4-,1'1’8‘0 af-J" .— -’V:‘1’I? h???" . T' "'°'.vr;,’.. ». .r amw were-m; 1:. (£9; ’0' (”l-’66: a" .l’. i";'.?' . ’ 'm' ‘7; A" 34m "ham ~r ' I. ’-3 . g .0. . ‘9' . CHILDREN'S SAME~*D;I.FFERENT IU‘DG-MENTS OF VARIOUS TRANSFORMATIONS OF LETTER-LIKE FORMS USING THE METHOD OF PAIRED COMPARISONS: EFFECTS OF TRANSFORMATION AND AGE OF CHILD Thesis for the Degree of M. A. ' MICHIGAN STATE UNIVERSITY M. JOSEPH SCHALLER 1969 T THESIS LIBRARYW Michigan State 5‘ University # _ [if ‘3'" "‘ @559 987 ABSTRACT CHILDREN'S SAME-DIFFERENT JUDGMENTS OF VARIOUS TRANSFORMATIONS OF LETTER-LIKE FORMS USING THE METHOD OF PAIRED COMPARISONS: EFFECTS OF TRANSFORMATION AND AGE OF CHILD BY M. Joseph Schaller This study was an extension, with several substantive and methodological changes, of Gibson, Gibson, Pick, and Osser's (1962) developmental study of the discrimination of letter-like forms. Gibson et al. designed standard figures incorporating features of English letters and then transformed these standards along dimensions which, with respect to the discrimination of English letters, they judged to be either critical (line-to-curve, rotation and reversal, breaking or closing a gap) or non-critical (perspective transformation). They then employed these forms in a match-to-sample procedure. Their gs, four- to eight-year—old children, were instructed to pick from among the transformations and one additional standard those forms which they thought matched the standard. M. Joseph Schaller Gibson et a1. related the error pattern.p9§t_hgg_for each type of transformation to the degree to which each type of transformation was critical for the discrimination of real objects and/or real letters. The perspective transformation (gag., tilting the figure back 45°), which presumably is irrelevant for discriminating both real letters and real Objects, yielded highest error scores (about 80%P60%), whereas transformations presumably relevant to letter discrimination but more or less irrelevant to real object discrimination (rotation, reversal, line-to-curve) were of medium difficulty. Transformations relevant for both letter and object discrimi- nation (break and close) were easiest of all. However, only one degree of the perspective transforma— tion was used, and its greater relative difficulty of dis- crimination might have accounted for the higher error rate. The current study therefore included two additional degrees of perspective change on the presumption that generalization of object constancy--if such generalization did account for the high error rate-awould not be peculiar to only the least discriminable of the transformations. Gibson et al. also pretrained their subjects with only rotation transformations of real letters. This procedure M. Joseph Schaller would seem to bias results in the direction of greater sensi- tivity toward rotations than toward other transformations. The current study therefore used no pretraining. The current study substituted the method of paired- comparisons for Gibson et al.'s match-to—sample method to insure that §§ looked at every combination of figures. By balancing the number of possible correct "same" and "different" responses, the present study also avoided possible response biasing. In agreement with Gibson et al., current results dis- closed a general decline with age in the number of errors on all transformations--except rotation and reversal. Errors on these transformations increased with age, whereas Gibson et al.'s scores decreased. A further point of difference came with separate analyses of these scores. Gibson et al. reported slightly more errors with up-down than with right- left reversals. The current study found an opposite and far stronger effect. The absence of pretraining on rotation- reversal figures in the current study is presumed to have accounted for both these differences. The results suggest that the children ignored dimensions of difference that would have been critical to the discrimination of real letters. M. Joseph Schaller Finally, error scores on the perspective transformations agreed with Gibson et al.'s results only for the original perspective transformation (},§,, very frequent errors across age; slight decrease with age). However, making the perspec- tive transformation less difficult as a discrimination drastically reduced the frequency of errors at all ages, so that the error curves for the additional perspective trans- formations overlapped those for line-to-curve and topological transformations. Thus, the current study found no evidence for Gibson et al.'s conclusion that object constancy general- izes from everyday experience to the discrimination of letter- like forms. When more pronounced perspective transformations were tested, there was no evidence that this transformation, as