Children's size judgments when size and distance vary: Is there a developmental trend to overconstancy?

JOURNAL

OF EXPERIMENTAL

CHILD

PSYCHOLOGY

22, 23-39 (1976)

Children’s Size Judgments When Size and Distance Vary: Is There a Developmental Trend to Overconstancy? MARTHA TEGHTSOONIAN ANDJANE B. BECKWITH Smith College A review of the experimental literature on size constancy in children shows that studies permitting unrestricted viewing in natural settings provide only limited support for the hypothesis, proposed by Wohlwill, of a developmental trend from under- to overconstancy. A study is reported in which subjects aged 810 18 years made magnitude estimations of height for targets whose height and distance from them varied. For distances up to 15 m, and heights from 5 to 50 cm, size constancy prevailed at all ages: The same number was assigned to a given height at every distance. If a developmental trend exists, it requires either younger subjects or greater distances to be revealed.

In daily functioning, we seldom act as if a far large object were a small one or a near small one large; in general, our behaviors are appropriate to the sizes of objects in our environment, regardless of how far or near to us they are. But laboratory studies have led some to conclude that distance does exert an influence on apparent size; in particular, it has been generally accepted that adult performance under “objective” instructions is marked by overconstancy (see, for example, Epstein, Park, & Casey, 1961; Wohlwill, 1963,197O; Baird, 1970). However, one of us (M. Teghtsoonian, 1974) has recently argued that the evidence for overconstancy in adults is neither compelling nor extensive and that constancy characterizes adult perceptual functioning. Indeed, Joynson, Newson, and May (1965) have found overconstancy to be the exception rather than the rule, and a recent extensive series of studies by Leibowitz and Harvey (1967,1969) has found only a constant degree of size overestimation, but no overconstancy, over a wide range of distances. One class of explanations for adult size constancy supposes that a person learns through experience to “correct” retinal size by information about distance; these explanations predict that in infancy, perceived size is largely influenced by retinal size, but that, since the child gains relevant experience as he grows older, he gets better at making the distance The research on which this report is based was supported in part by an award to the second author from a Sloan Foundation grant to Smith College and by grant MH 20047-01 from National Institute of Mental Health. We thank the staff and students of the Campus School of Smith College for their cheerful cooperation with us. Reprint requests should be sent to M. Teghtsoonian, Clark Science Center. Smith College, Northampton, Mass. 01060. The second author is now at Tulane University. 23 Copyright All rights

@ 1976 by Academic Press. Inc. of reproduction in any form reserved

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“correction.” In summarizing developmental trends in space perception. Wohlwill (1963, 1970) reached conclusions consistent with such learningthrough-experience hypotheses: (1) The primary development of size constancy occurs during infancy; (2) from early childhood to adulthood. a secondary development from underconstancy to overconstancy occurs, in the perception both of size and distance; (3) the degree of underconstancy or overconstancy depends not only on age but on distance, so that even young children exhibit constancy for short distances, and even adults exhibit underconstancy for long distances. Wohlwill (1963), of course. provided supporting data for these hypothesized trends from a variety of sources. His first conclusion, that size constancy develops during infancy, is consistent with Bower’s (1964) finding that retinal angle alone does not control the responding of 70- to 85-day-old infants to an object whose size and distance may differ from the original discriminative stimulus, but that underconstancy is exhibited by these subjects, since they respond at a lower rate to a test stimulus whose size is the same as, but whose distance is greater than, that of the SD. Wohlwill’s second conclusion, that underconstancy changes to overconstancy from childhood to adulthood, follows from the belief that underconstancy characterizes infants whereas overconstancy characterizes adults. However, if it is correct that overconstancy in adults is a doubtful phenomenon (M. Teghtsoonian, 1974), a review of studies using child subjects seems in order to evaluate the hypothesized developmental trend from under- to overconstancy. Two criteria were invoked in deciding what studies to consicter. (I) Our primary interest was in performance in natural environments; therefore, any experiment that used reduced settings or restricted viewing by fixing the head or covering one eye was eliminated from consideration. Such studies can be of interest and importance in analyzing the size-distance relation, but they do not provide a description of normal perceptual functioning. Indeed, experimental manipulation of setting and viewing conditions can, by appropriate selection of parameters, produce nearly any functional relation between judged size and distance (cf. Vogel & M. Teghtsoonian, 1972). An invocation of this criterion rules out studies by Cohen, Hershkowitz, and Chodack (1958). Piaget and Lambercier (1943a, 194313, 1946, 1951, 1956), and Lambercier (1946a, 1946b). In fact, there is a surprising paucity of studies of children’s size judging in natural settings with unrestricted viewing. (2) Of the studies that do approximate normal conditions, several do not meet a second criterion that an experiment should present the standard for judgment at several distances. As Wohlwill(l963) has pointed out, “If we consider that the concept of size constancy refers to the tendency of perceived size to rernuin invariant under changes in distance, it becomes apparent that, strictly speaking, it should be measured by obtaining size matches over a range of distances” (pp. 280-281). This is not a mere

