Size-distance perception in preschool children

JOURNAL

OF EXPERIMENTAL

Size-Distance

CHILD

PSYCHOLOGY

Perception EDWARD

MAURICE Brandeis

27, 166-184 (1979)

in Preschool

Children

TRONICK

HERSHENSON University

Children between three and six years of age matched the “apparent” and “real” size of familiar and unfamiliar objects 3, 6, or 9 feet away. Prior to the experimental sessions, the children were divided into two groups: (a) those who could distinguish the phenomenal from the real sizes of the arcs in the Jastrow illusion (the “Realists”) and (b) those who could not (the “Phenomenalists”). The results suggest that all children perceived size constancy up to distances of 9 feet solely on the basis of visual information.

The perception of size-at-a-distance or “size constancy” remains a problem for two different reasons: first, the two major theoretical positions propose different conceptions of the nature of constancy, and second, experiments on size-distance perception have not produced unequivocal results, regardless of theory. The theoretical differences are more easily understood; the psychophysicists or “flow” theorists, attempt to show that perceptual constancy can be produced solely by analysis of the optical input, whereas the empiricists, or “cue” theorists, attempt to show that constancy is a resultant of processes that combine information from the optic input with information from other sources. Leibowitz’ (1974) recent proposal that three different kinds of mechanisms are implicated in size-distance perception is a good example of the latter approach. He suggested that size perception is governed by (a) “oculomotor adjustments” of accommodation and convergence; (b) “perceptual learning” involving visual information; and (c) “cognitive learning” involving the nature of objects in the world. Indeed, Leibowitz This research was supported by Grant No. 19751 from the National Institute of Mental Health, USPHS, DHEW. Requests for reprints should be sent to Edward Tronick, Department of Psychology, University of Massachusetts, Amherst, MA 01003. 166 0022~0965/79/010166-19.$02.00/O Copyright @ I979 by Academic Press. Inc. Ail rights of reproduction in any form reserved.

SIZE-DISTANCE PERCEPTION

167

and coworkers demonstrated that the information provided by the first mechanism, oculomotor adjustments, is sufficient to account for size constancy up to distances of about one meter (Leibowitz & Moore, 1966: Leibowitz, Shiina, & Hennessy, 1972). The operation of the second mechanism, perceptual learning, may be inferred by comparing the performance of children with that of adults in size-distance experiments. For example, Leibowitz noted that children show progressively less size constancy with increases in distance of the stimulus object when given an unrestricted view of the visual scene (Leibowitz, Pollard, & Dickson, 1967), whereas adults produce similar functions only when viewing objects through a reduction screen that limits their vision to the stimulus object (Harvey & Leibowitz, 1967). Taken together, these observations suggest that perceptual development consists of learning to use the visual information provided by contextual stimuli in unrestricted viewing. Leibowitz’ proposal for a third mechanism, conceptual size, must also be based on inference, but more from an intuitive base than from an empirical one. This mechanism, being cognitive in nature, would be independent of stimulus input; it would draw information about distributions of sizes from structures in memory formed over the life history of the observer. Such things as verbal labels for objects, descriptive categories, or meaning structures that supply information about the “essential nature” of objects (the Transactionalists called this aspect of a stimulus its “thatness,” e.g., Ittelson, 1960) could also function in this manner by providing a boundary within which expected or probable sizes could occur. Size constancy is treated in an entirely different fashion within the framework of flow theory. In this view, visual space containing objects at different distances is perceived directly as a consequence of mechanisms available in the human eye-brain system (Gibson, 1950, 1966). These mechanisms analyze spatio-temporal transformations of the optic array (hence the term “flow”) to produce the three-dimensional properties of perceptual space. Within this context, size constancy is a property of perceived objects: an automatic consequence of the analysis of “higher level” invariants in the visual input. Lee’s (1974) description of “rigidity” is a recent instructive example of this approach. Rigidity is a property of perceived objects. It is explained as a direct consequence of certain relationships among points of stimulus texture projected upon a cylindrical surface: another way of saying that size and shape are perceived as constant over such transformations, or that size constancy is a property of the system. This interpretation ihuminates the difference between cue and flow theories: the latter assume that by taking motion into account, the optical stimulus includes, as an essential element, the changes in the positions of the optical texture elements

