The demonstration of capacity limitation

COGNITIVE PSYCHOLOGY 12, 75-96 (1980)

The Demonstration of Capacity Limitation

JOHN DUNCAN MRC Applied Psychology Unit

The study of divided attention has produced many apparent demonstrations of “capacity limitation.” Possible ambiguities in such demonstrations are considered for three major types of experimental situation: simultaneous inputs with separate responses; choice: and classification. Two issues emerge. First, demonstrations always rest on assumptions aboutprocess ser, i.e., the set of internal processes by which the task actually is performed. Alternative process sets are considered for situations of each type. Second, a demonstration of capacity limitation is made either by increasing the number of simultaneous processes, or by changing the bias between them. In either case effects unrelated to capacity limitation may influence the results. I f several processes contribute to a single response, some performance decrement must accompany an increase in their number, simply through the increased overall chance for error. I f the subject is biased toward one alternative in a choice or classification situation, the benefits enjoyed by this alternative may reflect not a preferential allocation of attentional capacity, but simply a willingness to decide in favor of this alternative with relatively little evidence.

Performance often suffers when a person tries to do two things at once. Traditionally this reflects excessive demands on some limited psychological resource or “capacity.” Though this resource has been characterized in different ways-as an ability to transmit information (Broadbent, 1958); to “translate” stimuli into responses (Welford, 1968); to assign modality- specific “analyzers” in the examination of stimulus input (Treisman & Davies, 1973); to expend pyschological “effort” (Kahneman, 1973)-the basic idea of capacity limitation is the same.

This general problem of divided attention has been studied in very many different ways. To name but a few there are experiments on dichotic listening (e.g., Broadbent, 1958), the “psychological refractory period” (e.g., Bertelson, 1966), choice reaction time (e.g., Hick, 1952), visual search (e.g., Shiffrin, 1975), memory scanning (e.g., Sternberg, 1966), and priming (e.g., Posner & Snyder, 1975).

Sometimes, though, it is not clear how much a particular result has to do with “capacity limitation.” For example, a great deal of interest has recently attached to the study of attention by “priming” (e.g., LaBerge,

This work was carried out at the University of Oregon, with the support of a postdoctoral research fellowship from the Science Research Council, London. Practically every person working in the Cognitive Laboratory at the University of Oregon during 1977 and 1978 helped with the improvement of early drafts. It is a pleasure in particular to express my deep gratitude to Mike Posner. Requests for reprints should be sent to John Duncan, MRC Applied Psychology Unit, 15 Chaucer Rd., Cambridge CB2 2EF, England.

75 OOlO-0285/80/010075-22$05.00/O Copyright @ 1980 by Academic Press, Inc. AU rights of reproduction in any form reserved.

76 JOHN DUNCAN

1973; Posner & Snyder, 1975). The basic experimental technique involves cueing the subject to expect a particular one of several potential altema- tive stimuli, with the idea that “attention” (some form of limited capacity) will be allocated preferentially to this one. Yet elsewhere in the experimental literature such cueing has been considered from rather a different point of view, as influencing the bias parameter in mathematical models of decision (e.g., Green & Swets, 1966; Laming, 1968). What is the relationship between these two approaches? Does the advantage enjoyed by a cued stimulus truly reflect some sort of capacity limitation?

As another example, some of the earliest discussions of capacity limitation arose in connection with the logarithmic increase of reaction times (RTs) with the number of alternatives (N) in a choice situation (e.g., Hick, 1952; Hyman, 1953). Yet later models based on signal detection theory rather than information theory (e.g., Green & Birdsall, 1964) gave scant attention to any concept of capacity limitation in their accounts of this result, emphasizing instead the simple statistical fact that, the more alternatives there are, the more chances there are for one to be chosen incorrectly. What is the relationship between these two types of approach?

Most studies of divided attention raise questions of this sort. In general, what constitutes a clear demonstration of capacity limitation? What other factors must be excluded? These questions will be considered in detail for three major types of experimental task: simultaneous inputs with separate responses; choice; and classification. The first step is to introduce some basic issues.

Capacity Limitation ISSUES

To identify a little more closely the idea of capacity limitation: Simulta- neously a subject is called upon to do (at least) two things. The task might be to identify two words presented simultaneously to left and right ears (e.g., Broadbent, 1958) or to choose and initiate two separate, speeded responses (e.g., Bertelson, 1966), or to match a letter against two stored members of a “memory set” (e.g., Stemberg, 1966), and so on. Sup- posedly there are two corresponding and distinct sets of internal processes, A and B. Both A and B are assumed to draw on some (theoreti- cally specified) psychological resource, e.g. (as above), a pool of “effort” (Kahneman, 1973), or a set of modality-specific “analyzers” (Treisman & Davies, 1973). Performance suffers if available resources are insufficient to support both A and B at once.

It is this basic idea that is of present concern. There will be no attempt to deal with particular issues: the exact nature of the limited resource; whether limitations are general or specific to a particular task or stimulus

DEMONSTRATION OF CAPACITY LIMITATION 77

modality (e.g., Allport, Antonis, & Reynolds, 1972; Treisman & Davies, 1973); whether they arise in perception or response (e.g., Treisman & Geffen, 1967); or in simple tasks such as energy detection or more complex tasks such as pattern recognition. Though these distinctions are obviously important, they are immaterial here. The intent is to address problems which apply in whatever context issues of capacity limitation arise.