CHILDREN’S

SIZE

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JUDGMENTS

methodological nicety, since an inequality between standard and matched comparison can be attributed either to a failure in constancy OYto an error in size estimation that is independent of distance (for a more extended discussion of this point, see M. Teghtsoonian, 1974). Thus, in the studies of Piaget and Lambercier (1943a, 1943b, 1946, 1951, 1956), Lambercier (1946a, 1946b), Zeigler and Leibowitz (1957), and Leibowitz, Pollard, and Dickson (1967) (the last two varied standard size and distance concomitantly, so that the same standard never occurred at two distances), it is not possible to decide whether the results indicate a change in matched size that depends on distance, or simply errors of underestimation or overestimation that are proportional to size but independent of distance. Among the studies using child subjects that satisfy these two criteria are those of Beyrl’ (1926), Jenkin and Feallock (1960), and Rapoport (1969). Of these three studies, two showed no change with age for children (between 8 and 14 years for Jenkin and Feallock, between 5 and 9 years for Rapoport). Jenkin and Feallock demonstrated constancy in children, overconstancy in adults. Rapoport demonstrated underconstancy in children, constancy in adults (although overconstancy could have been present but undetected). Both studies used small standard sizes (heights of 4 in. or less) and short distances (20 ft or less); thus the generality of their findings is limited. The only study that demonstrated consistent development is that of Beyrl, whose data indicate a large and orderly change, for judgments of a single size of standard (height 10 cm) over distances 2-11 m, from marked underconstancy in 2-year-olds to near constancy in IO-year-olds and adults. Thus, Wohlwill’s (1963, 1970) hypothesis of a developmental trend to overconstancy receives limited support from those few studies that permitted unrestricted viewing in natural settings and that used at least two separations between standard and comparison. However, a systematic evaluation of the hypothesis requires parametric studies that vary size and distance over considerable ranges for different ages, to assess the functional relation between the judged size and the distance of a target object of fixed size. The study to be reported here varied both size and distance over a ten-to-one range, and used the method of magnitude estimation (Stevens, 1956); subjects were asked to match numbers to the heights of rectangles that appeared at different distances from them, and also to match numbers to the distances of these target objects. The advantages of the direct psychophysical methods in studying size constancy have been detailed (R. Teghtsoonian and M. Teghtsoonian, 1970b): “(a) they permit the integration of questions about size constancy into the broader framework of the perception of size: (b) they allow the ex1 Neither of the authors reads German. the language our account is based on Wohlwill’s (1%3) description

in which Beyrl’s report of Beyrl’s study.

is written:

thus

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perimenter to dispense with a variable stimulus whose definite physical properties may exert undesirable constraints on judgments; (c) they enable the experimenter to obtain judgments of distance as well as size in the same situation with the same scaling techniques; and (d) they are quick and convenient” (p. 612). Despite these advantages, magnitude estimation may not be as useful a technique with children as for adults, although there are grounds for optimism in the outcome of a study by Dorfman and Megling (1966), showing that subjects 9- to 1 l-years-old could make magnitude estimations of loudness that were not different in exponent from those of adults. In the study reported here, subjects were ages 8, 10, 12, and 18 years. In the studies with adult subjects upon which the present study is modelled (R. Teghtsoonian & M. Teghtsoonian, 1970b), the exponent of the power function for area was the same at every distance. The apparent area of target objects of fixed area either increased slightly or remained invariant as distance increased up to 14 m. If, in the study to be reported here, adult subjects perform as they did in these previous studies, with constancy or slight overconstancy characterizing their judgments, Wohlwill’s (1963, 1970) hypothesis predicts that children’s judgments should exhibit underconstancy and that the youngest subjects should exhibit it to the greatest degree. The studies on which Wohlwill based his conclusions used size matching; i.e., the subject adjusts the size of a comparison figure to make it appear equal to the size of a standard figure; our experiment used number matching;i.e., the subject “adjusts” the sizes of assigned numbers to make them proportional to the sizes of standard figures. Figure 1 shows a schematic rendering of Wohlwill’s predictions adapted to an experiment in which number matching or magnitude estimation is the measure of apparent size: The distance from the subject of the target object is on the abscissa, and magnitude estimations of the size of the target object are on the ordinate. Constancy in adults is represented by a line with zero slope, indicating that the same number is assigned to a fixed target size as its distance from the subject increases; increasing underconstancy with younger ages is represented by lines with increasing negative slopes, indicating that smaller numbers are matched to a fixed target height as its distance from the subject increases. (Wohlwill’s hypothesis is not expressed quantitatively, so it is the relative placements of the functions that are specified). The primary purpose of the present study was to determine whether the outcome would conform to the prediction represented in Fig. 1. A second purpose was to compare size and distance scales obtained for children with those for adults. For adult subjects, apparent size is a power function of physical size (Stevens & Guirao, 1963). with exponent depending on the number of dimensions in the stimulus: Linear extents have an exponent of 1.0; areas, 0.8; volumes, 0.6-0.7 (M. Teghtsoonian, 1965). Only one size-scaling study has been carried out with child subjects; Siegel

