Dependent spatial channels in visual processing

COGNITIVE

PSYCHOLOGY

Dependent

9, 326-352 (1977)

Spatial

Channels

ALEXANDER~OLLATSEKAND University

in Visual Processing LORENZ DIGMAN

of Massachusetts

The present experiments were designed to test whether or not processing in visual information channels defined by spatial position is independent in the visual search paradigm. In Experiment 1 subjects were asked to judge whether or not a red square was present in a display of two colored geometric figures. Their mean reaction time (RT) to respond no to a “divided target” display in which one figure was red and the other was a square was about 100 msec longer than to control displays containing either two red circles or two green squares. This result is inconsistent with a spatially serial independent-channel model and with many spatially parallel independent-channel models. The relatively slow responding to divided target displays was replicated in Experiments 2 and 3, when subjects judged whether or not an “A” was present in a display of two alphanumeric characters, and a divided target display was one which contained two features of “A.” Experiments 4 and 5 demonstrated that the dependence observed in the first three experiments was probably the result of two mechanisms: crosstalk integration, whereby the target features are integrated across the two spatial channels, and repetition facilitation, whereby processing is facilitated (in some cases) when the two figures in the display are physically identical. Experiment 6 suggested that subjects organized the display in terms of spatial channels even when the task allowed subjects to ignore spatial location.

An important question in visual information processing is how information from various parts of the retina is integrated to enable a response. Much of the literature related to the issue of integration has been focused on the question of whether information in channels defined by disparate retinal or spatial locations is processed in parallel or in series. The task that has been most widely used to study the spatial integration of visual information is visual search. The subject is presented with a display of several figures (such as alphanumeric characters) that can be viewed in a single fixation. The subject is typically asked to push one lever if a target item (e.g., a “B”) is present in the display and to push another lever if it is absent (or if another target item is present). This research was supported by National Science Foundation Social Science Department Development Grant No. GU 4041 and by National Institute of Mental Health Small Grant No. MH 23968. The authors wish to thank Allan Porfert, Bernard Elliot, and Gary Kidd for their assistance in running subjects and Charles Clifton, David Meyer, and Arnold Well for their helpful comments and suggestions. Please send reprint requests to Alexander Pollatsek, Department of Psychology, University of Massachusetts, Amherst, Massachusetts 01002. 326 Copynghl All rights

~0 IV77 by Academic Press, Inc. of reproductmn ,n any torm reserved.

ISSN M)IO-0285

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Although many experiments have been conducted to determine whether visual search data are best fit by spatially serial or spatially parallel models (e.g., Atkinson, Holmgren, & Juola, 1969; Egeth, Jonides, & Wall, 1972; Estes & Wessel, 1966; Sternberg, Note l), few attempts have been made to investigate the assumption of channel independence that underlies the models tested. To elaborate, the most widely employed tests of those models involve measuring the effect of “display size” (i.e., the number of characters) on the dependent variable of interest (either response time, probability of correct response, or both). The simplest serial model assumes that the time to process N elements should be the sum of the times taken to process each element in turn if the process is exhaustive (e.g., when no target is present). If display elements are randomized, this assumption leads to the clear prediction that response time is a linear function of display size. On the other hand, the predictions of even the simplest parallel models are more complex. They postulate that the time taken to process N elements is the maximum of the times to process each of the N elements if the process is exhaustive. With certain special distributional assumptions (e.g., the processing times in all spatial channels are equal and have zero variance) the parallel model predicts no increase in reaction time (RT) as display size increases, while with most distributional assumptions, it does predict an increase. While parallel models do not predict linearity under most distributional assumptions, it is difficult to discriminate the serial model from many parallel models. This difficulty has led to more sophisticated experiments designed to discriminate between the two models, such as those using multiple and redundant target elements (e.g., Holmgren, Juola, & Atkinson, 1974; Wolford, Wessel, & Estes, 1968). However, most of the above experiments were not designed to test critically the basic assumption of channel independence that underlies both models. On a functional level, the assumption of channel independence has meant that overall processing time can be calculated as a relatively simple function of the processing times in each of the spatial channels (e.g., the sum in the serial model above or the maximum in the parallel model above). On a process level, the assumption of channel independence implicit in these models is that the features in a spatial channel are processed up to the level of deciding whether or not a target is present in that channel without influence from processing in other channels. In the following discussion, as in most of the literature, it is assumed that each of the spatially discrete items (e.g., alphanumeric characters) defines a spatial channel. The question of how a spatial channel would be defined in a typical real-world scene is beyond the scope of this article. However, if the naive definition above is not appropriate in this situation, the concept of spatial channels would appear to be of limited use.

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Recently several researchers in visual information processing have questioned the assumption of channel independence. Sternberg and Knoll (1973), in a synthesis of the literature on judgments of temporal ordering, proposed an analog of the logic of Sternberg’s “additive factors” method (Sternberg, 1969)to test channel independence. In three visual information processing experiments that were reviewed, the intensities of two light signals were factorially varied. Their test requires that the effects of the intensities produce additive effects (in the analysis of variance sense) on the “point of subjective simultaneity” in order for the independence hypothesis to be accepted. A significant interaction was obtained in one of the three experiments suggesting spatial positions may not always serve as independent channels in temporal ordering judgments. (However, Sternberg and Knoll suggest that there may be been methodological problems with the study that reported an interaction.) Estes (1972) proposed an interactive channel model for visual search on the basis of a complex visual search experiment. The major aspect of the data that led to Estes’ rejection of channel independence was that the number of characters in a display influenced processing time only if the nontarget elements were physically “confusable” with the target. Estes conceived of the interaction as a competition among spatial locations for feature extractors which have limited capacities. Wolford (1975) reviewed Estes’ experiments and other related research and proposed a complex interactive channel model which is consistent with several experiments in visual search that use accuracy of report (either forced choice or whole reportj as the dependent variable. A phenomenon that suggested an interactive channel model to Wolford was that the discriminability of peripherally presented letters falls off much more steeply when they have other letters near them. However, neither Estes nor Wolford provided rigorous arguments that demonstrated that independent channel models are inconsistent with these two phenomena. The aim of the present experiments was to test the hypothesis of independent spatial channels in a more direct way than in previous visual search experiments. (The concept of independence of spatial channels will be formulated more precisely in the course of describing the paradigm.) In Experiment 1, subjects were presented with a display containing two figures, each of which was either a red square (RS), red circle (RC), green square (GS), or green circle (GC). The task was to respond “yes” (by pressing a lever) if a red square was present and to respond “no” otherwise. (Red square is the target assumed in all subsequent discussion.) The critical display contained a red circle and a green square (RC, GS). We shall call such a display a divided target display, since it contains both “features” of the target but in different spatial locations. The two displays used for comparison, called the control displays, contained either two red circles (RC, RC) or two green

