Post-iconic visual storage: Chunking in the reproduction of briefly displayed visual patterns

COGNITIVE PSYCHOLOGY lo, 324-355 (1978)

Post-lconic Visual Storage: Chunking in the Reproduction of Briefly Displayed Visual Patterns

D. J. BARTRAM

Two experiments are reported which investigate the organization of visuo- spatial information in post-iconic storage. In both experiments, stimuli consisting of 10 disks randomly placed in a four-by-five array were tachistoscopically presented to subjects whose task was to recreate the pattern. In Experiment 2, reproduction was constrained (on a row-by-row basis) while in Experiment 1 it was unconstrained. The results of Experiment 1 showed that subjects recalled in terms of “chunks” of spatially adjacent disks, with most “chunks” consisting of about three of four disks. Within each sequence of 10 responses the probability of correctly recalling a chunk decreased with its serial position but was relatively independent of chunk size per se (for chunks containing seven or less disks). In addition, clear topographical variations in accuracy were found, which tended to covary srrongly wirh order of recall. In Experiment 2, rhe order of reproduction was prespecified (either top row down to bottom row, or bottom row up to top row) in order to induce chunking by rows. The direction of reproduction was cithcr

pre- or post-cued. The results of this study showed that subjects encode the stimulus, wherever possible, in a form which is compatible with the constraints imposed on recall order. The results for the postcued conditions provide strong support for the argument that topographical variations in accuracy are a function of variations in accuracy of encoding, and not simply a function of order of report. The results are discussed in terms of an attentional model. It is proposed that a general “anticipatory schema” (cf. Neisser, Cognition and Rrality, 1976) presets the distribution of attention in the visual field, preselects a set of coding heuristics, and subsequently interacts with the present stimulus pattern. Spatial discontinuities in the distribution of attention resulting from this interaction are regarded as “defining” chunks of stimulus elements.

Wilton and File (1975) have produced some evidence to suggest that positions of randomly located disks are remembered by organizing the disks into groups and then coding the positions of the groups relative to each other, rather than by relating the positions of each disk to some overall coordinate system. In their study, subjects were presented with a memory stimulus consisting of 12 disks randomly located on a plain background. Matching comparison stimuli consisted of either a subset of disks, selected at random from the 12, or one selected at random with the five adjacent

Requests for reprints should be sent to Dr. D. .I. Bartram, Department of Psychology, University of Hull, Hull, HU6 7RX, N. Humberside, England.

OOlO-0285/78/0103-0324$05,00/O Copyright 0 ,978 by Academic Press, 1°C. All rights of reproduction in any form rexrved.

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POST-ICONIC VISUAL STORAGE 325

to it. Recognition performance was significantly better under the adjacent condition. This result is consistent with the notion that disks were grouped by spatial proximity and then a general structural description was “written” to relate the groups to each other. The study, however, does not allow us to define these groupings with any precision.

Chase and Simon (1973) reached a similar conclusion in their work on perception in chess. Their subjects (a Master player, an advanced player, and a novice) were given two tasks: a perception task (in which they had to copy positions laid out on one board, onto another empty board) and a memory task (in which they were shown a board containing pieces for 5 set and then had to reproduce it from memory). In addition the layout of pieces on the board could be either random or from a real chess game. They adopted pauses in recall to indicate the segmentation of pieces on the board into perceived groups or “chunks.” This procedure is based on the assumption that if elements of a pattern are structured by the perceiver into chunks, then recall will involve two opera- tions: first, the recall of a chunk, and then the retrieval of information within that chunk. The time taken to recall successive chunks is assumed to have as its behavioral correlate a pause in the recall of the complete set of elements. This notion receives support from two main sources. First, it has been shown (e.g., McLean & Gregg, 1966) that pauses fall at the boundaries between experimenter-defined chunks. Second, Chase and Simon (1973) found the same structure for within-glance placement latencies (on the perception task) as for within-pause placement latencies (on the memory task). In addition the content of the pause-defined chunks in the memory task closely matched those of the glance-defined ones in the perception tasks. They argued that a pause represented the end of a chunk in the memory task and acted in the perception task as a signal to the subjects to take another look at the stimulus.

Their study provides good evidence that pauses in recall are behavioral correlates of the structure imposed by the subject upon the stimulus array. Furthermore, they showed that the efficiency of this structuring was dependent on the interaction between two factors. First, the level of expertise of the subject, and second, the relevance of that expertise to the particular stimulus presented. The Master player’s superiority was only apparent in his performance on tasks involving pieces laid out as in a real game of chess. Under these conditions there was a clear tendency for him to recall slightly more chunks than the novice, and more importantly, for those chunks to contain a greater number of elements.

A number of important conclusions can be drawn from this work: first, that structure in the stimulus array does not determine the structure in recall. The structure which the perceiver imposes upon the stimulus will be a function of the repertoire of chunk patterns (or chunk generation rules) he pos- sesses and the relationship between some subset of these and the structural

326 D. J. BARTRAM

constraints in the stimulus array. Second, inter-piece placement latencies can be used to segment recall into chunks. Both these conclusions, however, require qualification. Although spatial proximity was found to be a major factor determining chunking, chess pieces have properties other than location: They have color and identity and also have abstract relationships (e.g., of attack) to other pieces. In order to produce a correct recall, it is necessary to know at least the position, identity, and color of each element. Thus, it seems reasonable to assume that the sort of chunks Chase and Simon are considering are rather more complex than the groupings dealt with by Wilton and File (1975). Henderson (1972) has shown that position and item information (for letters placed randomly within a grid) are stored in partially independent forms. In chess, of course, position information is not independent of color and identity of piece (except on the random board). Even here, however, there is not a strict dependence between knowing if a square contained a piece and knowing what that piece was. With respect to the use of inter-piece placement latencies, Reitman (1976) has pointed out that this method of segmenting recall will only reflect underlying structure if the chunks are not nested or do not overlap. In her analysis of perception in Go, she found that Go patterns were seen in terms of overlapping clusters. As a result she was unable to find such a clear relationship between pauses and chunks.

Experiment 1 in the present study was carried out in order to investigate the use ofpauses in recall as a means of identifying chunks in the perception of simple random patterns (10 black disks randomly located within the cells of a five by four matrix). The criteria for empirically validating chunks, however, are rather different from those used by Chase and Simon (1973) and Reitman (1976). They are based on the notion that the interaction between the spatial layout of the stimulus elements and the organizational processes of the perceiver determines the distribution of attention across the stimulus array. This idea has received support from Pomerantz and Garner (1973) who showed that if two stimulus elements are grouped together during initial encoding of the stimulus array, selective attention to one of those elements is difficult, if not impossible, without producing some form of internal reorganization of the description of the stimulus. Similarly, Reed (1974) using an embedded-figures type of test, has shown that the way in which subjects initially encode a pattern affects the ease with which they subsequently recognize a part of that pattern. If the part happens to be explicit in their internal representation of the pattern, they have no difficulty. If, on the other hand, a redescription of the pattern is required, performance is adversely affected to a considerable degree. Furthermore, Pomerantz and Schwaitzberg (1975) showed that the grouping processes studied by Pomerantz and Garner (1973) were not simply automatic and under pre-attentive control. They were to some degree optional processes under the direct “strategic” control of the subject.


Thus the spatial layout of the pattern constrains, but does not determine, the subject’s perception of structure. The choice of encoding strategy is also very much affected by task requirements, as has been shown under a wide variety of conditions (e.g., Bahrick & Boucher, 1968; Tversky, 1969; Frost, 1972).

In the light of the above research, it seems that the perception of spatial structure can be conceptualized in the following general manner. The subject has available a repertoire of heuristics which operate, either auto- matically or under strategic control, upon the stimulus array to segment it into a number of discrete “chunks.” These heuristics may be relatively simple, embodying such Gestalt principles as proximity, common shape, color, texture, and so on, or may be relatively sophisticated involving abstract relationships, as in chess. The effect of the application of such heuristics to the stimulus can be conceptualized in terms of a redistribution of attention across the stimulus array. That is to say, the stimulus array is segmented into areas such that the level of attention varies between but not within areas. Thus each chunk is perceived as a unit rather than as a set of discrete elements. The operation of these structural heuristics on the distribution of attention can be illustrated by considering the experience of looking at a regular array of dots. If no conscious attempt is made to structure the array, one experiences a constantly shifting set of patterns of lines, squares and so on. It is relatively easy, however, to im- pose structure on such a stimulus by actively “looking for” certain configurations. Similarly, reversible figures can be reversed at will once one has learned the differential patterns of attention associated with the perception of each of the possible perceived structures.