a type, was any more difficult than the other types. CHILDREN'S SAME-DIFFERENT JUDGMENTS OF VARIOUS TRANSFORMATIONS OF LETTER-LIKE FORMS USING THE METHOD OF PAIRED COMPARISONS: EFFECTS OF TRANSFORMATION AND AGE OF CHILD BY M. Joseph Schaller A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF ARTS Department of Psychology 1969 I) ACKNOWLEDGEMENTS I am indebted to my thesis chairman, Lauren Harris, who originally became interested in this study, got me involved in it, and worked so hard with me through its various stages. I am grateful, too, to Drs. Ellen Stommen and Charles Hanley, for criticizing the thesis, and to Mr. Kent Thibideau and the teachers of Midway School in Holt, Michigan, for their generous help. Finally, thanks are due, of course, the children who participated in the study. I was supported by a National Defense Education Fellowship during the period of this research. ii TABLE OF CONTENTS List of Tables List of Figures Introduction The current study Method Subjects Materials and design Procedure Results and Discussion Identical-pair analysis Different-pair analysis Directions for further research Notes References iii iv 17 17 l7 19 23 27 29 42 47 48 LIST OF TABLES Table 1. Analysis of Variance Table - Grouped Transformations - Identical-pairs only. 28 Table 2. Analysis of Variance Table - Grouped Transformations - Different-pairs only. 30 iv LIST OF FIGURES Figure l. 'Letter-like' forms. Figure 2. Results for ”confusion errors' in Gibson et al.'s original study. Figure 3. Example of original perspective trans- formation. Figure 4. Example of perspective transformations used in current study. Figure 5. Apparatus for displaying forms in Gibson et al.‘s matching task. Figure 6. Example of a different-pair error. Figure 7. Example of an identical-pair error. Figure 8. Percent judged "same" for different- pairs. Figure 9. Percent judged "same" for different- pairs for the three degrees of perspective transformation. Figure 10. Percent judged "same" for different- pairs for the three line-to-curve transfor- mations. Figure 11. Percent judged "same" for different- pairs for the rotation and reversal trans- formations. 10 11 13 24 25 32 34 36 38 INTRODUCTION Interest in the psychology of reading and reading disability has stimulated much psychological research in recent years. Much of this research has centered on form discrimination and the discrimination of orientation, two perceptual skills critical for identification of letters of the English alphabet. A thorough review of studies related to the effect of orientation on discrimination of shape is provided by Howard and Templeton (1966). The classic study of the relation between shape orien- tation and letter discrimination is by Davidson (1935). She examined kindergarten and first-grade children's ability to distinguish the letters b, d, p, and q in a match-to-sample task. She found a general decline in errors with age, with right-left reversals accounting for approximately three times as many errors as up—down inversions and 1800 rotations. When pressed, however, the children admitted that some of the letters they had chosen were indeed "turned the other way." 1 From such evidence, Davidson suggested that the children indeed were able to recognize the same shape despite the different orientations, but were unconcerned with orienta- tion, and consequently made 'errors'. More recently, Rudel and Teuber (1962), using U-shapes and straight lines, showed that right-left mirror images were difficult for three-and-a-half- to eight-and-a-half-year- old children to discriminate, while up-down inversions were not; discrimination of opposed obliques was nearly impossible for the youngest children. One of the most influential studies of shape and orien- tation discrimination as these abilities might relate to reading skills was published in 1962 by Gibson, Gibson, Pick, in a paper entitled, "A developmental study of the and Osser, discrimination of letter-like forms". This study provided the impetus for the research to be reported here. For this Study, Gibson and her colleagues designed a group of standard letter-like forms. They then designed transformations which Varied from the standards along some of the dimensions which, 0n the basis of inspection of the English alphabet, they judged to be critical for the discrimination of English letters. The transformations they chose were: "line-to-curve" (changing one, two, or three of the straight lines of the figure to curves, or vice versa—-as in the change from a letter D to 0 or U to V); "rotation-reversal" (rotating the figure 450, 90°, 180°; reversing the figure, both up-to-down and right-to- left--as in d to q, d to b, etc.); and "topological" (break- ing a continuous line and closing open lines