DEPENDENT

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329

squares (GS, GS). Slower responses to divided target displays than to either control display would suggest a “crosstalk” mechanism in which the target features were integrated across the two spatial positions, that is, a violation of the independent channel hypothesis. To see how such a violation can be tested, we will first consider the predictions of the simple serial and parallel independent spatial channel models usually tested in the visual search paradigm before considering the concept of channel independence in greater generality. To avoid awkwardness, they will be referred to as “the serial model” and “the parallel model.” The prediction of the serial model is straightforward. If the time needed to reject a red circle as not being a red square is a and the time needed to reject a green square as not a red square is b, then the time to respond “no” to the divided target display (RC, GS) should bea + b + W, whereas the response times for the (RC, RC) and (GS, GS) displays should be 2a + W and 26 + W, respectively (where W is the “wastebasket” time or the time elapsed in all other stages of processing). Thus, according to the serial model, the response time for the divided target display should be equal to the average of those for the two control displays. On the other hand, the prediction of the parallel model depends on distributional assumptions. If the distributions a and b have no variability (parallel fixed times), then the response time for the divided target display is W + max(a, b), whereas the response times for the two control displays are W + a and W + b, respectively. Hence, a parallel fixed times model predicts that the response time to the divided target display should be equal to the maximum of the two control displays. No assumption-free predictions appear to be possible in the general case where a and b are random variables. However, if a and b are assumed to be statistically independent and if F(u ) is everywhere less than F( b ), or vice versa, then one can show that the response time to the divided target display should be less than or equal to the maximum of that for the two control displays (see Appendix). Thus both the serial independent channel model and a wide class of parallel independent channel models predict that the mean response time to the divided target display should be less than or equal to that of the maximum of the mean response times to the two control displays. However, if there is crosstalk integration of features between the two spatial channels, one might expect the response time for the divided target display to be significantly longer than for either control display, since the information that both target attributes are present could slow down responses to the divided target displays. Let us now attempt a more general formulation of an independent channel model. We assume that there are three stages of processing of interest: feature extraction, feature integration, and channel integration (see Fig. 1). The feature integration stage is assumed to take the features produced by the feature extraction stage, integrate them, and compare

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spatial Channel

of Processing

So11d lines represent the added dashed line indicates

a

Level

Exanples

Feature

Analyzers

Discrimination brightness, orientation, lines, etc.

Feature

integration

Discrimination of letters, colored geometric figures, objects.

flow of information across independent channels. one possible form of dependence or interaction.

of color. shape. vert7ca,

The

FIG. 1. A model of independent processing in spatial channels.

them to the target. The output of the feature integration stage is assumed to be unidimensional (reflecting the fact that features are integrated) and a monotone function of the similarity of the physical stimulus to the target. Presumably, this similarity is a weighted function of the similarity along the various dimensions, although for the purposes of this discussion, the only thing that needs to be assumed is that each physical stimulus has a number reflecting its similarity to the target. The channel integration stage takes the outputs of the feature integration stage and decides whether or not the target is present in any of the spatial channels. A finding that responses to the divided target display were significantly slower than those to either control display would be inconsistent with any model of the type discussed which assumed that the mean processing time in the feature integration and channel integration stages combined is a jointly monotone function of the similarity of the figure in each spatial channel to the target. Thus the dependence test, comparing the mean response time for the divided target display with the longer of the two mean response times for the control displays, has the potential for ruling out a wide class of independent channel theories. While it would be more elegant to have a test of channel independence that did not depend on other assumptions being made about processing, we feel that the present test is of fairly general interest. The separation of processing into a feature integration stage and a subsequent channel integration stage is presupposed by much of the visual search literature so that the proposed formulation is not more restrictive than others (e.g., Estes, 1972; Kinchla, 1974; Wolford, 1975). Furthermore, separation of processing into the two stages seems consonant with the intuition that the usual mode of processing is first an integration of features to form

DEPENDENT

CHANNELS

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figures or objects and then an integration of those objects to form a “scene.” While there is no conclusive evidence that processing follows that sequential pattern, the priority of feature integration within a channel is suggested by the finding that integration across features or “analyzers” within a channel is easier than integration of information across spatial channels (see Treisman, 1969, for a review). A violation of independence in a visual search task is also likely to have implications for whether or not processing in spatial channels is independent in other visual tasks as well. In a typical search task the stimulus elements are physically discrete, their spatial locations are reasonably predictable (in the present experiments, completely predictable), and there is no reason to believe that subjects are trying to form a unit of analysis larger than the stimulus element. Since all of these conditions would appear to encourage subjects to treat spatial locations as independent channels, one would expect independent-channel processing to be less likely in most other visual processing tasks. The first three experiments were conducted to determine whether or not there are violations of channel independence, using the above dependence test, and to explore the range of stimuli for which processing in spatial channels violates independence. Although the crosstalk integration mechanism is a plausible hypothesis for why divided target displays would take longer to process than the control displays, two other classes of mechanisms need to be considered. The first is that there could be an alternative (and possibly less interesting) mechanism which violates independence. The most plausible such mechanism is a repetition facilitation mechanism, whereby displays that contain identical figures or that contain figures with identical features would be processed more rapidly than an independent-channel model would predict. (This kind of effect could occur either with serial or parallel processing.) Thus responses to a divided target display could be slower than those to control displays simply because responses to the control displays are facilitated by repetition. In the first three experiments, the effects of the crosstalk integration mechanism and the repetition facilitation mechanism were partially confounded. Experiments 4 and 5, which had more complex tests for dependence, were performed to unconfound the potential effects of these two mechanisms. The second alternative to the crosstalk integration mechanism is that the subject need not integrate the features in each spatial channel as a stage of processing which is prior to integration of information across channels. One such model that predicts slow processing for divided target displays is the following. The channels are analyzed for color: If the target color is absent, there is ano response, but if the target color is present, processing is continued. The channels are then analyzed for form: If the target form is absent, the subject responds no, but if the target form is present, further

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processing is done to determine whether or not the target form and target color were in the same location. Such a model would explain slower responses to divided target displays than to control displays since an extra stage of processing would be required for divided target displays. However, even if the processing of features were assumed to be independent in each stage of such a model, the overall processing would be dependent in the sense that the presence of the target color in one channel would influence whether or not target form was processed in the other channel. Experiment 6 was conducted to test models of this type. In the task of Experiment 6, a determination of the spatial location of features was not required for a response: Subjects judged whether or not two target attributes, red and square, were both present in a display, regardless of their spatial locations. EXPERIMENT

1

Method Subjects. Seven students were drawn from an undergraduate subject pool. They received bonus credit in a course for participation in the experiment. Apparatus. The stimuli were presented through Gerbrand shutters on two random access Kodak Carousel slide projectors, which were focused on the same screen using a beamsplitting prism. A PDP-81 computer controlled the stimulus presentations and measured the response time (RT). Two copies of each slide were used (randomly) in each spatial position to minimize the possibility that the subject could identify the stimulus by some extraneous cue. Experimental design. The experiment was divided into blocks of 48 trials each. On each trial, the subject heard a I-set warning tone and then saw two figures presented simultaneously side by side. The universe of figures was: red square (RS), red circle (RC), green square (GS), green circle (GC). Each possible figure appeared in either spatial position randomly with a probability of %. For example, the probability of seeing a green square on the left and a green circle on the right (GS, GC) was l/16. The subjects had to indicate yes if either or both figures was a red square, and no otherwise. In this and succeeding experiments, yes responses were indicated by pushing a switch with the left index finger and no responses were indicated with the right index finger. The probability of ayes response was thus 7/16. The figures subtended an angle of approximately 2.5” horizontally, 0.5” vertically, and the separation between figures was approximately 0.5”. No fixation point was used, but the stimuli were shown in a small frame that delineated where they would appear. Each response terminated the stimuli for that trial. Feedback about the accuracy of the response was given after every trial, and RT feedback was given after every trial block. The subjects had four trial blocks on each of 2 days of the experiment. The first trial block of each day was treated as practice and not used in the present analysis.

