Spatial Extent of Attention to Letters and Words

Journal of Experimental Psychology: Human Perception and Performance 1983, Vol. 9, No. 3, 371-379 Copyright 1983 by the American Psychological Association, Inc. Spatial Extent of Attention to Letters and Words David LaBerge University of Minnesota The spatial extent of attention to visually presented letters and words was investigated using a probe technique. The primary task required subjects to categorize (a) five-letter words, or to categorize the middle letter of (b) five-letter words or (c) five-letter nonwords. The probe task required the subjects to respond when the digit 7 appeared in one of the five letter positions. Probe trials were inserted at the onset of letter and word processing in Experiment 1 and 5 msec after letter and word processing in Experiment 2. In both experiments, probe trials produced a V-shaped function of reaction times across probe positions for the letter-categorization task for word and nonword stimulus conditions. In contrast, a relatively flat reaction time function was found for the word-categorization tasks. An analysis of the data based on a quantitative model of attentional spotlight distributions suggests that the spotlight width in the letter tasks is one letter space, and the spotlight width in the word task is typically five spaces. Selection of stimulus channels has been regarded as a dominant function of attention since the pioneering work of Broadbent (1958). Recent studies of the visual mode have shown advantages in processing by early selection of color (e.g., Francolini & Egeth, 198; Kahneman & Henik, 198) and particularly of spatial position (Eason, 1969; Posneretal., 1978;Shulmanetal., 1979; Van Voorhis & Hillyard, 1977). Assuming that attention can be directed to a specific point in the visual field, one can ask how large an area around this point receives the benefit of selective attention. A likely reply is that, within limits, the size of visual attention varies with the apparent size of the physical stimulus. For example, we would expect the size of the attentional "spotlight" to be larger for a face than for the nose of that face, and therefore larger for a word than for a constituent letter of that word. This research was supported in part by Grant BSN- 794677 to the author from the National Science Foundation and by Grant HD-1136 to the Center for Research in Human Learning, University of Minnesota, from the National Institute of Child Health and Human Development. I am grateful to Tom Lacki, Tom Taylor, Robert Newcomb, and Chris Vye for their technical assistance, and to Janice Lawry for comments on an early draft of this article. Requests for reprints should be sent to David LaBerge, Department of Psychology, Elliott Hall, University of Minnesota, Minneapolis, Minnesota 55455. Estimates of the size of visual attention in letter identification tasks have yielded values of about 1 of arc (Eriksen & Hoffman, 1972, 1973). Size values for word-identification tasks seem to be unavailable in the literature, but some indirect evidence suggests that attention to words has a greater spatial extent than does attention to letters (Johnston & McClelland, 1974). The purpose of the present study was to explore a procedure by which the spatial extent of attention to letters and words could be compared. The procedure is based on the time it takes to switch attention to a probe after directing attention either to a single letter or to a whole word. Specifically, if attention is narrowly focused to identify the middle letter of a five-letter word, then a response to a probe displayed in the middle position should be faster than a response to a probe displayed in one of the other four positions. On the other hand, when attention is widely focused to identify a five-letter word, then response time to a probe should be invariant across the five letter positions. Furthermore, the narrow focusing of attention on the middle letter of a word may be influenced by the unitary property of a familiar word. To reveal possible effects of the unitary factor one could compare words with nonwords in the identification of the middle letter. The present study made estimates of the size of focal attention at two temporal points 371

372 DAVID LABERGE in the processing of letter and word targets. The first point of measurement, explored in Experiment 1, was at the onset of the target. By occasionally substituting a probe for a target, one should estimate the extent of focus at the moment the 7 target is displayed and note whether or not the subject was prepared for a stimulus of a particular size. The second point of measurement by the probe, explored in Experiment 2, was 5 msec after the onset of the letter or word target. Pilot studies had determined that 5 msec was sufficiently long to complete the processing of the target and yet not so long that subjects would be likely to change appreciably the size of focus used in the processing of the target. Method Experiment 1 Subjects. A total of 75 English-speaking undergraduate students from the University of Minnesota and the University of California, Irvine volunteered for sessions of approximately 25 min. Apparatus and display conditions. The presentation of trial events and the recording of responses were controlled by a Cromeraco Z8 microprocessor. All stimuli were displayed on a Hazeltine 2 CRT, which was placed approximately 44 mm from the eyes of the subject. The warning signal was a horizontal