Another point to be ignored concerns the distinction between “serial” and “parallel” processing. If A and B together require more than the total available resource, the system has two options. Either the two sets of processes may occur in turn, resources being shifted from one to the other (serial processing: Hick, 1952; Moray, 1969; Sperling, 1963; Stemberg, 1966; Welford, 1968), or they may be attempted simultaneously (parallel processing). For present purposes it does not matter which. In either case performance will suffer: Either one process must wait (and may lose relevant information) while the other takes place, or both processes occur together, but neither with sufficient allocated resource.

Many discussions of “attention” are not directly or obviously concerned with questions of capacity. For example, it is a commonplace that people select from their environment information especially relevant to current occupations or goals, and many experimental situations actually require this (e.g., Eriksen & Hoffman, 1973; Treisman, 1964). Though this might certainly be termed “selective attention,” selection here might have little to do with capacity limitation. Rejected information might be ignored simply because it is not needed, not because resources are insufficient for its use. The present paper will not be concerned with situations of this sort.

What then are the issues attending any attempt to demonstrate capacity limitations?

Process Set The definition of capacity limitation assumes two known sets of internal

processes, A and B. Can such internal process sets be known? In a given task stimuli might be “coded” in different ways, decisions based on different critical “cues,” responses chosen by different “strategies.” The process set chosen by the subject might well influence the task’s capacity demand.

Approaches to this problem vary. Sometimes empirical evidence suggests a particular process set, or sometimes one set has strong intuitive appeal. One goal of the present paper is to give some general idea of the sorts of process set that might be expected in various types of experimental situation.

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Confounding Factors Capacity limitations are typically measured in one of two ways. Ex-

perimental manipulations control either the number of supposed internal processes, or the type of bias in allocating capacity between them. The general expectancy is that performance will suffer as the number of processes is increased or as a particular process loses a part of its capacity allocation.

The most important issue to be addressed here concerns the relationship between observed performance decrements and inferred capacity limitations. In many commonly studied situations there is good reason to ascribe decrements, at least in part, to factors altogether different from capacity limitation. In some cases it is possible to show that such factors must necessarily make at least some (unspecified) contribution.

With these ideas in mind, I turn now to a detailed consideration of particular experimental situations.

INDEPENDENT RESPONSE SITUATIONS

The first type of situation is the most straightforward, and serves in some respects as the ideal against which others must be compared. The subject receives (at least) two inputs, simultaneous or so close in succession that responses to the two will overlap. Each input requires a separate, independent response.

Some examples from the literature may be useful. In many the dependent measure is accuracy. Some “tachistoscopic report” experiments (e.g., Sperling, 1963) provide a good example. A set of simultaneous visual stimuli (e.g., an array of letters) is briefly presented, and each one must be separately reported (separate responses). Similarly in hearing, simultaneous inputs might be presented one to each ear, and some decision about each be required. The inputs might be verbal (e.g., Broadbent, 1958; Ostry, Moray, & Marks, 1976) or nonverbal (e.g., Sorkin, Pohlmann, & Gilliom, 1973). In some cases the “simultaneous inputs” are two properties of a single object. Allport (1971) required report of the color and shape of tachistoscopically presented forms. Various types of response have been used. Each input may simply be identified and reported (Allport, 1971; Sperling, 1963). Identification may be supplemented by a rating of confidence in its accuracy (e.g., Long, 1975). Sometimes key depressions are substituted for verbal or written reports (e.g., Ostry et al., 1976; Sorkin et al., 1973). The important point is that there should be a separate response for each input.

In other studies the dependent measure is RT. Experiments on the “psychological refractory period” (Bertelson, 1966) provided a clear example. Two stimuli (e.g., letters) are presented either simultaneously or


close in succession, and each requires a separate, speeded response (e.g., a key depression). (When the stimuli are not exactly simultaneous, still the second typically follows before reaction to the first is over; so that still both could compete for common resources.) Another example is the use of “probe” RTs (e.g., Kerr, 1973; Posner & Keele, 1969). The stimulus for a (speeded) simple reaction is presented at some point during performance of another task. Again the simultaneous tasks have separate responses.

In other cases simultaneous inputs (and responses) are continuous rather than discrete. In an experiment by Shaffer (1975) the subject re- ceived simultaneous prose messages (one auditory and one visual) and tried continuously to repeat both back, one vocally and one by typewriter. Tracking tasks are also commonly used (e.g., Wickens, 1976).

In all these very different situations, separate stimulus inputs require separate, independent responses. This is the important feature to be borne in mind through the following discussion.

Process Set (a) Concurrent single-input processes. Typical assumptions about pro-

cess set may be illustrated with reference to dichotic listening. In a control condition the subject identifies a single word heard in the left ear. The processes of this task-the single-input processes-make some demand on psychological resources. So also do the processes of a second control, involving a single word in the right ear. Then in the dichotic (simultaneous input) condition, both words must be identified at once. The two concurrent sets of single-input processes now compete for common resources. Any performance decrements are due exclusively to this competition.