Thus, it is argued that structural heuristics operate by modifying the distribution of attention across the stimulus, and hence segment it into a number of higher-order discrete units. In order to be able to reproduce a stimulus pattern, it is necessary to have some form of internal representation of it which contains information both about the “units,” or “chunks,” themselves and their relative positions within the stimulus frame. Assum- ing that within such a representation or structural description the configuration of each chunk is defined, then its location in the stimulus frame may be encoded in a number of ways. For example, the description may have a linear format (where the location of one chunk is specified in relation to another, that other chunk in relation to a third, and so on) or a network format (where the position of a chunk is specified relative to a number of other chunks). Alternatively, relative positions may not be explicitly encoded, and each chunk may be independently assigned an address locating it within the stimulus frame. Which of these strategies of encoding is used may well depend on the nature of stimuli and task constraints. For example, a network format might well be used when the chunks themselves can be treated as elements within a higher-order

328 D. J. BARTRAM

chunk (e.g., repeated configurations forming a symmetrical pattern). When a random pattern of disks has to be encoded, however, it may be simpler to segment the disks into groups and then locate each group independently with respect to the stimulus frame [that is, to adopt at the level of chunks what Wilton and File (1975) refer to as a coordinate system].

EXPERIMENT 1

In this experiment, each subject performed a series of free-reproduction tasks, in which a stimulus (10 disks randomly located in a live by four matrix) was shown for 40 msec, and then after a I-set delay, the subject had to reproduce the stimulus pattern as accurately as possible on an empty grid by carrying out a sequence of 10 disk-placement responses. From the above conceptualization of the process of encoding spatial displays, the following hypotheses can be drawn about subjects’ behaviour in this task.

(1) The Adjacency Hypothesis. For the stimuli used (in which all the elements are the same size, shape, and color) given that recall is unconstrained, chunking is likely to be mediated by spatial proximity. That is, temporal pauses in recall should tend to occur between the placement of spatially nonadjacent disks, but not between the placement of spatially adjacent disks.

(2) The Within-Chunk Constancy Hypothesis. If the distribution of attention across chunks is uniform and the chunk acts as a single unit in recall, then the probability of correctly placing a disk on the response board should be a function of the probability of correctly reproducing the chunk that disk belongs to, and not simply a function of the serial position of that disk in the response sequence.

(3) The Size-Zndependence Hypothesis. If a pattern is familiar or meaningful, it may be treated as containing fewer chunks than if it is unfamiliar or meaningless. In the present case, a subjectively complex or “difficult” pattern may be treated as containing relatively more and relatively smaller chunks than one which is subjectively less complex. This follows from the notion that the structural heuristics operate to segment the stimulus into a minimal number of well-defined groups. Thus, overall, if serial order effects in recall are taken into account, the probability of correctly recalling a chunk should be independent of its size.

(4) The Sequential-Zndependence Hypothesis. If the locations of chunks within the stimulus frame are independently encoded (i.e., chunks are given some form of coordinate reference), then the probability of correctly reproducing a chunk should be independent of whether the preceding chunk in the response sequence was correct or not.

Method Subjects. Three male and three female undergraduates from the University of Hull were

tested individually, each having a single 1-hr session. With the exception of one left-handed female, all subjects were right-handed. They were not paid.

POST-ICONIC VISUAI STORAGE

‘Positive’ ‘Negative’

329

Left - RlQht CW8rSal

Left-Right reversal and Inversion

FIG. 1. Examples of stimuli used in Experiments 1 and 2 (see text for explanation)

Srimulus marerials. Stimuli were produced by randomly locating 10 black disks in the cells of a five by four grid, such that the probability of a disk being in any cell of the matrix was .5. The master matrix was 20 x 16 cm. with each disk having a diameter of 3 cm and being located centrally within its cell. Five random orders were produced to make five master patterns, all the patterns being asymmetrical about both vertical and horizontal axes. Each master pattern was then used to generate a balanced set of eight patterns in the following way (see Fig. 1).

A “negative” ofthe master pattern was produced by removing disks from the filled cells and placing them in the empty cells. Then, for both “positive” and “negative” masters, three other patterns were generated by (a) left-right reversal, (b) inversion, and (c) inversion with left-right reversal. Thus five balanced sets of eight stimuli each were produced. By using “positive” and “negative” patterns it was ensured that across all 80 test stimuli, each cell was filled in 40 patterns and empty in 40 patterns. The reversals and inversions were carried out so that particular configurations of disks occurred equally often in all parts of the matrix. In addition. IO other randomizations were used to generate IO practice stimuli. Black on white slides were made of all the patterns with the grid-lines removed (one copy of each of the 10 practice stimuli and two copies of each of the 40 test patterns).

Appurutus. Stimuli were back-projected onto a 7.5 x 6-cm screen from a Kodak Carousel projector fitted with a cable-release-operated shutter and a Triac dimmer-control. The bright- ness of the display was adjusted so that the stimulus could be clearly seen without producing a negative afterimage at offset. The subject triggered the shutter by using the cable release which was placed to the right of the response table (to the left for the left-handed subject). The subject was seated so that his eyes were between 60 and 70 cm from the screen, the stimulus subtending a horizontal visual angle of between 7”8’ and 6”8’, and a vertical visual angle of between Y43 and 4”54’. Each disk subtended a visual angle of between l”4’ and o”54’. A small pencilled cross was present in the centre of the screen as a fixation point. It was visible when the screen was blank but not noticeable when the stimulus was presented.

On a table between the screen and the subject was a white board divided into 20 5-cm squares arranged in the same five by four pattern as the original matrix, and a row of 10 black disks, each 3.75 cm in diameter. Above the board was a 16-mm tine camera (Eumig C16)

330 D. J. BARTRAM

fitted with a solenoid-operated cable release, which took one picture of the board every second.’

Design and procedure. Subjects were told they would be shown single brief (40-msec) exposures of patterns which they would have to reproduce on the response board. They were instructed to fixate the center of the screen and to use their preferred hand both to operate the shutter and for placing the disks, one at a time, onto the grid. The physical constraints present in the layout of the apparatus ensured that there was a delay of at least 1 set between exposure and the first response. (In fact the delay was normally of the order of 2 to 3 set, thus allowing plenty of time for the icon to fade.)

All 10 disks had to be used on every trial. Subjects were told to guess when not certain, but to make sure that at the end of each trial they had tilled all those cells they were sure should be filled, and left empty all those cells they were sure should be empty. They were al- lowed to move disks after they had been placed on the board (though this rarely happened). Each trial was initiated by the experimenter turning on the camera. As soon as the subject heard the camera running, he pressed the cable release and began his recall.

The experiment was divided into one practice block of 10 trials and eight test blocks of 10 trials each, with a short break between each block. The first four test blocks contained all 40 stimulus patterns in random order, while the second four test blocks contained the same 40 stimuli in different random orders both within and between blocks. Subjects were not told that stimuli were being repeated. Blocks were arranged so that for any given stimulus, at least 15 min elapsed between the two presentations.

Subjects were encouraged to carry out their reproduction as quickly as possible. During the practice period they were given feedback about the time taken to reproduce each stimulus and were encouraged to complete each reproduction in not more than 15 sec. All were responding in under 15 set by the end of the practice block. Their speeds were checked throughout the experiment on about 50% of the trials (though no feedback was given unless a reproduction took longer than 15 set). In this manner a high degree of uniformity in response times was obtained, both within and between subjects. (For the 233 test trials which were timed, 96% fell within the range 10 to I4 set, with an overall range from 7 to 18 sec.)

No feedback about errors was provided, but subjects were told at the beginning that

’ Three pilot studies were carried out prior to Experiment I. Pilot 1 involved one subject whose performance in an Experiment I situation was recording with the tine camera running at I6 fps. From this record, it was possible to produce distributions of inter-piece placement latencies for adjacent and nonadjacent pieces, for various time intervals (e.g., less than I set, between 1 and 2 set, and over 2 set). From this analysis, it was clear that the vast majority of adjacent placements had interpiece placement latencies of close to or under I set, while the vast majority of nonadjacent placements had inter-piece latencies of over 2 sec. On the basis of this pilot study, it was decided that very little information would be lost by recording at a rate of only 1 fps, using a “blank” frame to indicate a chunk boundary. in addition, while still laborious, data analysis was made much easier by having the data recorded in this way. Pilot 2 again only used one subject and looked at the effect of organizing the disks in the array. As reported below, this led to near faultless performance, with chunks of all 10 disks being correctly reported on a number of occasions. Pilot 3 was carried out to assess the effects of exposure duration. As reported below, three subjects were run, each subject having some trials at 40 msec, some at 200 msec and some at I sec. While there was no clear difference in performance on the first two conditions, the I-set exposure did produce a clearly different pattern of results (see below. These effects of exposure time require further study, as the strategy adopted by the subject is likely to depend upon his knowledge of factors such as for how long the stimulus will be available, whether it will be presented more than once, and so on, as well as his knowledge of the type of stimulus being presented and response requirements.


“normally” people only got about six or seven right out of IO, so they were not to worry about making mistakes.

Data recording and methods of analysis. Two main methods of scoring were used: First, each subject’s reproductions were analyzed topographically, and second, serial order effects within each response sequence (i.e., a sequence of IO disk-placement responses made to a stimulus) were analyzed. For the topographical analysis a measure of accuracy (Pc) was calculated by averaging the “hit” and “correction rejection” rates for each cell, for each subject across trials. This provides a measure independent of response bias for each cell of the matrix.