string of five "#" items. The stimuli that followed the warning signal always consisted of a horizontal string of five items, which were displayed in the same locations as the items of the warning signal. A letter on the CRT subtended visual angles of.43 vertically and.29 horizontally, based on a distance of approximately 44 mm from eye to screen. The space between letters was approximately.8. The string of five letters therefore subtended approximately 1.77 of visual angle. A response panel in front of the subject contained a button, 25 mm in diameter, that the subject was required to press when the letter string or probe was a member of a positive set. When a letter string or probe was a member of a negative set, the subject was required to withhold the button press. Stimuli and trial types. There were three test conditions that differed in the type of primary categorization task required (word vs. letter) and the type of stimulus display (word [W] vs. nonword [NW]). In the word condition, primary stimuli consisted of five-letter nouns. Positive set items were familiar names (e.g., ALICE) and negative set items were nouns from the common categories of furniture, musical instruments, and dwellings. In the letter (W) condition, the positive set of primary stimuli consisted of familiar five-letter words in which the middle letters were from the Set A through G. Negative-set items were words in which the middle letter was from the Set N through U. In the letter (NW) condition, primary stimuli were nonword anagrams of the positiveand negative-set items in the letter (W) conditions. These stimuli were constructed by maintaining the middle letter and rearranging the remaining four letters to yield an item with low pronounceability. Each primary item appeared only once. In addition to primary trials, all conditions included probe trials. Probe stimuli consisted of four "+" signs and one critical item, a 7, T, or Z, which appeared randomly in one of the five positions of the display string. On these trials, 7 was the positive item and T and Z were the negative items. Procedure. Subjects were tested individually in a normally lighted room. Each subject was assigned to one of the three testing conditions previously described. Testing consisted of two practice and two test blocks. A trial began with a warning signal that appeared randomly in one of four positions spanning approximately 7 cm horizontally. After a duration of 1,25 msec, the warning signal was replaced by either a primary stimulus or a probe stimulus, which remained on until the subject responded or for a maximum of 1,5 msec. The intertrial interval showed a blank screen for 75 msec. The first practice block consisted of 25 probe trials. The item 7 appeared three times at each of the five positions, and the items T and Z each occurred once at each position. Subjects were instructed to respond with a button press only if a 7 appeared; if a T or Z appeared, they were to let the trial pass without a response. Errors of commission and omission (misses) were signaled by an error message at the end of the trial. The second practice block consisted of 5 trials made up of 2 probe trials plus 2 primary stimulus trials from the positive and 1 from the negative set as defined for each of the word, letter (W), and letter (NW) conditions. In the word condition, subjects were told to respond when the primary display was the name of a person. For the letter (W) and letter (NW) conditions, they were told to respond when the middle letter of the primary display was from the Set A through G. Subjects were told to treat the probe stimuli as they had in the previous block. Practice was followed by two 8-trial test blocks each containing 45 positive and 15 negative primary stimulus trials and 2 probe trials. On the probe trials, the positive item 7 appeared three times in each of the possible five positions. A brief rest period was given halfway through each block of test trials. To promote a strategy of preparing for a primary letter-string display rather than for a probe display, subjects were shown their mean reaction times to the primary trials at the end of the second practice block and at the end of each test block. They were encouraged to improve their reaction times to the letter-string stimuli while keeping errors to a minimum. Results The average reaction times of correct responses to the probe stimuli are shown in Figure 1. Each point is based on approximately 15 observations. The findings of main interest are the V-shaped patterns of reaction time for both letter (NW) and letter (W) conditions, and the relatively flat pattern

SPATIAL EXTENT OF ATTENTION 373, L.tt.r(NW) Letter(W) Word Position of Probe Figure 1, Mean reaction time to the probe stimulus as a function of probe position. (The probe was presented at the time that a letter string would have been displayed. W and NW refer to word and nonword, respectively.) for the word condition. The first analysis of variance (ANOVA) was designed to test these reaction time curves for a quadratic component approximating a V pattern. For each block, a subject's mean reaction time to each of the five probe positions was subtracted from the overall mean of these reaction times to yield five difference scores. The ANOVA of these difference scores indicated a significant effect of probe position, F(4, 288) = 11.71, p <.1, and a significant quadratic effect of probe position across the three conditions, F(l, 72) = 35.64, p <.1, as well as a