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Testing OrganizationPreferences in Serial PatternLearningCees van Leeuwen aa Faculty of Psychology , University of Amsterdam ,the NetherlandsPublished online: 06 Jul 2010.

To cite this article: Cees van Leeuwen (1991) Testing Organization Preferences inSerial Pattern Learning, The Journal of General Psychology, 118:2, 139-145, DOI:10.1080/00221309.1991.9711139

To link to this article: http://dx.doi.org/10.1080/00221309.1991.9711139

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The Journal of General Psychology, 118(2), 139-145

Testing Organization Preferences in Serial Pattern Learning

CEES VAN LEEUWEN Faculty of Psychology

University of Amsterdam, the Netherlands

ABSTRACT. Subjects studied a series of colored dots for 60 s and then performed a memory reproduction task for which they chose alternative puzzle pieces from a set. Series were presented repeatedly until subjects made a completely c o m t reproduc- tion. The puzzle pieces contained parts of the series that were expected to interact with the groups identified by spontaneous perceptual organization. By assuming that same grouping in series and puzzle pieces would be preferred, the preferences could be predicted on the basis of an economy principle. The preferences obtained were in accordance with the predictions.

SOME APPROACHES OF PERCEPTUAL ORGANIZATION have as- sumed the existence of a generic mechanism that is somehow sensitive to the regularity of the perceptual pattern (Hatfield & Epstein, 1985), as determined according to descriptive economy. Leeuwenberg (1971) made attempts to specify economy within a coding system of visual patterns (see also Pomer- antz & Kubovy, 1985). In this article, I show, however, that a measure based on a few common-sense assumptions may already provide very accurate pre- dictions.

I simply assumed, following Restle’s (1970) study, that a run of one or more identical elements in a series may form a group. For instance, in the series a a a b c c, there are three groups: (a a a)(b)(c c). For nonidentical elements, I assumed that each occurrence of a repeating subseries may count as a group-for instance, (a b)(a b)(a b). These combined assumptions led

I thank S. Handel for comments on an earlier version of the manuscript and Anny Bosman for performing the experiment.

Requests for reprints should be sent to Cees van Leeuwen, Faculty of Psychol- ogy, Department of Psychonomy, University of Amsterdam, Roetersstraat 15, 1018 WB Amsterdam, the Netherlands.

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140 The Journal of General Psychology

to (a b)(c c)(a b)(c c)(a b) and (a b c)(c)(a b c)(c)(a)(b) as possible groupings, among others, for the series a b c c a b c c a b .

I predicted that the grouping chosen contained the least possible number of groups, in this case the former one. This hypothesis may be specified into a quantitative prediction with the aid of Equation 1, which is similar to one used for the same purposes by Buffart and Leeuwenberg (1983). In this equa- tion, Po , B) indicates the preference for a grouping A over a grouping B, NA and N, indicate the number or groups in A and B , respectively, and k indi- cates a parameter.

(1)

A paradigm familiar from the domain of serial patterns was used for testing the prediction (van Leeuwen, Buffart, & van der Vegt, 1988). Subjects study a series of colored dots, partially covered by a mask sliding over the pattern. After a 60-s inspection, the whole series must be recovered from puzzle pieces containing parts of the series. If the groups on the puzzle pieces do not correspond to the ones obtained during the inspection, the reconstruc- tion is expected to be more difficult. The original groups and the ones on the pieces get confused, for instance, because the perceiver must rework the orig- inal interpretation before the puzzle can be laid. Two alternative sets of puzzle pieces were compared, each corresponding to a grouping of the series. If the number of groups corresponding to one set is indicated as N,, and the other as N,, the preference for one set of segments can be calculated with Equa- tion l .

> B) = NBk 1 W A k + N B k )

Method

Subjects and Stimuli

Seventy-six undergraduate students were paid or received course credits for participation. All were unfamiliar with the task. Four subjects had to be dis- missed for not finding a correct solution to the task after 10 successive trials.

The series used are shown (with letters representing the colored dots) in Series 1 and 2.