The analysis of serial order effects was carried out on the tine-film record. For each trial, the first frame of the film containing a response was numbered “I” and the succeeding frames from “2” to “n,” where “n” was the frame containing the 10th response. As frames were taken at the rate of one per second, these numbers directly represented time for recall (from the first response) in seconds. (Whenever two responses occurred within a single frame it was possible to discriminate order by the fact that the subject’s hand was always visible over the second of the two responses.) The actual time interval between responses were used in the analysis of chunking.

The criterion used to define achunk boundary within a response sequence was the presence of one or more frames (in the film record) which did not contain a new response. A pilot study’ had shown that the inter-piece placement latencies within chunks were nearly all under I set, with interchunk pauses being in the order of 2 to 3 sec. The adoption of the above criterion implies that all inter-piece latencies in excess of 2 set will be treated as chunk boundaries, while for latencies between I and 2 set the probability of an “empty” frame occurring (and hence a boundary being inferred) will increase uniformly from 0 to 1. It was felt that this criterion represented the simplest way of reflecting the temporal structure revealed in the pilot study.

From this analysis, a number of measures were obtained: the number of chunks in each response sequence for each subject; the number of elements they contained; and the proportion of chunks correctly recalled (i.e., all disks in their right places) as a function of size and serial position in recall. In addition, for each position in the response sequence, the proportion of correct responses (i.e., independent of chunking) was calculated. The two measures, proportion of correct chunks and proportion of correct responses as a function of serial position, were corrected for guessing to produce the measures: Pee, the probability of thejth recalled chunk being entirely correct: and Per,, the probability ofthe ith response in a sequence being correct.*

* In Experiment I corrections for guessing were carried out on the following basis. It is assumed that a subject either knows a particular response to be correct, or guesses. In the latter case, the probability of correctly making a single response is 5. Thus if a subject makes, for example, 95 correct responses and 5 error responses, we can assume that the five error responses indicate that five of the correct responses were correct guesses, and thus the number actually known by the subject was 90 not 95. In general, then, if p is the probability of correctly guessing a response or sequence of responses, then the number of such responses (or sequences of responses) which were correct by chance is given by: Number incorrect x p (I - p). This number is subtracted from the observed number correct. The resulting number is then used in determining Per and Pee values. In the case of Per, p = S, in the case of Pee, p = .5”, where n is the number of disks in the chunk. Hence Pcri is the probability of the ith response, in a sequence of 10 responses, being correct, and is given by: Pcri = (Ncri - Neri/Ncri + NerJ, where Ncri is the number of correct responses at the ith position in the sequence, and Neri is the number of incorrect responses at that position. Similarly, Pee, is the probability of getting thejth recalled chunk completely correct. For each value of n, where n is the number of elements in the chunk, Pee, is given by:

332 D. J. BARTRAM

TABLE 1

MEAN Per VALUES WITH CORRECTION FOR GUESSING AS A FUNCTION OF SERIAL POSITION WITHIN THE RESPONSE SEQUENCE”

Serial position in response sequence

1 2 3 4 5 6 7 8 9 10

Mean Per across subjects .9417 .9250 .7875 .6500 .5375 .3208 .1833 .0875 -.0375 -.0167

” Means across six subjects and 80 trials per subject in Experiment 1.

Results

Serial order effects and chunking within response sequences. Table 1 shows the overall decrease in the proportion of correct responses, corrected for guessing (Per), as a function of serial position in the response sequence. From this it would appear that Per decreases to reach an asymp- tote at chance level by about response eight. If subjects are recalling patterns in terms of a number of discrete chunks, however, rather than as a set of 10 independent responses, one would expect Per to be a function of the serial position of chunks in recall, not simply a function of the serial position of individual responses, (Within-Chunk Constancy Hypothesis). That is to say, given that a chunk is recalled, Per within that chunk should

pee = Ncc, - Net, (.5n/(l - .Sn)) I Nccj + Net, ’

where Nccj is the number of entirely correct chunks of size n in thejth position and Necj is the number of chunks ofthat size containing at least one incorrect response. In Experiment 2, Per values were not computed, as all the necessary information was contained in the PC values (as order of report was positionally defined). For PC (row) values, the situation was not as simple as for Pee in Experiment 1. Initially, two different correction procedures were tried. The first was based on the assumption that each row was treated as consisting of five elements (each having one of two possible states: disk present or disk absent). On this assumption p = .55 = .0313, and is constant. The second method considered both the probability of obtaining the correct configuration of responses in a row (p = .5”, where n is the number of disks in that row) and the probability of correctly locating that configuration, by chance, in the correct position in the row (P,,). This latter probability is given by the reciprocal of the total possible number of ways of locating a given configuration of n disks in a row of five cells. Assuming that these two probabilities (p and P,,) are independent, their product gives the probability of correctly reporting a row by chance. It was found that neither of these methods of correction had much effect on the pattern of results. The first had a uniform effect on all PC (row) values, while the second reduced PC (row) values to between .9 and .94 of their observed values. As there was no need to make comparisons between chunk values and single response values (as in Experiment 1; see Table 3 and Fig. 3), and as there was no basis for deciding between the alternative methods, the final decision was not to apply any correction to the data.


relatively constant, only dropping between chunks. Thus, the relatively smooth decrease in Per seen in Table 1, may be produced by averaging across a number of individual “step functions” having variable “tread” lengths, with the number of steps corresponding to the number of chunks in recall and the length of each step corresponding to the number of responses in each chunk. The data were examined to test this hypothesis.

For each subject, each response sequence was analyzed in terms of the chunks it contained using the method described above. The number of chunks per response sequence varied from 1 to 6, with a mode of 3. Over 86% of all response sequences contained between two and four chunks. The overall means and standard deviations of the number of responses per chunk are shown in Table 2. Only the first three chunks had a mean size greater than 2, and only chunks one and two had modal sizes greater than 1 (the mode of Chunk, was 4, and for Chunk, was 3). Examination of the raw data suggests that for the most part Chunk,-, consisted of single responses at chance level.

In order to test the “step-function” hypothesis, mean Per values for the first and last responses within each of the first three chunks were obtained (excluding chunks of size 1). It was not possible to calculate mean Per values for each position within a chunk, as there was insufficient data if chunks were partitioned by size as well as by serial position. If the hypothesis is valid, there should be little difference between Per for the first and last responses within a chunk, but a relatively large decrease in Per from the last response in one chunk to the first in the next. The results of this analysis are shown in Fig. 2 (where the two probabilities for each chunk are plotted about the median location of the chunk in the response sequence, with the distance between the two being equal to the mean size of the chunk). This clearly supports the hypothesis, as the relatively smooth decrease in Per (Table 1) becomes discontinuous when chunking is taken

TABLE 2

MEAN AND MODAL SIZES OF CHUNKS AS A FUNCTION OF SERIAL POSITION IN RECALL (EXPERIMENT 1)”

Serial position of chunk in recall

1 2 3 4 5 6

Modal size 4 3 1 1 1 I Mean size 4.24 3.282 2.145 1.472 1.241 1.200 SD 1.747 I .499 1.404 0.730 0.501 0.447 Number of chunks (N) 480 472 394 199 58 15 Number correct (N cc) 346 134 108 71 20 6

I1 When the number of correct chunks are corrected for guessing (see footnote 2) only Chunk, and Chunk, have Pee values above .05 (.7083 and .1440, respectively).

334 D. J. BARTRAM

6- L

a” 4-

. Chunk2

.

2-

Chunk3

o---- ----- --*A-

I 1 I 1 I I I I 1 1 1 2 3 4 5 6 7 6 9 10

Medmn posltion

FIG. 2. Mean Per values for the first and last responses in each of the first three chunks, plotted about the median positions of each chunk in the response sequence, with the distance between the two values for each chunk being equal to the mean size of that chunk (Experiment 1).

into account. Also, only Chunk, and Chunk, have first and last Per values which are above the chance level. Mean Pccj values have been computed for each chunk size.2 The results for Pee, are shown in Fig. 3. For Chunk,, Pcc2 values of .2445, .2350 and. 1282 were found for chunk sizes 2,3, and 4 respectively. For all other chunks and all other Chunk, sizes (1,5,6,7, and 8), Pee values were less than .05.