168

TRONICK

AND

HERSHENSON

over time. As a consequence, properties such as rigidity (i.e., the constancy of size) may be elevated to the status of axioms. The claim is, of course, that when time is introduced as a variable, the optic array contains enough information to specify a unique percept of a rigid object moving in space. Cue theory, on the other hand, historically has rested upon the demonstration that the proximal stimulus does not provide enough information to produce a unique percept. Hence the need for “cues” or “clues” from other sources (perceptual, motor, or cognitive) in order to determine which object is “out there.” The difficulty in understanding the outcomes of size-distance experiments is more subtle. It is a direct consequence of the fact that “size constancy” is most frequently understood as describing the occurrence of a particular set of phenomenal events, namely, the perception of unchanging size with change in perceived distance from the observer. Given this definition, even the relatively simple task of size matching is difficult to interpret because different functions relating matched-size to distance are produced by different instructions (e.g., Leibowitz & Harvey, 1967, 1969: Rapoport, 1967, 1969), and it is not clear which of these functions best describes the perceptual experience of the observer. Three types of instructions have been used: (a) “objective” instructions, where the subjects are told to match the “real size” of the stimulus object: (b) “apparent” instructions, where subjects are told to match size according to the way the stimulus object “looks”: and (c) “retinal” instructions, where subjects are told to match “projective” or “visual angle” size. When adults perform a size-matching task, “objective” instructions generally produce matches approximately equal in size to the real (physical) size of the stimulus: “retinal” instructions produce matches approximately equal in size to the projective size or visual angle size of the stimulus object (slightly larger in “full cue” situations): and “apparent” instructions produce matches somewhere between these two, condition (Leibowitz & but generally closer to those of the “retinal” Harvey, 1967, 1969). In some instances, “apparent” and ‘&retinal” instructions do not produce functions which can be distinguished from one another (Leibowitz & Harvey, 1969; Rapoport, 1967). Given these findings, the problem for the theorist is clear: which function best describes what the observer sees? In discussing their results, Leibowitz and Harvey suggested that “apparent” instructions produce size matches that best represent the phenomenal experience of the observer (i.e., that the observer is indeed matching how a stimulus “looks” when asked to do so). Under this assumption, the size-distance functions obtained suggest that the phenomenal experience of size decreases with distance for adults. Moreover, the function is closer to projective size than to real size over a wide range of distances. If the function obtained under “apparent” instructions does indeed

SIZE-DISTANCE

PERCEPTION

169

represent adult size perception, then “size constancy” should not be called a “perceptual” phenomenon (i.e., perceived size is not constant with change in perceived distance). Thus, the simple act of evaluating the relationship between “experimental instructions” and “size-matching” affects our understanding of a fundamental property of perceived visual space. In this sense, it becomes more than a simple experimental description of the act of “size-matching”; it becomes a basis for eliminating the entire class of theories that incorporate size constancy as a fundamental property of perceived visual space. Furthermore, suppose it is correct to assume that matches made under “apparent” instructions reflect phenomenal size perception, and to conclude that size constancy is not a property of the phenomenal experience of the subject. What, then, produces the accurate real-size matches obtained under “objective” instructions? The answer to this question clearly calls for an additional channel of information to supplement the perceived size given by the visual system. Many possible sources have been identified, among them a “learned judgmental ability” based on cognitive (memorial) information (Leibowitz er al., 1967). or learned “attitudinal” states (Carlson, 1960, 1962; Carlson & Tassone, 1963). Empirical support for the position that size-constancy matches require learning has come more directly from experiments with children. Clearly, if a response in the adult is the result of learning, then the learning should be demonstrable in the young. In one such experiment, Rapoport (1967) measured size matches under two different instructions and found that two different size-matching functions were not obtained for young children but were produced by children beyond nine years of age. She concluded that this developmental trend represented the acquisition of the ability to assume an “objective attitude” (i.e., an improvement in the children’s judgmental ability). The finding that children’s size matches are more accurate when given binocular (as opposed to monocular) information (Leibowitz ef al., 1967) has also been cited as support for the empiricist position. Since adults do not show this monocular-binocular difference, adults may supplement the visual information with cognitive information, while children may rely primarily on purely visual input. Despite the chain of logic and the supporting data, there is some direct evidence that does not support Leibowitz and Harvey’s contention that “apparent” instructions produce size matches reflecting the phenomenal experience of the subject. Zeigler and Leibowitz (1957) instructed their subjects to tell the experimenter when the comparison stimulus “looks as high as” the standard stimulus (an “apparent” instruction). Adults produced size matches that were close to the real size of the stimulus for distances between 30 and 100 feet. Under the Leibowitz and Harvey interpretation, these data would indicate that adults &I manifest phenomenal size constancy. Moreover, Zeigler and Leibowitz found that chil-

170

TRONICK

AND

HERSHENSON

dren’s size-matches fell between real size and visual angle size for the same range of distances. Again, under the Leibowitz and Harvey interpretation, these data would indicate that phenomenal size increases with age until, in adulthood, it approximated the real size of the stimulus objects. Of course, one could also argue that the instructions of Zeigler and Leibowitz were not explicit: that they could have been interpreted to mean the same thing as the “objective” instructions and, consequently, that these data do not conflict with the notion that “size constancy” matches reflect the degree to which a subject has acquired the ability to use ‘&cognitive” information to interpret phenomenal experience. To avoid the need to interpret the subjects’ understanding of verbal instructions in size-matching, Rapoport (1969) used a size discrimination task, attempting to hold task difficulty, task “attitude” and motivation constant across ages. The task was described to children and adults as selecting the “biggest” or “littlest” triangles from sets of five, mounted on model trains, and then to “call the trains home” in order of decreasing or increasing size by pressing the appropriate switches. In the first part of the task, objects were at the same distances, and in the second part, objects were at different distances. Rapoport found that all age groups were highly accurate and that there were no differences due to age. But, once again, the problem of interpretation arises because the results do not unequivocally separate the various possible contributions to the discriminitive response. Rapoport assumed that the instructions and the equal-distance test produced an implicit understanding in the subjects that “size” was the only factor to be used. But how were the subjects to know whether the size they were supposed to evaluate in the discrimination task size? The initial corrections took place was “real” size or “apparent” while the subjects were learning the task in the equal-distance test, where real size and apparent size were identical. When the objects were placed at different distances (i.e., when the subjects were forced to “take distance into account” in making their size discriminations), they could have produced “size constancy” discriminations (correct size judgments) in two very different ways: (a) they could have perceived the appropriate sizes directly and simply based their discriminations on perceived size; or (b) they could have modified their perceptions with a “cognitive correction” for distance, Thus, Rapoport’s results simply document the fact that children as young as 54 years of age can make accurate size discriminations for objects at different distances. They do not explain the mechanism underlying the ability. Thus, there remains some confusion about the instructions used in size-matching experiments, the size-distance functions produced, and the relationships between the experimental results and the subjects’ phenomenal experience. The experiments reported below were an attempt to clarify these relationships for young children. The ability of preschool