Similar assumptions would be typical in any independent response experiment. A condition with (at least) two separate inputs X and Y occur- ring together is compared with controls involving only X or Y. Any difference in performance reflects the fact that concurrent sets of single-input processes compete for common resources.

(b) Grouping. Perhaps grouping is the most obvious alternative. Though the subject receives together two separate inputs X and Y, there may not be a separate set of processes dealing with each one. Rather, grouped decisions may concern their combined state.

Some examples may make this clear. Consider the special case of “simultaneous inputs” which in fact are two properties (e.g., size and color) of a single visual object. These are to be separately reported. Garner (1974) has argued that for some (“separable”) property pairs (e.g., size and form) it indeed makes sense to think of each being separately judged (concurrent single-input processes, above). However, other (“integral”) pairs (e.g., hue and saturation) apparently combine to form a new, unitary

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property. For integral properties a grouping analysis is obviously required. Even though hue and saturation are to be separately reported, perceptual judgements will concern the combined property.

Rather similar is the phenomenon of “response grouping” in the psychological refractory period situation. There is often a strong tendency for the two speeded responses to occur simultaneously or in some other fixed temporal relationship (e.g., Kahneman, 1973; Schvaneveldt, 1969). Again they have been emitted as a unit rather than independently.

If grouping occurs, responses to the separate inputs X and Y must be scored not separately but as a unit. As an example, let X and Y each be binary, taking values X1,X2 (corresponding responses x1,x2) and Y,, Y2 (corresponding responses yl,y2). Given the pair of inputs X,Y1, response probabilities are:

PbYY,) = a, P(X,Y~ = by PkiYI) = c, ~Cwd = d.

In the absence of grouping we should conclude that the processes iden- tifyingx are accurate with probability (a + b), those for Y with probability (a + c). But with perceptual grouping (e.g., for a pair of integral stimulus properties) these separate processes do not exist. It makes sense only to conclude that the combined response is correct with probability a, and the probabilities of three different types of error are b, c, and d, respectively.

Similarly with response grouping in the psychological refractory period situation: Evidently it would be senseless to derive separate RTs for the two reactions. Only the latency of the unitary, combined response can be considered.

(c) Emergent processes. The classical Gestalt argument in perception is that a whole stimulus may be more than the sum of its parts. Similarly here, when inputs X and Y occur together their combination may define problems (and corresponding internal processes) absent with only one.

A suggestion by Treisman (1979) provides one good example. Sup- pose that the subject identifies two simultaneous, complex stimuli (e.g., a red triangle and a blue square). One problem may be organizing their components into the correct bundles. Failure may result in apparent com- binations of features actually separate in the display (the “illusory con- junctions” red square or blue triangle). Obviously this problem cannot exist (at least in the same sense) with a single stimulus: It is emergent from the combination of the two.

Similar arguments might apply in the psychological refractory period situation. Suppose that one input S, is a tone at 500 or 1000 Hz, receiving response R, with the middle- or forefinger of the left hand; and the other S, is a letter A or B, receiving response R2 with the middle- or forefinger


of the right hand. In a single input control condition, the only response choice will concern the two fingers of one hand; there will perhaps be no element of choice between hands. Will this remain true in the dual input condition? When the tone occurs, will the response be chosen only from the two fingers of the left hand, or will there also be some emergent element of choice between hands? Again a new problem may be defined by the combination of tasks.

A psychological refractory period experiment by Triggs (1969) suggests a particularly clear example. S, (a light in one of two positions, up or down) appeared on the subject’s left, and R, (a movement in one of two directions, up or down) was made with the left hand. For some subjects the stimulus-response mapping was “corresponding” (response in the direction of stimulus) while for others it was “crossed” (response oppo- site to stimulus). R, was similar, with stimuli and responses on the right. Thus four conditions were produced by factorial combination of left and right mappings. Performance was especially poor when left and right mappings were different, one “corresponding” and one “crossed.” Dun- can (1979) has confirmed that under these circumstances subjects have difficulty choosing the correct mapping for each reaction: Often there is a characteristic type of error, with the incorrect mapping applied to the (correctly identified) stimulus. Thus when two reactions with different mappings are combined, a new problem again is defined by their combination.

An analogous problem attends the attempt to perform different actions simultaneously with the two arms (e.g., tapping the head while rubbing the stomach). Each arm suffers some tendency to perform the action assigned to the other.

In general, when several inputs (or actions) occur together, their cum- bination may define problems (and corresponding internal processes) absent with only one.

Confounding Factors If there is grouping or some emergent process, then process set is

specific to the conditions in which simultaneous inputs X and Y occur together, and no simple comparison with controls involving only X or Y is possible. Otherwise however this comparison seems very directly to reflect capacity limitation. There are none of the confounding factors to be discussed for other types of experiment.

CHOICE

In choice, the subject receives one from a known set of alternative inputs, and is to decide which. Thus there is a separate response for each alternative. In many experiments the dependent measure is accuracy.

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Alternatives might be barely audible tones at different frequencies (e.g., Tanner, 1956); weak visual stimuli at different locations (e.g., Shiffrin, Gardner, & Allmeyer, 1973); auditory words in noise (e.g., Miller, Heise, & Lichten, 1951); and so on. When the dependent measure is RT this is the familiar “choice reaction time” situation (e.g., Hick, 1952; Hyman, 1953). The stimulus must be identified and its appropriate response chosen as fast as possible. There is no need to detail the wide variety of stimuli, responses, and stimulus-response relationships used in these studies. There are several good reviews (e.g., Audley, 1973; Broadbent, 1971; Theios, 1975).