Results The mean RTs for each of the 16 stimulus conditions are presented in Table 1. Since mean RTs were almost identical on Day 1 and Day 2 (F < 1) and since there was no interaction of practice with stimulus conditions (F < l), the data were averaged over the 2 days. The overall error rates were low (2.0%) and slightly higher in conditions with longer mean RTs.

333

DEPENDENT CHANNELS TABLE 1

MEAN REACTION TIMES (MILLISECONDS) AS A FUNCTION OF STIMULUS DISPLAY FOR EXPERIMENT I (AVERAGED OVER 2 DAYS OF PRACTICE)

Left figure Right figure

RS

RC

GS

GC

RS

383

422

417

428

RC

399

419

492

406

GS

u 389

545

376

373

GC

388

414

377

365

Note. See text for stimulus code. Times surrounded by black lines are “yes” responses. Other times are “no” responses.

Since the highest error rates were associated with the divided target cells, it was unlikely that violations of independence discussed below were produced by subjects having differing speed-accuracy tradeoffs when responding to different stimulus displays. Clearly, the mean RTs for (RC, GS) displays (the divided target displays) were by far the slowest. The mean RT of the two divided target displays was 99 msec slower than the mean RT to (RC, RC) displays, r(6) = 5.44,~ < .002, which was 43 msec slower than the mean RT to (GS, GS) displays, t(6) = 4.79, p < .Ol. This finding rules out the large class of independent spatial channel models discussed in the introduction since they all predict that the mean RT for the divided target display would be less than or equal to that of the maximum of the control displays. The data of Experiment 1, furthermore, rule out any independent channel model that postulates that response time is monotone with processing times in the various spatial channels. EXPERIMENT

2

Experiment 1 demonstrated that two figures defined by color and form were not processed independently, at least with the levels of practice employed. However, there may be combinations of dimensions or features that can be processed independently. Consider the figures, A, V, A, V: upright A (UA), inverted A (IA), inverted V (IV), and upright V (UV). They can be defined by the two dimensions, “presence or absence of a crossbar” and “direction of wedge.” If this definition of the stimuli is psychologically correct, and if there is dependence between the channels, then one should obtain results analogous to those of Experiment 1. If the task is to say whether or not there is an upright A in the display, the

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mean RTs for (IA, IV) should be longer than those for (IA, IA), or (IV, IV). This is because both target features, “presence of crossbar” and “wedge pointing up” are present in the former display but not in the latter ones. Method Design. The structure of the experiment was identical to that of Experiment 1. The only difference was that the set of stimuli was changed to upright A, inverted A, upright V, and inverted V; the subject’s task was to indicate whether or not a UA was present somewhere in the display. The subjects, as before, were run for 2 days, with four trial blocks per day, and 48 trials per trial block. The first trial block on each day was treated as practice and discarded. Eight undergraduate students drawn from the same pool as in Experiment 1 were used as subjects. Apparatus and stimuli. The stimuli were displayed on a Hewlett-Packard X-Y Scope. Plotting of the stimuli, timing of the experiment, and measurement of the RTs were done on a Hewlett-Packard 2114B computer. The sides of the “A”s and the “V’s were points defining 45” lines, and the crossbars for the “A”s were halfway up the figure. In this experiment, a “f” was used as a fixation point and a warning signal. The onset of the “+” preceded the onset of the display by 1 set and its duration was 500 msec, and it appeared in the center of the display. The figures subtended a visual angle of approximately 2.0” horizontally and 0.5” vertically, and there was a separation of approximately 0.7” between figures.

Results

The data for Experiment 2 are displayed in Table 2. The mean RT was 37 msec less on Day 2 than on Day 1, F(1,7) = 12.3, p < .Ol, and there appeared to be a different pattern of results for the 2 days. Accordingly, the data for the two days are presented separately. Clearly, the overall RTs were much slower than in Experiment 1; however, it is not clear whether this was due to simple visual discriminability differences, changes in the apparatus, or something more profound. Error rates were only slightly higher than in Experiment 1 (3.0%) and the highest error rates were in the divided target cells. The dependence test employed in this experiment was the difference between the mean RT for (IA, IV) and that for (IA, IA). The size of this difference was 88 msec on Day 1 and 14 msec on Day 2. The Day 1 effect was significant, t(7) = 5.09,~ < .Ol, and was about equal to that of Experiment 1. The Day 2 effect was not significant, t < 1, but the difference between the Day 1 effect and Day 2 effect is only marginally significant, t(7) = 1.85, p about equal to .05, one-tailed. (IA, IA) was 72 msec slower than (IV, IV), t(7) = 2.70, p < .05. Thus processing on the first day with alphabet-like stimuli is inconsistent with a large class of independent channel theories. However, since the size of the effect was very variable on Day 2, it seemed advisable to repeat Experiment 2 utilizing more practice in order to assess the stability of the dependence effect with these stimuli.

335

DEPENDENT CHANNELS TABLE 2 MEAN

REACTION

TIMES (MILLISECONDS) AS A FUNCTION DISPLAY FOR EXPERIMENT 2

OF STIMULUS

Right figure Left figure

Day 2

Nore. See text for stimulus code. Times surrounded by black lines are “yes” responses. Other times are “no” responses.

EXPERIMENT

3

Method The stimuli and task were identical to those of Experiment 2. The only difference was that the subjects had 5 days of practice rather than 2. The subjects were four graduate students at the University of Massachusetts who were paid for their participation.

Results The overall pattern of results was the same as that for Day 1 of Experiment 2 (see Table 3). While the dependence effect decreased somewhat with practice, it was still 85 msec on Day 5. The average dependence effect was 90 msec, t(3) = 4.26, p < .025, and the decrease with practice was insignificant, F < 1. Thus it appears that the dependence effect is large and reasonably stable for both classes of stimuli. Accordingly, it is likely that there is a reasonably large class of stimuli for which some notion of dependence (defined with respect to the model of Fig. 1) will be needed in order to explain visual search. The following experiments were conducted to explore the nature of this dependence.

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TABLE 3 MEAN REACTION TIMES (MILLISECONDS) AS A FUNCTION OF STIMULUS DISPLAY AND DEPENDENCE EFFECTS (MILLISECONDS) AS A FUNCTION OF DAY FOR EXPERIMENT 3

Left figure Right figure

IA

UA

IV

uv

447

430

Mean reaction times

uv

I

535

491

Dependence effecta Mean

Day

Value of contrast

1

2

3

4

5

106

9.5

80

86

86

90

a Contrast is mean of (IA, IV) minus mean of (IA, IA).