CHILDREN’S

SIZE JUDGMENTS

DISTANCE

27

0F TARGET

FIG. 1. Outcome predicted by an extension of Wohlwill’s (1963) hypothesis concerning developmental trends in space perception to an experiment in which subjects of different ages make magnitude estimations of the height of a target of fixed height that occurs at varying distances from them.

and McBurney (1970) had subjects age 6 to 13 and adults match force of handgrip to line length. One can estimate from their data the exponent relating number to line length: Over all subjects, the value is 1.2, but there are age-related changes, with the youngest subjects having the highest exponents. For adults, apparent distance is a power function of physical distance with an exponent of 1.0 or less for outdoor settings (Gibson & Bergman, 1954; Gibson, Bergman, & Purdy, 1955; R. Teghtsoonian & M. Teghtsoonian, 1970a) and around 1.2 or higher for indoor settings (Kiinnapas, 1960; M. Teghtsoonian & R. Teghtsoonian, 1969) when a method of magnitude estimation is used. The only study that has used groups of different ages is that of Harway (1963); it was based on a method developed by Gilinsky (Note I), whose study included five children, 5- 11 years old. The differences between magnitude estimation and this method, in which the subject produces a series of equal-appearing intervals at increasing distances, makes it difficult to compare Harway’s results to those cited above. All his subjects showed increasing underestimation of a 1-ft interval as distance increased; 5, 7-, and IO-year-olds exhibited a larger error than 12-year-olds and adults. These results suggest the possibility that visual space is foreshortened for children of 10 and younger. A third purpose of this study was to see whether, in a cross-modal matching task, precision in judgment increases with age, as Gibson (1969) has suggested is characteristic of perceptual task performance. Siegel and McBumey (1970) found adults to be somewhat more variable than children in a cross-modal matching task, whereas Bond and Stevens (1966) found little difference. METHOD Stimulus Materials

The targets were 25 white cardboard rectangles; there were five heights (equally logarithmically spaced, at 5.08,9.14,16.5,29.7, and 53.6 cm), with

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each height occurring in five widths (25, 37.5. 50, 62.5, or 75 percent of its height). Each rectangle had a support attached to its back so that it could be placed on the floor with its base parallel, and its height at a 90” angle, to the floor. The distances used were equally logarithmically spaced at 1.52, 2.74, 4.88.8.53, and 15.2 m from the front legs of the chair on which the subject sat when making judgments. The room used was agymnasium about 17 m long. The subject sat at one end of the room looking out along an imaginary line about 3 m from one wall that ran from him to the opposite end of the room and along which the target rectangles were placed at the five distances, inconspicuously marked with tape on the floor. The entire gym was in full view ofthe subject; lighting was through windows along both sides of the room and from overhead lights. Procedure

The subject was seated so that the front legs of his chair were at distance zero. The following instructions were read: I’m interested in finding out how big things look to people of different ages. I’m going to show you some rectangles, like this one; they will be different heights and at different distances away from you, anywhere from right in front of you to way at the back of the gym. For each rectangle I show you, I want you to tell me how tall it looks, from the floor to the top of the rectangle, by giving it a number. You can give any number you want to the first rectangle; then. if the next rectangle is taller, you would give it a bigger number, and if it is shorter, you would give it a smaller number. And however much taller or shorter it is, make the number that much bigger or smaller. Then you will do the same for each of the other rectangles. The rectangles will be at different distances away from you, but it is how tall they are. and not how far away. that is important. Do you have any questions? (If the subject asked whether he should give his answers in inches and/or feet, the experimenter answered. “You may if you want to, but you don’t have to.“)

The 25 rectangles were presented in a randomly-determined order, different for each of the 16 subjects of a given age, but repeated across age groups. The five widths for each height were matched to the five distances randomly, with the restriction that each height occur once at each distance. This was intended to ensure that the subject could not recognize the same rectangle being presented at different distances and assign a remembered number to it. The experimenter placed a rectangle at the appropriate distance, then returned to a position about midway from nearest to furthest distance, and to one side of the line on which the target objects were placed. The experimenter signalled the subject, who assigned a number to the height of the rectangle and then looked away while the experimenter removed that rectangle and put the next one in place. Approximately 20 min was required to give instructions and obtain judgments for 25 rectangles. Then the following instructions for distancejudging were read:

CHILDREN’S

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JUDGMENTS

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So far you have been doing fine. Now I would like you to do something a little different. You have been assigning numbers to how tall the rectangles look: now I want you to assign numbers to how far away they look. The further away the rectangle looks. the bigger the number you should give it. Any questions?