Process Set

(a) Information theory analyses. The first approach to process set in choice is based on information theory (e.g., Hick, 1952; Welford, 1968). Consider a case in which there are four alternative inputs, e.g., a square array of lights in a spatial choice reaction task. Each could be represented as a pair of values on two independent, binary dimensions, e.g., horizontal and vertical position. This is a logical possibility even when inputs are not obviously two-dimensional; e.g., a horizontal row of four lights. Here we have the basic idea of information theory analyses. Any set of N alternative inputs is coded into log,N binary dimensions. An input is identified by taking log,N binary decisions, one for each dimension. In- creases in N increase the number of dimensions and decisions required. Any accompanying performance decrement (increase in RTs or decrease in accuracy) is assigned to capacity limitation.

“Serial dichotomization” models provide a simple example (e.g., Welford, 1968). They suppose that only one binary decision can be taken at a time (capacity limitation). The log,N decisions are taken in sequence. Choice RT is indeed roughly proportional to log N (e.g., Hick, 1952; Hyman, 1953).

The assumption of coding into independent, binary dimensions has never been clearly tested. On the whole, it is not at all easily justified. Suppose that in a two-choice task the alternative stimuli are the symbols “square” and “circle.” To change the task to four-choice, the further symbols “triangle” and “cross” are added. Intuitively it is not at all clear that this corresponds to the addition of a single extra binary choice to the perceptual situation.

(b) “Present -absent” processes. Another possibility is to suppose that for each of the N alternatives the subject makes a separate “present-absent” decision. The input is identified as the single alternative shown to be “present.” The number of decisions of course increases directly with N. An accompanying performance decrement is again assigned to capacity limitation.


An example is provided by the recent “memory scanning” models of choice reaction performance (e.g., Falmagne, Cohen, & Dwivedi, 1975; Theios, 1973, 1975). Performance is based on a set of associated stimulus and response representations. The input is compared in turn with each stimulus representation, until when a match is found the corresponding response is made. Obviously RTs will increase with increasing N. Again capacity limitation is reflected in the necessity for serial matching.

One must be very careful here. In choice the central thing is really the relationship between alternatives. For example, the difficulty of choice evidently depends on similarity of alternatives. This can be concealed by models having for each alternative a separate “present-absent” decision.

Consider a typical spatial choice RT task. In the two-choice case there are two alternative stimulus lights B and C, to either side of fixation. To increase N to four, two new lights A and D are added, one to either side of the original display. Any “present-absent” decision concerning B might be completely different in the two cases (Duncan, 1976; Komblum, 1965). In the two-choice task B need only be discriminated from a light (C) on the other side of fixation. In the four-choice task there is another light (A) to the same side of fixation. These two rather different discriminations might require completely different types of process.

A model developed by Tanner (1956) rests in part on separate “present-absent” processes for each alternative, but acknowledges too the importance of the relationship between alternatives. The task was to decide which of several alternative weak tones (differing in frequency) had occurred in noise, with accuracy the dependent measure. First, the subject was supposed to accumulate separately information concerning each alternative (frequency): Capacity limitation influenced these separate “present-absent” processes. Then however the separate sets of evidence were compared, and the alternative most strongly indicated was chosen. This really is the requirement in choice: not to assess separately whether each alternative is “present,” but to decide which most seems to be present.

This suggests a criticism of recent work by Shiffrin and his colleagues (Shriffrin, 1975; Shiffrin, Craig, & Cohen, 1973; Shiffrin & Gardner, 1972; Shiffrin, Gardner, & Allmeyer, 1973; Shiffrin & Grantham, 1974). The experiment of Shiffrin, Gardner, & Allmeyer (1973) may be taken as an example. In the “simultaneous” condition there was a single observation interval during which a weak visual stimulus was presented at one of four corners of a square. The subject was to choose which corner had contained the stimulus, the dependent measure being accuracy. In the “successive” condition each trial was split into two halves. The stimulus appeared either during a first observation interval, in one of two (known)

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alternative comers, or during a second interval, in one of the remaining two. Just as in “simultaneous,” however, there was always one stimulus, and the subject waited till the end of the trial to announce which corner had contained it. The argument was this: In “simultaneous” it was neces- sary to examine all four comers at once, but in “successive” attention could be confined to two at a time. “Successive” performance should then have been superior, given capacity limitation. (Note again the idea of dividing attention between separate “present-absent” processes for each comer.) As in other experiments, Shiffrin, Gardner, & Allmeyer (1973) found no such result. Though the great merit of this experimental technique will be discussed shortly, it does ignore the importance of comparing evidence from the four comers. In “successive” evidence from the first observation interval could not have been compared with that from the second, without an intervening period of storage. Memory losses may have seriously weakened performance in this condition. Much the same applies to other choice tasks in which Shiffrin has compared “simultaneous” and “successive” performance.

Confounding Factors (a) Number of inputs. A performance decrement generally accompanies

an increase in N; and as we have seen is often ascribed to capacity limitation. However, even in the complete absence of capacity limitation some such performance decrement must occur.