In the introduction, two mechanisms were discussed that might account for the dependence effect observed in Experiments 1-3, integrative crosstalk and repetition facilitation. In Experiments 1-3, the two mechanisms were confounded, since the control displays had two identical figures. Hence, the dependence effect may have resulted either from integrative crosstalk slowing down processing of the divided target displays or from the second of two identical figures in the control displays being processed more rapidly than predicted by an independent channel model. Accordingly, a more complex design was employed using three attributes per dimension. In the case of the colored figures, the color attributes were red (R), green (G), and yellow (Y), while the form attributes were square (S), circle (C), and triangle (Tr). For the alphabet-like figures the attributes for the “wedge” dimension were “wedge up,” “wedge down,” and “no wedge” (parallel lines), and for the “crossbar” dimension were “crossbar,” “no crossbar,” and “external crossbar” (see Fig. 2). The three-attribute per dimension design allows for comparisons to be made in which the identity of the figures can be balanced across comparisons. In the following discussion, the universe of the colored geometric objects will be used as exemplars with a red square assumed as the target for simplicity; however, the tests were applied to both sets of stimuli and more than one target was used in each experiment.

337

DEPENDENT CHANNELS Wedge Dimension Wedge Up

Wedge Down

NO Wedge

Crossbar

External Crossbar

F3~. 2. Stimuli used in Experiment 5.

One test for crosstalk integration that is free of possible influence from a repetition effect due to identical form is a comparison of the mean of the RTs to divided target displays [(RC, GS), (RTr, GS), (RC, YS), (RTr, YS)] with the mean RTs for a control display of two red figures that are not identical (RTr, RC), which is presumably slower than a (YS, GS) display. This test, Crosstalk Test 1, is a refinement of the dependence test previously employed. While a parallel fixed-times model predicts that the mean RT to the divided target display would be equal to that of the slower control display, a serial model predicts that it would be equal to the average of those of the two control displays [(RTr, RC) and (YS, GS)], and most parallel distributed times models predict it would be intermediate between those of the two control displays. Thus if processing were basically something other than parallel with fixed-times, there could be a crosstalk effect that slows down processing of divided target displays but is not large enough to override the “naturally” slower processing of the slower of the two control displays (RC, RTr). Accordingly, a more sensitive test, Crosstalk Test 2, was employed. Intuitively, this tests whether or not the presence of a square slows down RT equally when red is present and when red is not present (again assuming a red square is the target). The contrast employed was the difference between two differences in mean RTs: (a) a divided target display [(RC, GS), (RC, YS), (RTr, GS), (RTr, YS)] minus a display containing one red figure but no square [(RC, GTr), (RC, YTr), (RTr, CC), (RTr, YC)]; and (b) a display containing one square but no red [(GS, YC), (GS, YTr), (YS, GC), (YS, GTr)] minus adisplay containing neither red nor square [(GC, YTr), (GTr, YC)]. It should be noted that all displays used in this comparison have two different forms and two different colors.’ A spatially serial independent channel model predicts a value of 0 for this ’ Crosstalk Test 2 is symmetric with respect to dimensions. Thus for a red square target, the test could be equally well stated “tests whether or not the presence of red slows down RT equally when square is present and when square is not present.” Algebraically, if difference (a) is u - v and difference (b) isx - y , then the above restatement is equivalent to rearranging (a)-(b):(U-v)-(X-y)=(u-x)-(v-y).

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contrast since differences (a) and (b) would both be equal (in the example) to the difference in processing time between a nonred square and a nonred nonsquare. On the other hand, a parallel fixed-times model predicts a negative or zero value for this contrast: Difference (a) would be equal to 0 since a red circle or red triangle would take the longest to process, and hence the presence of a square of a different color would be irrelevant; on the other hand, difference (b) would be greater than or equal to 0 depending on whether or not processing a nonred square takes any longer than processing a nonred nonsquare (i.e., on whether or not form is processed given that the figure is not red). Moreover, a parallel distributed times model also predicts a negative or zero value for this contrast if one assumes (a) statistical independence and (b) that the cumulative distribution functions for red figures and square figures are everywhere less than or equal to those for figures that are neither red nor square (see Appendix for a proof). However, if there is integrative crosstalk between the channels, then one would expect that the value of this contrast would be positive since squareness should slow down processing more in the presence of red than when red is absent. Thus a positive value of this contrast will be taken as evidence for integrative crosstalk. The design also allows one to test for possible repetition facilitation effects. Since the repetition tests are fairly straightforward, discussion will be deferred to the results and discussion section. EXPERIMENT

4

Method The method was identical to that of Experiment 1 except that three values were used per dimension. The colors were red, green, and yellow, and the forms were square, circle, and triangle. The forms were the same size as in Experiment 1 and the viewing conditions and visual angles subtended by the figures were also the same. The stimulus probabilities were adjusted to make the response probabilities the same as in Experiment 1: (a) Target stimuli were presented (in either location) with probability equal to 1/4;(b) any stimulus that had exactly one attribute in common with the target was presented (in either location) with probability equal to l/8; and (c) any stimulus that had neither attribute in common with the target was presented (in either location) with probability equal to l/16. Twelve undergraduate and graduate students at the University of Massachusetts, who were paid for their participation, served as subjects for 3 days each. Three had a red square as a target, three a red circle, three a red triangle, and three a yellow square. On each day, the subjects had eight trial blocks of 51 trials each. The first trial block on each day and the first trial in each subsequent trial block were discarded as practice.

Results and Discussion Although there was a decrease in RT over days, the pattern of results was reasonably similar on the 3 days. Tests were run on the contrasts reported below in order to assess their reliability over days. While there

DEPENDENT

CHANNELS

339

was some general tendency for most differences to decrease with practice, all changes over days were insignificant. Hence, to clarify exposition, a single value was taken for each contrast for each subject averaged over the 3 days. In a few cases, where there appeared to be interpretable individual differences, reliability was assessedfor individual subjects. The majority of tests below assessed the reliability across subjects. The error rates were about 2% and tended to be higher in conditions with longer mean RTs. The two most important tests were the tests for crosstalk integration (see Table 4). In Crosstalk Test 1, we cannot reject the null hypothesis of independence if a parallel fixed-times model is assumed since the mean RT for divided target displays was actually a bit less than for the slower of the two control displays. (However, there were differences between the results for the different targets, a point that will be discussed later.) This negative result suggests that much of the dependence effect obtained in Experiment 1 was due to some version of the repetition facilitation mechanism. However, if a serial model is assumed, independence can be rejected. The value of the contrast measuring the difference between divided target displays and the average of the two control displays was 25 msec, t( 11) = 2.56,~ < .05. On the other hand, the contrast used in Crosstalk Test 2 had a value of 33 msec, which allows us to reject both the serial independent channel model and a large class of parallel independent channel models, even for displays that had no identical features (see Table 4). The data of Experiment 4 also provide evidence for a repetition facilitation effect. The effect of the identity of the two figures was assessedfor three classes of figures (see Table 4, Facilitation Tests l-3). Two other tests for facilitation by identity were conducted (see Table 4, Facilitation Tests 4 and 5): facilitation by identical form for figures having different colors (one of them the target color) and facilitation by identical color for figures having different forms (one of them the target form). The pattern of results in the repetition tests is relatively clear: (a) The physical identity of two figures speeds up processing only if they are red; and (b) given a difference on either the form or color dimension, identity on the other dimension does not appear to affect processing time. The lack of a repetition effect for identical color is noteworthy since color appears to be processed on all trials. While the contrast in Facilitation Test 1 was consistently greater than 0 for all subjects, it appeared to be less for the three subjects who had a red triangle for a target (the average serial test value was 12 msec for these three subjects). Another reflection of this difference was that these three subjects violated independence in Crosstalk Test 1; the values of the contrast were 51,49, and 44 msec for the three subjects and the t values for the three subjects were: 3.32, p < .002; 2.23, p < .05; and 1.92, p -=c.lO, re-