A randomly-selected rectangle was placed at the five distances, one at a time and in random order. This portion of the procedure required about 5 min. Subjects Child subjects were students at the Smith College Campus School, a private school many of whose students are the children of cohege faculty. IQ scores are not available for these students. Subjects were selected from class lists to fall into specified age ranges; 8:0-9:0, IO:O-11:0, and 12:0- 13:O. All children who met theage criterion were run as subjects, and it was necessary to stretch the age boundaries somewhat to fill groups. Each age group had 16 subjects, with means and ranges as follows; 8:7 (8:0-9:l). IO:2 (9:8- ll:O), and 12: 1 (11:8- 13:9). Adult subjects were volunteers who received credit in an introductory psychology course for participating. The mean age of the 16 adults was 18 years (17-20). RESULTS

AND DISCUSSION

The height judgments were 1ogarithmicaIly transformed (a transformation that preserves the ratios of judgments, as well as tending to normalize response distributions of magnitude estimations and to equate their variances). Bartlett’s test for homogeneity of variance yielded F(4,15) = 3.09; p > .OS, so the log judgments were subjected to an analysis of variance. The results are easily summarized: of the main effects; Age, Target Height, and Target Distance, only Height showed a significant F (F(4,240) = 1281.6; p < .Ol); none of the two-way interactions was reliable, although the Age x Height interaction (F( 12,240) = 2.10; .05 < p < . 10) should be noted; the triple interaction was not reliable. Size Judgments

as a Function

of Distunce

Did apparent size show a systematic change as viewing distance increased? Fig. 2 shows the results separately for each age. At a given age, there are five curves, each one representing height judgments for a target of given physical height at each of the five target distances. (Height judgments, on the ordinate, are plotted on a logarithmic scale; target distance, on the abscissa, is on a linear scale.) Although there is variability, the overall impression given by Fig. 2 is that a given height appears about the same at 1.5 as at 15 m. That impression is born out by the analysis of variance of log height judgments: The main effect of Distance was not

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20-

ten

eight l -*

\

l -----m-------e

.“L.- .

1.

i4 IO 6

i4

6

0 TARGET

DISTANCE

(M)

FIG. 2. Number matches to target heights as a function of distance, with target height (shown in centimeters in the column at the right of the figure) as a parameter, for four ages. Distance of the target height from the viewer is shown on a linear scale. The geometric mean of the numbers matched to the target height is scaled logarithmically. In each age group,,each of 16 subjects made one judgment for each height-distance combination.

reliable, nor were the Age x Distance and the Age x Distance x Height interactions. For these 8- to 18-year-old subjects under these viewing conditions, apparent size was invariant with distance: that is, constancy prevailed. A clearer picture of the relation between apparent size and viewing distance emerges if height judgments are pooled over all five target heights; this is an acceptable procedure, since the analysis of variance showed that the Height x Distance interaction was not reliable. The pooling was accomplished by taking the geometric mean of all height judgments at a given target distance. Although the main effect of Age was not reliable, 12and 18-year-olds did use slightly larger numbers, and thus had higher mean judgments, than the two younger age groups; the overall geometric means

CHILDREN’S

SIZE JUDGMENTS

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FIG. 3. Number matches to target heights as distance varies, pooled across five target heights. for four ages. Each point represents the geometric mean of-80 judgments (5 heights x 16 subjects); the judgments were modulus-equalized by multiplying each subject’s judgments by a factor that made the geometric mean of his judgments equal to the grand geometric mean of all judgments (see text for discussion).

of height judgments for 8-, lo-, 12-, and 18-year-olds, respectively, were 3.2,3.2,4.1, and 4.1. To facilitate visual comparison, the functions for the four age groups shown in Fig. 3 were realigned by equating these geometric means across ages: Each function is positioned vertically so that its geometrio mean is 3.6. Figure 3 should be compared to Fig. 1, and two features should be noted. First, there is no systematic trend in size judgments with increasing distance for 8-, lo-, and lZyear-olds; neither do these ages show underconstancy (represented in Fig. 3 as in Fig. 1 by a line with negative slope) nor do they appear to be moving toward overconstancy (represented by a line with positive slope). Second, the 18-year-olds do show a consistent growth in judged size with distance, but the change is not reliable. These size-as-a-function-of-distance curves are similar to those reported by R. Teghtsoonian and M. Teghtsoonian (1970b) for their Experiment II, which used an identical design, presented irregular polygons as targets, and requested number matches to target area from a group of subjects drawn from the same population as the 18-year-aids in the present experiment; they found that number matches for a given target area were invariant with distance over the range 1.5- 14 m. The results agree in part with those of Jenkin and Feallock (1960), who showed constancy for ages 8 and 14, but the overconstancy exhibited by their adult subjects was not found. The results disagree in part with those of Rapoport (1969), who found underconstancy in 9-year-olds, and those of Beyrl (1926), who found a developmental trend from underconstancy at age 8 to near constancy at age 10 and for adults. The lack of agreement among these studies is not surprising, in view of the many differences in design, method, viewing situation, and stimulus identity and value, but this very diversity precludes any firm conclusion about the sources of disagreement.