A model based on information theory illustrates the point. In any two- choice task there is a single binary decision. It is correct with probability p. Correspondingly the probability of a correct response is also p. In any four-choice task there are two binary decisions. Let there be no capacity limitation, so that for each decision the probability correct remains at p. Yet both must be correct for a correct response: probability onlyp2. Even though individual decisions remain equally accurate (no capacity limitation) a performance decrement (decline in response accuracy) accompanies an increase in N, for simple statistical reasons. The number of underlying processes has been increased, and all must be correct for a correct response.

The generalization to RT tasks is straightforward. The usual requirement is to keep error rates constant as N increases. To allow this, each binary decision must actually become more accurate. Since the accuracy of a decision increases with the time devoted to it, this requires an increase in RTs. In the absence of known speed-accuracy tradeoff func- tions, the expected increase in RTs is uncertain, but might be substantial.

Green and Birdsall (1964) had developed a similar argument with a different assumed process set. Their analysis of choice accuracy assumed, like Tanner (1956), separate “present-absent” processes accumulating evidence for each alternative, followed by comparison and


selection of the strongest. There is one correct alternative and N-l incorrect. As N increases, so also must the chance that one of the incorrect alternatives is strongest. There simply are more incorrect alternatives, and thus a greater chance that one at least will be stronger than the correct alternative. With this model, and assuming no capacity limitation (i.e., that the accuracy of individual “present-absent” processes is independent of N), Green and Birdsall (1964) were able to lit with extreme preci- sion the extensive data of Miller et al. (1951) on choice accuracy in the identification of auditory words in noise. Laming (1968) has taken a very similar approach to RT tasks.

The basic point is extremely simple and quite independent of the assumed process set. Any increase in N correspondingly increases the number of supposed underlying processes. We need not specify the exact nature of these (e.g., independent, binary decisions; or processes separately accumulating evidence in favor of each alternative). It need only be that each process is prone to error. The more chances for error there are, the worse must overall performance be. Of course capacity limitation would only be implicated if the individual processes became less efficient as their number increased. Since some performance decrement will occur whether or not this is true (and since without assumptions about process set and speed-accuracy tradeoff the size of this decrement cannot be predicted) it is very hard to obtain any firm evidence concerning capacity limitation in a choice task.

The contrast with the independent response situations considered earlier is worth noting. In those situations supposed sets of internal processes, one for each input, are associated with separate responses. (This of course is assuming no grouping or emergent process.) If one process becomes less accurate as the number of simultaneous processes is increased, this is directly detected and directly reflects capacity limitation. In choice on the other hand a single response reflects the combined outcome of all processes. Since its accuracy is reduced by the tendency to error of every process, some performance decrement must accompany an increase in the number of processes (i.e., an increase in N), even if individual processes remain equally accurate (no capacity limitation). ’

’ The argument that a performance decrement must accompany an increase in N may seem to conflict with findings in well-practiced tasks such as digit and letter naming. In these tasks RTs seem sometimes to be independent of N. That effects of N should decrease with practice is unsurprising, but that they should vanish altogether is more so. Probably they never really do. A review of 15 digit- and letter-naming studies (Duncan, 1976) showed a mean difference of 24 msec between two- and eight-choice RTs with a standard deviation of 19 msec. Thus the difference, though slight, is probably real. A further possibility has been raised by Fitts and Switzer (1962). In some conditions subjects may always treat the task as if any digit (letter) could occur, so that the apparent manipulation‘ofN has no psychological reality.

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One last point is worth noting. The technique of comparing “simultaneous” and “successive” observation conditions, discussed earlier in connection with the work of Shiffrin, does successfully solve this problem of varying N. In the experiment of Shiffrin, Gardner, & Allmeyer (1973) for example, N, the number of alternative spatial locations, was fixed at four in both “simultaneous” and “successive” conditions, it being important to remember that, in “successive,” no decision was made until the end of the trial, when the stimulus could potentially have occurred at any one of the square’s four corners. In a simple statistical sense therefore the two conditions were equivalent. (For example, on the analysis of Green and Birdsall (1964), in each condition there were three incorrect alternatives and therefore three chances for one of these to indicate a stimulus more strongly than the single correct alternative.) Even so “successive” imposed less of a capacity demand. Though criticized earlier for its assumptions about process set, the work is important as suggesting a potential measure of capacity limitation unconfounded by changes in N, and I shall return later to possible modifications that might be used in other contexts.

(6) Bias. Instead of N, bias may be the critical experimental variable. For example, one stimulus may be more probable than the others. As expected, performance is better on this stimulus than on its alternatives (e.g., Hyman, 1953; Laming, 1968).

This result has been related to capacity limitation in various different ways. The “memory scanning” models of CRT performance (e.g., Fal- magne et al., 1975, described earlier) provide an example. Repre- sentations of each stimulus alternative are scanned in turn until one matches the input. Probable alternatives are identified quickly because they are scanned first. More generally, those decisions which serve to identify a probable alternative are taken early. The treatment of models based on information theory is rather similar (e.g., Rapoport, 1959).

There is however a more obvious approach to the problem of bias. If an alternative is highly probable, the system may simply decide in its favor with relatively little evidence.