SIZE-DISTANCE

PERCEPTION

171

children to distinguish real from phenomenal size in an illusion task was assessed prior to the experimental session. Some children were able to make this distinction, while other children were not. That is, some children describe the illusion only in terms of their phenomenal (illusory) experience, and cannot tell the difference between their experience and the real world (Braine & Shanks, 196.5; Piaget &L Szeminska, 1952). The fundamental assumption underlying the experiments was that children who could not differentiate real from phenomenal size in the Illusion Test would describe their phenomenal experience in a size-matching task, no matter what the instructions or the stimuli. The logic suggested that these responses must be “pure” phenomenal descriptions because these children did not yet possess the cognitive operations for distinguishing real and illusory sizes. Thus, the pretest provided an independent criterion for evaluating the subjects’ responses to “objective” and “apparent” instructions in the size-matching task. EXPERIMENT

I

Following Piaget (Piaget & Szeminska, 1952), Braine and Shanks (1965) have reported that, prior to about five years of age, children are generally incapable of making the distinction between real and phenomenal size. One of the illusions children saw in their experiment was the Jastrow illusion (see Fig. I). This illusion is typically demonstrated with two arcs of the same size, however, in order to make the difference between real and illusory sizes more distinctive, the arcs used in the test were slightly different in size. The arcs were shown in two positions: a superimposed position, where the smaller arc was placed on top of the larger arc, and an illusory position, where the smaller arc was placed below the larger arc. In the illusory position, the smaller arc looked larger than the larger arc. Braine and Shanks found that, when questioned about the real and phenomenal sizes of the arcs in the illusory conditions, children below the age of five equated the real size of the arcs with their phenomenal experience of the size of the arcs despite the fact that they had been given clear visual information in the superimposed position about the relative sizes of the arcs, and a verbal explanation that one of the arcs looked larger but was really smaller. Similar observations were made using other illusions. In this experiment, this developmental difference was exploited to provide an independent assessment of a young child’s performance in a size-matching task. Each child was given two tests prior to the exp&mental sessions: (1) a Size Judgment Test to determine whether they understood and could use correctly the words “bigger,” “smaller,” and “the same size as”; and (2) an Illusion Test to assess their ability to distinguish the real from the phenomenal sizes of the arcs in the Jzstrow illusion. The Illusion Test provided the basis for separating the children into two

172

TRONICK

AND

HERSHENSON

groups: (a) the Realists (those who could distinguish the phenomenal from the real sizes of the arcs) and (b) the Phenomenalists (those who could not). In the experimental test, size-matches were measured for objects at different near distances in a full-cue setting. The children were instructed to match size according to how big or small the objects “looked.” According to Braine and Shanks, the Phenomenalists interpret all instructions in the same way, and match phenomenal size. Thus, if the Phenomenalists’ size-matches corresponded to the real size of the stimulus object, it could be concluded that “size constancy” is a description of their phenomenal experience of size. On the other hand, if their size matches approximated projective size, then it could be argued that “projective size” is a description of the phenomenal experience of size in young children. Since the Realists did distinguish real from phenomenal size in their response to the Jastrow illusion, their size matches, made in response to “apparent” instructions, could also be interpreted as representative of their phenomenal experience of size. Thus, in a similar fashion, the conclusion that “size constancy” is a description of their phenomenal experience of size is warranted if their size matches approximated the magnitude of the real object. Indeed, if both groups gave similar size matches, it would lend more credence to the conclusion. On the other hand, if the two groups differed, then it could be suggested that the Realists’ responses were influenced by “cognitive” factors. Pretests Size judgment test. The stimuli in the Size Judgment Test were two sets of eight 6 in by 9 in cardboard cards with cutout forms pasted on them. In one set, the shapes were squares and in another set they were diamonds. Each card had a standard and a comparison form. The standard ranged from I$ to 1%in on a side in & in steps (the 1% in stimulus was omitted in order to limit the number of judgments while providing a 4 in maximum standard-comparison difference). Within each set of eight cards, four cards had a green standard and a yellow comparison, and four had the reverse. The separation of the shapes on the cards was approximately l+in. During testing, the tester sat opposite the child at a child-sized table and read the following instructions: “We are going to play a game called ‘Big and Little.’ I am going to show you two things, and I want you to tell me if one is bigger or smaller than the other or if they are both the same size.” The tester then held up one of the cards and asked: “Does the yellow (green) thing look bigger or smaller than the green (yellow) thing, or do they both look the same size?” The tester responded “Good” to all answers. No attempt was made to train the children. After recording the