in the figure-- as in the transformation of an O to a C). They also included one set of transformations which they presumed were not critical for distinguishing English letters-awhich, indeed, must be ignored in reading letters--schematically changing the angle of View as it would be changed in tilting the figure back 450 and as in turning the figure sideways 450 (Both are "perspective" transformations.). Their set of transformations and standards is included in Figure 1. Gibson et al. used these forms in a match-to-sample task with four- to eight-year-old children. Their design allowed for their subjects to make two kinds of error: con- fusing a transformation with a standard (“confusion error") and failure to detect the true match ("omission error"). The omission errors were not analyzed because they were in- frequent and unsystematic. The results of their analysis of confusion errors are depicted in Figure 2. Gibson et a1. related the error patterns for a particu- lar type of transformation to the extent to which they presumed allll 1.! I! III] .xmfiuopmm.sm spas pmxumfi mum .mtumpsmum. Hagan on Hmoflucopfl one £0fl£3 msoHDMEuommsmupl.H0pu0H. xfiw omoaa ..Houuma. some mo Show .pumtsaum. on» msoam m GESHOU .Ammsfipmeg sEsHoo may ca # a >9 ovumofiocflv @H can .MH .HH .oa msEsHoo CH wouoHQUp .hpsum usonnso exp Mom posmfimOp Axomnluaflu 3b: can can umoalusmam 3o: osuv msoflumEuommsmnu o>fluoommnom Hmsoflufittm Hsom may msam .mHImH was .NH .mIH .m msEDHoo Ga pmuoamot .Ammmav ummmo pom Moan .somnaw .comnaw noumm .mEuom .oxfialuoppoa. Hmcamfiuo any mo poumflmcoo >psum useHHso opp 2H poms flasfiflum .mEuom .oxfialnoupvq. .H ousmfim '0‘ ‘ Transformation SIE'IIE—k 3 I I «3‘5 ‘I’ I>< 'QK IfimflIEIVQSTNQQII IJIZSIIII *ZIIIII’NU< §m~I+IZSIIR~+ZOIS Ib hggLu—ZLKWVC 5W XIV} zwy72uA32Ixm< IIIEMVMHIHdFYCA . ImRVQWRDOXQérfoéI—I/V .IMKHIEUVEEYKQprxw< myflgkvflwmfiwmw< .p .p (I) I4 A.moma .Hommo can .Mofim .aomnHG .cownawv .hunum Hmnamflno m..Hm um comnaw ca =mnouuo cofimnmcoo= How muanmom .m anumflm mm 2. mad 0. . m . m h m 0 ¢ q + _ _ _ _ a , 0 3060.30... 350-0723 ON 0..» Enigma u cot—tom 1 3:03.23 IllTlllllllJFAUmw mzammm Mcomn 5 80883 % that type of transformation to be critical for discrimination of real objects and, in the case of their older subjects, who they expected would have learned to read, for the discrimina- tion of real letters. Accordingly, they viewed the resulting high rate of error across all ages with perspective trans- formations as reflecting the operation of object constancy generalized to the discrimination of the letter-like forms. That is, according to Gibson (1963) in a later discussion of the study, "perspective transformations...indicate not a different object but a change in position of the §§m§_object. They must be tolerated in order for size and shape constancy to be possible" (pp. 181-2). In addition, ”perspective transformations...must be tolerated in reading (they are produced by holding a book at different angles, for instance)" (Gibson, 1963, p. 182). On the other hand, breaking or clos- ing a gap in a contour (topological transformation) is critical for object and letter discrimination. This trans- formation yielded fewest errors for all groups of children, and error rates were relatively low (15%) even for the pre- schoolers. In contrast to these transformations, Gibson et al. suggested that rotation and reversal and line-to-curve transformations are generally irrelevant for real object discrimination but relevant for letter discrimination. Rotations and reversals denote, again, a change in position of the same real objects, but denote a different letter. Changes of lines to curves "perhaps...indicate a change of state (not a different object) in plastic or living objects. Such changes would occur in facial expression, for instance" (p. 182, Gibson, 1963). But in the alphabet such changes denote a different letter, so that Gibson et a1. concluded that the initially high rate of error and its subsequent decrease with age resulted from the increasing detection of features critical to the discrimination of letters during the period from four to eight years, the period when the child begins learning to read. The current study. The current study attempted to take into account several methodological aspects of the original study which, it was thought, might bear importantly on the results. The most striking finding, the high rate at all ages of confusion error on the perspective transformations, seems on closer examination to have been possibly an artifact of difficulty of discrimination. The standard and its perspective trans— formation differed from one another by a ratio of approximately 7 to 10. Examples of several of the comparisons required are depicted in Figure 3. These figures seem