significant interaction of quadratic effect by condition, F(2, 72) = 3.7, p <.3. None of the other interactions was significant, nor was the effect of blocks significant. Post hoc tests performed separately on each condition showed significant quadratic effects for the letter (NW) condition, F(\, 24) = 22.4, p <.1, and the letter (W) condition, F( 1,24) = 17.4, p <.1, but not for the word condition, F(l, 24) = 1.69, p >.2. The word condition showed no significant effect of position. Taken together these tests confirm that the letter tasks produced a V-shaped reaction time curve and the word task produced a relatively flat reaction time curve. The average percentage of errors for probes in the letter (NW), letter (W), and word conditions were 9.8, 9.7, and 13.1, respectively. An ANOVA of these averages showed no significant effects. No tests were performed on misses because they occurred less than 1% of the time. An ANOVA of the raw, nontransformed reaction times of Figure 1 indicated significant main effects for probe position, F(4, 288) = 11.74, p <.1, letter-string condition, F(2, 72) = 7.3, p <.1, and blocks F(l, 72) = 6.14, p <.2. No interactions were significant, although the Position X Condition interaction closely approached significance. Post hoc pairwise comparisons of condition means showed significant differences between the word condition and the letter (W) and letter (NW) conditions (p < ), but the lat ter two conditions did not differ significantly from each other. The average reaction times to the letterstring displays of letter (NW), letter (W), and word conditions in the two test blocks were 515, 565, and 476, respectively. An ANOVA indicated a significant overall effect for conditions, F(2, 72) = 16.17, p <.1, and for blocks, F(l, 72) = 22.88, p <.1. None of the interactions was significant. All post hoc pairwise comparisons between condition means showed significant differences (p < ). The average percentage of errors to the letter-string displays of letter (NW), letter (W), and word conditions were 2.8, 2.7, and 3.7, respectively. No main effects or interactions were significant. Method Experiment 2 Subjects. Sixty native English-speaking undergraduates at the University of California, Irvine volunteered for sessions of approximately 25 min. Apparatus and stimulus materials. The apparatus and the three types of letter strings and probe stimuli were the same as used in Experiment 1. The letter-string items were selected from the sets of items used in Experiment 1. Design. A trial of a test block began with a primary letter-string display that was replaced by a probe stimulus. As in Experiment 1, the probe stimulus was a 7, T, or Z embedded in a row of four "+" signs. The subject pressed the button only if both the letter-string and the probe were members of positive sets. Thus, in the word condition, the subject was to respond only if a person's name was followed by a display containing a 7. Likewise, in the letter (W) and letter (NW) conditions, a response was required only if the middle letter of the five-letter string was from the Set A through G and the following display contained a 7. Each of the two test blocks of the word condition contained a total of 55 trials, 35 trials in which a name was followed by a probe 7, 1 trials in which a name was followed by a probe T or Z, 5 trials in which a non-name was followed by a probe 7, and 5 trials in which a nonname was followed by a T or Z. The test blocks for the letter (W) and letter (NW) conditions were constructed in the same manner, except that letter-string displays were

374 DAVID LABERGE judged according to the middle letter instead of the whole word. The first practice block presented probe stimuli only, 2 displays containing a 7, 5 containing a T, and 5 a Z. The second practice block presented letter strings only. For each of the three conditions, there were 15 letter strings that required a response and 15 letter strings that did not. The items were taken from the set used in the second practice block of Experiment 1. Each primary item appeared only once. Procedure. Subjects were tested individually in a normally lighted room. Subjects were assigned to one of the three primary stimulus conditions and given two practice blocks and two test blocks. Verbal instructions were supplemented with cards showing examples of all types of displays. The instructions for the first practice block were the same as those given in Experiment 1. Subjects were told to respond only to a 7 embedded in a row of "+" signs and to refrain from responding to a T or Z. For the second practice block the subjects were told to respond only to the letter strings in the positive set. No probes appeared in this block. In the instructions for the two test blocks, the subjects were told to respond only if the letter string was a member of the positive set and the probe that followed it was a 7. A trial began with a display of a letter string that was always positioned approximately in the center of the screen. The duration of the letter string was 5 msec. This particular duration was selected because it appeared to produce the fastest reaction times in a pilot study in which durations from 1 msec to 8 msec were used. The letter string was replaced by a probe stimulus that remained on the screen for 1,5 msec unless terminated by a response. The duration of the intertrial interval was 75 msec. Results The average reaction times of correct responses to the probe stimuli are shown in