SIZE-DISTANCE

PERCEPTION

173

response, the tester presented a new card and repeated the question, The order of presentation was balanced within subjects for left-right position of the standard and for color. Zllusion rest. The stimuli were two plastic arcs, one painted black and one painted white, made from & in thick plexiglass. The white arc measured 53’ and the black arc measured 50“. Figure 1 shows the two arcs which produced the Jastrow illusion in the superimposed, illusory, and nonillusory or real positions. When superimposed, the white arc extended

FIG. I. The two plexiglass arcs which produced the Jastrow illusion in the Illusion Test in the (a) superimposed, (b) illusory, (c) real positions.

174

TRONICK

AND

HERSHENSON

4 beyond the black arc. Both arcs measured 18 in from inner to outer circumference. There were five steps in the Illusion Test. The first step assessed the child’s susceptibility to the illusion. Steps 2 through 5 provided the child with increasingly more information about the difference between the real and the phenomenal (illusory) size of the arcs. All steps (i.e., changes in the amount of information presented) and all parts of steps (i.e., changes in the positions of the arcs) were repeated twice. To begin the test, the tester read the same instructions used with the Size Judgment Test. The arcs were then placed in the illusory position, where the real size (white bigger) and the phenomenal size (black bigger) did not correspond (Fig. lb). The tester then asked the “Phenomenal” question (i.e., the question which stressed how the arcs looked to the child): “Does one of these things /ooL bigger or smaller than the other, or do they look the same size?” If the child’s response indicated that the black looked bigger, an “illusory” response, the tester continued with the “Objective” question (i.e., a question about the physical dimensions of the arcs): “IS the white thing really bigger or smaller than the black thing, or are they both really the same size?” The two arcs were then moved into the nonillusory position (Fig. lc). In this position the phenomenal appearance corresponds to the objective reality [i.e., the larger (white) arc looks bigger]. The tester then repeated the Phenomenal and Objective questions. In the second step, the two arcs were superimposed so that real size and phenomenal size corresponded (Fig. 19f This position clearly provided enough information to distinguish real from phenomenal size. The tester then asked the Phenomenal and Objective questions, in that order. If the child did not notice the extension of the larger (white) arc beyond the smaller (black) arc, the difference was pointed out. The tester then separated the arcs into the illusory position and the two questions were repeated. If the child failed to answer the two questions correctly (i.e., in real terms) when the arcs were in the illusory position, the tester went to the third step, The arcs were again superimposed and the tester corrected the child saying: “No, you were wrong! Now you can see that the black thing is reall) smaller than the white thing. It only looked bigger before.” The arcs were again placed in the illusory position, and the Phenomenal and Objective questions asked. If the child again failed to respond correctly, the tester repeated the correction statement while the arcs were superimposed. In addition, the child was asked to place and hold his/her finger on the “really bigger thing” (Step 4). The arcs were then separated and the questions asked again. If the child still did not answer correctly, the final step was introduced. With the arcs superimposed, the tester repeated and emphasized

SIZE-DISTANGE

PERCEPTION

175

the correction statement. The arcs were then placed in the illusory position and the tester asserted: “I think the white thing is reuily bigger, even though it looks smaller. Which one do you think is reullv bigger and which one do you think looks bigger?” The steps were sometimes modified according to the child’s responses. For example, some children would insist that the two arcs were the same size when they were superimposed. In this case, the tester would have the child place a finger on the arc he/she said was bigger when separated. The arcs were then superimposed, producing a conflict between “really bigger” and “really the same size.” In other instances, a child might fail at Step 3 but pass at Step 4. In this case, the third step would be repeated to determine if the child could now pass that step.’ At the conclusion of the sequence, the tester and an observer independently judged whether the child discriminated real from phenomenal size in the Illusion Test. Those children who could make the discrimination were called “Realists” and those who could not were called “Phenomenalists.” It should be clear that the Phenomenalists were those children who persisted in describing the objective world in terms of their own phenomenal experience in the face of direct visual and tactile evidence to the contrary, and also in the face of statements by the tester to the contrary. Subjects. The subjects were six children, ages 4-O to 5-6, who were attending a nursery school. Pretest results. All children demonstrated an ability to understand and use size concepts correctly. Four of the six children were classified Phenomenalists and two Realists. In each instance, the tester and observer agreed in their categorization of the children’s behavior. Size Perception Viewing$eld. Two 3 ft by 6 ft tables were placed end-to-end to form a single viewing field 3 ft by 12 ft. The field was covered by a patterned cloth containing & in green dots in straight rows and offset columns on a white field. The viewing field was placed in a nursery school classroom which had recessed lighting that minimized shadows. Stimuli. The stimuli were four plywood triangles, two painted red and two blue, measuring 6 in. in altitude. The Standard stimuli (one red and one blue) had mounts along their bases permitting them to stand upright on the viewing field. A red or a blue Comparison stimulus was mounted on a mechanism which raised or lowered them through openings in the tables supporting the viewing field at distances of 3, 6, or 9 ft. The height of the ’ The corrective features of this procedure required a great deal of sensitivity to each child tested by the examiner, Amy Hershenson. She managed to test children in Experiments I and II without upsetting a single child, by making the procedure a game that the children enjoyed.