physically very similar, and when one considers that they were less than one inch in size in the actual matching task, it seems probable that they would be judged identical for reasons having to do more with basic discrimination difficulty than with generalization of object constancy. The current study therefore included three stages of each perspective transformation for each standard, making the discrimination range from difficult to simple. Examples are shown in Figure 4. The operation of object constancy presumably would not be peculiar to only one part of this range, so one would expect that if the child is not respond- ing to the perspective transformation because it is irrelevant, he would respond similarly at all levels; that is, he should be no more likely to say that perspective 2 or perspective 3 is different from the standard than to say that perspective 1 (the original) is different from the standard. Another important change was in method of stimulus presentation. Gibson et al. put each of their standard forms in the center of the upper row of a display appara- tus (depicted in Figure 5) and instructed the subject to scan the appropriate row below searching for any form which was exactly like the standard. It seems that this procedure .NmmH .Hmmmo new .xowm .comnaw .GOmnHw an coma mcoflumfinommzauu w>fluoommnom Hacflmfiuo mo OHQEaxm .m unnmflm coflumEHommzauu Momn1pafla wnmccaum zoflumfinommcmuu “moaluzmam 10 m m>auovmmnum N o>auoommuom Ho>auoommnom mcoflumahommcmnu xomnluaas .mwsum m..am uo somnaw a“ coma soHumEHommsmnu us“ we H 0>Hu loommnom .hosum uconuno on» a“ com: meowmeuommzauu o>fiuuommuom eons“ on“ no vamEuxm .e onnmflm euaucaum mcofluwfiuommcmup umoaluzmam m o>fiuoommumm N o>fluoommnom H 0>fluoommupm l .m .m 11 12 might have been very confusing for the younger children, a conjecture lent some support by Gibson et a1.'s comment that the experimenter had to redirect the attention of subjects who lost their places or seemed not to be looking at every letter (1962, p. 899). It also seemed that their method could not control for response bias because the subjects could not have had the opportunity to make an equal number of correct "same" judgments and correct "different" judgments. In effect, the procedure required the child to reject many more forms as different than he could accept as same. Response bias has been shown to be an error factor of differential strength across chronological age. (Gibson et a1.'s procedure thus had the potential to increase artifactually the number of "omission errors" and decrease the number of "confusion errors" because subjects would be set to respond "different" even when two forms were actually identical. The younger children then might be more susceptible to this factor than would the older children. However, judging from the fact that Gibson et a1.'s "omission errors" were too few to be analyzed, it seems that such an effect, if it existed at all, was very weak. Nevertheless, it appened that a different Figure 5. Apparatus for displaying forms in Gibson et a1.'s matching task (Gibson, Gibson, Pick and Osser, 1962). 13 l4 procedure should be instituted for the extension study under- taken here.) The method of paired-comparisons therefore was substituted for the match-to-sample procedure.‘ Pairing every transfor- mation of each letter with its standard and with itself produced 396 paired comparisons, exactly half of which re- quired a 'same' judgment to be correct. The last important change in the current study was the decision to ngt_giyg pretraining. Gibson et al. reported that their instructions "...were given very explicitly, so as to make absolutely clear that only an exact match was wanted. A demonstration was given first with very large sample forms (real letters) which included two reversals. The E asked if they were the same and corrected §_if he responded incorrectly. Repetition and other terms such as "equal" or "exactly alike" were used if necessary. Then g was given a practice row on the matrix board, again with real letters, but with a standard at top and filled board so that conditions simulated the final task” (Gibson, Gibson, Pick, and Osser, 1962, p. 899). Judging from this description, Gibson et a1.'s pre- training apparently used only one dimension (reversals) of their total set of dimensions and then tested for differential 15 sensitivity to the entire set. This procedure could have biased their results in the direction of greater sensitivity toward the pre-emphasized dimension. It seems, however, that the use of pretraining in re- search of this kind, even with all dimensions included, poses a problem nonetheless. The assumption here is that Gibson et a1. intended to explore the possibility that features which the child has learned are