Effects of chunk size on Pee. If reproduction is carried out by recalling a sequence of chunks, rather than a sequence of responses, then not only should the probability of a correct response within a chunk remain relatively constant across serial positions within that chunk, but also the probability of a chunk being correct should simply be a function of the serial position of the chunk in recall. In other words, for a given position in recall, Pee should not be dependent upon chunk size per se (Size-In- dependence Hypothesis). Because Pcc2 values were around chance level for all but chunk sizes 2, 3, and 4, it was only possible to test this prediction for the first chunk. In addition to the Pee, values calculated for each chunk length, two other sets of values were calculated: a set of “predicted” values and a set of “null hypothesis” values. The predicted values of Pee were based on the Size-Independence Hypothesis and were calculated on the assumption that the mean Per for the first response in the response sequence (Per,) to the power of n (where n is the chunk size) gives the probability of Chunk, being correct. The “null hypothesis” values were calculated on the assumption that Per values within chunks were independent (contra the Size-Independence Hypothesis). Thus, decreases in Pee, with increases in chunk size should be a function of the overall decrease in Per with serial order in recall. The values shown in Fig. 3 were


obtained using the following formula:

Pee (null) = (Per, X Per, x . . . Per,),

where n = chunk size, and the Per values are those shown in Table 1. Thus both the null Pee and predicted Pee functions are derived from Per values, which do not depend on prior segmentation of individual sequences into chunks, while the observed Pee values are derived from the segmented response sequences. 2 Examination of Fig. 3 suggests that the hypothesis is confirmed for chunk sizes 1 to 7. Between sizes 7 and 8 there is a clear discontinuity, and for sizes 8 and above the data are consistent with the null hypothesis (which at these levels is that performance has fallen to chance level). There is also a discontinuity in the frequency of occurrence of chunks of a given size between 7 and 8 (see Table 3).

In Table 3, the Size-Independence Hypothesis and the “null” or “Re- sponse-Independence Hypothesis” (as defined above) and used to predict the number of incorrect chunks for each chunk size. Wilcoxon’s t test was used to compare the fit of the Predicted values and the Null Hypothesis values to the observed data. There was a highly significant difference between the Null and Observed values (t = 0 p < .OOl) but no difference

1 2 3 4 5 6 7 8 9 10

CHUNK SIZE

FIG. 3. Variations in mean Pee values as a function of chunk size, for Chunk,, together with “predicted” and “null hypothesis” values (see text for explanation) (Experiment 1).

336 D. J. BARTRAM

TABLE 3

DIFFERENCES BETWEEN ACTUAL NUMBERS OF INCORRECT CHUNKS AT SERIAL POSITION 1,

THE NUMBERS PREDICTED BASED ON HYPOTHESIS (3) (P), AND THE NUMBERS

EXPECTED UNDER THE NULL HYPOTHESIS (N)

Chunk size Frequency

Observed number

incorrect (0) (0 -P) (0 -N)

8 9

10

21 0 48 3 94 12

130 35 8.5 35 59 21 26 11 6 6

8 8

-1 -1 -2 -3 -4 -18 +7 -37

+12 -30 +3 -33 +2 -14 +4 0 +2 0 +4 0

a The (0 - P) values represented an error in prediction of 6.69%, while for the (0 - N) values the error is 29.37% across chunk sizes 1 to 7 (where percentage error is defined as the absolute sum of errors of prediction divided by the total number of chunks, expressed as a percentage).

between the Predicted and Observed ones (r = 8.5, not significant) for chunks of up to seven elements. The above analyses provide a validation of the method of scoring chunks, and also provide strong support for both the Within-Chunk Constancy Hypothesis and the Size-Independence Hypothesis.

Con$guration ofchunks. The Adjacency Hypothesis was tested by comparing the proportion of adjacent response pairs within chunks with that between chunks. (An adjacent response is one where responsei is placed in a square which has at least point-contact with the square containing responsei-l.) The number of adjacent and nonadjacent responses were counted and categorized as either involving or not involving a pause. It was found that when there was no pause, 89.2% of the response pairs were adjacent (and 10.8% nonadjacent), while if there was an intervening pause (i.e., across chunk boundaries), only 14.7% were adjacent (and hence 85.3% were nonadjacent). These figures strongly confirm the Ad- jacency Hypothesis, that chunking is mediated by spatial proximity.

Examination of the actual configurations of all chunks (for sizes between two and seven elements), regardless of orientation, reveals a clear relationship between “simplicity” of figure and frequency of usage (See Table 4). Configurations other than those shown can be considered idio- syncratic in that they each occurred less than 1% of the time and also tended to be amalgams of those shown, or mainly, to be chunks con-


TABLE 4

BASIC CONFIGURATIONS OCCURRING AT LEAST 1% OF THE TIME IN SUBJECTS

REPRODUCTIONS, ORDERED BY FREQUENCY OF OCCURRENCE WITH PERCENTAGE

FREQUENCES AND CUMULATIVE PERCENTAGE FREQUENCES GIVEN”

00 00 0 000 000 0 0 0

Rank Percentage Cumulative

percentage

1 2 3 4 5 18.77 14.14 8.59 5.81 5.30

18.77 32.91 41.50 47.31 52.61

00 000 00 00 0: 0 0 E 00


percentage

6 7 8 9 10 5.22 4.71 4.38 3.03 2.86

57.83 62.54 66.92 69.95 72.81

00 000 :0 : E :‘i: 0 0 0 0

0 : 0


percentage

11 12 13.5 13.5 15.5 1.94 1.85 1.52 1.52 1.43

74.75 76.60 78.12 79.64 81.07

0: 000 00

000 R 0 0:

00 00


percentage

15.5 18 18 18 1.43 1.35 1.35 1.35

82.50 83.85 85.20 86.55

’ Total number of chunks examined (i.e., all those between sizes 2 and 7 across all six

subjects) = 1188.

taining one nonadjacent pair of disks (e.g., oo 0). All six subjects showed similar frequency distributions of usage of configurations.

Relationships between Chunk, and Chunk,. The Sequential-Inde- pendence Hypothesis predicts that for any pair of chunks from a response sequence, the accuracy with which the first is reported should not affect the accuracy with which the second is reported. This was tested by examining each Chunk,-Chunk, pair from those response sequences in which Chunk, consisted of either two, three, or four elements (i.e., those cases where Pee, was above chance). Counts were then made of pairs in which: (a) both

338 D. J. BARTRAM

chunks were completely correct; (b) both were incorrect; (c) only the first was correct; and (d) only the second was correct. The resulting two by contingency table (Chunk, correct vs incorrect by Chunk, correct vs incorrect) was subjected to an x2 analysis, with the result: x2 = 0.012 (df = 1, N = 330, .9.57 <p < .9). The values of P(Chunk, correct 1 Chunk, correct) andP(Chunk, correct 1 Chunk, incorrect) were found to be .3158 and .3012, respectively. Separate analyses of contingency tables for each subject (collapsed across Chunk, sizes) and for each Chunk, size (collapsed across subjects) produced a significant result for only one of the subjects (x2 = 4.806, df= 1, N = 51, p < .05). This was due, however, to P(Chunk, correct 1 Chunk, correct) being less than P(Chunk, correct 1 Chunk, incorrect), and hence is counter to any notion of sequential dependence.

Overall, the above analyses provide strong support for the notion of Sequential Independence, implying that either each chunk’s position is independently addressed or that it is related to some overall higher order structural description, or schematic map, of the pattern. The idea that the position of Chunk, is defined by reference to that of Chunk, is clearly not supported.

The Size-Independence Hypothesis makes the further prediction that the accuracy of Chunk, should be unaffected by the size of Chunk,. This was tested by taking all those Chunk,-Chunk, pairs (for Chunk, sizes 2 to 4) in which Chunk, was correct.,A contingency table was then drawn up with the variables: Size of Chunk, (From 1 to 7) and Accuracy of Chunk, (correct vs incorrect). The proportion of these chunk pairs in which both chunks were correct was found to decrease as the size of Chunk, increased: for Chunk, sizes 1 to 7, these proportions were .400, .588, .346, .267, .161, .187, and .182, respectively (x2 = 19.867, @ = 6, N = 230,~ < .Ol). This appears to contradict the Within-Chunk Constancy Hypothesis. This relationship, however, can be interpreted in two main ways. First, it could be due to a limit on the total number of stimulus elements which can be encoded, regardless of chunking. This would, of course, be contrary to the Size-Independence Hypothesis. Alternatively, the effect may be due to the fact that increases in the size of Chunk, are confounded with increases in the delay to onset of recall for Chunk,. It is possible to discriminate between these two explanations by selecting all pairs where both Chunk, and Chunk2 are correct and then testing for the presence of an inverse relationship between the size of Chunk, and the size of Chunk,. The presence of such a relationship would support the Encoding-Limit Hypothesis, while, if the “Forgetting” Hypothesis is correct, no such size trade-off within pairs would be expected. All completely correct Chunk,-Chunk, pairs were classified by size of Chunk, (which was found to vary from one to seven elements) and size of Chunk, (which was found to vary from one to five elements). In order to carry out a x2 analysis of the resulting seven by five contingency table, it was


necessary to combine a number of categories to avoid low expected fre- quencies. The final analysis, carried out on a four levels of Chunk, by three levels of Chunk, table, produced the result: x2 = 9.38, df = 6, N = 101, .2 < p < .I. This lack of any clear relationship between the two variables supports the “Forgetting” Hypothesis. As the x2 value was fairly large, however, it was felt necessary to carry out a more powerful test. This was done by producing a frequency distribution for the combined sizes of Chunk,-Chunk, pairs (with total sizes varying from two to 10 elements) and then comparing this with an “expected” distribution based on the assumption that the sizes of the two chunks are independent. This expected distribution was produced by calculating expected values for each of the 35 cells in the contingency table described above, and then, for each combined size of Chunk, and Chunk,, summing the appropriate set of expected values; for example, for a combined size of four elements, the cells for sizes 1 and 3,2 and 2, and 3 and 1 were summed. The resulting observed and expected distributions were compared using the Kolmogorov- Smimov one-sample test (D = .058, N = 9, not significant).