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RELATIVE

AND BECKWITH

TARGET

HEIGHT

FIG. 4. Number matches to target heights, pooled over distances. for four ages. Both axes are scaled logarithmically. The points for S-year-olds are plotted against presented target height (in centimeters); for ease of display. each succeeding function is displaced horizontally by half a log cycle, so that ratios of target heights. but not their absolute values, are preserved. The ordinate shows the obtained values for number matches at each age. Each point represents the geometric mean of 80 judgments, 5 from each of 16 subjects. The fitted lines all have a slope of I. 10 and represent the least-squares fit to log number match, pooled over ages, as a function of log target height.

The present results provide no support for Wohlwill’s (1963, 1970) hypothesized developmental trend from under- to overconstancy. They by no means force its abandonment, for at least three reasons. First, the youngest subjects were 8 years; underconstancy might exist in younger subjects. The use of number as the matching continuum in this study placed a lower limit on the age of subjects; 8-year-olds are probably the youngest group who would be able to use numbers to match ratios of size. To extend our study to younger ages will mean the use of some other matching continuum, such as line length or sound pressure of noise (Bond & Stevens, 1969) which all ages can adjust with equal ease. A second reason to retain Wohlwill’s hypothesis is that the longest distance was 15 m; 8- to IZyear-olds might have shown underconstancy at greater distances. Indeed, Wohlwill (1963) concluded that degree of underconstancy depends both on age and distance, and that even young children may show constancy over short distances. If, in Fig. 3, we compare judgments made at the nearest distance to those at the furthest distance, 8- and lo-year-olds show a decrease in the mean judgment from 1.5 to 15 m, whereas 12- and 18-year-olds show an increase. At the furthest distance used, there are indications of a developmental trend, and it is an open possibility that distances greater than the 15 m used here would reveal it more clearly. Yet a third reason to hesitate is concluding that there is no developmental trend is that little is known about the effect of instructions on magnitude estimation of size. Gilinsky (1955) and Leibowitz and Harvey (1967, 1969)

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JUDGMENTS

33

have shown that with size matching, “objective” instructions produce quite different results from “apparent” and “retinal;” Rapoport (1967) has shown that after 13, but not before 9, years of age, “objective” instructions produce different results from “apparent.” Our instructions correspond most closely to “apparent,” which some authors believe favor constancy. Perhaps the use of “objective” instructions would produce overconstancy in older age groups (although it does not seem likely that it would produce underconstancy in younger ones). The ambiguity of these results relative to Wohlwill’s hypothesis, and the lack of agreement among the studies reviewed, points up the necessity for further research in a variety of natural settings, so that the functional relation between apparent size and distance can be precisely specified for wider ranges of age, size, and distance, and for different instructional sets. Size Scales

The geometric means of the height judgments pooled over distances are shown as a function of the target heights for the four ages in Fig. 4. The 12and 18-year-olds used numbers slightly larger than those used by younger subjects, but the lack of an Age effect indicates that these differences are not reliable. If power functions are fitted separately to the points for each age, the exponents are 1.05, 1.09, 1.23, and 1.06, for 8-, lo-, 12-. and 18-year-olds, respectively. However, the nonsignificant F for the Age x Height interaction indicates that the slopes do not differ among ages. Consequently the straight lines in Fig. 4 represent the single best-fitting power function for height judgments pooled over ages: Apparent

Height

= k Height’.‘O

The exponent of 1.10 means that height judgments are a slightly accelerating function of physical height. The value corresponds fairly well to exponents reported for adults- 1.OO(Stevens & Guirao, 1963), 0.98 (M. Teghtsoonian, 1965). and 1.09 (for the most closely comparable range, reported by R. Teghtsoonian and M. Teghtsoonian, 1971). The exponent slightly greater than 1.Omay reflect the small range of physical stimuli (10 to I), which acts to increase the exponent somewhat (R. Teghtsoonian, 1973). The striking aspect of these findings is the lack of change with age: 8-, IO-, and 12-year-olds exhibit apparent height scales that are like each others’ and those of adults. This is not surprising, given the phenomenal simplicity of length as a stimulus attribute; it is difficult to imagine what additional perceptual development might occur between 8 and 18 years to change length perception. It is reassuring, however, since it indicates that subjects as young as 8 years can follow instructions to assign numbers that are proportional to heights in such a way that their average response is no different from that of 18-year-olds.

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These results are in partial conflict with those of Siegel and McBurney (1970), who had subjects match force of handgrip to line length and number. If one analyzes their data in the way suggested by Stevens (1971) and described by Cross, Tursky, and Lodge (1975) to obtain the regression-free exponent relating number and line length, the result is that the exponent declines with age from 2.0 at age 6 to 0.8 for adults. However, ages 8, 9, 10, 1I, and 13 years have exponents I. 14, 0.8 1, 1.69, 1.06, and 0.83, respectively; the mean of 1.11 is close to that for the child subjects in this study. The possibility remains that a developmental trend would have been revealed in this study had younger subjects been used. Distance Scales The five distance judgments from each subject were transformed logarithmically, and the best-fitting straight line for them as a function of log target distance was determined by the method of least squares; the slope of this line is the exponent, and the additive constant the scale factor, of an individual power function. An analysis of variance of the individual exponents yields a nonsignificant F (F < 1) for the effect of age. Unlike the subjects in Harway’s (1963) experiment, these subjects showed no change in distance judgments between 10 and 12 years; to the contrary, the three younger ages and adults all judged distance in the same way. An analysis of variance of the individual scale factors also yields a nonsignificant F (F(3,60) = 1.15; p > .05) for the effect of age. The 12-year-olds used the