either critical or noncritical for the discrimination of real objects (and later, of real letters) would be the basis for his judgment of sameness or differentness of two-dimensional or non- representational letter-like forms. In other words, the assumption, so far as the purposes of the current study are concerned, is that Gibson et a1.'s interest was in what the child responds to as critical, or to put it somewhat differ— ezntly, in what, in the child's judgment, is a difference that makes a difference. If this assumption is correct, then giving pretraining and then correcting the child for what in: the experimenter's estimation is an error would beg the Very question under consideration. That is, this procedure WGuild teach the child what the experimenter thinks makes a difference (what the experimenter thinks is a critical feature). III (other words, it would seem that the question of interest 16 is the child's understanding of "same" and "different", the assessment of which should be induced from his systematic responses, not taught him beforehand. Therefore, subjects were not pretrained in the present study. METHOD Subjects The subjects were public grade—school children with a history of no previous participation in psychological research. Ninety-six children were tested individually: 12 boys and 12 girls at each of four grade levels: kinder- garten, 2nd, 4th, and 6th. Mean chronological ages were: kindergarten - 6 yrs., .04 mos.: 2nd - 8 yrs., 2.71 mos.; 4th — 10 yrs., .67 mos.: 6th - 12 yrs., 1.67 mos.1 Materials and design The stimulus materials used were the same figures de— signed by Gibson, Gibson, Pick, and Osser (1962) plus the additional four "perspective" transformations of each figure developed for the current study--two additional slant-left transformation, with size ratios to the standard of 6:10 and 5:10 (Gibson et a1.'s size ratio was about 7:10) along the horizontal axis, and two additional tilt-back transformations, with size ratios to the standard of 6:10 17 18 and 5:10 along the vertical axis. The total set of figures consisted of 12 x 17 = 204 stimuli (depicted in Figure l). The additional perspective transformations are designated by a # in the column headings. A total of 396 paired comparisons were designed from these stimuli. To avoid biasing the gs' responses (toward "same" or "different"), the presentation set contained equal numbers of actually identical and actually different pairs. For each transformation of each standard, one pair was in- cluded which consisted of the figure paired with itself (identical-pair), and one pair was included which consisted of the figure paired with its standard (different-pair). All standards also were paired with themselves to obtain a baseline measure for each 'letter'. A selection of different- pairs (taken from the diagonal in Figure l--Al, B2, C3, etc., through L12), one of each letter and 12 of 16 of the trans- formations, was added to the different-pair set to equalize the number of identical- and different-pairs in the presenta- tion set. The reversal transformations posed prdblems with some figures, since they still were identical to the standard. It therefore was necessary to omit these figure-transformations (six in all-—marked with an asterisk in Figure 1) from both 19 the identical-pair and different—pair sets. Procedure Since 396 paired comparisons would have constituted too long a task, the total set was divided systematically into approximate quarters, with each quarter included in a separate book, one book for each subject. Each book consisted of either 98 or 100 pages, with one stimulus pair on each page. The identical—pair set and the different-pair set were each randomly ordered and then combined using Gellerman (1934) series to reduce the possibility of successful patterned responding. For each of the different-pairs, the standard was alternately placed on the right or left side according to Gellerman series. The forms were drawn on 3%" square paper and were placed side by side, about two inches apart, in the center of each page. The entire stimulus set was quartered in such a way that, as nearly as possible, children in each sub-set saw each 'letter' the same number of times, though they did not see the same '1etter'-transformation combinations. Four gs were required, then, to Obtain data on the entire set of pairs. The four stimulus books were assigned evenly among the eight grade-by-sex groups. Each child came alone from his classroom to the testing room and sat at a low table on which the appropriate book 20 was placed. Smaller children were boosted on the chair so that all gs viewed the book from approximately the same angle (about 200 to 300 from perpendicular to the plane of the book). The experimenter sat next to the