340

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TABLE 4 TESTS OF CROSSTALK Name of COntraSi

INTEGRATION

AND REPETITION

FACILITATION

VallJe (msec)*

Description”

Crosstalk Crosstalk test I

(See text>

Crosstalk test 2

Gee text)

IN EXPERIMENT

t(ll)

P

-1.34

.20

33.2

3.28

.Ol

integration -20.3

Identity

4

of figures

Facilitation test I

Mean of displays with two different red nonsquare figures minus mean of displays with two identical red nonsquare figures.

61.1 38.9 (Parallel)

3.53 2.24

.Ol .OS

Facilitation test 2

Mean of displays with two different square nonred figures minus mean of displays with two identical square nonred figures.

7.2

I.41

.20

Facilitation test 3

Mean of displays with two different nonred nonsquare figures minus mean of displays with two identical nonred nonsquare figures.

2.6

.22

-

Identity

of attribute

Facilitation test 4

Mean of displays with two different nonsquare forms. one red and one nonred, minus mean of displays with two identical nonsquare forms, one red and one nonred.

5.2

2.0

.I0

Facilitation test 5

Mean of displays with two different nonred colors, one square and one nonsquare, minus mean of displays with two identical nonred colors. one square and one nonsquare.

12.2

I.6

.20

” Descriptions all assume that a red square is the target. (All figures are nontarget figures.) b In parallel tests, the maximum of the identical displays (for each subject) was used as the second contrast rather than the mean. Parallel tests were done only when serial test was significant.

term

in the

spectively (all dfs 92). Since the triangles were appreciably longer than the other two forms (as the three forms were equated for area), subjects with a red triangle for a target may have been able to ignore all aspects of form besides length. Thus since circle and square were about the same length, it may not have made a difference whether the display contained (RS, RS), (RS, RC), or (RC, RC) as all may have been subjectively identical. Regardless of the details of the explanation, the differing results for subjects with a red triangle target suggest that the repetition facilitation effect is not limited to objective physical identity. To summarize, the results of Experiment 4 demonstrated that independence was violated in two ways. Crosstalk Test 2 demonstrated a crosstalk integration effect, although Crosstalk Test 1 showed that the effect was not large enough to violate a parallel fixed-times model (except for red triangle targets). There was also a repetition facilitation effect for displays with identical forms, but only when there were two figures on the display that both had the target color.

DEPENDENTCHANNELS EXPERIMENT

341

5

Method The structure of Experiment 5 was the same as Experiment 4 except that the alphabetic stimuli were employed. The figures employed were as in Experiments 2 and 3, except that the set was enlarged as described earlier by having three features per attribute: “A”, “V”, and “//“, and ” “, “mm*‘,and “- -“, (see Fig. 2). Twelve graduate andundergraduate students served as subjects for 3 days each. Six used an upright A as a target and six used an inverted V as a target. They were paid for their participation.

Results

The general pattern of results of Experiment 5 was fairly similar to that of Experiment 4. Crosstalk Test 1 showed that divided target displays were on the average 1 msec faster than the slower controls (two nonidentical figures that were the same as the target on the crossbar dimension). Thus one cannot reject independence if a parallel model is assumed. However, if a serial model is assumed, one can reject independence since the value of the contrast between divided target displays and the average ofthe control displays was 15 msec, t (11) = 4.28,~ < .002. On the other hand, Crosstalk Test 2 produced strong evidence for crosstalk integration (see Table 5). There appeared to be no reliable differences between patterns of responding to the two targets. The tests for repetition effects for identical figures against a serial independent channel model were significant for Repetition Tests l-3 (see Table 5). However, the tests against a parallel model were significant only when both figures matched the target on the wedge dimension (Test 2). As in Experiment 4, identity on one dimension did not facilitate processing if the figures were different on the other dimension (see Crosstalk Tests 4 and 5 in Table 5). The overall error rate was about 3% and the error rate tended to be higher in conditions with longer RTs. Tests of serial versus parallel processing. Although display size was not varied, there are two tests that help to distinguish between spatially serial and spatially parallel models using the data of Experiments 4 and 5. The first is a test for an effect of the position of the target in displays that contained targets. The simplest parallel models would predict no position effect, while the simplest serial models would predict a position effect if subjects had any biases about the order of testing the figures. The data of Experiments l-5 were analyzed and a significant position effect was found, suggesting a bias toward left-to-right scan (see Table 6). Thus the serial position data favor a serial model over the simplest parallel models. A second test would ideally be a comparison of displays containing two different nontarget figures, (X, Y), with displays containing identical elements, (X, X) and (Y, Y). A serial model predicts that the mean RT to (X, Y) should be equal to the average of those to (X, X) and (Y, Y) while a Dependence.

342

POLLATSEK

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TABLE

5

TESTS OFCROSSTALK INTEGRATION AND REPETITION FACILITATION IN EXPERIMENTS Name of CO”tE3St

Description”

Crosstalk

Value (msecY

r(lI)

P

integration

Crosstalk test I

(See text,

-1.4

-.27

Crosstalk test 2

(See text1

29.0

4.91

.oOl

Facilitation test I

Mean of displays with two different crossbar nonwedge-up figures minus mean of displays with two identical crossbar nonwedge-up figures.

54.1 13.5 (Parallel)

6.01 I.06

,001

Facilitation test 2

Mean of

displays with two different noncrossbar wedge-up figures minus mean of displays with two identical noncrossbar wedge-up figures.

35.0 19.2 IParallel)

4.83 2.35

.NlI .OS

Facilitation test 3

Mean of displays with two different noncrossbar nonwedge-up figures minus mean of displays with two identical noncrossbar nonwedge-up figures.

22.2

2.57

.05

3.9

.6

-

5.1

I.5

Identity

identity

of figures

of attribute

Facilitation test 4

Mean of displays with two figures different on wedge. one with crossbar, one without. minus mean of displays with figures same on wedge. one with crossbar. one without.