RELATIVE

TARGET

DISTANCE

FIG. 5. Number matches to target distances for four ages. Both axes are scaled logarithmically. The points for 8-year-olds are plotted against the presented target distances (in meters); for ease of display, each succeeding function is displaced horizontally by half a log cycle, so that the ratios of target distances, but not their absolute values, are preserved. The values on the ordinate for number matches are those obtained for each age. Each point represents the geometric mean of I6 judgments, one from each subject. The fitted lines all have a slope of 0.93 and represent the least-squares fit to log number match, pooled over ages. as a function of log target distance.

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35

largest, and 18-year-olds the smallest numbers, but the differences are not reliable. The functions for apparent distance are shown for each age in Fig. 5. The fitted line represents the single best-fitting power function for distance judgments pooled over age. As the exponent of 0.93 indicates, the function is slightly decelerating. The results are unlike those previously reported for adult subjects in an indoor setting; the exponents reported for apparent distance indoors are around 1.2 (M. Teghtsoonian & R. Teghtsoonian, 1969) and perhaps higher for a ten-to-one stimulus range. One possible explanation for this difference is that the subjects’ distance judgments were influenced by the prior height judgments. However, neither for all groups combined nor for each group separately was the correlation coefficient r between height exponent and distance exponent reliable (for ages 8, 10, 12, and 18, respectively, r(15) = +.42, -. 10, +. 12, and +.07, with p > .05; for all ages combined, r(63) = +.lO, p > .05). Apparently, the judgments of height did not exert a significant influence on the judgments of distance that followed them. In fact, a t test of the difference between the mean of individual distance exponents (0.93) and the mean of individual height exponents (1.10) shows that it is reliable (t(63) = 4.88; df = 63;~ -=c.Ol). The failure to obtain the expected value of the distance exponent is puzzling; we spectulate that it may be related to the relatively undifferentiated visual context provided by the gymnasium setting. It does not alter the fact that there is no change in distance exponent with age from 8 to 18 in this particular setting. Respovtse Variability

Gibson (1969, pp. 452-454) has suggested that, even when central tendencies do not differ among ages, a major developmental change may be an increasing precision in judgment on perceptual tasks. In our data, increasing precision might be reflected in better-fitting power functions for older subjects; a convenient measure of this is r*, which gives the proportion of the variance in log judgment associated with changes in log target height or distance. For height, the mean r* increased from 0.92 for 8-year-olds to 0.98 for 18-year-olds; an analysis of variance (F(3,60) = 6.50; p < .Ol) and a subsequent Newman-Keuls test showed that 18-year-olds differed reliably 0, 5 .05) from 8- and lo-year-olds. For distance, the mean r2 increased from 0.95 to 0.99 (F(3,60) x 4.11; p < .05), with the only reliable difference (p I: .05) between 8 and 18 years. We also asked whether response distributions for a given stimulus value are more variable for younger subjects. One difference revealed by the response distributions is that there is a progressive shift toward giving a number close to the target object’s actual height in inches (but not to its distance in feet) as the subject grows older: The height in inches of the

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TEGHTSOONIANANDBECKWITH

target predicts the modal number match for 18-year-olds. but not for 8-year-olds. The fact that each subject selected his own modulus in the number-matching task, and that different ages differed in their selection, means that response distributions may not be directly comparable across ages. To compensate for the free modulus, a modulus-equalization procedure was applied (each subject’s judgments at a given distance were multiplied by a factor transforming them so that their geometric mean equalled the geometric mean of judgments from all subjects at that distance). For height, modulus equalization produces similar distributions for 8- to 12-year-olds, but more compact distributions for 18-year-olds; the mean standard deviations of log judgments (pooled across heights and distances) are about 0.15 for the younger groups but 0.08 for the 18-year-olds. For distance, the effects of modulus equalization are similar, but the influence of age is attenuated; the mean standard deviation of the response distributions decreases only from 0.11 to 0.08 as age increases from 8 to 18. The analyses on variability of response as a function of age suggest three major conclusions: (1) For all age groups, the power functions fitted to individual height and distance judgments accounted for over 90% of the variance in those judgments, indicating the performance of younger subjects closely resembled that of older subjects. not only in central tendency but in precision of judgment. (2) The small but reliable increase in precision of height judgments with age was associated with an increasing tendency of older subjects to judge height in inches and with less intersubject variability of older subjects in numbers chosen for a given height. One may speculate that 18-year-olds have had more practice at judging height in inches and concomitant feedback about their correctness than younger subjects, and that this results in the use of a “memory inch” as a standard, greater precision in estimating the number of “memory inches” in a given target height, and greater similarity among subjects in their estimates. (3) Older subjects are not more likely to give numbers closely approximating target distance in feet, and there is less age-related difference in precision and response variability of distance judgments. Perhaps there is a greater increment in practice between 8 and 18 years in making height judgments than in making distance judgments, and perhaps also less feedback available as to the correctness of distance judgments, especially for longer distances. Suitability

of Magnitude

Estimation

for Developmental

Studies

The outcome of this study shows that magnitude estimation is a useful technique for subjects as young as 8 years. Experimenters found that subjects understood and followed instructions easily and appeared to enjoy