176

TRONICKANDHERSHENSON

Comparison above the viewing field was measured on a scale mounted on the back of the triangle. When moving, the Comparison traveled at a rate of 7 in. per min, Procedure. A child was seated at the end of the viewing field and presented with the Standard and Comparison at one of the nine possible distance combinations. The tester controhed the movement of the Comparison, At the beginning of a trial, the tester asked the Phenomenal question: “Should I make the blue (red) triangle bigger, or smaller, or leave it the same, so that it looks the same size as the red (blue) triangle?” When the child said “Stop.” the tester repeated the question to allow the child to modify the initial setting. When the child was satisfied with the size match, the next trial began. The child watched while the assistant changed the distances of the stimuli. Each child was assigned to a left or right position of the Standard, and to a color of the Standard (e,g., red Standard always on right). All Standard- and Comparison-distance combinations were used, and each combination received an ascending followed by a descending trial. The order of combinations was random. Results and Discussion

An analysis of variance was performed on size matches for subjects nested in groups (Phenomenalist or Realist) crossed with distance of the Standard, distance of the Comparison, and direction of the Comparison (ascending or descending). Direction of movement of the Comparison was the only variable that yielded a significant difference [F (1,4) = 34.68, p < .05]. The descending series produced size matches that were, on the average, 12% larger, and the ascending series produced matches that were 3% smaller than the real size of the Standard triangle. A Brunswik Ratio (BR) was calculated from the formula: BR = (PSE VA)/(C - VA), where PSE is the point of subjective equality, VA is the size of a visual angle match, and C is the size of a constancy match. The Brunswik Ratio transforms the PSE scale such that visual angle matches produce BRs of 0.00 and constancy matches produce BRs of 1.00. Mean Brunswik Ratios for ascending and descending matches at the three distances of the Standard are given in Table I for the Realists and the Phenomenalists separately. The children’s size matches were close to the real size of the stimulus object, especially for the ascending series. The descending series was not as accurate, especially for the 9 ft distance, but this directional difference was probably artifactual; it is not likely that the phenomenal size of an object changes as a function of the direction of movement of the Comparison stimulus. Since there were no differences in matched size between the Realist and Phenomenalist groups, it is possible to conclude that al] children saw the Standard as being the same size at al] distances tested. In summary, the size matches of children between the ages of 4 and 54

SIZE-DISTANCE TABLE MEAN

BRIJNSWIK

RATIOS

Lou

SIZE

177

PERCEPTION 1 MATCHES

DESCENDING DIRECTION OF THE COMPARISON AT 3, 6, AND 9 FEET FOR CHILDREN PHENOMENALISTS OR REALISTS

FOR ASCENDING FOR THE CLASSIFIED L%’ = 6)

Distance

of the

AND

STANDARD AS

standard

(ft)

3

6

9

Ascending

I .02

.92

.92

Descending

I.05

Phenomenal&s

Ascending

.99

1.07

.9.5

I.23 .97

Realists Descending

1.07

I.10

1.29

years, made under “apparent” instructions, suggest that they experience perceptual size constancy over distances up to 9 ft. EXPERIMENT II if Realists and Phenomenalists perceive size-at-a-distance in a similar way, do they have a different understanding of the relationship of distance to real and apparent size? Experiment II was designed to answer this question by changing the size-matching instructions from the Phenomenal question to the Objective question. Other changes were also introduced to make it easier for the children to differentiate real from phenomenal size: the visual information was reduced and cognitive information increased by (a) separating the Standard and Comparison fields to eliminate relative size information, (b) blindfolding the subjects between trials so they could not see the assistant change the stimulus distance, and (c) introducing a familiar-size test series. Moreover, a large number of subjects were tested, and the method of constant stimuli was used in the hope of reducing variability. Method Subjects. The subjects were 31 children, aged 4-O to 5-3, who were attending a nursery school. Pretests. The Size Judgment Test and Illusion Test used in Experiment I were administered in the same way, except that only the square forms of the size judgment cards were used and each card was judged twice instead of once. Color and position of the Standard were balanced across subjects for the two sets of judgments, and the order of presentation of the cards was random. The two raters independently classified 15 children as Phenomenalists