Facilitation test 5

Mean of displays with two figures different on crossbar. one with wedge-up. one without, minus mean of displays with two figures same on crossbar, one with wedge-up, one without.

two

.20

” Descriptions all assume that an uprlght A is the target (ix., crossbar and wedge-up). All figures are nontarget figures). a In parallel tests, the maximum of the identical displays (for each subject) was used as the second term in the contrast rather than the mean. Parallel tests were done only when serial test was significant. (Parallel test 3 was not done since there were many missing data cells.)

parallel fixed-times model predicts it to be equal to the maximum. (Parallel distributed times models that assume statistical independence and nonintersecting cumulative distribution functions make intermediate predictions.) However, as discussed previously, the repetition effect makes interpretation of such a test difficult. Hence, the actual tests that were used compared (X, Y) displays to (X, X’) and (Y, Y’) displays, where X and X’ signify two roughly equivalent stimuli and Y and Y’ signify two other roughly equivalent stimuli. Clearly, the test has little power unless the mean RTs for the Xs are significantly different from those for the Ys. For example, the only interesting test in Experiment 4 is a comparison of (RC, GTr) with (RC, RTr) and (GC, GTr). The test for the serial model would be (RC, GTr) minus the mean of the other two, while the test for the parallel fixed-times model would be (RC, GTr) minus (RC, RTr).

343

DEPENDENT CHANNELS TABLE 6 TESTS OF POSITION EFFECTS IN EXPERIMENTS l-5

Experiment

Position effect” (msec)

t

df

P

6 7 3 II II

.05 ,001 .lO .Ol .05

Displays with target stimuli 31 87 40 16 28

2.81 6.34 3.06 3.54 2.57

Divided target displays Pilot* 1 2 3 4 5

69 53 26 27 34 1

2.83 1.99 1.90 I .55 3.22 .I2

.02 .I0 .I0 .Ol

-

(LPosition effect for target stimuli is the mean RT when target is on left minus the mean RT when target is on right. Position effect for divided target displays is mean RT when figure that matches target in color or on the crossbar dimension is on the left minus mean RT when that figure is on the right. * Pilot experiment was identical to Experiment 1 except that subjects were only run for 1 day and that the stimulus frequencies were unbalanced due to programming error.

There were no analogous tests in Experiments l-3 with any power since (X, X) and (Y, Y) displays invariably contained identical figures. The outcome of the tests in Experiments 4 and 5 is relatively straightforward: a parallel fixed-times model can be easily rejected while a serial model makes good predictions in three of the four tests (see Table 7). In fact, most of the (X, Y) displays were actually a little faster than the average of (X, X’) and (Y, Y’) displays, although this difference tended to go away with practice. While the outcomes of these two tests do not rule out parallel distributed times models, they suggest that fairly unusual distributional assumptions would be needed to explain the present data with a spatially parallel model. Discussion Repetition effects. The negative outcomes of Repetition Tests 4 and 5 demonstrated that identity of features on one dimension did not facilitate processing when the two stimuli differed on the other dimension. On the other hand, physical identity facilitated processing (with respect to a spatially serial model) with only a few exceptions. The first exception is

344

POLLATSEK

AND DIGMAN

TABLE

7

TESTS OF SERIALVERSUSPARALLELPROCESSINGINEXPERIMENTS~AND~ Value (msec) Experiment 4 4 5 5

X’

Y’

RC,RT GS,YS

GC,GT GC,GT

A ,7+

v.1 I

v ,H

VA I

YC,YT YC,YT 47 t 4.4 t

f(ll)

P

SeriaP

ParalleP

Serial

Parallel

Serial

Parallel

14.6 -12.5 25.5 4.0

59.0 -1.8 49.9 23.6

.8 -.8 2.5 .5

4.6 -.4 5.8 3.6

ns

.ool

.z

.Zl .Ol

ns

o X and Y are given with reference to a RS target for Experiment 4 or an “A” target for Experiment 5. * The serial test is [(X, X’) + (Y, Y’) - 2(X, Y)] and the parallel test is (X, X’) - (X, Y). (See text for fuller explanation.)

that displays with different nontarget colors and identical forms were processed no slower than displays with identical nontarget colors and identical forms. Since color must have been processed in almost all cases, this result implies that identical color does not facilitate processing (at least for the colors used in the present experiments). The facilitation effect for identical figures clearly gets smaller the less similar the display figures are to the target (see Tables 4 and 5). This suggests some sort of model whereby the figures are processed dimension by dimension in a self-terminating fashion and processing is facilitated only by equality on the dimensions processed. The problem with such a model is to explain why there was not facilitation for arrays in which there was identity on one dimension. Thus the data on facilitation present a bit of a puzzle. Crosstalk: order of testing changed or integration of features? There appear to be two classes of explanations of crosstalk integration staying within the basic framework of Fig. 1. To simplify discussion of these explanations, we will assume that the target is RS and the dimension processed first is red. However, the arguments below do not depend on a particular dimension being invariably processed first and are readily extended to the alphabetic stimuli used in Experiments 2,3, and 5. We will also assume spatially serial processing, since the data favor serial over parallel processing (albeit weakly). The first class would claim that the first stimulus merely influences the order of testing the features of the second, so that the dimension tested last on the first figure would be the dimension tested first on the second figure. Thus when the first figure is a red circle, the form of the second would be tested first (since color and then form would be tested on the red circle), while when the first figure is a yellow circle, the color of the second figure would be tested first (since only the color of the yellow circle would be tested). When the second figure is agreen square, processing time would be longer if form is tested first, since both attributes would be tested, whereas

DEPENDENT CHANNELS

345

form would not be tested if color was tested first. Thus a green square would take longer to process when preceded by a red circle than when preceded by a yellow circle. On the other hand, the processing time for a yellow triangle would be affected less by the color of the first figure, since only one attribute of the yellow triangle would be processed regardless of whether color or form was tested first.2 Hence, such a model could predict a positive value for the contrast in Crosstalk Test 2. A second class of models would claim that the memories of the features of the first figure influence the processing of the second. For example, if the first stimulus was a red circle, the subject would test both the color and form so that memories of both red and circle would be present when the second figure was processed. Such a model would predict crosstalk integration if we further assume that the presence of “red” in memory: (a) caused the form of the second figure to be tested even when it was not red; and (b) caused a delay in the response when the second figure was a square, possibly because the color of the second figure would have to be rechecked. Both of these models predict that the order in which figures are tested in a divided target display should make a difference. There should be dependence only when the red circle is tested first: According to the first model, when the green square is processed first, the attributes of the red circle would be processed in the usual order (color first, form second); according to the second model, when the green square is processed first, its squareness would not be processed and not in memory so that there would be no interference with the processing of the red circle. Since the analysis of target position effects suggested that subjects usually process the left stimulus first (see Table 6), both models predict that processing times for divided target displays would be longer when the figure that matches the target on color (or crossbar) is on the left. Such a position effect (which is also a violation of independence) was obtained in most of the experiments, although the effect was marginal in many cases (see Table 6). While the experiments were not designed to distinguish between the two above models, they do provide some relevant evidence. The first model predicts a facilitation effect in a display like (RC, RTr) for processing the second red nonsquare figure, and this facilitation effect was not observed. According to the first model, both dimensions of a red nonsquare figure are usually processed; however, ifprocessing of another red figure precedes it, only its form would be processed since its form would be tested first. Therefore, one would expect the difference in RT between (RC, RTr) and * To make quantitative predictions, one would have to make assumptions about the time to make both positive and negative decisions on each dimension. If we assume that the time to make either a positive or negative decision on form isx and on color is y, then difference (a) in Crosstalk Test 2 would be x + z, difference (b) would be x - y + z and (a) - (b) would be y (where z is the difference in processing time between a red circle and a yellow circle).