Together, the above analyses strongly support the “Forgetting” Hy- pothesis interpretation of the relationship between Chunk, size and accuracy of Chunk,, and hence no rejection or modification of the Sequen- tial-Independence Hypothesis is necessary.

Topographical variations in accuracy (Pc) The values of PC averaged across subjects for each cell of the matrix are shown in Fig. 4. These results show clear topographical variations in accuracy of report, with an overall decrease in accuracy from the top left-hand corner of the matrix to the bottom right. Variations in PC were examined with a three-way analysis of variance with repeated measures on two factors (row and columns) and with sex as the third factor. The differences between rows [F(3, 12) = 11.65, p < .005] and between columns [F(4, 16) = 12.15, p < .005] were significant, and there was no interaction between the two (F < 1).

Variations in PC are closely related to variations in the order in which responses were made: i.e., the top right-hand corner tends to contain the most accurate responses and the earliest responses in the response sequences. From the location in the matrix of the 10 responses in each sequence, the mean rank position in recall (fi) for each of the 20 cells was calculated for each subject. Pearson product-moment correlations were then calculated for each subject between R and PC, for each of the 20 locations. The obtainedr values varied between - .655 and - .898 (p < .005 in all cases), showing a strong relationship between the two variables. It is not possible at this stage, however, to determine the extent to which changes in PC are simply a function of order of report (i.e., due to decay or interference effects occurring during the recall period) and the extent to which they are a function of encoding variables (i.e., due to differences in the accuracy with which different areas of the matrix are encoded).

340 D. J. BARTRAM

1

1 2 3 4 5

Columns

FIG. 4. Mean PC values across subjects for each cell of the matrix (Experiment 1).

Experiment 2 was carried out to unconfound differences in accuracy of encoding and order of report.

It might be expected that subjects would have difficulty in producing an even distribution of responses across the matrix. For example, they might use up more than half of their responses on the first 10 cells of the response board. Any systematic response bias of this type should produce a correlation between the probability of a response being made for each location (Pr) and R for that location. Correlations between Pr and I? were calculated for each subject. The obtained values of r varied between +.2792 and + .0112 (all nonsignificant) from which it can be concluded that no important response bias of the above type exists.

Summary of Results

The results provide strong support for the validity of the method adopted to segment response sequences into chunks. The chunks obtained in this way had the following properties. First, they tended to consist of adjacent disks. Second, the probability of a response within a chunk being correct was predictable from the probability of the first response in that chunk being correct, rather than from the serial position of that response in the response sequence. Third, while the number of chunks recalled varied from 1 to 6 per sequence, only the first two were recalled at above chance


level (these two accounting for about 70% of all responses), and for the second one, only sizes 2, 3, and 4 were above chance. A clear pattern of topographical variation in accuracy was found, though this was confounded with topographical biases in order of report.

Analyses of variations in accuracy with chunk size and of the relationships between Chunk, and Chunk, provide strong support for all four of the main hypotheses proposed in the introduction.

EXPERIMENT 2

Experiment 2 had two aims: first, to see whether the variations in PC found in Experiment 1 are due simply to a tendency to respond on a top- left to bottom-right basis (the “Decoding hypothesis”), or whether this bias itself is determined by an initial uneven distribution of attention across the stimulus display, resulting in more accurate encoding of some areas than others (the “Encoding hypothesis”), and second, to utilize the op- portunity provided by the experiment to extend the previous findings on chunking to a task in which chunks are defined by the experimenter.

Unconfounding Ordrr of Report and Directions of Scan

The procedure adopted was analogous to that used by Scheerer (1972). He presented a row of letters tachistoscopically, and the subject was required to report the string in either a left-to-right or a right-to-left order. A cue indicating direction of report was provided either before or at varying time intervals after the exposure. When the cue occurred before (or immediately after) the exposure, report was best for the material report first. When the cue was delayed, report was best for the material on the left of the display, regardless of order of report. This suggests that there is normally an attentional bias in favor of the left-hand side of the display, though this bias can be changed if a cue occurs either before the exposure or when the iconic image is still available.

In the present experiment (using the same stimuli as Experiment l), subjects were told to treat the patterns as consisting of four rows and to reproduce each pattern either starting with the top row and proceeding from left to right along each row down to the bottom (condition T-B), or by starting with the bottom row and proceeding in a right-to-left fashion along each row up to the top one (condition B-T). For the first group of subjects, the order of report was specified 1 set after each exposure (Post- Cued group), while for the second group, stimuli were divided into blocks of 10 trials, with the order of report being specified before each block (Pre-Cued group).

For condition T-B, both groups should produce a pattern of results similar to that found in Experiment 1, with perhaps a stronger top-to- bottom decrease in accuracy. In both these groups, for condition T-B the

342 D. J. BARTRAM

Encoding and the Decoding hypotheses predict the same outcomes, as the attentional bias and order of report are compatible.

If pre-cueing enables the subject to modify the way he distributes his attention over the stimuli array, then the Pre-Cued group under condition B-T should produce an “inversion” of the top-to-bottom effect predicted for condition T-B.

Condition B-T for the Post-Cued group is the crucial one in which order of report and distribution of attention should be incompatible (if the hy- pothesized top-left to bottom-right attentional bias does normally occur). The Decoding hypothesis predicts that for both the Pre- and Post-cued B-T groups accuracy of report should decrease from the bottom to the top of the matrix. However, according to the Encoding hypothesis, in the Post-Cued group, the top line will have the advantage of being well at- tended to and the disadvantage of being reported last, while the bottom line will have the advantage of being reported first and the disadvantage of receiving relatively less attention. By comparing, within the Post-Cued group, the top line for (T-B) report with the top line for (B-T) report, and the bottom line for (T-B) report with the bottom line for (B-T) report, it will be possible to estimate the effect of order of report with spatial location held constant. Similarly, by comparing the top line for (T-B) report with the bottom line for (B-T) report, it will be possible to estimate the effect of spatial location with order of report held constant; the existence of such an effect would be strong support for the Encoding hypothesis.

Induced Chunking in a “Serial-Reproduction” Task

In the introduction it was argued that the way in which a pattern is structured is a function of constraints in the stimulus, the organizational processes possessed by the perceiver, and the task requirements, Thus it was predicted that by constraining subjects to reproduce patterns as four discrete rows, they would be “set” to see the patterns in this way and hence segment the patterns into four row-chunks. By doing this, subjects would avoid the necessity of reorganizing the stimulus representation prior to recall. As Reed (1974) showed, subjects find such reorganizations very difficult to carry out.

If subjects are treating rows as units (i.e., chunks), then the following predictions can be made. From the Within-Chunk Constancy Hypothesis it follows that the left-to-right decreases in PC found in Experiment 1 should not occur under the Induced chunking conditions. Instead, PC values should be relatively constant within rows and drop, in a step-like fashion, between rows, Second, from the Size-Independence Hypothesis it follows that the proportion of correctly reported rows, PC (row), should not be a function of the number of disks in that row. Third, given the strict relationship between order of recall and spatial location, it might be expected that row chunks would be encoded into a linear structural de-


scription form. Hence, contrary to the Sequential Independence Hy- pothesis, a dependency should be found under these task constraints, between the probability of correctly reporting a given row and whether or not the preceding row was correctly reported.

Method Subjects. Twelve University of Hull students each took part in one individual I-hr ses-

sion. Three male and three female subjects were assigned to each group (Pre- and Post- Cued). All subjects were right-handed. They were not paid.

Appuratus and stitnu/us murerials. The stimuli and apparatus were the same as used in Experiment 1, except that the tine camera was not used (as order of report was fixed and pauses were no longer used as the criterion for segmenting chunks).

Design und procedure. The procedure on each trial was the same as in Experiment 1, except that subjects were constrained to reproduce patterns on a row by row basis. For the Post-Cued group, the Experimenter gave the command “top” or “bottom” (for conditions T-B and B-T, respectively) I set after the subject had pressed the cable release. For the first 40 trials, the order of T-B and B-T trials was randomized, there being 20 of each type. In the second 40 trials, the first 40 stimuli were repeated in a different random order, and the cue given for each stimulus was the opposite of that given on its first occurrence.

In the Pre-Cued group, subjects were instructed before each block of IO trials to reproduce all 10 patterns in the same order (either T-B or B-T). The 40 test stimuli were divided into four blocks of IO each. Within each block of IO, the stimuli were in one random order for their first occurrence and in a different random order for their second occurrence (trials 41-80). Each block of IO occurred once as a T-B block and once as a B-T block for each subject. Within subjects the order of T-B and B-T blocks was balanced in the following way. For half the subjects the eight blocks of IO occurred in the order: T-B, B-T, B-T, T-B: B-T, T-B, T-B, B-T. For the others the order was reversed.