CHILDREN’S

SIZE JUDGMENTS

37

the task. The ability of all ages to command numbers adequate to match the stimulus ranges and the comparability of ages in precision of judgment confirm experimenters’ impression of the suitability of the method for child subjects. Possibly the youngest subjects would not be able to maintain comparable performance if stimulus ranges were increased beyond the ten-to-one range of the present study. Although subjects younger than 8 years are unlikely to have had the instructions and experience that allow them to use the ratio properties of numbers in the matching situation, Bond and Stevens (1969) showed that 5-year-olds can match brightnesses to loudnesses, and Siegel and McBurney (1970) that 6- to 13-year-olds can match handgrip to line length, so that cross-modal matching may allow the use of direct psychophysical techniques with much younger subjects by substituting other matching continua for numbers. SUMMARY

AND CONCLUSIONS

The apparent size of a target object when the physical height of the target and its distance from the viewer were varied was measured by the method of magnitude estimation: Subjects 8, 10, 12, and 18 years old assigned numbers to represent the height and distance of target objects that varied from 5 to 54 cm in height, and from 1.5 to 15 m in distance. Subjects of all ages could perform the required task with adequate precision. Apparent size and distance scales were the same for children as for young adults: apparent height increased as a slightly accelerating function of physical height, whereas apparent distance increased as a slightly decelerating function of physical distance, for all ages. Apparent height did not change with distance at any age. This outcome does not provide support for the hypothesis that there is a developmental trend from underconstancy to overconstancy, but rather shows that constancy characterizes size judgments not only of young adults but of children; it does not rule out the possibility that younger subjects may exhibit, or greater distances induce, underconstancy. REFERENCES Baird, J. C. Psychoph.vsicu/ ancc/ysis qf visucrl space. Oxford: Pergamon Press, 1970. Beyrl. G. ijber die Grossenauffassung bei Kindern. ZPifschriffir P&ro/ogie. 1926. 100, 344-371. Bond. B.. &Stevens, S. S. Cross-modality matchingofbrightness to loudness by 5-year-olds. Perception

& Ps.vchophysics,

1%9.

6, 337-339.

Bower. T. G. R. Discrimination of depth in premotor infants. Psychononzic Science, 1964.1, 368. Cohen, W., Hershkowitz, A.. & Chodack. M. Size judgment at different distances as a function of age level. Child Development. 1958, 29, 473-479. Cross. D. V., Tursky. B.. & Lodge. M. The role of regression and range effects in determination of the power function for electric shock. Perception & Psychophysics, 1975, 18, 9- 14.

38

TEGHTSOONIAN

AND BECKWITH

Dorfman. D. D.. & Megling. K. Comparison of magnitude estimation of loudness in children and adults. Purce@ort & P.ryc.ho~p/‘?sics, 1966, 1, 239-241. Epstein. W.. Park, J., & Casey. A. The current status of the size-distance hypotheses. Psychologicul Bulletin, I % I , 58. 491-5 14. Gibson, E. J. Principles of perceprlctrl /rtr~lin,q trnd de\‘~lo/>mrnt. New York: AppletonCentury-Crofts. 1969. Gibson, E. J.. & Bergman. R. The effect of training on absolute estimation of distance over the ground. Jortrnul of E.~perimentul Psychology, 1954. 48, 473-482. Gibson. E. J., Bergman. R.. & Purdy. J. The effect of prior training with a scale of distance on absolute and relative judgments of distance over ground. Journul of’ E.vperimenfuf P.~.vcholog?‘,

1955. 50, 97- 105.

Gilinsky.

A. S. The effect of attitude upon the perception of size. Ameriwn Journul of Pswholog~. 1955, 68, 173- 192. Harway, N. I. Judgment of distance in children and adults. ./o~rr~/l of Experimentul Psychology. 1963. 65, 385-390. Jenkin. N.. & Feallock. S. M. Developmental and intellectual processes in size-distance judgment. Amrricun Journul of Psychology, 1960. 73, 268-373. Joynson, R. B., Newson, L. J.. & May. D. S. The limits ofoverconstancy. Qlrcrrreu/~Jolrrntr/ of Experimentul Psycholog.~, 1965. 17, 209-2 16. Kiinnapas. T. Scales for subjective distance. Scundinuriun Journul qf’Psycho/o,q.v. 1960. 1, 187- 192. Lambercier, M. Recherches sur le developpement des perceptions: VI. La Constance des grandeurs en comparaisons sCriales. Archives de Psychologie, Gen>r~e. 1946a. 31, I-204. Lambercier. M. Recherches sur le dCveloppement des perceptions: VII. La configuration en profondeur dans la Constance des grandeurs. Archirjes de Psychologie. Gen&,e, 1946b. 31, 287-323.