child so that he could turn the pages of the book with one hand and record the child's responses with the other. Responses were recorded onto prepared computer cards. The experimenter opened the book to a blank page and spoke the following instructions from memory: "In this book there are pictures of make- believe letters. There are two letters on each page; one letter will be in the space over here (§_pointed to empty space), and the other letter will be in the space over here (§_points). I want you to tell me whether the two letters are ju§£_the_§§m§_or whether they're different from each other _i_11 2.111 273.1. So you say "same" if they're exactly the same in every way, and say "different" if they're not exactly the same in every‘way. "Just look at the letters. If the color of the paper sometimes is a little different, that doesn't matter, or if there are some smudges or little marks 21 on the paper here and not over here, that doesn't matter. Just say "same" if the letters are just the same, and say "different" if the letters are 225.just the same. Do you understand? ‘OK. Let's begin. And I'm going to keep track of what you say on these cards here (indi- cating computer cards){ The instructions for kindergarteners and first-graders were elaborated as follows: “So if the two letters are exactly the same, what will you say? (§_waited for correct reply.) And what will you say if the two letters are not exactly the same?" (E waited for correct reply.) Then §_asked S, on the first trial, "Are these the same?" and repeated this question for five trials following. (This latter procedure seemed necessary for the younger children, who often said nothing until prompted this way. In some cases, the question induced young children to say "yes" instead of "same" for the rest of the trials.) No pretraining was given. If §_asked what made a pair different, §.replied, "That's up to ygg. YOu tell me if y22.think they're different in any way." If E thought §fs interest flagged, §_encouraged him by saying, "Only a few 22 more," or "Almost done." All responses were noted, including multiple judgments of same and different to the same stimuli and questions and comments to the experimenter. When §_had completed the trial he was told he had done very well and was thanked for his participation. RESULTS AND DISCUSSION In Gibson et a1.'s study, the child's judgment that a transformation, objectively different from the standard, was the same as the standard was called a "confusion error". In the current study, this is analogous to the child's judging a different-pair (Figure 6) as the same and shall be called a "different-pair error". On the other hand, when a child in Gibson et a1.'s study failed to pick out a matching standard in the rows, he was said to have made an "omission error". This error type could have included both true omissions, that is, actually failing to detect the matching standard, and errors in judgment, that is, deciding that the matching standard was in fact different. In contrast, the paired-comparisons procedure in the current study insured that the child looked at each and every pair. When he made an error with an identical-pair (Figure 7), it was an error in judgment alone; this shall be called an "identical—pair error". 23 Figure 6. Example of a different—pair error. If the child said that these figures were the same, he made a different- pair error. ('Letters' actual size.) 24 Figure 7. Example of an identical-pair error. These two figures, on the other hand, are identical. If the child said that these figures were different, he made an identical- pair error. ('Letters' actual size.) 25 26 Analysis of variance was the main statistical test used. Preliminary analysis indicated that the effect of 'book' did not reach significance [(3 = 2.44, <_i_f_ = 3/64, E = 0.073.) A unique set of one-quarter of the 'letter'- by—transformation stimulus combinations comprised each 'book'. The 'letter'-by-transformation variable (which produced a significant interaction: §:= 11.96, Qf_= 165/9215, p< .0005) was thereby nested within 'book'. This interaction undoubtedly accounted for the nearly sig- nificant effect of 'book'.]