Signal detection theory provides one well-known implementation of this idea. In the simplest case there are two alternative inputs, X and Y. From trial to trial, the decision is supposedly based on evidence varying continuously between strongly in favor of X and strongly in favor of Y. Evidently some criterion (p) must be set, such that a decision of “X” will be made if the evidence falls to one side, “Y” if it falls to the other. If Y is made less probable than X, the criterion should ideally be adjusted in X’s favor (Green & Swets, 1966). The result of course is an increase in probability correct for X, a decrease for Y.

The generalization to RT experiments-like those for which models based on capacity limitation have been developed-is straightforward.


The “accumulator” models discussed by Audley and Pike (1965) illustrate the general approach. Successive samples of (noisy) information are taken from the input. For each stimulus alternative there is a separate counter or accumulator. Each information sample favors one or the other alternative, and the appropriate counter is incremented. This process continues until one counter reaches a criterion value. Setting criteria is a matter of balancing speed and accuracy. The lower a criterion, the faster it will be reached (shorter RTs); but it will be reached more often when the corres- poing stimulus alternative actually is absent. Again the ideal solution is to set the criterion lower, the more probable the stimulus is (e.g., Laming, 1968). This account of the relationship between RT and stimulus probability is quite different in spirit from those based on capacity limitation.

The reader may be left with a doubt over how criteria are set. Is there some psychological limitation (perhaps equivalent to capacity limitation) which constrains criteria to vary reciprocally, so that if the criterion for X is reduced, that for Y must be increased? It is worth emphasizing that no such thing is implied by these models. Typically we should expect criteria to vary reciprocally, since ifX is made more probable, Y must necessarily become less probable. But this is not through any limitation (e.g., capacity limitation) imposed by the system-potentially all criteria might simultaneously be reduced. This is simply not expected because it is not an ideal reflection of relative stimulus probabilities, implying simply that all responses will become faster but less accurate.

It may then be a mistake to ascribe bias effects to capacity limitation. A bias toward a probable alternative may imply no more than that a decision in its favor will be made with relatively little evidence.

CLASSIFICATION

Classification situations are perhaps the most interesting in the experimental literature. Very widely studied, they present problems closely similar to those just considered for choice. The input is classified as belonging to one of two (or more) alternative groups. For present purposes, “classification” will be taken to include all situations in which groups of alternative stimuli share a common response.

There are several good examples. In “visual search” (e.g., Atkinson, Holmgren, & Juola, 1969) the subject decides whether or not an array of visual forms (e.g., letters) contains a prespecified target (e.g., the letter E). There are typically only two responses, “Target present” or “Target absent,” and all possible stimulus arrays are classified into these two groups. In “uncertain frequency detection” (e.g., Swets, 1963) the subject decides whether or not a tone occurred in noise. The tone might be at one of several different (known) alternative frequencies, but the common response “Tone present” is appropriate whatever the frequency. In “memory scanning” (Stemberg, 1966) the subject memorizes a set of

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target characters (e.g., letters) and is then presented with a “probe” to be classified as member or nonmember of this “positive set.” Again there are only two alternative responses, and it is irrelevant which member of the positive (or negative) set actually is presented. In “same-different matching” (Egeth, 1966; Posner & Mitchell, 1967) the subject receives a display of two stimuli (e.g., colored shapes, letters) and classifies the pair as “same” or “different.” Again these are the only two alternative responses, and all possible stimulus pairs are simply classified into these two groups. Many other examples could be given-a single response might be appropriate for either of two circles of different sizes (e.g., Garner & Felfoldy, 1970), or two lights in different positions (e.g., Posner, Nissen, & Ogden, 1978), and so on. The important thing is that different stimuli should share a common response, and therefore that differences between them are irrelevant to the task.

Process Set (a) Separate tests. Items can often be classified into two groups by a set

of separate tests. If any one gives a “positive” answer then one response is made; if all are “negative” the other response is chosen by default.

In visual search, each item in the array might be classified as “target” or “nontarget.” If any one is a target the positive response is made, otherwise the negative. In uncertain frequency detection there might be a test for a tone at each possible frequency. The positive response is made if any tone is found, otherwise the negative. In memory scanning the probe might be matched against each member of the positive set. The positive response is made if any match occurs, otherwise the negative. In same- different matching each attribute of the two forms (e.g., color, shape) might be matched. A “different” response is made if any mismatch occurs, otherwise “same.”

In the typical experiment, the number of tests is increased systematically, by increasing array size in visual search, the number of alternative tones in uncertain frequency detection, positive set size in memory scanning, number of relevant attributes in same-different matching, etc. Performance decrements (typically increased RTs) are ascribed to capacity limitation (and often, in particular, to serial processing).

Of course the possibility of “emergent” processes, considered earlier for independent response situations, arises with equal force here. Again a combination of separate tests may be more than the sum of its parts. The argument of Treisman (1979) should be recalled as one example: When simultaneous stimuli are identified, one problem may be organizing their perceived features into the correct bundles. In visual search for example features of the letters P and K might recombine to form the “illusory conjunction” R. Another obvious possibility arises in same-different


matching of multidimensional stimuli. There might well be some emergent conflict if the test on one dimension gives the answer “same,” but that on another dimension gives “different.” Again this is a problem defined, not with reference to a single test, but with reference to their combination.