Leibowitz. H. W., & Harvey, L. O., Jr. Size matching as a function of instructions in a naturalistic environment. Journul of E.rperimental Psychology, 1967, 74, 378-382. Leibowitz. H. W., & Harvey. L. O., Jr. Effect of instructions, environment, and type of test object on matched size. Journal of Experimenrul Psychology. 1969, 81, 36-43. Leibowitz. H. W., Pollard, S. W.. & Dickson. D. Monocular and binocular size-matching as a function ofdistance at various age levels. AmericrJnJoltrnuloJ’Psvchology. 1967.80, 263-268. Piaget. J.. & Lambercier. M. Recherches sur le developpement des perceptions: II. La comparaison visuelle des hauteurs g distance variables dan le plan fronto-parallkle. Architaes de Psychologie. Get&se, 1943a, 29, 173-253. Piaget. J., & Lambercier. M. Recherches sur le developpement des perceptions: III. Le probleme de la comparaison visuelle en profondeur (Constance de la grandeur) et l’erreur systematique de I’Ctalon. Archivrs de Psychologie. Gen&e, 1943h, 29, 253-308. Piaget, J., & Lambercier. M. Recherches sur le d6veloppement des perceptions: VIII. Transpositions perceptives et transitivite operatoire dan les comparaisons en profondeur. Archives de Psychologie, Gent-se. 1946. 31, 325-368. Piaget, J., & Lambercier. M. Recherches sur le dCveloppement des perceptions: XII. La comparaison des grandeurs projectives chez I’enfant and chez l’adulte. Archi,,e.s de Psychologie, Gen3ve. 1951, 33, 8l- 130. Piaget, J., & Lambercier. M. Recherches sur le dCveloppement des perceptions: XXIX. Grandeurs projectives et grandeurs rCelles avec ttalon &loigne. Archilvs de Psychologie, Geneve. 1956, 35, 257-280. Rapoport, J. L. Attitude and sizejudgment in school age children. Child De\Be/opment. 1967. 38. 1187- 1192.

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SIZE JUDGMENTS

39

Rapoport. J. L. Size-constancy in children measured by a functional size-discrimination task. Journal of Experimental Child Psychology, 1969, 7, 366-373. Siegel, A. W., & McBumey, D. H. Estimation of line length and number: A developmental study. Journal of Experimental Child Psychology. 1970, 10, 170- 180. Stevens, S. S. The direct estimation of sensory magnitudes: Loudness. American Journal of Psychology. 1956,69, l-25. Stevens, S. S. Issues in psychophysical measurement. Psychological Rer+ws. 1971, 78, 426-450.

Stevens, S. S., & Guirao, M. Subjective scaling of length and area and the matching of length to loudness and brightness. Journal of Experimental Psychology, 1%3,66, 177- 186. Teghtsoonian, M. Thejudgmentofsize.American JournalofPsychology, 1%5,78,392-402. Teghtsoonian, M. The doubtful phenomenon of over-constancy. In H. R. Moskowitz. B. Scharf, &J. C. Stevens (Eds.), Sensation and measurement. Dordrecht. Holland: D. Reidel, 1974. Teghtsoonian. M., & Teghtsoonian, R. Scaling apparent distance in natural indoor settings. Psychonomic

Science,

1969,

16, 281-283.

Teghtsoonian,

R., & Teghtsoonian, M. Scaling apparent distance in a natural outdoor setting. Psychonomic Science, 197Oa, 21,215-216. Teghtsoonian, R., & Teghtsoonian. M. The effects of size and distance on magnitude estimations of apparent size. American Journal OfPsychology, 1970b. 83,601-612. Teghtsoonian, R., & Teghtsoonian, M. The apparent lengths of perimeters and diameters define a ratio smaller than pi. American Journal of Psychology, 1971, 84, 437-438. Teghtsoonian. R. Range effects in psychophysical scaling and a revision of Stevens’ law. American

Journal

of Psychology,

1973, 86, 3-27.

Vogel, J. M?, & Teghtsoonian, M. The effects of perspective alterations on apparent size. and distance scales. Perception & Psychophysics, 1972, 11, 294-298. Wohlwill, J. F. The development of “overconstancy” in space perception. In L. P. Lipsitt & C. C. Spiker (Eds.), Advances in child development and behavior (Vol. I). New York: Academic Press, 1963. Wohlwill, J. F. Perceptual development. In H. W. Reese&L. P. Lipsitt(Eds.), Experimental child psychology. New York: Academic Press, 1970. Zeigler, H. P., & Leibowitz, H. Apparent visual size as a function of distance for children and adults. American Journal of Psychology, 1957, 70, 106- 109.

REFERENCE NOTES 1. Gilinsky, A. S. The effect of growth on the perception of visual space. Paper read at Eastern Psychological Association, New York, April l%O. RECEIVED: April 14, 1975: REVISED: October 1, 1975.