346

POLLATSEKANDDIGMAN

(GC, RTr) to be less than the difference between (RC, YTr) and (GC, YTr). This comparison was made in the “Serial Tests” on lines 1 and 3 of Table 7. The positive values indicate that if there is a difference between the two differences, it is in the opposite direction to the prediction of the model. On the other hand, the second class of models might predict a small difference in the observed direction if there is greater interference with the processing of the second figure when more attributes of the first are stored in memory. Thus the data imply that the crosstalk integration effect is, in fact, produced by integration of target features rather than by an alteration of the order of testing the features of the second figure. Furthermore, since the crosstalk integration effect was obtained using the alphabetic stimuli in Experiment 5, it is quite implausible that the crosstalk was between verbal codes. It does not seem likely that an upright A was coded verbally as “crossbar, wedge up” (nor did any subject report doing so). Crosstalk: another class of models. An alternative explanation for the present data might be in terms of a model which posits that the display is analyzed for the presence of the target features prior to the analysis that locates the features. As mentioned in the introduction, while such a model might be independent in some sense of the term, it would be radically different from the usual models of visual search in that feature integration is not prior to channel integration. A simple version of such a model, the simple dimensional model, is (in the case of colored geometric objects) that the subject: (a) tests the display for the presence of the target color; (b) tests for the presence of form; and (c) tests whether or not the target attributes are in the same location if the results of the first two tests are both positive. This model is consistent with several features of the data from Experiments 1 and 4 if one assumes that processing can terminate if the outcome of either test (a) or (b) is negative: (a) Mean no RTs to displays that contained the target color were longer than those to displays that did not contain it; (b) meanno RTs were virtually unaffected by the presence of the target form in the display when the target color was not present; and (c) mean RTs to divided target displays were slow relative to other no RTs. On the other hand, several aspects of the data of Experiments 1 and 4 were inconsistent with such a model: (d) Yes responses were much faster than no responses to divided target displays; (e) yes responses were faster than those to displays that had red but not the target form; and (f) responses to two different red nontarget forms (in Experiment 4) were generally no faster than those to divided target displays. However, these three inconsistencies may not be critical in rejecting a dimensional model. Comparisons (d) and (e) may be flawed since they are comparisons across yes and no responses and thus the differences observed may reflect differences in a later “response selection stage” of processing. While the size of difference (d) (about 100msec in both Experiments 1 and 4) appears to be larger than the usual observed dif-

DEPENDENT

CHANNELS

347

ferences between yes and no responses attributed to response selection differences, the hypothesis that the observed differences were produced by a response stage cannot be rejected out of hand. Furthermore, difference (f) might be explained within the framework of the dimensional model by postulating that one or both of the first two stages takes longer for displays with two red objects than for displays with one red object, such as the divided target display. (A dimensional model might also explain the results of Experiments 2, 3, and 5 with the modification that subjects start with the wedge dimension on some trials and the crossbar dimension on others. However, since evaluation of such a model is clearly more difficult, discussion will be limited to the colored geometric forms.) EXPERIMENT

6

In an effort to test the simple dimensional model more rigorously, a sixth experiment was run. Experiment 6 was identical to Experiment 1 except that the task was to respond yes if the attributes red and square were both present, regardless of location, and no otherwise (i.e., the same task as in Experiments 1 and 4 except that the correct response to divided target displays is yes). According to the simple dimensional model, one would expect that responses to divided target displays and displays with red squares should be faster than in Experiment 1 since the third processing stage is unnecessary in Experiment 6. On the other hand, one would expect that response times to all other displays should be about the same in the two experiments, since the third stage is irrelevant for these displays in both experiments. Therefore, it seems reasonable that subjects would process according to such a model in Experiment 6 if they did so in Experiment 1. The most crucial test of a dimensional model is a comparison of divided target displays (RC, GS) with (RS, GC) displays. One would expect that mean RTs should be about equal in the two conditions since the same response, “yes,” is made to the same attributes in the two conditions. Method The procedure was identical to that of Experiment 1 except for the change in task described above. Eight undergraduates, drawn from the same pool of volunteer subjects as those in Experiment 1, served as subjects for 2 days each. They received extra credit in their courses for their participation. On each day they had four trial blocks of 48 trials each. The first trial block on each day was treated as practice and not analyzed.

Results and Discussion While Day 2 responses were 58 msec faster than Day 1 responses, F( 1,7) = 37.8, p < .OOl, and while the pattern of results appeared some-

348

POLLATSEK

AND DIGMAN

TABLE 8 MEAN

REACTION

TIMES (MILLISECONDS) AS A FUNCTION DISPLAY IN EXPERIMENT 6

OF STIMULUS

Left figure Right figure

RS

RC

GS

GC

Day 1 RS

428

418

413

418

RC

418

441

483

501

GS

431

5.53

438

473

497

459

409

GC

Day 2

NOW. See text for stimulus code. Times surrounded by black lines are “yes” responses. Other times are “no” responses.

what different on the two days, certain effects were consistent across days (see Table 8). Responses to displays containing red squares were much faster than those to the divided target displays. Perhaps the best test of this difference is between the (RC, GS) divided target displays and (RS, GC) target displays, since the same attributes were present in both displays. The value of this contrast was 90 msec, t (7) = 4.37,~ < .Ol. Thus a dimensional model cannot explain the data of Experiment 6 unless some assumption is added that could account for the fact that the target attributes are harder to locate when they are in different positions. One such assumption would be that when red is located, form is evaluated starting with the location in which red was detected. Thus for (RS, GS) displays subjects would only have to test one form, while for the (RC, GS) displays they would have to test both forms. However, there are several problems with such a model. The most serious is that the above hypothesis would predict that mean RTs to (RS, RC) displays would be something like 45 msec (one half of 90 msec) slower than those to (RS, GC) or (RS, GS) displays since subjects would have to test 1 l/2 forms in the former case and only one in the latter case. However, responses in Experiment 6 were no slower to (RS, RC) displays (388 msec) than to either (RS, GC) or (RS, GS) displays (387 msec.).3 Since simple di-

DEPENDENT

CHANNELS

349

mensional models appear to have serious problems in simultaneously explaining the data of Experiments 1,4, and 6, and since they do not naturally explain the observed repetition effects, they will not be discussed further. Thus it appears that subjects organize displays into spatial channels even when the task allows them to ignore spatial location, as in Experiment 6. More complex models of this class may explain the present data. One model that seems plausible is one in which (a) red, (b) square, and (c) red square are all tested in parallel. Yes responses to target displays would be faster than those to divided target displays if(c) is assumed to be faster than the slower of (a) and (b). No responses to divided target displays would require another stage after completion of (a) and (b) and thus would also be relatively slow. Position effects for target displays would be explained by postulating process (c) to be spatially serial. However, such a model does not readily explain several aspects of the data. It does not explain the position effect observed for divided target displays. It does not easily explain why responses to divided target displays were usually faster than those to the slower control displays in Experiment 4, and it can explain why facilitation effects require the identity of the figures only if process (c) is involved in no responses as well as yes responses. In addition, such a model would be a dependent channel model in two senses: first, that feature testing across channels is going on after feature integration [i.e., process (c)l; and second, that testing for squareness in one of the spatial channels is dependent on the color in the other channel. Furthermore, such a model seemsto be in danger of being able to predict any logically possible outcome of any visual processing experiment. GENERAL

