Effects of redundancy on information-reduction tasks

.JODRNAL

Effects

OF EXPERIMENTAL

of

CHILD

Redundancy

7, 195-202 (1969)

PSYCHOLOGY

on

Information-Reduction

Tasks1

Thirt,v elementary school children sorted dot patterns that were cithrl asymmetrical or symmetrical about (a) a vertical axis, (b) a horizontal axis, or (c) both, Asymmetrical patterns were sorted faster and with fewer errors than the symmetrical patterns (p < .OOl) . Stimulus redundancy interfered with rapid visual discrimination presumably by reducing stimulus uniqueness and distinctness. When the complexity of the input was sufficient to force the Ss to reduce ihe stimulus to distinctive parts, the retarding effects of redundancy on discrimination were in direct relation to the amouni of redundancy and independent of the Ss’ cahronological age’.

Posner (1965) proposed a taxonomy of psychological tasks based upon the relation between input and output’ information required for perfect performance on the task, This taxonomy consists of three types of tasks: (a) Information-conservation tasks in which the S is required to 1)~ serve all of the input information in his response and any increase 01’ decrease in information during transmission represent:: error; (b1 information-addition tasks which involve information creation, so that the output information must exceed the input if the S is to perform the task; and (c) information-reduction tasks which require the S to produce a subset of the stimulus input. The loss of information does not represent error, but rather is necessary to produce the required output. Paraskevopoulos (1967, in press) found t,hat, in information-conservation tasks, performance is a function of the amount and the form of stimulus redundancy as well as the Ss’ chronological age and int’elligence. The present study investigat,ed tht effects of stimulus r+ dundancy on information reduction tasks. METHOD

Sti~t~uli. The stimuli matrices. The procedure

consisted described

of eight-dot by Attneave

patterns embedded in (1955) was adopted to

‘The report is based upon a dissertation submitted in partial fulfillment of the requirements for doctoral degree at the University of Illinois. The author is indebted to the members of his dissertation committee, Professors H. W. Hake, S. Jones, S. A. Kirk, K. Scott, and M. Tatsuoka. for their valuable guidance in planning and conducting the study. 195

196

IOANNIS

PARASKEVOPOULOS

generate the patterns. The dots were arranged in the following four variations : (a) Asymmetry. The position of each dot was independent of the position of any other dot in the pattern (Fig. la) ; (b) Bilateral Symmetry. Only the dots in the left half portion of the pattern were determined independently. The right half portion of the pattern was a

(cd Asymmetry

(cd. Horizontal FIG. 1. Sample of dot patterns symmetry.

(b). Bilateral

Sym.

(d).Double

for asymmetry,

Sym.

Symmetry

bilateral,

horizontal,

and double

image of the left half (Fig. lb) ; (c) Horizontal Symmetry. The bilateral patterns were turned 90”. The direction of turn was randomly determined. Thus, the bilateral and horizontal patterns were identical in all respects but in orientation (compare Fig. lb with lc) ; and (d) Double Symmetry. Only the positions of the dots in the upper left quadrant were determined independently. The rest of the dots were placed so that they were symmetrical both horizontally and vertically (Fig. Id). For each mode, seven different patterns were generated and six black and white photographic copies for each pattern were obtained. One copy was mounted on cardboard to be used as a model in the sorting task. The other five copies were pasted on playing cards; these comprised the deck to be sorted. Apparatus. Seven rectangular boxes, one for each model card, were put together side by side. Above these boxes a panel was installed to hold the cardboard with the model cards. A photograph of the apparatus, as viewed by the S, is shown in Fig. 2.

mirror

INFORMATION-REDUCTION

TASKS

197

Procedure. Each S was tested individually. Sitting in front of the apparatus, the S was presented with the model panel and corresponding deck of cards. To counterbalance carryovers of fatigue, practice or boredom effects, each S was presented with a different permutation of the four modes. The examiner instructed the S to sort the cards by matching them with the model cards as quickly as possible. Following any questions by the S, the instructions for speed and accuracy were reemphasized. For each S, the time for sorting and the errors in matching were recorded for each mode.

FIG. 2. T&kg

appuntus

Statistical analysis. Time and errors were analyzed by multivariatc analysis of variance with repeated measures. To stabilize the variance the time scores were replaced by their reciprocals and the error scores by their square roots (Edwards, 1963). The nature of the differences was explored by means of discriminant analysis (Jones, 1960).

EXPERIMENT

I

Subjects. Twenty-four children attending upper elementary grades served as 8s. Results. The mean time and error scores are presented in Fig. 3. The variance and covariance matrices for the transformed scores and the mean squares and cross-products matrices are given in Table 1 and 2. The differences between the centroids of the four modes was statistically significant (Fs,Isz = 330.29; p < .OOl). To explore the source of this difference, discriminant analysis was performed.

