THE UP-AND-QOWNvMETHQD- A ‘E‘ECHNEQUE FOR GBTANING PSYCHWHYSKZM. DATA Thesis br fin) Degree of M. A. MECH'QGAN STATE UNEVERSITY Dominic .1. Zerbciéc, 3.2: 19763 LIBRARY Michigan State 0:11ch)! ABSTRACT THE UP-AND-DOWN METHOD - A TECHNIQUE FOR OBTAINING PSYCHOPHYSICAL DATA by Dominic J. Zerbolio, Jr. Psychophysical techniques, used to obtain points of subjective equality in visual illusions for different age levels, suffer from such inherent flaws as Error of the Standard, Starting Position Effects, and Central Tendency or Context Effects Other factors not controlled by standard techniques include decreasing illusion through repeated exposure and differences in attention span between younger and older subjects. These factors may be related to age and, therefore, confound the measurement of Per- ceptual Deve10pment. The Up-and-Down Method, because of its one-exposure-per-subject testing procedure, the simplicity of the response it requires, and the short time necessary to administer it, minimizes or circumvents those difficulties arising with other psychophysical techniques. Data are presented for five visual illusions; the Ponzo, the Modified Ponzo, the Horizontal-Vertical with Intersect, the Horizontal-Vertical without Intersect, and the Miller~Lyer; for both sexes at seven age levels: kindergarten through fifth grade, and adults; and compared to data found with psychophysical techniques. Reasons are discussed for preferring the Up-and-Down Method. THE UP-AND-DOWN METHOD - A TECHNIQUE FOR OBTAINING PSYCHOPHYSICAL DATA By Dominic J. Zerbolio, Jr. A THESIS Submitted to Michigan State University in partial fulfillment of the requirements. for the degree of MASTER OF ARTS Department of Psychology 1963 ACKNOWLEDGEMENTS The author wishes to express his sincere appreciation to Dr. Charles Henley for his assistance, guidance, and sense of humor, all of which were instrumental to the completion of this thesis. He also wishes to thank Dr. D. M. Johnson and Dr. M. Ray Denny for their helpful and penetrating criticism and advice. He is grateful to the Elliot Bond, Midway, and Sycamore Schools of Holt, the Marble School of East Lansing, and the Central School of Okemos for their cooperation in providing the space, the subjects, and the information necessary for this study. Without their help, this research would not have been possible. Last, but not least, the author thanks his wife, who labored long and hard under very trying conditions--typing from my handwritten manuscript. ii TABLE OF CONTENTS Page INTRODUCTION ................... . ............................ 1 THE UP-AND-DOWN METHOD ..................................... 4 METHOD ..................................................... 8 RESULTS ................................................... 24 DISCUSSION ...................................... . ..... ....38 SUMMARY ...... ........................................ ..... 46 BIBLIOGRAPHY..............................................47 APPENDIX.00......OOOOOOOOOOOOOOOOOOOCOOOOOOOOOO0.000.000.050 iii LIST OF TABLES TABLE Page 1. The interval between cards in the series used, the number of cards, the range of the variable line, and the length of the standard for each illusion ............................................ l4 2. Age ranges for each sample... ....................... l6 3. The mean, standard deviation (corrected according to the d/SD ratio), and effective sample size for each grade and sex of each illusion ............. 25 4. Analysis of variance for the Ponzo Illusion ......... 27 5. Analysis of variance for the Mbdified Ponzo Ill-“Sic“ ........ ......OOOOOCCOOO......‘OOOOOOIOOO.0.28 6. Analysis of variance for the Hbrizontal-Vertical with InterseCt IlluSiOnOOOOOOOOOOOOOO ..... 0.000.000.31- 7. Analysis of variance for the HOrizontal-Vertical without Intersect Illusion............... ....... ....33 8. Analysis of variance for the Mbller-Lyer Illusion ....... ... ...... ... ........ .................35 iv FIGURE Page 1. The Ponzo Illusion ...... . ............................ 9 2. The Modified Ponzo Illusion ......................... 10 3. The Horizontal- Vertical with Intersect Illusion. ........................................... ll 4. The Horizontal-vertical without Intersect Illusion ............................................ 12 5. The Muller-Lyer Illusion............................13 6. Test Card No. 1.....................................20 7. Test Card No. 2.....................................21 8. The means for the Ponzo Illusion.............. ...... 29 9. The means for the Modified Ponzo Illusion...........30 10. The means for the Horizontal-Vertical with Intersect Illusion........ ..... .... ..... .. .......... 32 11. The means for the Horizontal-Vertical without Intersect Illusion....... ........................... 34 12. The means for the Muller-Lyer Illusion .............. 