DISCUSSION

The present finding of dependent spatial channels in the visual search task raises some general questions about the visual search paradigm in particular and visual processing in general. As mentioned in the introduction, the visual search paradigm seems to be one in which the subject is encouraged to treat spatial channels as independent since the spatial 3 Two other aspects of the data in Table 8 also suggest parallel processing: The position effect for displays with targets is only 11msec (averaged over the two days), and responses to displays with two targets are no faster than responses to displays with one target. While there was little difference (5 msec) between (RS, RC) displays and (RS, GS) and (RS, GC) displays in Experiment 1 as well, (RS, RS) displays were about 25 msec faster than displays with only one target element. Thus the results of Experiments 1 and 6 provide some trouble for any serial model. However, if one uses the approximately 40 msec difference between (RC, GC) and (GS, CC) as the difference in processing time between a red circle and a green square, the predicted difference between (RS, RC) and (RS, GS) would be about 20 msec, which is not too different from the observed value of 5 msec in Experiment 1 (other parameters would be needed to predict the sizes of the other two results mentioned). What makes the result particularly bad for the dimensional model is that it has to relate half of a 90 msec effect to these small effects.

350

POLLATSEK

AND DIGMAN

positions are defined by physically distinct patterns and there is no sense or order to the overall array on a higher level; it is a random array of stimuli. The fact that processing appears to be dependent in the visual search paradigm suggests that the range of tasks for which processing occurs in independent spatial channels is limited. Independent processing may occur in the same-different task, although the fact that mean RT sometimes decreases as set size increases (Dondieri & Zelnicker, 1969) suggests that the spatial channels defined by the figures may not combine in any simple fashion in that task either. Furthermore, as mentioned in the introduction, Sternberg and Knoll (1973) report one experiment suggesting that processing in spatial channels may not be independent in a temporal order judgment task, which seems to be another very “primitive” visual judgment. When the task is made more complex, or the larger properties of the display are made less arbitrary, spatial channels defined by figures such as alphanumeric characters appear to be clearly dependent. A wide variety of familiarity effects have been reported. For example, visual search for a target letter is faster if a string of letters form a work than if they do not (e.g., Krueger, 1970). Since the display letters are the same in both the word and nonword strings, and since the position of the target and other possibly confounding variables are counterbalanced, such a familiarity effect cannot be explained by an independent channel model that assumes spatial channels defined by the individual letters. Familiarity effects have also been observed in a variety of other detection tasks (e.g., Biederman, 1972; Reicher, 1969) as well as same-different tasks (e.g., Eichelman, 1970; Pollatsek, Well, & Schindler, 1975). One way in which the dependence effects in the present experiments might be related to familiarity effects is the following. A reasonable theory of familiarity effects is that they are produced (at least in part) by sequential processing of an array in which information from parts of the array processed first allow for more rapid processing of the remaining parts of the display. For example, in the processing of words, people may typically process the letters of a word in a more or less left-to-right order using their knowledge of English orthography and the memories of the first letters to process the last letters more efficiently. If this kind of processing is normal, since most displays are meaningful, people may find it difficult to process arrays other than in this sequentially dependent fashion. Furthermore, since there were about as many displays with identical items as divided target displays and since the facilitation effects were about as large as the crosstalk effect, it may not have been disadvantageous for subjects to process displays sequentially, even in the present experiments. On the other hand, one might try to explain familiarity effects by postulating that the units of perception are larger for familiar stimuli and, for example, a six-letter word might be in two or three rather than in six units or channels. Thus the figure or character may be too small as the

351

DEPENDENT CHANNELS

spatial unit of analysis in the present experiments as well. However, phenomenologically, figures such as alphanumeric characters do seem to be units and the repetition facilitation effect seems hard to explain if they are not. Thus it may be that both the character and some higher-order spatial unit of analysis are meaningful psychological entities in visual processing tasks. Similarly, the present experiments provide evidence for two levels of analysis at a given spatial location: The crosstalk integration effect suggests that the “feature” is a meaningful unit while the repetition facilitation effect suggests that the figure is also a meaningful unit. If many such levels of analysis are used in a rapid process such as that employed in the visual search task of the present experiments, adequate models of most visual processing tasks are likely to be quite complex. APPENDIX

For the following discussion, let X,, X2, XB, and X4 be the random variables representing the time it takes to process one red circle, one green square, one green triangle, and one yellow circle, respectively. We assume that red square is the target. Leff, and Fi be the distribution function and cumulative distribution function for Xi. Let Mij represent the random variable which represents the maximum of Xi and Xj. (A) We wish to prove that if F,(t) < F,(t) and if Xi and Xj are statistically independent, then E(M,,) > E(MJ > E(M.&. Proof: It can be easily shown that if Xi and Xj are independent, then f(M,j) = Fifj + FJJ. Thus,

0: E(M,,) - E(M12) =

t(F, - Fdf,dt + 0

I

33 tF&f1 - fMt . 0

Integrating the first term on the right side of the equation by parts yields, m E(MlJ

-

E(M,,)

=

tF,(Fl

-

Fz)

-

0

= F,(F,

- F,)dt.

0

The first term can be shown to be zero if the variance is finite (it obviously is for a finite upper limit of integration), and since F, is assumed less than F2, the second integral is negative and thus the right hand side is positive. Hence E(M,,) > E(M,,). A similar argument shows that E(Mn) ’ E(Mz). (B) We wish to prove that if F,, F2 < F,, F, and if Xi and Xj are independent for all i and 1, then T = [E(M,,) - E(M13)] - [E(M42) - E CM,,)1 < 0. Proof: Again using the fact thatf(Mij) = F& - Fjfi, T= I

cc t (Fz - Fd(fi 0

- f;W

+

CD t(F, 0

- Fdcfi

-.fM.

352

POLLATSEK

AND DIGMAN

Integrating the second term by parts yields,

- F&f. t(F,- Fd(F2 - F3) - m(F,- F‘$)(Fz 0

0

Again, if finite variances are assumed, the first term is equal to zero. Since F, < F4 and F, < FBI the second integral is positive and hence T < 0. It should be noted that the expressions derived allow for calculations of T and E(M,,) - E(M,,) if the cumulative distribution functions for the components are known or can be estimated. REFERENCES Atkinson, R. C., Holmgren, J. E., & Juola, J. F. Processing time as influenced by the number of elements in a visual display. Perception and Psychophysics, 1969, 6, 321-326. Biederman, I. Perceiving real-world scenes. Science, 1972, 177, 77-80. Dondieri, D. C., & Zelnicker, D. Parallel processing in visual same-different decisions. Perception

and Psychophysics,

1969, 5, 197-200.

Egeth, H. E., Jonides, J., &Wall, S. Parallel processing of multielement displays. Cognitive Psychology, 1972, 3,674-698. Eichelman, W. H. Familiarity effects in the simultaneous matching task. Journal of Experimental Psychology,

1970, 86, 275-282.

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REFERENCE

NOTE

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