198

IOANNIS

PARASKEVOPOUI,OS

6 Upper Qradrr

Oou blr

C

Horiz.

Bilat.

Atym.

I co : a a w

Upprr

Grader

2 ; A

Fm. 3. Mean time and error scores of the four modes for upper grades and kindergarten children.

TABLE VARIANCE

AND

COVARIANCE

1

MATRICES

OF TIME

AND

Upper elementary grades Mode Double Bilateral Horisontal Asymmetrical

Time .3437 - .3053 .1999 .1612 .2128 - .0499 .3071 1.0597

o All numbers have been multiplied

70.2260 79.8115 28.6244 by 100.

ERROR

SCORES’

Kindergarten

Errors 88.9711

elementary

Time .

.1062 - .9554 .2364 - 1.0911 .0877 -1.5824 .1529 - .7525

Errors 20.6654 12.8869 60.9876 9.7684

INFORMATION-REDUCTION

TABLE MEAN

Variables

SQUARES

AND

CROSS-PRODUCTS

2

MATRICES

Time Errors Time Errors

TIME

OF

AND

ERROR SCORES~

Kindergarten

Upper elementary grades Subjects

Time Errors

199

TASKS

Subjects

.6213

170.1207

1.4620

.6360 -5.3420

ndf 23

Modes 2.9016

15.58

I, l1.f .-I

16, x’J’L2

rul,f :-:

68

Modes .2929

nc!f

-33.7038

595.87‘2

1

-2.0710

3

Error term .16“8

Error term

.3185

36.3888

ndj’

.o’L13

69

.0281

tulj~ 19. cKJ49

I.5

L’Mean squares and cross-products values have been multiplied by 100. The first discriminant function accounted for 93% of the variance. Each variable accounted for equal portions of the discriminatory power of the function; time accounted for 51% and errors for 49%. This discriminant function was Vu = .0642 (Errors) - .09979 (Time). Large scores on a discriminant function indicate that performance is relatively high on variables with positive coefficients and relatively low on variables with the negative coefficients. Inversely, small discriminant scores indicate that performance is relatively low on variables with positive coefficients and high on variables with negative coefficients. The time scores, however, were transformed by reciprocal transformation; thus, small transformed scores signify large scores in the original scale. Therefore, large scores on the obtained discriminant function indicate both large Time and Error scores; inversely, small discriminant, scores indicate both small Time and Errors scores. Figure 4 presents the order of the mean discriminant scores for the Asym. _

poublr

ljor!z. Bilat. Grodrr

i) Upper

A8Ym.

lioriz.

Doublr Bilat.

ii)

00

.05

Kindrrgarton

.I0 Mean

Dircriminant

.I5

.20

Scorrs

FIG. 4. Mean discriminant scores of the four modes for upper elementary grades and kindergarten children. ’

200

IOANNIS

PARASKEVOPOULOS

four modes. The largest mean discriminant score was for bilateral and horizontal symmetry; the smallest was for asymmetry. These results suggest that the time spent, and the errors made sorting the asymmetrical patterns were the smallest of the four modes. The longest time spent and the most errors made were in sorting the bilateral and horizontal patterns. Discussion.. The results suggest that, unlike with memory tasks (Paraskevopoulos, in press), symmetry retards performance on discrimination. Similar retarding effects of the stimulus redundancy were observed in experimental situations involving reaction time with visual stimuli (Gregg, 1954) and recognition of visual forms and word lists (Anderson and Leonard, 1958; Dale and Baddeley, 1962; Deese, 1956). Discrimination probably requires the selection of but few unique characteristics of each stimulus (information-reduction task) which reliably differentiate one pattern from the others. This sampling strategy has been observed in several experimental situations (Forsman, 1966; Munsinger, 1965). The more irregular a stimulus is, the more unique characteristics it presents for selection. Randomness provides more and easier discriminable combinations of details and, thus, permits the S to reduce the amount of information he must process before he can respond correctly. Symmetry, with the constraints it introduces, limits the degrees of freedom for pattern variations, thus increasing the similarity and subsequent confusability. Therefore, the retarding effects of redundancy on discrimination can be attributed to the differences in homogeneity between symmetrical and asymmetrical patterns. The nondifferential performance on bilateral and horizontal symmetry bears out the notion of within-mode pattern homogeneity. The bilateral and horizontal patterns in the present experiment were identical in all respects but in orientation. The practically equal performance on these two modes might be due to the fact that both modes provided equal probabilities for distinctive figure cues. It was expected, under the premise that the amount of redundancy is in direct relationship to confusability, that the double symmetry patterns being the most redundant, would be the most difficult to sort. The results, however, did not support this expectation. Double symmetry was harder to discriminate than asymmetry but easier than either bilateral or horizontal symmetry. This incongruent finding might be explained in terms of extreme easiness of the double symmetry patterns of the present complexity for the subjects tested. As the subjects themselves reported, in sorting asymmetrical, bilaterally, and horizontally symmetrical patterns, they tried to locate parts of the patterns which were distinct and to match the patterns in terms of these parts. But, in classifying the double symmetry, they “worked” with the whole pattern.