Figure 2. Each point is based on approximately 28 observations. As in Experiment 1, quadratic effects were tested by transforming each subject's mean absolute reaction time to a difference score based on the overall g 55 K C, Letter (NW) L«tt«r(W) Word Position of Probe Figure 2. Mean reaction time to the probe stimulus as a function of probe position. (The probe was presented 5 msec after the letter string was displayed. W and NW refer to word and nonword, respectively.) mean of the five position scores in a block. The ANOVA showed a significant effect of probe position, F(4, 228) = 16.12,.p <.1, and a significant quadratic effect of probe position across the three conditions, F(l, 57) = 28.11, p <.1, as well as a significant interaction of quadratic effect by condition, F(2, 57) = 4.88, p <.2. No other interactions were significant, nor were blocks significant. Post hoc tests performed on each condition showed significant quadratic effects for the letter (NW) condition, F( 1,19) = 23.14, p <.1, and for the letter (W) condition, F(l, 19) = 1.96, p <, but not for the word condition, F(\, 19) =.6, p >.4. There were no significant interactions. The outcomes of these tests are similar to the outcomes of the tests in Experiment 1 and support the claim that the letter tasks produce a V-shaped curve of reaction time, and the word task produces a relatively flat curve of reaction time. The average percentage of errors for letter (NW), letter (W), and word conditions were 3.4, 3.2, and 2.8, respectively, but the error analysis showed no significant effects. The percentage of misses (<1%) was too small for a meaningful analysis. An ANOVA of the raw, nontransformed reaction times of Figure 2 showed a significant effect of probe position, F(4, 57) = 7.39, p <.1. There were no other main effects, nor were any interactions significant. The analysis of reaction times to the letter strings alone was available only from the second practice block because in the test blocks the letter string was always followed by a probe and the reaction times were timed from the onset of the probe. The average reaction times to letter strings alone for the letter (NW), letter (W), and word conditions were 676, 713, and 612, respectively. An ANOVA showed a significant effect of condition, F(2, 57) = 4.88, p <.2. Post hoc pairwise comparisons indicated a significant difference in reaction times only between the letter (W) and word conditions. The percentage of errors to the letter-string displays for the letter (NW), letter (W), and word conditions were 6., 6, and 4, respectively, but differences between these conditions were not significant. The percentage of misses (< 1 %) was too small for a meaningful analysis.

SPATIAL EXTENT OF ATTENTION 375 Discussion The pattern of results from the two experiments seems to indicate that the focus of attention given to a letter has a smaller spatial extent than does the focus given to a word. This conclusion is based on the assumption that increases in reaction times to the probe stimulus reflect increases in the distance that attention is shifted. For the letter tasks, the estimated change in reaction time is approximately 2 msec when the probe is shifted one letter position. Apparently, the obtained times to shift attention closely agree for shifts measured just before and immediately after the target letter was processed. A theoretical account of these data may be derived from a model of attention described in the Appendix. The characteristics of the attention spotlight, which are of main interest here, are its width and position within the letter string. The model assumes that the spotlight width takes on integer values ranging from one to five letter spaces, with the restriction that the spotlight always falls within the boundaries of the string of five letters. The unit of area is defined as the distance between the centers of two adjacent letters, that is, a space. Fo{ present purposes we assume that width and position yield a total of 15 different spotlights: The one spotlight of Size 5 extends across all 5 spaces; two spotlights of Size 4 extend across Spaces 1-4 and 2-5; three spotlights of Size 3 extend across Spaces 1-3, 2-4, and 3-5; four spotlights of Size 2 extend across Spaces 1-2, 2-3, 3-4, and 4-5; and finally, five spotlights of Size 1 extend across each of the 5 spaces. In any given task, the subjects may adopt one or more of these 15 spotlights. For simplicity, it is assumed that each task has one distribution of spotlights for all subjects and that the probes occur equally often in the five locations. When this distribution is determined, we can derive the theoretical latency points. The first distributions to be estimated from the data are those for the letter tasks. Fortunately, the estimations in these cases are very easy because the best fit to the obtained latencies in all four letter tasks is a pair of symmetric linear functions that meet at a point coinciding with the center position. The spotlight that gives rise to this V curve is always centered at the middle position and has a width of one space, or about.35 of arc. If the spotlight width was greater than one space, or if there had been a distribution across several locations of a spotlight having a width equal to one, then the obtained curve would resemble a U more than a V. Assuming that the spotlight in the letter tasks has a width of one space and is positioned at the center of the letter strings, one can estimate the time to shift