All subjects were given a block of 10 practice stimuli under the appropriate cueing conditions. As in Experiment 1, speed of response was monitored and they were encouraged to complete their response sequences within I5 sec. As before, they had no trouble doing this (the mean time for the trials which were timed during the main part of the experiment was I1 set, with a range from 7 to 17 set).

Subjects were instructed to use all the disks by the time they had reached the end of the last row. If they were left with one or two disks, they were told to place them somewhere on the board, and if they used up all their disks before reaching the end, they were told they could move disks already placed. As in Experiment I, they were told to ensure that at the end of each trial they had filled all those cells they knew should be filled and left empty all those they knew should be empty. [In fact, out of a total of 960 trials, subjects ran out of disks on only 15 trials (I .56%) and had disks left over on only seven trials (0.73%).] Overall, they seemed to have no difficulty understanding the instructions. On three occasions, one of the Pre-Cued group began her reproductions in the wrong direction. These trials were repeated later in the session.

Data recording and analysis. For each cell of the matrix, for each subject, values of Pr (response probability) and PC (accuracy) were calculated, as in Experiment I. In addition, the proportion of correct rows as a function of row position and number of disks per row was computed for each subject [PC (row)]. No correction for guessing was used as variations in chunk size were balanced within rows.*

Results

Topographical variations in PC, Pr, and Pc(row). The mean values of PC across subjects within each condition are shown in Figs. 5A and B and

344 D. J. BARTRAM

1.0 - ----m Pre - cued

.9 )--. T-B

-B-T

*8

0.7 - a

.4 -

0 “‘4’ I I I / I I I I I I I I I I I Al 12345 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Serial Order

1.0 r Post-cued

.---. T-B

a- B-T

l -_. \

.9 - ‘\.. .* _-1

.8 - &

0.7 - 0.

.6 - d

.5------- - _ -A

.4 l-

o II”’ , 6) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Serial Order

FIG. 5. Mean PC values across subjects for each cell of the matrix for the Pre-Cued (A), and the Post-Cued (B) groups, as a function of the temporal order in which the cells were responded to (Experiment 2).

the mean Pc(row) values in Table 5a. A number of points suggest that subjects were treating rows as chunks. First, the fact that PC values show a U- shaped pattern of change across columns rather than the steady decrease from first to last reported cells in each row (found in Experiment 1) provides weak support for the Within-Chunk Constancy Hypothesis. Sec- ond, and related to this, is the clear step-like variation in PC between rows.


TABLE 5

PROPORTION OF CORRECT Rows, PC (ROW), AS A FUNCTION OF (a) CONDITIONS

AND POSITION AND (b) NUMBER OF STIMULUS ELEMENTS PER Row

(4 Row

Top Bottom

Condition I 2 3 4

Pre-Cued T-B .8458 .2917 .0625 .0708 B-T .0542 .0792 .2167 .7375

Post-Cued T-B .7250 .I833 .0583 .0750 B-T .2917 .1042 .0833 .3625

(b) Number of disks per row

1 2 3 4

Pc (row) .41 .45 .48 .39

From Fig. 5 and Table 5 it appears that, as in Experiment 1, only two chunks can be reliably reported at above chance level. [The significance of the fact that for condition B-T (Post-Cued) these were the first and last rows will be discussed below.] Third, the errors made by subjects are also consistent with the view that they were encoding rows as units. For example, the middle two rows were frequently interchanged at recall, and strong vertical cues to location (e.g., a vertical line of disks in the stimulus) did not appear to prevent mislocation within a row. Analysis of the incorrect rows revealed that 52.6% contained the wrong number of responses, 28.57% contained the right number in the wrong configuration, and 18.82% were mislocations of correct configurations. Finally, variation in number of disks per row also had very little effect on Pc(row) values as predicted by the Size-Independence Hypothesis (see Table 5b).

An analysis of variance was carried out on the PC values for each subject, with Groups (Pre- vs Post-Cued) and Sex as between-subject factors, and rows, columns, and conditions (T-B vs B-T) as within-subject factors. [A second analysis of variance carried out on the Pc(row) values produced the same pattern of results as the first, and hence is not reported.]

A significant effect of columns was found [F(4, 32) = 5.41, p < .05] but this did not interact with any other factors (F < 1.24 all cases). This suggests that the U-shaped variation in PC within rows is relatively stable across all conditions. While there was no systematic linear relationship between Pr (response bias) and overall order of report (correlations between Pr and order of report for the conditions varied between -.092

346 D. J. BARTRAM

and +. 126, all nonsignificant), within each line Pr did vary in a systematic fashion, being low at the ends of each line and high in the middle (see Table 6). This, together with the variation in PC within rows (see Fig. 5) suggests the presence of an “anchor effect.” Chunks which contain a disk which is adjacent to the frame of the matrix may be more easy to locate in recall than those which do not. Furthermore, the combination of high PC and low Pr values for columns 1 and 5 suggest that subjects are both more accurate and adopt more stringent criteria for making responses in these columns than they do for the central three columns.

The overall difference in performance between the first to last reported rows was significant [F(3, 24) = 324, p < .005] as were the interactions between Rows and Groups [F(3,24) = 40.13,~ < .005] and between Rows, Groups, and Conditions [F(3, 24) = 15.37, p < .005]. Analysis of these effects showed that the decrease in PC from the first to last reported rows was greater for the Pre-Cued group and that Conditions interact with the Rows effect only in the Post-Cued group (as would be expected from examination of Fig. 5). Overall, the effect of Conditions was only significant for the Post-Cued group [F(l, 8) = 6.03, p < .05]. Thus, the analysis of variance provides strong support for the Encoding hypothesis; the Decoding hypothesis would predict that no interactions should occur between Con- ditions (T-B vs B-T) and rows (by order of report) for either group of subjects. Correlations between PC and order of report, confirm that condition B-T (Post-Cued) succeeded in unconfounding accuracy and order of report. The obtained values of y were as follows: Pre-Cued (T-B) = .8962; Pre-Cued (B-T) = .9338; Post-Cued (T-B) = .8395; Post Cued (B-T) = .0203.

Spatial location and serial position effects. The results from the Post- Cued group can be used to estimate the effects of spatial location and

TABLE 6

MEAN Pr VALUES (PROBABILITY OF A RESPONSE), AVERAGED ACROSS SUBJECTS AND Rows.

FOR EACH COLUMN OF THE MATRIX, TOGETHER WITH THE SPEARMAN RANK-ORDER

CORRELATIONS (Ye) BETWEEN MEAN Pr (ACROSS SUBJECTS) AND ORDER OF REPORT FOR THE 20 CELLS OF THE MATRIX FOR EACH

OF THE FOUR CONDITIONS (EXPERIMENTS)

Columns

Group Condition I 2 3 4 5 f-s

Post-Cued T-B B-T

Pre-Cued T-B B-T

” ns = not significant.

.4313 .5427 .5385 .5406 .4469 - ,062s ns”

.4973 .5817 .4802 .5479 .4729 -.0504 ns

.4021 .5188 .5458 .5813 .4521 -.0921 ns

.4281 .5656 .5260 .5458 .4344 +.1256 ns


TABLE 7

THE EFFECTS OF SERIAL POSITION IN RECALL AND SPATIAL LOCATION FOR THE

POST-CUED GROUP, EXPERIMENT 2, AS SHOWN BY MEAN PC VALUES

(ACROSS SUBJECTS AND COLUMNS) FOR THE TOP AND BOTTOM Rows OF THE MATRIX

Serial Position Effect

Top Row Bottom Row

Mean PC Top,,-,, - Top,,-,, .8892 - .I983 = .I809

Bottom,,-,, - Bottom(TmB,

.6942 - .5425 = .I517

Spatial Location Effect

First Row Last Row

Mean PC

Firs&T-B) - First,,-,,

.8892 - .6942 = .I950

Last,,-,,, - Last,,-,,

.I083 = .5425 = .1658

serial position on accuracy of reproduction. The difference in accuracy between the two top rows and between the two bottom rows from conditions T-B and B-T provide an estimate of the effects of serial position while holding spatial location constant. Similarly, by comparing the top row (T-B) and the bottom row (B-T), and by comparing the bottom row (T-B) and the top row (B-T), estimates of the effect of spatial location can be obtained with serial position held constant. The results of these comparisons are shown in Table 7. (Given the nature of probability scal- ing, these differences should be regarded as only ordinal estimates.) This shows quite clearly that as well as there being a decrease in accuracy with order of report, there is also a decrease in accuracy (from the top to the bottom of the stimulus) which is independent of serial position effects. This adds further strong support to the Encoding hypothesis and suggests that order of report, under free-reproduction conditions, reflects differences in the accuracy with which information was encoded. The nature of the relationship between accuracy of encoding and order of report is discussed more fully later.

