0.5, 0.5 (b), and 0.75, 0.25 (c). Heavy vertical lines show where the criteriashould be for each of these probabilities assuming that observers are optimal and use the same ␤ as in the single and͞or dual-same conditions. In practice,observers display a conservative behavior under all conditions so that these criteria are closer to each other than shown. Vertical dotted lines show the meansof the N- and the two S-distributions. The actual internal response distributions (N and S) remain unchanged under all experimental conditions, so that a giventarget yields a constant dЈ across all conditions.
individual distribution so that the predicted response criteria for criteria as those assessed under the single and͞or dual-same such dual-same conditions should not differ from those observed conditions. The open symbols in Fig. 3a represent the actual under single conditions. Note that this model bears only on how ⌬cAs between the same stimuli as measured in the single and͞or observers use the internal response distributions in the decision dual-same cases. Overall, ⌬cAs under the dual-different condi- process whereas leaving these distributions, and therefore, sen- tion are smaller than those under the single and dual-same sitivity, unaffected by the experimental manipulations. Indeed, conditions (‘‘attraction’’; Fig. 2b) by an average of 0.44 (for an the present data show no systematic dЈ changes with these In a multistimulus environment, precues (and for that matter, In Fig. 3a, the ‘‘unitary distribution’’ model is used to predict postcues) are helpful for optimizing performance when they are the cA differences (⌬cA) between the two stimuli in the dual- used to tag stimulus probabilities but not stimulus strengths.
different pairs (closed symbols). This was achieved by using the Observers decide on the presence͞absence of a signal in relation observers’ dЈs and ␤s as assessed for the same stimuli and to the internal response distribution associated with a given stimulus probabilities as under the single and dual-same condi- external event (7). Optimal decisions in the presence of more tions. Fig. 3 b and c provides an illustration of how this was than one stimulus require the appraisal of the internal events accomplished (see legend). Predictions of the unitary distribu- distributions associated with each stimulus. The present data tion model lie very close to the line of perfect fit (the diagonal show that human observers cannot do so even though the of slope 1) and account for 80% of the variance. On the different signals are spatially disjoint and unambiguously de- alternative, standard Signal Detection Theory assumption that noted by consistent precues. Instead, observers appear to use the observers keep track of and independently use each of the two composite distribution generated by the two simultaneously internal distributions associated with the two stimuli under the occurring stimuli and use it as a unitary distribution to set their dual conditions, the dual-different case should yield the same criteria in accordance with the specified signal probabilities as PNAS ͉ October 24, 2000 ͉ vol. 97 ͉ no. 22 ͉ 12383
(in)efficiently as in a single-stimulus environment. The global different strength signals are randomly mixed in one experimen- effect of this behavior is that, relative to the impoverished tal block. Not knowing the specific signal (among many) to which (single-strength) environments, the criteria they use in more an internal response distribution should be associated, observers ecological ones are displaced to higher values on the sensory have no means of keeping track of these distributions; as a scale (more misses) for the weaker signals, and to lower values consequence, they place their detection or classification criteria (more false alarms) for the stronger ones, provided that the in relation to a global internal response distribution representing external events considered are behaviorally relevant. This fact the ensemble of relevant stimuli. In the present experimental generalizes to conditions where the paired stimuli are of orthog- format, however, observers could and actually did keep perfect onal orientations or different spatial frequencies, or are pre- track of the stimulus identity by using the polarity of the precue and postcue circles. This is indicated by the fact that the criteria The present results may bear on the well-known neuropsy- obtained under the single and dual-same conditions for the same chological disorders of blind-sight (9), hemineglect (10), and signal probabilities are practically identical (Fig. 2a). Why then extinction (11). Consequences of cortical injury, these conditions couldn’t observers adjust their criteria in relation to each of the refer, respectively, to the relatively efficient behavior toward two distinct internal response distributions generated under the objects which the patients claim not to see, to their neglect of half of their sensory space, or of some simultaneously occurring One may pose that, whatever the sampling resources of the stimuli. Presumably, patients of this kind are in a situation system as a whole, it devotes them all to sampling one (intensive) analogous to the one studied here. Given that they present a reality at a time to reach a decision bearing on this reality. If critical sensitivity drop contralateral to the injury, and on the equivalent criterion shifts were to be observed within the context assumption of a homogeneous physical world, such patients of discrimination tasks along dimensions other than intensity might displace their response criterion toward the mean of their (e.g., shape, color, and velocity), this could be regarded as a internal responses along the nonaffected sensory space. They fundamental constraint imposed by the unity of action (or will then ignore the weaker internal responses generated in the decision) on this reality (17). An alternative interpretation of the affected areas. Criterion shifts under these neurological condi- present results would be that the sampling resources of the brain tions have been invoked (12, 13) and actually observed (14).
are limited [e.g., to 7 Ϯ 2 samples or chunks (18) or less (8)] and The criterion shifts assessed in the present study depend on that they cannot be distributed across external events without a both the specific strengths (or dЈs) and the probabilities of the significant loss in accuracy. One way or another, the global use stimuli involved in the detection task. They are quantitatively of a unitary internal response distribution in judging multiple accounted for by a model whereby, for a given stimulus proba- simultaneously occurring events might account for the unity of bility, observers use the same likelihood ratio criterion in a the (visual) world as experienced and as acted on. Of course, single-stimulus (uniform) or multistimulus environment but the generality of this statement is subject to further studies compute the current likelihood ratios needed for the comparison of the present phenomenon in a variety of multidimensional with this number from the unitary internal response distribution generated by the ensemble of stimuli on which they have to decide. This behavior is to be expected in detection (15) or We thank Randolph Blake, Patrick Cavanagh, Elliot Freeman, Avi scaling͞classification experiments (6, 16) where nontagged, Karni, Stanley Klein, Larry Maloney, and Joshua Solomon for valuable comments on earlier versions of this paper and Yoram Bonneh for providing the software. This work was supported in part by a joint §Gorea, A. & Sagi, D. (2000) Investig. Ophtal. Vis. Sci. Suppl., 41, S751 (abstr.).
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