attention one space in either direction by using the obtained slopes of the latency curves of the letter tasks. The estimated shift times are 19 msec for Experiment 1 and 21 msec for Experiment 2. These values may be treated as the units of the time to shift attention for each experiment. The theoretical curves for the letter tasks are simply integer multiples of the unit of shift time. The derivation of a flat theoretical curve for the word category tasks is rather simple when a spotlight of Size 5 is assumed. However, before concluding that subjects adopted a spotlight of this large size, one should examine an alternative possibility. Suppose that the spotlight size for the word was the same as for the letter tasks, that is, a width of one space, but the location of the spotlight was distributed equally across the five positions. Would this rectangular distribution of spotlight locations produce equal latencies for each location? The answer, computed by the equations in the Appendix, is no. A rectangular spotlight distribution produces a latency curve that is distinctly concave upward. This shape is also predicted from rectangular distributions of a width of two, three, and four spaces. The question may be rephrased to ask whether any distribution of locations of a spotlight of Size 1 exists that would yield a flat latency curve. The answer, derived from computations in the Appendix, is that the only distribution of spotlight locations that satisfies this condition is one in which the first and fifth positions each occur with probability of, whereas the three inner positions occur with a probability of zero, This extreme U type of distribution seems intuitively to be a very unlikely candidate to account for the reaction times of the word condition.

376 DAVID LABERGE If we turn to spotlights of size greater than one, we immediately see that symmetric distributions of Sizes 3 and 4 always produce a minimum latency at the middle position because this position is always covered by the spotlight regardless of its location within the letter string. According to the reasoning in the Appendix, a spotlight of Size 2 can always be shown to produce curves in which the endpoints have greater latencies than do the inside points for any symmetrical distribution of spotlight locations. Thus we are left with a spotlight of Size 5, centered at the middle letter position, as the only reasonable candidate responsible for a flat latency curve. Although statistical tests failed to show a significant position effect for the two word conditions, the small rise in latency at the end of the word in Experiment 1 and the small rise at the beginning of the word in Experiment 2 suggest that subjects may sometimes bias the location of the spotlight toward the left just prior to the presentation of the word and sometimes toward the right at the end of word processing. What this implies is that the subjects' distribution of spotlight sizes included some sizes less than five that were located off center. The theoretical choice of spotlights of different sizes and positions to mix with the spotlight of Size 5 seems less constrained by the data than one would like. One can perhaps rule out the addition of a spotlight of Size 1 that is always located in either Positions 1 or 5 because this would produce a linear slope when averaged with the spotlight of Size 5. Neither of the word-condition curves appears linear. The simplest combination of spotlights needed to fit the data of the word condition seems to be a mixture of three spotlights of Sizes 3, 4, and 5 in the proportions.15,.25, and.6, respectively. For Experiment 1, the three spotlights are assumed to be positioned with common endpoints on the left side, and for Experiment 2, the common endpoints are on the right side. In view of these considerations, it would seem that the obtained probe reaction time curves for the word tasks did not arise by maintaining the same size of attention as obtained in the letter tasks and distributing the center of focus across the five positions. Rather, the data and the theoretical analysis are more compatible with the view that the size of focus in the word task was typically as wide as five letter spaces or 1.77 of arc. We can conjecture that the size of focus in the word task was sometimes less than five letters. In this event, there may have been a slight bias in the position of the center of focus, with the direction of bias depending on when during processing one measured the focus. Although the data reported here suggest that the size of focus does not exceed five letter spaces, the data do not preclude the possibility that longer words could yield larger estimates of size of focus. Similarly, the present data do not impose a lower bound on the size of focus. The properties of the spotlight metaphor that the present model addresses are the specification of spatial area of variable size and location over which visual information is integrated by attention operations (LaBerge, 1973a; Treisman & Gelade, 198). For the present tasks, a narrow spotlight width in the letter conditions restricts the area of visual integration to a single letter, whereas the broader spotlight width in the word conditions permits integration over four or five letter positions. The property of mobility enables the probe to map distances over which the spotlight shifts. Neither the model nor the data speak to the general shape of the spotlight area other than to specify its width. However, if