178

TRONICK

AND

HERSHENSON

and 16 as Realists. They never disagreed in their classifications. The ages of the Realists ranged from 4-O to 4-10 with a median of 4-6. The ages of the Phenomenalists ranged from 4-3 to 5-3 with a median of 4-8. The difference in ages between the two groups was significant [l (29) = 2.17, p < .025], in a direction opposite to that expected from the results of Braine and Shanks. That is, there were a number of “old” Phenomenalists and “young” Realists among the children selected. There were no differences between the groups in their ability to use and understand size concepts [F (1, 27) < 1.001. An analysis of size judgments using age as a covariate did not yield a significant age effect. The differences in size judgments were not related to the sex of the child. VietiGng.fklds. Two identical 3 ft. by 12 ft. viewing fields were positioned SO as to form a right angle. The fields were covered with cloth containing a pattern of + in. diameter white dots in straight rows and offset columns. Sfimuli. Two sets of stimuli were used: a Familiar Size set and an Unfamiliar Size set. The Familiar Size set was constructed by photographing an unfolded half-gallon milk container, printing a series of color enlargements and reductions, and then folding the prints into milk-carton shape. This produced a series of 15 identically shaped and proportioned “milk cartons” varying only in size. The Standard stimulus of this set was the normal sized milk carton (Stimulus Number 8 in the series) which measured 9+ in by 3%in and subtended a vertical visual angle of 7.V at 6 ft and 5.01’ at 9 ft. The other stimuli increased or decreased by $ in linear steps from this size. Although the original series consisted of 15 stimuli, preliminary testing showed that neither Realists nor Phenomenalists failed to discriminate stimuli two steps smaller or three steps larger than the Standard as different from the Standard. Therefore, only six stimuli (Numbers 6 through I I in the series) were used in the Comparison series. The Unfamiliar Size series was made from yellow construction paper in the shape of rectangular solids with the same dimensions as the Familiar Size series. Procedure. Each child was assigned at random to the Familiar or the Unfamiliar series, and to a left-right position of the Standard. The child to be tested was seated in the alcove between the two viewing fields. The Standard stimulus was always at 6 ft and the Comparison stimulus was at 9 ft. The tester asked the child the Objective question and the response was recorded. After each judgment, the child was blindfolded and an assistant changed the Comparison stimulus according to a prearranged random sequence. Each stimulus was matched eight times. Since no single dimension of the stimulus is an adequate measure of its “size,” the Comparison stimuli were simply assigned numbers (6 through 11) corresponding to their order in the sequence. Stimulus Number 8 was the same size as the Standard.

SIZE-DISTANCE

PERCEPTION

179

Results and Discussion

A “point of subjective equality” was determined for each child by transforming the percentage of “same” responses to z-scores. Straight lines were fit to these scores by the method of least squares, under the assumption that Stimulus Number 8 (the Comparison equal in size to the Standard) corresponded to the origin of the z distribution. The value on the abcissa that corresponded to the ordinate z = 0.00 on the least-squares line was taken as the PSE (Guilford, 1954). Brunswik Ratios were then calculated from the PSEs. A three-way analysis of variance of z-scores (Groups x Familiarity x Stimuli) yielded only one significant effect: the main effect of Stimulus Size [F (3,81) = 141.82,~ < .OOl]. This outcome confirms the fact that the size matches were related to the changes in size-distance combinations. A separate trend analysis showed that there was a linear increase in the percentage of “same” responses with stimulus size for each Group x Familiarity cell. The Phenomenalists and the Realists did not differ in their size matches even when asked to match to the “real” size of the object. Indeed, none of the other changes, introduced to make it easier for the children to differentiate real from phenomenal size, had an effect. Overall, the performance was similar to that of the first experiment: the size matches were a reasonable approximation to the real size of the Standard object (average BR was .92). Thus, the finding that the size matches of the Phenomenalists and Realists alike approximate size constancy even under “objective” instructions supports the conclusion from the previous experiment that children 4 to 54 years of age experience perceptual size constancy for near distances up to 9 ft. EXPERIMENT

Ill

In Experiment II, the introduction of Familiar Size information resulted in slightly more accurate matches by the Phenomenalists for the Familiar series than for the Unfamiliar series, but no difference for the Realists. Although these differences were not significant statistically, if this trend held up, it would be paradoxical (Familiar Size information should improve the performance of the Realists, the group more cognitively advanced). The third experiment evaluated this “tendency” in the performance of separate groups of Realists and of Phenomenalists, tested under Objective and Phenomenal instructions. A new set of Unfamiliar stimuli was constructed to make the objects more similar in shape and surface pattern to the milk cartons. Method

su6jecfs. The subjects were 48 children, aged 3-8 to 5-6, who were living in a graduate student housing project.