INFORMATION-REDUCTION

TASKS

201

It seems that the present complexity was not sufficient to force the subjects to encode only parts while soring double symmetry. The informa.tion load of the double symmetry with 8 dots was far below the subjects’ capacity. In another experiment Paraskevopoulos (1967) found that the mean errors in recall for these patterns was negligible. To test the hypothesis of light information load two alternatives were offered: (a) To const)ruct more complex double symmetry patterns (probably 16-dot patterns) and to administer them to the same subjects; or (br to use the stimuli of the present study with younger children. The second alternative was followed and carried out in Experiment II. EXPERIMENT

II

Subjects. Six 5-year-old children served as Ss. In a recall experiment t Paraskevopoulos, in press) it was found that kindergarten children made substantial number of errors in reproducing from memory g-dot patterns and that the mean error differences among the four modes were statistically different. It was, therefore, assumed that the load of the g-dot patterns was far beyond the capacity of kindergarten children. Results. The mean error and time scores are presented in Fig. 3. The variance and covariance matrices and the mean squares and crossprodurts matrices are presented in Tables 1 and 2. The differences between tlic centroids of the four modes were stat,istically signifirant (Fc,:cs = 20.18; p < .OOl) . Discriminant analysis yielded the function T’k = 9094 (Errors) + 1.000 (Time) accounting for 99% of the variance. The mean discriminant scores for the four modes are presented on Fig. 3. The smallest mean discriminant score was, as in the case of the upper elementary school children, for asymmetrical patterns indicating that the least time and fewest (rrors were made in sorting asymmetrical patterns. The mean diseriminant score for double symmet.ry was the largest indicating that the t.ime spent and errors made in sorting the double symmetry patterns mere the largest of all modes. Bilateral and horizontal patterns were of intermediate difficulty. The findings suggest’ed that whenever the complexity of the input is sufficient to allow Ss to decode only parts of thr input, the retarding effect of redundancy on discrimination is direct]? related to the amount of redundancy. Consistently in Experiments I and II and in a pilot study (Paraskevopoulos, 1967) with 8-year-olds it was found that symmetrical patterns were more difficult to sort than asymmetrical patterns. This findings suggests that the retarding effects of redundancy on the performance of information reduction tasks is independent of the ,$’ rhronological age.

202

IOANNIS

PARASKEVOPOULOS

REFERENCES

N. S., AND LEONARD, J. A. .The recognition, naming, and reconstruction of visual figures as a function of contour redundancy. Journal of Experimental

ANDERSON,

Psychology, ATTNEAVE,

1958, 56, 262-270.

F. Symmetry,

of Psychology,

information,

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and memory

for patterns. American

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H. C. A., AND BADDELEY, A. D. Alternatives in testing recognition memory. Nature Lond., 1962, 196, 93-97. DEESE, J. Complexity of contour in the recognition of visual form. USAF W$DC TR 56-60, February, 1956. EDWARDS, A. L. Experimental design in psychological research. New York: Holt, 1963. FoRSMAN, R. G. Age differences in the effects of stimulus complexity and redundancy on pattern discrimination in a visual search task. Unpublished doctoral dissertation, University of Illinois, 1966. GREGG, L. W. The effect of stimulus complexity on discriminative responses. D.~LE,

Journal

of Experimental

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1954,48,

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JOSPS, L. V. Some illustrations of psychological experiments designed for multivariat,e statistical analysis. The Psychometric Laboratory, University of North Carolina, Chapel Hill, N. C., 1960. MTJNSINGER, H. Tachistoscopic recognition of stimulus variability. Journal oj Experimental

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Psychology,

1965, 2, 186-191.

I. N. Symmetry: its effects on recall, preference and discrimination of visual pattern in relation to age and intelligence. Unpublished doctoral dissertation. University of Illinois, 1967. PARASHEVOPOULOS, I. N. Symmetry, recall and preference in relat,ion to chronological age. Journal of Experinzental Child Psychology, 1968, 6, 258-264. POSNER, M. I. Memory and thought in human intellectual performance. British Journal of Psychology, 1965, 56, 197-215. PARASKEVOPOULOS,