it were assumed that the contour of an object such as a letter or word is the dominant factor in determining spotlight shape, then one might infer that the height of both letter and word spotlights is approximated by the vertical extent of a letter. For a typical word, an oblong shape would seem more appropriate than a circular shape, considering that in a typical line of text other words are located in close proximity above and below the target word. Whether or not a subject could maintain a given shape or width of attention in a blank field without an object to mold its shape is an interesting issue for further research. There is another property implied by the spotlight metaphor that one could incorporate into the model described in the Appendix. The common notion of a physical spotlight implies a fixed quantity of energy such

SPATIAL EXTENT OF ATTENTION 377 that when the spotlight is narrowly focused, more energy falls on a given unit of area than when it is widely focused. Applying this inverse size-energy relationship to the present data, one might expect to find faster processing of a probe in the center position when attention is narrowly focused on the middle letter than when attention is broadly focused across four or five letters of a word. However, in three out of four comparisons across the two experiments, the word condition shows the faster probe reaction time at the center position. From a statistical viewpoint, the only significant differences in overall probe reaction times occurred in the first experiment in which the word condition yielded the faster reaction times. Thus one could be led to the paradoxical conclusion that a wider focus of attention increases the total available energy such that the processing energy at the center position remains constant or even increases. Alternatively, one might construe the slower responding to the primary task of the letter conditions as indicating the expenditure of more resources (Norman & Bobrow, 1975) or effort (Kahneman, 1973) than was the case for the primary task of the word condition. This drain on available resources by the primary tasks reduces the remaining amount of resources that can be allocated to the detection of a probe. Assuming a fixed resource capacity across the two types of tasks, it follows that fewer resources were available for the probe in the letter conditions and hence these tasks showed slower overall probe reaction times. To account for differences in demand for resources by the tasks, one might assume that the process of narrowing the spotlight to the center position in the letterdetection tasks requires resources to inhibit or overcome competing claims on the spotlight from neighboring letter items. In the word-detection tasks there was no need to narrow the spotlight because there were no other items nearby to attract attention to themselves (LaBerge, 1973b; Shiffrin & Schneider, 1977) and compete with the word item for attention. As for the significant difference in reaction times to the primary tasks of the letter (W) and letter (NW) conditions in the first experiment, one might suggest the possibility that individual letters compete more strongly for attention when they are embodied in a word than when they constitute a nonword. From these informal considerations, an energy or resource variable in these tasks would seem to operate in an additive fashion, and therefore to change the intercept of the reaction time function, rather than interact with size and/or movement time to produce a change in the slope of the function. However, before representing the resource variable more formally in a reaction time equation, its role in these kinds of tasks should be clarified by experiments that manipulate it systematically. Finally, there is another type of model that might account for the major features of the present data without the assumptions of a moving spotlight having a variable size. Assume that the spotlight size is determined by the boundaries of the group of five items in the displays and therefore has a fixed width for both the letter and word conditions. The changes across these conditions would be represented by different distributions of energy or intensity within the spotlight. For the letter condition, the intensity distribution could assume an inverted-v shape, and for the word condition the distribution could be flat. By appropriate choice of parameters for these distributions, one might deduce the pattern of slopes obtained for the two types of tasks and possibly the differences of reaction times to primary and probe stimuli across the conditions. In such a model one might interpret the intensity variable as clarity or ease of feature extraction at given spatial locations. References Broadbent, D. E. Perception and communication. London: Pergamon Press, 1958. Eason, R. G., Barter, R., & White, C. T. Effects of attention and arousal on visually evoked cortical potentials and reaction time in man. Physiology and Behavior, 1969, 4, 283-289. Eriksen, C. W., & Hoffman, J. E. Temporal and spatial characteristics of selective coding from vjsual displays. Perception & Psychophysics. 1972, 12, 21-294. Eriksen, C. W., & Hoffman, J. E. The extent of processing of noise elements during selective encoding from visual displays. Perception & Psychophysics, 1973, 14, 155-16. Francolini, C. M., & Egeth, H. On the nonautomaticity of "automatic" activation: Evidence of selective seeing. Perception & Psychophysics, 198, 27, 331-342.