. Data from every four same-sex, same-grade, different-'book' subjects were pooled to form data for one 'grand-subject' for the main analysis. This pooling of 'books' resulted in the inclusion of 'book' var- iance in the error terms, producing a more conservative test of significance. The necessary omission of pairs for the six 'letter'- transformations for which no Objectively different trans- formations could be formed produced six blank cells per 'grand—subject' (1,3,, per four actual subjects). To facilitate analysis these cells were filled with the average value across 'letters‘ for that transformation for each 'grand-subject' individually.2 As in the Gibson et a1. study, identical-pair errors in 27 the current study were substantially less frequent than were different-pair errors (_F_‘_ = 611.09, (if = 1/6128, 2 < .0005; all transformations included.). The identical-pair and the different-pair judgments will be considered separately. Identical-pair analysis There seemed no reason to suppose that any of the identical transformation pairs should produce any more errors in judgment than any of the identical standard pairs, since each transformation, paired with itself, was merely another pair of identical 'letters', and since every child had unlimited time to make each judgment with the stimuli still in view. (Other stimulus presentation methods, such as tachistoscopic presentation, might be expected to produce markedly different error rates for the different transfor- mations as well as for different letters; 3;, Howard and Templeton, 1966.) In fact, the transformation effect was not quite so strong as the'letter’effect in the identical- pairs (_F_ = 4.68, _d_f_ = 11/176; 2HpommmHmm new N wbfiuommmnwm .awnwv .Hm um somnaw >9 Gems emoau Mano mum Gwendosw msoHumEHommcmne .mufimmlucmnowmwc Mom =wEwm= emmesn ucmoumm .m eusmfim wadmo :5 iv ucN ox fllf'IlOrll _ _ « 'l'llO.IIHIIIlO.I 603230.? [I'D 'll'lo J / II II .I / 3.50:2 -05.. // II \\\\V¢ I nYIII.I|.IIHHU“U.||nAWHPcILWI1'4[1.1. \\.\\ \\ l1: IIO\\ .0333. 1 \ I ‘ 13:20 O\ [I . m [Ari I ll / II I / II _ 3:02.de // ll 10 32 (80883) ,,3wvs,, asoanr as 33 transformation pairs). we will examine the perspective transformations first. Comparison of error scores with perspective transformations 2 and 3 with the error scores for Gibson et a1.'s original transformations (perspective 1), shown in Figure 9, discloses a marked decrease in number of errors as the degree of objective dissimilarity increases. In fact, the error scores for degree 2 of the perspective transformation parallels almost exactly the scores for the line-to-curve transformation for both Gibson et a1.'s and the current study. The third degree of perspec- tive change parallels the findings of both Gibson et al. and the current study on the topological transformations. (For degree of perspective change, §.= 239.15, g§.= 2/1725, ‘p<1.0005.) These data support the surmise raised earlier that Gibson et a1.'s original perspective transformation effect was simply an artifact of stimulus discriminability. That is, these findings challenge Gibson et a1.'s interpre- tation of their own findings in terms of generalization of object constancy to the discrimination of letter-like forms. A simpler interpretation seems indicated: for perspective transformations, the tendency to judge two different forms as different increases as the paired forms become more physically different. .eoflumEHommsmuu w>fluoummumm Hmsamfiuo m..Hm uw somnww me A m>fluommmumm .soflumauommcmnu o>auommmumm mo mwmumme messy may now mufimmlpsmnmmmfle How amEmm= wwmesm useonem .m musmam madmw 5m 53v new 0x. on)“ 10 z _ T + m 2,203.39”. N 320328 91 / .. . 3:03.22”. .. 3:03.935 _ocozzuuq ON 0e. 00 Om (ways) ,,3wvs,, 039mm 93 34 35 The current data also do not support the conclusion that "errors decrease, after four years, depending on whether 'they are now critical for letter differentiation.... Confusions Vflith relevant transformation types drop out. Irrelevant ones (do not." (Gibson, 1963) Granting Gibson et a1.'s point that -these perspective transformations are completely irrelevant 'to the reading task, errors on perspective transformations in the current study nevertheless decreased with age at the same rate as on any of the other transformation types. These interpretations of the data in terms of the effects of increased discriminability and of increasing age can also explain the rest of the findings in the current study, and in Gibson et a1.'s study by implication. It does not appear necessary to invoke special hypotheses to explain each of the different curves. The same decrease in errors with in- crease in physical difference, as in the perspective trans- formations, is found in the line-to-curve transformation; errors decrease as a direct function of the number of lines changed to curves or curves changed to lines (§.= 8.43, g; = 2/861, 24.001). In addition, the number of errors declines with grade level, as in the perspective transforma- tions. These data are depicted in Figure 10. Gibson et al., in fact, reported a similar effect within their line-to—curve .mzoaumEHommcmHu 0>HsoloulmcHH wens“ exp How mnflmmlucmumMMHe How =wEMm= Ummesn pceonem .oa eusmam wooH saooloulms .Hmmue>mu puma lowlanmfiu "mum mcoflumanommsmuu o>am 0:9 .mcoHumsnommcmnu ammuo>mu can coflumuou osu Mom mufimmlucmumMMflo mom =oEmm= oomosn unmouom .HH Gunmen mo