(b) Selective processes. If inputs share a common response (i.e., if they are to be classified into the same group) then differences between them are irrelevant and might ideally be ignored. This raises the possibility of a selective process. Inputs are coded into relevant and irrelevant dimensions. The relevant dimensions distinguish stimuli from different groups (i.e., stimuli requiring different responses). All differences within groups are along the irrelevant dimensions. Only the relevant dimensions are processed; all decisions are based on these, and irrelevant dimensions are ignored.

In any classification situation this ideal strategy (rather like the ideal coding of information theory) is a logical possibility. It depends only on the ability to code inputs into suitable dimensions. These dimensions need be neither intuitively obvious nor easily specifiable.

The problem has been widely studied using stimuli with easily specifiable relevant and irrelevant dimensions. An experiment by Gamer & Felfoldy (1970) provides an example. The four alternative stimuli-circles drawn on cards-were to be classified into two groups of two. One response was appropriate for either a 7/8- or a l-in. circle with an inscribed diameter 15” clockwise from the vertical. The other was appropriate for a 7/8- or l-in. circle with the diameter 15” counterclockwise. Here it is clear that all (irrelevant) variation within stimulus classes concerned size, while all (relevant) variation between classes concerned angle. Selective perceptual processing only of the relevant dimension is intuitively plausible in a case like this, and indeed the typical goal of such experiments is to discover pairs of dimensions for which it is possible.

However, in other cases, and especially with practice, a similar strategy might be developed even when the nature of relevant and irrelevant dimensions is not intuitively clear. Suppose that an experiment’s four stimulus alternatives are digits, to be classified into two groups of two in an RT task. Thus one key is to be depressed for either member of one pair, a second for either member of the other pair. It may well be that, as the task continues, subjects discover some single perceptual characteristic distinguishing the two members of one pair from the two members of the other (e.g., Bertelson, 1965; Rabbitt, 1968). Then the task could be performed by selective processing only of this characteristic.

These examples concern selective perceptuuf processing. More generally, we might suppose any classification task to be organized into various different (perhaps successive) stages (cf. Sternberg, 1969). Taking memory scanning (Sternberg, 1966) as an example, we might perhaps distin-

90 JOHN DUNCAN

guish at least (1) a perceptual stage in which some representation of the probe is formed; (2) a classification stage in which it is classed positive or negative; and (3) a response stage in which the appropriate one of the two alternative responses (typically key depressions) is chosen. (Presumably then Stemberg’s (1966) suggestion that the probe is compared in turn with each member of the positive set would concern the second stage.) It may be useful to consider different stages quite separately, and to ask separately for each stage whether some form of selective process is possible.

For example, consider a task like Stemberg’s (1966) memory scanning, but with a well-learned distinction between positive and negative sets. Thus the positive set might ah be digits, the negative set letters (e.g., Shiffrin & Schneider, 1977). There might be no single perceptual feature distinguishing these sets, so selective processing at stage 1 might be im- possible. Assume on the contrary that the probe is fully identified. Given such identification, a single (learned) semantic feature (“letter” or “digit”) might become available. All later stages might be selective processes based on this semantic feature. A similar idea is reflected in various “direct access” models of performance in this situation (e.g., Corbal- lis, 1975).

As far as the stages of response selection are concerned, selective processing might be achieved in almost any classification task. By the time these stages are reached, all information distinguishing inputs from the same class might well have been discarded. Suppose again that in Stemberg’s (1966) (ill-learned) memory scanning the probe is matched in turn against each member of the positive set. The only information considered by later stages of response selection might then be whether or not any match was found, the single relevant feature distinguishing positive from negative probes.

Thus the problem of process set is somewhat complex in a classification task. Selective processing might generally be achieved by the stages of response selection. The important question is the point at which it is achieved, i.e., the point at which information distinguishing stimuli from the same class is discarded. Presumably performance often reflects a rather complex combination of different types of process going on at different stages of the task.

To the extent that selective processing is perfectly achieved, no issue of capacity limitation immediately arises, since there are not obvious simultaneous processes competing for common resources.

Confounding Factors (a) Number of tests. As we saw many classification situations (visual

search, uncertain frequency detection, unpracticed memory scanning, same-different matching of multidimensional stimuli) may require a set


of “separate tests” whose number can be increased systematically (by varying array size, the number of alternative frequencies, positive set size, number of relevant dimensions). Just as in choice however it is a mistake to assign resulting performance decrements simply to capacity limitation. Again a single response (the classification) reflects the combined outcome of the whole set of simultaneous processes. Increasing the number of processes increases the overall chance of error; so that even in the absence of capacity limitation some performance decrement must occur.

Green (1958) and Swets (1963) have discussed the problem for uncertain frequency detection. If there is a separate test for a tone at each possible frequency, then the overall chance of a “false alarm” must increase with the number of frequencies. For visual search, Eriksen and Spencer (1969) and Gardner (1973) have argued that, as the size of the array increases, so also does the chance of some nontarget being incorrectly taken for a target. Speed-accuracy tradeoffs, as in the choice situation, may allow this effect to show up in RT rather than accuracy. Much the same point has been made in a variety of different contexts (e.g., Kinchla, 1977; Lappin & Uttal, 1976; Shiffrin, 1975). As before, the exact extent of this effect-and hence of any further contribution from capacity limitation- often cannot be assessed.