1. a e c d e c d a a c a e a c b b d b d a a b e e b e b d 1 A . a e c d e e d a a c a e a c b b d b d a a b e e b e b d 1 B . a e c d e c d a a c a e a c b b d b d a a b e e b e b d 2 . b e b e a e d a c a a d b a b d a b a c d e c d 2 A . b e b e a e d a c a a d b a b d a b a c d e c d 2B. b e b e a e d a c a a d b a b d a b a c d e c d

Since alternative sets of puzzle pieces were compared, I predicted preference for an organization in terms of preference for puzzle pieces. For both Series

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~ ~ ~ L e e u w e n 141

1 and 2, there were two alternative sets of puzzle pieces from which the disk could be reconstructed completely. Sets 1 A and 1 B of Series 1 both consisted of eight puzzle pieces, four puzzle pieces of 3 dots alternated with four puzzle pieces of 4 dots. Sets 2A and 2B of Series 2 both consisted of six puzzle pieces, three puzzle pieces of 3 dots alternated with three puzzle pieces of 5 dots. The mask that partially covered the series revealed 7 or 8 dots, equaling the number of elements contained by two adjacent puzzle pieces.

Hochberg (1968) demonstrated that subjects are able to recover the struc- ture of a pattern from successive partial views of it. This is possible for series like Series 1 and 2 only, insofar as the structure contains groups not larger than the size of the window in the mask (van Leeuwen et al., 1988). We may, therefore, limit ourselves to groupings that span exactly two adjacent pieces (7 or 8 dots). With these assumptions, I determined for each alternative pair of adjacent pieces the least number of groups. The assumption that a group cannot extend over a border of a piece led to the groupings shown in Table 1, from which the preferences for alternative segments can be predicted using Equation 1.

Materials

Series consisted of yellow, blue, red, green, and brown dots. To make sure that eventual effects of beginning and ending point were eliminated, a series of dots was placed along the border of a disk (Figure 1). This disk was made of neutral grey cardboard and was surrounded, and partially covered, by an envelope of black cardboard.

Subjects could rotate the disk in both directions behind the cover to in- spect all the dots on the disk. They inspected the series of dots by turning the disk at their own preferred rate for 60 s. The cover posed an upper limit to the number of dots that subjects were able to perceive simultaneously. In this experiment as well as in the next one, the window was constructed in such a way that seven or eight dots were visible at the same time. The cover also prevented a subject from using spurious two-dimensional position cues to memorize the disk (e.g., two elements of the same color on opposite sides of the disk).

Two sets of disks, Qpe 1 and Type 2, were constructed. Qpe 1 disks were versions of Series 1, and qpe 2 disks were versions of Series 2. There were two remappings of the variables to colors and two straight or mirror images, constituting four different versions of Disk 1; add the same number of versions of Disk 2 for a sum of eight different disks. Type 1 disks were reconstructed with eight puzzle pieces from Set I A and eight from lB, 16 pieces for each version, constituting 64 puzzle pieces. Qpe 2 disks were re- constructed with six puzzle pieces from Set 2A and six from 2B, 12 pieces

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142 The Journal of General Psychology

TABLE 1 Response Alternatives (Puzzle Pieces) and Corresponding Grouping as

Predicted by Restle (1970)

Puzzle pieces from Corresponding Cluster Sets A and B grouping No. of groups

aec decd aecd ecd aac aeac aaca eac bbd bdaa bbdb daa bee bebd beeb ebd beb eaeda bebea eda caa dbabd caadb abd aba cdecd abacd ecd

5 3 5 5 4 5 5 5 8 6 7 7 6 6

Note. Each number of groups was determined according to Restle's (1970) description system. Grouping for cluster 2A, is obtained without the extra assumption mentioned in the discussion.

for each version, constituting 48 puzzle pieces. Puzzle pieces correspond to the clusters 1 A, through 2B, in Table 1.

Procedure

A Type 1 disk was randomly assigned to 40 subjects, and a Type 2 disk to 36 subjects. Each subject was allowed a 60-s inspection of the disk. Next, the subject was asked to give the disk to the experimenter. The subject then was provided with all the puzzle pieces that make up the disk just studied (64 puzzle pieces for Disk 1; 48 for Disk 2).

The puzzle pieces were presented like a shuffled deck of cards spread out on the table. Subjects could select puzzle pieces from the deck and complete the disk out of the puzzle pieces selected. This part of the task had no time restrictions, and subjects were allowed to try out or replace puzzle pieces freely during the reconstruction. When the reconstruction of the disk was entirely correct, the experiment ended. Otherwise, the inspection and subse- quent puzzling were repeated (a maximum of 10 times) until the reconstruc- tion was correct.