180

TRONICK

AND

HERSHENSON

Pretests. The Size Judgment Test and the Ihusion Test used in Experiment II were administered in the same way in Experiment III. Twentyfour children were classified as Phenomenalists and 24 as Realists. The two raters never disagreed in their classifications of the children. The ages of the Phenomenahsts ranged from 3-9 to 5-5 with a median age of 4-9. The ages of the Realists ranged from 3-8 to 5-6 with a median age of 5- I. There were no differences between the two groups due to age, and no effect of age on any of the variables. The differences in size judgments were not related to the sex of the child. Viewing fields. The viewing field was made from a single large table measuring 4 ft x 124 ft covered with the same patterned material used in Experiment II. The field was illuminated by a row of incandescent lamps to the left of the table, producing shadows from objects placed on the viewing field. StirmA. Stimuli Numbers 6 through 10 of the Familiar series were used in Experiment III. A new Unfamiliar series was constructed that was identical in size and shape to the Familiar series. Lines and quadrangles were drawn on the yellow construction paper to make a patterned surface for the Unfamiliar objects. Procedure. Each subject was assigned at random to one of eight conditions, receiving either Phenomenal or Objective instructions, and seeing either the Familiar or the Unfamiliar series of stimuli, on either the left or the right side. The order of presentation of the stimuli was random. Each stimulus was matched 10 times. In all other respects, the procedure was the same as in Experiment II. Results and Discussion An analysis of variance on z-scores for subjects tested in (Groups x Instructions x Familiarity), crossed with Stimuli, yielded a significant main effect of Stimuli [F (2,70) = 185.78, ,D < .OOI]: and two significant interactions: Groups x Familiarity [F (1,39) = 6.61, p -C .025]; and Groups x Instructions [F (1,39) = 4.20, p c .05]. A separate trend analysis showed a linear increase in percent “same” responses with stimulus size for each Group x Instruction x Familiarity cell. Mean Brunswik Ratios for size matches under Phenomenal and Objective instructions were I .03 and .98 for Phenomenalists, and 1.OOand I .05 for Realists, respectively. Post hoc critical difference tests showed that Phenomenalists and Realists did not differ in their size matches under Phenomenal instructions. However, given Objective instructions, the Phenomenalists produced size matches that were slightly smaller than the real size of the Standard, and the Realists produced slightly larger matches. Although these differences are in the appropriate direction (i.e., the Realists’ matches may be interpreted as “overcompensations”), the differences were too small to be taken as evidence that different mechanisms were at work in the two groups of children. Indeed, the size

SIZE-DISTANCE

PERCEPTION

181

matches of the Phenomenalists under Phenomenal instructions were also slightly larger than the Standard, and were closer to those of the Realists than to the Phenomenalists under Objective instructions. Mean Brunswik Ratios for size matches for the Familiar and Unfamiliar series were .98 and 1.03 for Phenomenalists, and 1.05 and .98 for Realists, respectively. Again, both Realists and Phenomenalists showed a high degree of perceptual size constancy for both Familiar and Unfamiliar stimuli. Post hoc critical difference tests showed that Phenomenalists did not produce size matches that differed for Familiar and Unfamiliar stimuli. However, the Realists matching the Familiar stimuli produced size matches that were slightly larger than the standard. Once again, the effect was small and, although statistically significant, does not seem robust enough to be taken as evidence for the action of a “cognitive” mechanism. GENERAL

DISCUSSION

In three separate experiments, children were assigned to one of two groups according to their ability to differentiate between the real size and the apparent size of the arcs of the Jastrow illusion. The Phenomenalist groups consisted of children who reported the illusory size as the “real” size of the arcs, despite additional information about the relative sizes, and statements about what the tester believed to be the case. The Realist groups consisted of children who said that the real and the apparent sizes of the arcs were different when placed in the illusory position. Yet, despite the striking differences in the cognitive abilities of the members of the two groups, there were no major differences between the Phenomenalists and the Realists in their size matches of objects at distances up to nine feet. All children produced fairly accurate matches of objective size in all experiments. These results suggest a number of interrelated conclusions. First, the conclusion on which all others hang, is that the size matches produced by the Phenomenalist children should be understood as accurate indices of their perceptions of size. This conclusion is based solely on their performance in the Illusion Test, and not on the outcomes of the size-matching task. It rests on the observation that these children did not make the distinction between real and illusory size in this test, and on the conclusion that they could not do so because their cognitive abilities had not yet developed to the point where such a distinction was possible. Thus, it is not surprising that the size matches produced by the Phenomenalists were essentially the same regardless of the instructions. For Phenomenalist children, “real” size and “apparent” size mean the same thing. Thus, it seems safe to say that the Phenomenalists did not respond differently under “real” and “apparent” instructions because they could not; they always responded as if given “apparent” instructions. Moreover, since

182

TRONICK

AND

HERSHENSON

their size matches approximated the real size of the stimulus object for all near distances tested, it also seems safe to conclude that they exhibited perceptual size constancy. The same conclusion cannot be made for the Realists. Clearly, in an illusory situation, the Realists could make the distinction. The fact that they did not differentiate between the Objective and the Phenomenal instructions in the experiment may be interpreted as either (a) a lack of difference between what they saw and what they knew about the stimuli, or (b) an inability to make the distinction in the size-matching task, even though they could make the distinction in the illusory task. The first interpretation rests on the assumption that the outcome of the Illusion Test provides evidence that Realists possess a kind of general cognitive ability to separate “real” size from “phenomenal” size, whetzever they differ (i.e., that the ability demonstrated in the Illusion Test is not taskspecific). Moreover, it suggests that the Realists should have been able to analyze any lack of correspondence between what they saw and what they knew about the stimuli, and should have been able to match size accordingly, given the two different instructions. The fact that their size matches were essentially the same under both instructions would lead to the conclusion that there was no basis on which to distinguish real from apparent size (i.e., that apparent size corresponded to real size). The similarity between the Realists’ size matches and those of the Phenomenalists lends support to this interpretation. The second interpretation suggests that the ability to differentiate real from apparent size is task-specific, and that different task abilities mature at different ages. This interpretation is supported by Rapoport’s (1967) finding that only children above the age of nine produced different size matches in response to “apparent” and “objective” instructions. Children below nine did not respond differentially to the two instructions in that experiment. But it is not clear how to relate the size matches of the younger children in Rapoport’s experiment to those of the four- and five-year-olds in these experiments; the latter produced size matches very close to constancy whereas Rapoport’s children produced size matches between 85% and 93% of real size. These differences in “accuracy” of matched size could be accounted for by the difference in the distances used: Rapoport’s variable stimulus was at 24 ft, more than twice as far as the longest distance seen by the children in these experiments. Thus, the question of interpreting the size matches of the Realists must be left unresolved. Either they were “Realists” in the illusion task but “Phenomenalists” in the size-matching task, or they were “Realists” in both tasks who were reporting a correspondence between real and apparent size in the size-matching task. Regardless of which interpretation is correct, their size matches should be understood as reflecting what they saw-and what they saw was size constancy.