It is worth returning here to the technique of comparing “simultaneous” and “successive” observation intervals, considered at length earlier in connection with the work of Shiffrin, Gardner, & Allmeyer (1973). I have tried recently to modify this technique to give, in visual search, a measure of capacity limitation unconfounded by changes in array size (Duncan, in press). The task was visual search for digit targets among letter non-targets, with brief exposures and accuracy as the dependent measure. The four-character arrays formed a cross (plus sign) centered on the fixation point. As usual target position was immaterial: the subject simply indicated whether any target was present. In the “simultaneous” condition all four characters were exposed at once. In “successive” a known pair (e.g., those above and below fixation) were presented in a first exposure, the others in a second exposure 1 set later; but still at the end there was only a single decision about the whole set of four. As argued before, though in both conditions the same total number of characters was presented (giving the same total number of chances for a “false alarm”), still capacity demands were relatively slight in “successive” since only two characters appeared at a time, so that still given capacity limitation this should have been the easier condition.

In the similar experiment of Shiffrin, Gardner, & Allmeyer (1973) described earlier the subject was to choose which location contained the “target,” raising the possibility that information from different locations

92 JOHN DUNCAN

(and different exposures in “successive”) was to be compared. In the visual search task used here, though, such comparison was unnecessary since it could never have been important to decide which of two perceived characters was more like a target. This technique again promises a measure of capacity limitation unconfounded with changes in array size, and here rests on intuitively plausible assumptions about process set.

(b) Bias. Measures using bias in the classification situation have recently become popular. One stimulus from a group sharing a common response is made especially probable, or otherwise “cued” or “primed,” The work of LaBerge (1973, 1975) provides a good example. In one experiment (LaBerge, 1973) the single response key was to be depressed if either an orange light or a lOOO-Hz tone occurred. One or the other modality was precued as highly probable, and to this modality attention was supposedly “assigned.” As expected, RTs were decreased for the expected but increased for the unexpected modality. In the latter case, attention had presumable to be “switched” between modalities before any response could be initiated.

The “cost-benefit” studies of Posner (e.g., Posner & Snyder, 1975; Posner et al., 1978) involve much the same analysis. In an experiment by Posner et al. (1978), the single key was to be depressed if a light occurred either to right or left. A precue for one side decreased RTs on that side but increased them on the other. Again a need to “switch” attention between sides was implicated.

Though analyses of this sort have substantial intuitive appeal, the argument applied earlier to choice applies again here. A bias toward one input may imply, not the preferential allocation of some limited capacity, but simply that the system will decide in favor of this alternative with relatively little evidence. An “accumulator” model of the LaBerge (1973) experiment may make this clear. For the light and the tone there are separate counters or accumulators. The key is depressed if either counter reaches a criterion. Each criterion is set lower-and RTs hence are shorter-the more probable is its corresponding stimulus.

Again, no limitation of the system (analogous to a capacity limitation) requires that, if one criterion (e.g., for the light) is lowered, the other (tone) must be raised. This typically is to be expected simply because of the structure of the experiment-as one stimulus becomes more probable, so the other becomes less. In fact both could be made more probable (reducing the probability of a “catch” trial with no stimulus). In this case we should expect both criteria to be lowered at once.

This possibility-that bias in part reflects not any limited capacity but rather a change in the amount of evidence required for a decision-must be considered in many “priming” situations.


CONCLUSIONS

Two general points have emerged from this discussion. First is the issue of process set. Alternative process sets exist for any experiment. Origi- nally I had hoped to offer general rules for choosing between them, but eventually I was unable to discover these. Experimenters can only be urged to use their own greatest ingenuity, both in imagining potential alternative process sets and in choosing between them. At least it is clear that the problem cannot be ignored. If there is grouping in an independent response situation it will be misleading to assume instead that the simultaneous input condition involves two concurrent sets of single-input processes (e.g., Schvaneveldt, 1969; Kahneman, 1973). No analysis of a choice task should ignore the possibility that at some point evidence favoring different alternatives will be compared (Shiffrin, 1975). No classification situation can be understood without a grasp both of the stage of the task most importantly influencing the results, and of whether selective processing is achieved at this stage. So the list might be continued.

The second point concerns confounding effects, having nothing to do with capacity limitation, that can arise during attempts to change the number of simultaneous internal processes or the bias between them. When a single response reflects the combined outcome of a set of simultaneous processes, simple statistical considerations must reduce its accuracy (and/or speed) as the number of processes is increased. Similar- ly, if a particular input is highly probable, the system may simply decide in its favor with relatively little evidence. When these effects occur, experimenters must again use their greatest ingenuity to isolate from them any separate effects of capacity limitation.

It would be a pity to put off certain types of experiment for reasons like this. There is substantial intuitive appeal for example in the idea of Posner et al. (1978) that, when an input from a particular point in space is highly probable, attention is preferentially allocated to that point. Sitting at one’s desk one can easily “see” this effect. But serious efforts must be directed toward disentangling this from simple bias, in the sense of requiring little evidence for an expected input. Much the same is true for each of the other types of experiment I have considered.

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(Accepted June 18, 1979)

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The demonstration of capacity limitation