Relationship between accuracy ofjrst and second reported rows. The relationship between first and second reported chunks was examined for the Pre-Cued group only (because of the problem of the low level of recall for the B-T Post-Cued condition on the second reported row). It was found that: P(Second Row Correct 1 First Row Correct) = .2819, while P(Second Row Correct 1 First Row Incorrect) = .1731. A x2 test was carried out on the First Row Correct vs Incorrect by Second Row Correct vs Incorrect contingency table, and a significant effect was found [x2 = 4.48, df = 1, p < .05] showing that performance on the second reported row is indeed related to accuracy of performance on the first reported row, as was predicted.

348 D. J. BARTRAM

DISCUSSION

The present experiments and those by Chase and Simon (1973), Wilton and File (1975), and Reitman (1976) provide strong support for the notion that information about spatial relationships within a visual pattern is or- ganized into chunks in Post-Iconic Visual Storage (PIVS) and that these chunks have identifiable behavioral correlates. The form these chunks take appears to be dependent upon a number of variables. In chess and in Go they are affected to some degree by the functions pieces serve in the game. In the present study, in Experiment 1, it was found that configurations tended to consist of relatively simple patterns of three or four adjacent disks. In Experiment 2, however, the strategy of coding by spatial proximity was not used. Instead the task requirement to reproduce the pattern in a fixed order appeared to induce coding by rows. Thus it seems that subjects can select, to some degree, coding strategies which are compatible with recall requirements. Not only did the types of chunks differ between the two experiments (configurations of spatially adjacent disks as opposed to linear sequences of spaces and disks), but also the locational “demands” of the two tasks differed. In Experiment 1, subjects had no cues to chunk-location (apart from the frame of the response board), while in Experiment 2, locations were predefined in terms of rows. In the latter case there would be a considerable advantage to be gained by encoding chunks into a strictly linear sequence (i.e., Row,-Rowz-R~~3-Ro~4).

Differential predictions were made concerning the two tasks (free vs constrained reproduction) which were supported by the data. First, as already mentioned, when recall is constrained, subjects appear to encode the stimulus in a form compatible with the mode of recall. The degree of control the subject has over the encoding strategy appears to be quite specific. In the Pre-Cued conditions, subjects were able to switch their encoding strategy according to whether recall was T-B or B-T. When recall was post-cued, however, encoding was only compatible with the T-B recall order. For the B-T condition there was a strong interaction between mode of encoding and order of recall. It seems that subjects will normally relate their encoding strategies to the expected mode of recall. That is, when recall order is prespecified, they will distribute their attention in favor of those areas of the stimulus which are to be recalled first. When recall order is not specified (or is post-cued) they will normally bias their distribution of attention toward the top of the display, and if free to do so, will order their recall in terms of the area of the stimulus which received most attention. The fact that the results for both T-B conditions in Experiment 2 were so similar implies that in both Post-Cued conditions subjects adopted the strategy of using their “normal” pattern of attentional bias (as shown in Experiment 1). If they had tried to anticipate order of recall or had adopted some procedure of switching encoding


strategies, then, on some occasions recall in the T-B conditions should have been adversely affected, making the results for T-B Post-Cued differ from those for T-B Pre-Cued.

The second differential predictions concerned the processes involved in locating chunks within the response frame. In Experiment I a number of procedures might have been adopted: forming chunks into linear or network structures or independent addressing of chunks. The data were more consistent with the notion of independent addressing than with the alternatives. That is, it is suggested that each chunk has attached to it an “address” which specifies its location within the stimulus (and, therefore, the response) frame. Only by implication do such addresses provide relative information about the positions of other chunks. This notion of “Independent Addressing” presupposes the existence of some general internal spatial representation [cf. Hochberg’s (1968) notion of a “schematic map”] within which location can be specified. Phillips (1974), in his discussion of short-term visual storage, argues that “the schematic visual representation is a figural articulation of the sensory representation that shows how selected elements can be related to each other to form figures or parts of figures” (p. 289). His proposed “schematic visual memory” seems to have very similar properties to the post-iconic visual storage studied in Experiment 1.

Even with independent addressing, the location of the first chunk in recall effectively constrains the possible locations of subsequent ones. Not only can chunks not overlap, but also there tend not to be any points of contact between chunks (only 14% of second chunks had one or more disks adjacent to a first chunk disk). This implies that placement of the first chunk may effectively reduce by nearly one half the area of the response board available for locating Chunk,.

Even given these locational constraints, the Sequential Independence Hypothesis was strongly supported in Experiment 1 (there being no relationship between the accuracy of Chunk, and that of Chunk,). In Experi- ment 2, a different pattern of dependency was expected, due to the basic linear constraints imposed on recall order. The results were consistent with this, as the probability of the second reported row being correct was .2819 if the first row was correct, but .I731 if the first row was incorrect.

Characteristics of PIVS

The present studies were not intended to answer questions about the fate of memory traces in PIVS. A number of tentative conclusions, however, can be drawn from the data. One important point to make is that a capacity of PIVS is not reflected in the fact that no more than two chunks could be recalled at above the chance level. This seems tc reflect a limit on the amount of information which can be output in this type of task. Ex-

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amination of the results from the Post-Cued conditions suggests that at least three, if not all four rows are initially available for recall. Whether or not Row2 and Row4 are recalled depends upon recall order (which, of course, is specified after encoding). It also seems probable that some information is available about Rows, but this is never reproduced. This assertion is based on the assumption that the accuracy with which Row2 and Row, are initially encoded should be between the levels associated with Row, and Row*. If both these latter rows can be recalled, when reported first, then the intermediate rows should also be recallable, if they were reported first. Given this assumption, in order to account for the obtained results, it is then necessary to argue that the rate of loss of information about a particular row is inversely related to the amount of attention initially allocated to that row (i.e., to the efficiency with which it was encoded). This implies an interaction between efficiency of encoding and order of recall.

The present studies cannot give any indication as to why information is lost (decay, interference, differential rehearsal, or some combination of these). Such questions could possibly be answered by using some form of probed-reproduction task, where only a single row had to be reproduced, the location of the row being post-cued. However, it is worth pointing out that in the B-T Post-Cued condition the last reported row (i.e., row,) was reported at above chance level. This represents recall after an interval of approximately 10 set of potentially highly interfering activity. As mentioned above, the storage system being examined here seems to have temporal parameters similar to those reported by Phillips (1974), who used block-patterns on a square matrix in a recognition task. He provides evidence for a schematic short-term visual memory of limited capacity, which is post-iconic and which becomes gradually less effective as the interval between presentation and recognition is increased up to 9 sec.

In Experiment 1, chunk size could vary from one to 10 disks. Exam- ination of the data, however, revealed that only those temporal groups of responses containing less than eight disks could validly be regarded as con- stituting chunks (see Fig. 3). In the relatively small number of instances when sequences of more than seven responses were scored as chunks, it seems likely that either the scoring procedure missed a break in the sequence or that subjects had attempted to form too large a grouping. Which- ever is the case, for patterns such as these, seven disks provide an upper limit on the chunk size, with chunks generally consisting of three or four disks. Thus, for patterns like those used in the present study where each element is statistically independent of the others, the “Magical Number 7” (Miller, 1956) appears to provide a clear upper limit on reproduction performance. It is interesting to note that none of the completely correct Chunk, and Chunk, pairs contained a Chunk, with more than seven elements in it (nor were there any Chunk,‘s with more than five elements).

POST-ICONIC VISUAL STORAGE 3.51

Analysis of Chunk,-Chunk, pairs, however, showed that this limit was not a limit on the total number of elements encoded but was a limit on the maximum number of elements per chunk. One of the pilot studies carried out’ used one subject under the same conditions as Experiment 1, but with stimuli in which the arrangement of disks was not random (the patterns were either symmetrical or contained repetitions of groupings). Under these conditions, only two out of 40 response sequences contained any errors, no more than two chunks were ever used, and a large number of chunks consisted of all 10 disks (patterns containing two spatially dis- tinct groupings, however, were all reproduced as two chunks). This result is consistent with the way it was proposed that chunking heuristics operate (see the Size-Independence Hypothesis above). That is, they operate to segment the pattern into the smallest number of “well-defined” parts, in order to minimize the load on PIVS, while maximising the total amount of information encoded. A pattern is “well-defined” in relation to the extent to which it is familiar, meaningful, or in general, can be related to information in long-term storage. Chase and Simon (1973), for example, found that not only did the chess master produce more chunks when recalling real games, but his chunks were also larger. His knowledge and experience of chess enabled him to treat larger subsets of stimulus elements as “well-defined” configurations.

Chunking and the Distribution of Attention

Clear topographical variations in recall were found in both Experiments. In Experiment 2 these effects were shown to be due to more than just serial order effects in recall. It seemed that certain parts of the display were more accurately encoded than others. Apart from the condition where subjects were pre-cued to recall from the bottom upward, there was a clear bias toward the top and, in Experiment 1, the left-hand side of the display. This pattern of results is similar to what would be expected in a free-viewing situation from what is known about general biases in the order and frequency of eye fixations in different areas of a large display (Buswell, 1935).