SIZE-DISTANCE

183

PERCERION

What conclusions can be drawn about the mechanisms producing perceptual size constancy in these preschool-aged children? If accommodation and convergence can account for constancy up to distances of one meter (Leibowitz, Shiina, & Hennessy, 1972), then the accuracy of the matches at 3 ft can be explained, but another mechanism is required to explain the accurate perceptions at 6 and 9 ft. Since “cognitive learning” appears to be ruled out (for many reasons. see above), the mechanism that produced the constancy perceptions must have involved visual information. Unfortunately, implicating visual information as the source of the constancy matches does not permit a choice between the two alternative theoretical positions. Since no age differences were discovered, there is no way to tell whether the visual information was used by a mechanism inherently part of the human eye-brain system, or whether the mechanism was acquired by a process of learning. REFERENCES Braine, M. D. S., & Shanks, B. L. The development Verbal

Learning

and

Verbal

Behavior,

of conservation

of size. Jourtzul

of

1965, 4, 221-242.

Carlson, V. R. Overestimation in size-constancy judgments. American Journa/ of Psycho/ogy, 1960, 73, 199-213. Carlson, V. R. Underestimation in size-constancy. American Journa/ ofPsycho/ogy, 1962, IS, 462-465. Carlson, V. R., & Tassone, E. P. Size-constancy and visual acuity. Perceptual and Motor Skills. 1963, 16, 223-228. Gibson, J. J. The perception of the visua/ war/d. Boston: Houghton Mifflin, 1950. Gibson, .l..J. The senses corzsidered as perceptual systems. Boston: Houghton Mifflin, 1966. Guilford, J. P. Psychomefric rnefhods. New York: McGraw-Hill, 1954. Harvey, L. O., Jr., & Leibowitz, H. W. Effects of exposure duration, cue reduction, and temporary monocularity on size matching at short distances, Journal qf the Optica/ Society

of America,

1%7.

57, 249-253.

Ittelson, W. H. Visual space perceptiorz. New York: Springer-Verlag, 1960. Lee, D. N. Visual information during locomotion. In R. B. MacLeod & H. L. Pick, Jr, (Eds.), Perception: Essays in honor o~J. J. Gibson. Ithaca: Cornell University Press, 1914. Pp. 250-261. Leibowitz, H. W. Multiple mechanisms of size perception and size constancy. Hiroshima Forum

for

Psychology,

1974,

1, 47-53.

Leibowitz, H. W., & Harvey, L. 0.. Jr. Size matching as a function of instructions in a naturalistic environment. Journa/ of Experimentu/ Psychology, 1967, 74, 378-382, Leibowitz, H. W., & Harvey, L. 0.. Jr. The effect of instructions, environment, and type of test object on matched size. Journal oj Experimental Ps.ychoiogy, 1969, 81, 36-43. Leibowitz, H. W., & Moore, D. Role of changes in accommodation and convergence in the perception of size. Journul of the Opticul Society of-America, 1966, 8, 1120-l 123. Leibowitz, H. W., Pollard, S. W., & Dickson, D. Monocular and binocular size matching as a function of distance at various age levels. American Journu/ ofPsycho/ogy, 1967.80, 263-268.

Leibowitz, Perceptiun

H. W., Shiina, K., & Hennessy, R. Oculomotor adjustments and size contancy. and

Psychophysics,

1972,

12, 497-500,

184

TRONICK

AND HERSHENSON

Piaget, J., & Szeminska, A. The chi/d’s conception of number. London: Routledge & Kegan Paul, 1952. Rapoport, J. L. Attitude and size judgment in school age children. Deve/opmenta/ psycho/ogy, l%7, 38, 1187-l 192. Rapoport, J. L. Size constancy in children measured by a functional discrimination task. Journal of Experimental Child Psychology, 1969, 7, 366-373. Zeigler, H. P., & Leibowitz- H. W. Apparent visual size as a function of distance for children and adults. American Journal of Psychology, 1957, 70, 106-109. RECEIVED: January 24, 1978;

REVISED:

May 5, 1978.