36 LIST OF FIGURES INTRODUCTION The typical investigatidn of perceptual develOpment attempts to measure the perceptual thresholds for several age levels. For example, if a perceptual illusion is being investi- gated, thresholds for several age levels are plotted and connected to form a perceptual develOpment curve. All such studies have used psychOphysical techniques as assessment instruments. However, these techniques can be criticized on many grounds. The purpose of this study is twofold; first, to demonstrate that the Up-and-Down Method is an adequate measurement instrument, and second, to show that it is free from the criticisms which specifically apply to psychophysical techniques. Wohlwill (1960) roughly divides the criticisms of perceptual development studies into two categories. The first category includes errors in investigational design, analysis, and procedure. An insufficient number of subjects at any age level or an inadequate number of age levels assessed are likely to disguise the 'true' shape of the development curve. lack of control in data collection may yield incomparable data across age levels. The use of inapprOpriate statistical techniques, such as analysis of variance when the data are curvilinear, may erroneously lead the researcher to conclude that age levels do not differ. All of the above criticisms can be eliminated by careful design and execution of research. Wohlwill's second category deals with specific flaws which are inherent in certain psychOphysical techniques that have been used to assess the perceptual levels. Wohlwill indicates these as: (1) Starting Position Effects, which occur with the Method of Limits (Piaget and Lambercier, 1951; wapner and Werner, 1957); (2) Error of the Standard, an overestimation of the standard stimulus as in the Method of Constant Stimuli (Piaget and Lambercier, 1943); (3) a Context or Central Tendency Effect, which appears when the comparison stimuli are presented in an ordered series to be matched to a constant standard (Lambercier, 1946). At least the last of these has been shown to be functionally related to age, i.e., decreases with increasing age according to Tempieri (1955) as cited in Wehlwill, 1960. Considering that the psychophysical methods have been the only research tools available, and that these methods assess many age related changes, it becomes apparent that the resultant empirical curves are not due to perceptual develOpment alone. Along with the above defects, a few others can be mentioned. First, successive presentation of the same illusion to a single subject can produce a change in the amount of illusion perceived. This is the case with the Muller-Lyer Illusion where the end result is a decrease in the amount of illusion perceived (Judd,l902; Kohler and Fishback, 1950). The amount of change per exposure is not known nor is it known how children are affected. Another consideration is the difference in attention span between young subjects and adults. Younger subjects confined to an experimental situation should be more likely to lose interest in the material being presented. This loss of attention could very well account for the larger individual differences reported for pre-school and early school subjects (Walters, 1942). The last criticism concerns the comparability of the responses over age levels. In some psychOphysical techniques, a degree Of procedural SOphistication is necessary to be able to respond. When young subjects lack this SOphistication, their responses are difficult to compare with those of Older individuals. All of these flaws; design, procedural, methodological, and logical; must be considered in interpreting the meaning of develOpmental curves obtained with standard psychOphysical techniques. The fact that they exist casts doubt on the efficacy of standard techniques ES‘tOOIS for assessing perceptual develOpment. The solution to this problem demands an assessment technique that can control or circumvent these various unwanted age-related contributions to developmental trends. The Up-and-Down Method is such a technique. THE UP-AND-DOWN METHOD The Up-and-Down Method (Dixon and Mood, 1948) was originally devised for dosage-mortality work as an alternative to the Probit Method. In such work, the problem is finding the average dose of a drug that will kill an organism. Any organism subjected to a toxic substance may be killed by it, build up a tolerance to it, or become so sensitized that a later lesser dosage will result in death. The result is that a single ex- perimental organism can be dosed just once. If the organism does die, one cannot be sure that a lesser dosage would not have killed it. The Probit Method requires testing several groups, each at a predetermined dosage level, and calculating the average dose which will produce death from the percentages of deaths occurring in all groups. At best, it demands large samples, and if the predetermined dosage levels deviate from the average dosage level, the efficiency of the technique drops rapidly. The Up-and-Down Method needs fewer subjects and automatically con- centrates testing at or near the mean dosage needed to produce the sought-for effect However, this method requires subjects to be tested individually whereas groups can be tested simultaneously with the Probit Method. As an example of the application of the Up-and-Down Method, Dixon and Massey (1957, pp 318-327) consider dynamite caps that explode if drOpped from a sufficiently great