In the final correct solution, choices could have been made from both alternative sets of puzzle pieces (A or B). Puzzle pieces from alternative sets

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VAN Leeuwen 143

FIGURE 1. Disk and puzzle pieces.

belonged together in pairs. For instance, if the leftmost puzzle piece Q e c from 1A is used in the reconstruction of Series 1, the correct reconstruction can only be made if the next puzzle piece is d e c d. But a pair chosen does not restrict the adjacent pairs. Thus, for Series 1, four independent choices could be made, and for Series 2, three of them.

Results and Discussion

Predictions shown in Table 2 were obtained from Equation 1 with k = 2. These preferences are overall in accordance with the model ( r = ,867, rs = 3.88, p < .012). The fit becomes better if it is assumed that the reversal of the chunk d b on the puzzle piece d b a b d (2A2) has not been detected and thus d b and b d could be treated as groups, as in (d b)(a)(d b). In that case, 2A2 becomes (c)(a a)(d b)(a)(b d). five groups according to Restle's (1970) description system, and preference predictions for these pieces be- come very similar to the actual data, as shown in parentheses in Table 2, resulting in a correlation of r = .997 (r, = 29.67, p < .001).

The experiment illustrates that for the present restricted set of data, a common-sense grouping criterion like the one adopted here, is strong enough to yield correlations that are equal in size to the ones generally reported by Leeuwenberg and his colleagues. This result could be viewed as challenging the uniqueness of the Leeuwenberg preference measure. Perhaps even more because, despite several years of training in the field, I was unable to find a coding for these series that yields an equally good fit.

Of course, it is not my intention to replace Leeuwenberg's preference measure with the one proposed here. I immediately grant any claim that, de-

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144 The Journal of General Psychology

TABLE 2 Percentages of Predicted and Observed Preference for Puzzle Pieces

Percentage of preference Cluster No. of groups Predicted Observed

5 3 5 5 4 5 5 5 8 6 7 ( 5 ) 7 6 6

.26

.74 S O .50 .61 .39 .50 .50 .36 .64 .50 (.66) S O (.34) .50 .50

.28

.72

.so

.so

.59

.41

.50

.50

.37

.63

.67

.33 S O S O

Note. Each number of groups was determined according to Restle’s (1970) description system. Numbers between parentheses are based on the extra assumption mentioned in the discussion.

spite its apparent elegance, this measure is completely ad hoc and in a new test would deliver a much lower correlation. Leeuwenberg’s measure, simi- larly to the present one, emerged from attempts to fit a restricted set of data (although not quite so restricted as the present one).

Theoretical justifications for the measure have been given (Buffart & Leeuwenberg, 1983; Van der Helm, 1988), but these were post hoc instead of explanatory. It is my belief that a measure will have to derive its validity not from its goodness of fit but in the productivity of its suggestions of how a representation is obtained. In this respect, Leeuwenberg’s measure and the present one are equal.

REFERENCES

Buffart, H., & Leeuwenberg, E. (1983). Structural information theory. In H.-G. Geissler, H. F. J. M. Buffart, E. L. J. Leeuwenberg, & V. Sarris (Eds.), Modern issues in perception (pp. 48-72). Amsterdam: North-Holland Publishing Com- pany.

Hatfield, G. C., & Epstein, W. (1985). The status of the minimum principle in the theoretical analysis of visual perception. Psychological Bulletin, 97, 155-186.

Hochberg, J. (1968). In the mind’s eye. In R. N. Haber (Ed.), Contemporary theory and research in visual perception (pp. 309-331). London: Holt, Rinehart & Win- ston.

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Leeuwenberg, E. (1971). A perceptual coding language for visual and auditory pat- terns. American Journal of Psychology, 84, 307-349.

Pomerantz, J. R., & Kubovy, M. (1985). Simplicity and likelihood principles. In K. Boff, L. Kaufman, & J. Thomas (Eds.), Handbook of perception and human per- formance (Vol. 2, pp. 36/1-36/46). New York: Wiley.

Restle, F. (1970). Theory of serial pattern learning: Structural trees. Psychological Review, 77, 48 1-495.

Van der Helm, P. (1988). Accessibility and simplicity of visual structures. Unpub- lished doctoral dissertation, University of Nijmegen, the Netherlands.

van Leeuwen, C., Buffart, H., & van der Vegt, J. (1988). Sequence influence on the organization of meaningless serial stimuli: Economy after all. Journal of Experi- mental Psychology: Human Perception and Performance, 14, 48 1-502.

Received September 10, 1990

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