The variations found in the present studies can be interpreted in two main ways. First it can be argued that they imply an attentional scanning process, in which the focus of attention shifts from the top down to the bottom of the display, in a manner analogous to shifts in eye fixations for larger displays. As Noton and Stark (1971, p. 42) propose “a shift in attention can be executed either externally, as an eye movement or in- ternally, depending on the extent of shift required.” This view would also be consistent with Scheerer’s (1972) interpretation of his data in terms of a left-to-right scanning process. Movement of the focus of attention down the display would be related in time to the decay of the icon, resulting in the obtained topographical variations in accuracy.

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The second alternative explanation is that information is encoded in parallel from all parts of the display and that the amount of processing “work” done in a given time varies across the display; that is, processing is very efficient around the focus of attention and becomes increasingly less efficient with increasing spatial distance from that focus. The alternatives are not mutually exclusive. The latter does not deny the possibility of attentional shifts occurring (with or without concomitant eye movements), but rather asserts that it is not necessary to postulate such shifts in the present case. This is supported by the results of one of the early pilot experiments’ in which three subjects were tested under the same conditions as Experiment 1, but with only 20 trials on each of a number of different exposure durations (40, 200, and 1000 msec). There was little difference between the 40- and 200-msec conditions, but a clear difference in strategy on the lOOO-msec condition. Here there was a clear tendency for the first two chunks to come from the top and the bottom of the display, with the middle being filled in last. (These first two chunks were both reported at the same general level of accuracy as Chunk, in Experiment 1). This suggests an encoding strategy in which attention is initially focused at the top of the display, then shifts, during the exposure, downward. Recall then follows the strategy of recalling the best encoded chunk first, the results showing a form of recency and primacy effect for the first two chunks recalled. While too much reliance should not be placed on the small amount of data generated by the pilot studies, they do support the view that it is unnecessary to postulate any form of sequential scanning mech- anism involving spatial shifts in attention focus to account for the results of Experiments 1 and 2, as such scanning only seems to occur with longer stimulus exposure durations.

If, as Experiment 1 and 2 show, more than one chunk can be reported from a single “glance,” does this not invalidate Chase and Simon’s (1973) and Reitman’s (1976) use of the perception task as a means of identifying chunks, as it is based on the assumption of one chunk per glance? It seems likely that subjects will adopt slightly different strategies in the two tasks. In a task where they know they can look back at the stimulus, they do not need to attempt to take in the whole stimulus with the first glance and may therefore concentrate on “quality” (one perfect chunk) rather than “quan- tity” (a number of nearly correct chunks). Thus the limit of one chunk per glance may reflect the choice of a particular task-related strategy by the subject rather than anything more fundamental.

If the distribution of attention at any one time is a function of the spatial distribution of processing “effort,” then clearly the spread of that distribution, as well as its focus is important. Mackworth (1976) has examined the way the “useful field of view” varies in size as a function of stimulus and task variables. He defines the useful field of view as “the area around the fixation point from which information is being processed, in the sense


of being stored or acted upon during a given visual task” (p.307). For present purposes, it would be better to redefine the center of the useful field of view in terms of the focus of attention, rather than the fixation point [as Kaufman and Whitman, in Noton and Stark (1971), have shown the fixation point does not necessarily coincide with the focus of attention]. From Mackworth’s (1976) results, it appears that the size of the useful field of view varies with processing load, and he showed that it constricts sharply when a high density of detail has to be processed. In general, it seems that its size can be related to the attentional demands made upon the perceiver; that is, it is a joint function of the density of detail in the stimulus, the nature of the response criterion, and the efficiency of the perceiver’s mode of processing. The differences between Chase and Simon’s (1973) perception and memory task can be explained in terms of subjects adopting different useful fields of view in the two types of task: a relatively small field of view in the perception task, and a wider one in the memory task. In the present study, the stimuli contained less detail, but were less meaningful, and also were only briefly presented on one oc- casion. Under these conditions, it seems that the useful field of view was “set” to encompass nearly all of the stimulus.

The Role of Anticipatory Schemata

The results of Experiment 2 suggest that the process of perceiving the patterns presented to subjects in the present studies can be considered as being initiated before the stimulus occurs. Prior to presentation the subject knows (a) what general type of stimulus will be presented, (b) when it will occur (in that the task was self-paced), and (c) he can prepare more or less explicit responses procedure. Thus, it seems likely that prior to pushing the cable release, the subjects can “preprogram” their distribution of attention and effectively preselect a relevant subset of chunking heuristics. This is similar to Neisser’s (1976) idea of setting up “anticipatory schema.” In the present case such schema can be quite specific and may control the position and size of the useful field of view, a “set” to form certain types of chunks (based on either spatial proximity or position within the same row), and a procedure for structuring recall. When the stimulus occurs, the general distribution of attention programmed by the anticipatory schema is modified by the operation of the chunking heuristics upon the configurations of disks actually presented. It is this modified schema which may be considered as containing information about the chunks and their positions, and the information about response format.

Conclusions

It has been suggested that performance in the present experiments has to be understood not simply in terms of a subject responding to a visual

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stimulus, but rather in terms of a number of interrelated phases: first, a preparatory phase for setting up an “anticipatory schema,” the form of which depends upon stimulus, task, and subject variables, and which presets a general distribution of attention or processing “effort” across the display, and a form of encoding appropriate for the task; and then the presentation of the stimulus resulting in a modification of this attentional pattern. Essentially, it is suggested that the distribution of attention, the preparatory attentional “set,” becomes discontinuous, as a function of the operation of chunking heuristics upon stimulus information; the discontinuities “define” the chunks in that attention is uniform within chunks and variable between chunks. Hence Pomerantz and Schwaitzberg’s (1975) assertion that selective attention to elements within a chunk is difficult can be turned around: A chunk is a chunk, because the distribution of attention across the elements forming that chunk is uniform. Finally, the third phase involves the reproduction of the stimulus pattern.

The attentional model outlined in this paper provides a framework for understanding the results not only of the present study but also the related work of Chase and Simon (1973), Wilton and File (1975), and Reitman (1976). It is hoped to extend the present paradigm to examine the encoding of real visual scenes and to test the general hypothesis that “grouping heuristics” similar to those examined in the present study operate to structure the real perceived world by acting upon and modifying our spatio-temporal distributions of attention.

REFERENCES

Bahrick, H. P., & Bahrick P. Independence of verbal and visual codes of the same stimuli. Journal of Experimentul Psychology, 1971, 91, 344-346.

Buswell, G. T. HUM people look ur pictures. Chicago: University of Chicago Press, 1935. Chase, W. G., & Simon, H. A. The mind’s eye in chess. In W. G. Chase (Ed.), Visual

information processing. New York: Academic Press, 1973, Pp. 215-281. Frost, N. Encoding and retrieval in visual memory tasks. Journal of Experimental Psychol-

ogy, 1972, 95, 317-326. Henderson, L. Visual and verbal codes: Spatial information survives the icon. Quarterly

Journal of Experimental Psychology, 1972, 24, 439-447. Mackworth, N. H. Stimulus density limits and the useful field of view. In R. A. Monty and

J. W. Senders (Eds.), Eye movement undpsychologiculprocesses. New York: Wiley, 1976. Pp. 307-321.

McLean, R. S., & Gregg, L. W. Effect of induced chunking on temporal aspects of serial recitation. Journal of Experimrntul Psychology, 1966, 74, 455-459.

Miller, G. A. The magical number seven, plus or minus two. Psychological Reviews, 1956, 63, 81-97.

Neisser, U. Cognitive psychology. New York: Appleton-Century-Crofts, 1967. Neisser, U. Cognition und Reulity. San Francisco: Freeman & Co., 1976. Noton, D., & Stark, L. Eye movements and visual perception. Sc,ienfijc Americun, 1971,

224, 34-43. Phillips, W. C. On the distinction between sensory storage and short-term visual memory.

Perception und Psychophysics, 1974, 16, 283-290.


Pomerantz, J. R., & Gamer, W. R. Stimulus configuration in selective attention tasks. Perception and Psychophysics, 1973, 14, 565-569.

Pomerantz, J. R., & Schwaitzberg, S. D. Grouping by proximity: Selective attention measures. Perception and Psychophysics, 1975, 18, 355-361.

Reed, S. K. Structural descriptions and the limitations of visual images. Memov and Cogni- fion, 1974, 2, 329-336.

Reitman, J. Skilled perception in Go: Deducing memory structures from inter-response times. Cognitive Psychology, 1976, 8, 336-356.

Scheerer, E. Order of report and order of scanning in tachistoscopic recognition. Cunudian Journal of Psychology, 1972, 26, 382-390.

Tversky, B. Pictorial and verbal encoding in a memory search task. Perception and Psycho- physics, 1969, 4, 225-233.

Wilton, R. N., & File, P. E. Knowledge of spatial relations: A preliminary investigation. Quarterly Journal of Experimentul Psychology. 1975, 27, 251-258.

(Accepted March 6, 1978)

Documents

Post-iconic visual storage: Chunking in the reproduction of briefly displayed visual patterns