378 DAVID LABERGE Johnston, J. C., & McClelland, J. L. Perception of letters in words: Seek not and ye shall find. Science, 1974, 184, 1192-1193. Kahneman, D. Attention and effort. Englewood Cliffs, N.J.: Prentice-Hall, 1973. Kahneman, D., & Henik, A. Perceptual organization and attention. In M, Kubovy & J. Pomerantz (Eds.), Perceptual organization. Hillsdale, N.J.: Erlbaum, 198. LaBerge, D. Attention and the measurement of perceptual learning. Memory & Cognition, 1973, /, 268-276. (a) LaBerge, D. Identification of two components of the time to switch attention: A test of a serial and a parallel model of attention. In S. Kornblum (Ed.), Attention and performance IV. New York: Academic press, 1973. (b) Norman, D. A., & Bobrow, D. J. On data-limited and resource-limited processes. Cognitive Psychology, 1975, 7, 44-64. Posner, M. I., Nissen, M. J., & Ogden, W. C. Attended and unattended processing modes: The role of set for spatial location. In H. L. Pick & I. J. Saltzman (Eds.), Modes of perceiving and processing information. Hillsdale, N.J.: Erlbaum, 1978. Shulman, G. L., Remington, R. W., & McLean, J. P. Moving attention through visual space. Journal of Experimental Psychology: Human Perception and Performance. 1979, 5, 522-526. Shiffrin, R. M., & Schneider, W. Controlled and automatic human information processing: II. Perceptual learning, automatic attending, and a general theory. Psychological Review, 1977,54, 127-19. Treisman, A. M., & Gelade, G. A feature-integration theory of attention. Cognitive Psychology, 198, 12, 97-136. Van Voorhis, S., & Hillyard, S. A. Visual evoked potentials and selective attention to points in space. Perception & Psychophysics, 1977, 22, 54-62. Appendix Derivation of Probe Latencies from Spatial Distributions of Attentional Focus For the present analyses it is assumed that probes occur equally often in each of the five positions and that the time involved in adjusting the attentional spotlight is entirely due to shifting the location of the spotlight. Any time involved in changes of spotlight size is assumed to be negligibly small relative to spatial shifts of the spotlight. Spotlights of Width One Letter Space Let j denote the position of the spotlight at the moment the probe is displayed. Let q } denote the probability that the spotlight is in the jth position, ;' = 1 to 5. Let / denote the position of the probe, / = 1 to 5. Let si t = (j - j) denote the number of spaces between j and / that the spotlight shifts to focus on the probe. Let u denote the latency in msec of a shift of attention across one space in the right or left direction. Let c denote a constant in msec. Then the equation expressing the latency (L) to a probe at position i is 5 L(i) = c + u 2 qjjj - HI i-t where q, is a density function such that Z «, - i. J-l In particular, we seek the distribution of spotlight positions that will produce a constant probe latency, k, across the five probe positions (i.e., we v seek the column vector [q,] that renders L[i] equal to k for i = I to 5). To find the five entries of q t we solve a set of six simultaneous equations: Five equations of the form 5 2 = k, where k is a weighted average of shifts, plus the equation 2 q, = 1. i'i This set of six equations in six unknowns may be represented by the matrix equation SQ = L, where ' 1 2 3 4-1 1 1 2 3-1 2 1 1 2-1 S = 3 2 1 1-1 4 3 2 1-1 1 1 1 1 1 The values of Q are found by solving Q = S 'L, where

SPATIAL EXTENT OF ATTENTION 379 - The solution is -1-1 -1 - - 2 Thus the distribution of spotlight positions that yields a constant probe latency for all probe positions assigns trie probability of to the two end positions and zero for all other positions. This result may be generalized to sets of positions greater than one. Spotlights of Width Greater Than One Letter Space For spotlight widths of 2, 3, and 4, neighboring spotlights overlap each other (e.g., the three spotlights of Width 3 extend from Positions 1 to 3, 2 to 4, and 3 to 5). Thus Positions 2, 3, and 4 are each covered by more than one spotlight position, whereas the End Positions 1 and 5 are each covered by one spotlight position. As a consequence, the probability of a spotlight covering a given position is always less for the end positions than for the internal positions. This inequality between the end positions and their neighboring positions always produces a greater latency for the end position compared to its neighbor, thus yielding an overall latency curve that is concave upward. Received September 7, 1982 Revision received December 6, 1982