height. When a single cap drOpped from a given height explodes, there is no way to determine if it would have detonated if drOpped from a lesser height. Conversely, if the cap does not explode, the powder in it will be more closely packed as a result of the impact, thus changing its explosive characteristics and making it useless for further study. Estfmating the mean explosion height of dynamite caps by the Up-and-Down Method involves selecting several testing heights from which individual caps are to be" drOpped. The height of each trial drop except the first is determined in advance by the results of the preceding trial; the height initially chosen for the first dr0p is determined in advance by the tester. As an example, call the heights ho, hl’ and h2° These heights differ by a given interval "d” such that h0 I d = hi and hl { d = h2. Next, suppose that capl is drOpped from hl’ the level predetermined by the tester for the first drop. If cap1 does not explode, capz will be dropped from h2’ the next greater height. If capl does explode, the next lower height, ho will be used for capz. In this way, the test height of any single cap except the first depends on the reaction of the previous cap at the height from which it was drOpped. Although it does not make a great deal of difference what the first level is, the method is most economical if that level is close to the true mean, If the first cap is dropped from a level departing grossly from the true mean, the method is self-correcting and after a few trials, will concentrate testing around the mean. Unlike the Probit Method, the Up-and-Down Method does not suffer a great loss in efficiency if the test levels chosen are not close to the true mean. There are a few restrictions on the use of the Up-and-Down Method. First, the method uses approximately one-half of the total number of observations collected, e.g., either the number of caps that explode, or the number that do not, whichever is smaller. Thus, the mean (R) and standard deviation (SD) estimates are based,in effect, on about onefhalf of the total sample tested. The R and SD estimates thus can be very misleading when based on total sample sizes of forty or less, since the effective sample sizes would be less than twenty. Secondly, the method requires that the variate under con- sideration be normally distributed, a cOmmon assumption in psycho- physical scaling techniques. This can be checked readily enough by plotting data on normal probability paper. If normality does not exist, then normalizing transformation procedures are required. A final restriction is peculiar to the method. The ease of analysis depends on the relative size of "d", the interval between test levels, and the SD Of the variable being measured. Dixon and Mead (1948) offer two methods of SD determination. The first is a simple linear approximation whereas the second is a tedious inter- polation technique. The adequacy of the first, the linear approxi- mation, depends on the size of the d/SD ratio using the SD calculated by it. As long as this ratio is between .5 and 2.00, the more com- plicated estimation technique does not yield a better SD approximation. When this ratio exceeds 2.00, the simple SD estimate is no longer satisfactory and the more tedious approximation technique is warranted. Use of the simpler form is preferable considering the calculation involved, but depends on an advance estimate of the SD such that a "d” can be chosen so that the resultant d/SD ratio falls between the .5 to 2.00 limits. In most cases, a little preliminary testing will approximate the SD Of the variable closely enough so as not to force the use of the more difficult technique. On paper, because of its one-eXposure-per-subject technique, the Up-and-Down Method appears immune to criticisms involving Error of the Standard, Starting Position Effects, Attention Span Differences, Methodological SOphistication, and Response Comparability. The purpose of this research is to demonstrate the practical utility of this method for the measurement of changes in susceptibility to illusion as a function of age. METHOD Apparatus Five visual illusions were chosen for this study, primarily because equipment necessary to present them is easily transported. They were the: l Ponzo (Figure l) 2. Modified Ponzo (Figure 2) 3. Horizontal-Vertical with Intersecting Lines (Figure 3) 4. Horizontal-Vertical without Intersecting Lines (Figure 4) S. mller-Lyer (Figure 5) The literature contains develOpmental curves Obtained using psychophysical techniques for all of these illusions except the Mbdified Ponzo. Each illusion appears in its indicated figure as it was presented to the subject. All illusions were drawn in india ink on white 5" x 8" unlined filing cards. Several cards were drawn for each illusion. Cards of a given illusion differed only in the length of the variable line, e.g., the standard line Of the Muller-Lyer illusion was two inches in length on each of the seven cards in its series whereas the variable line length varied from 1.75 inches as the smallest in the series to 3.25 inches in the largest. The standard and variable lines are indicated in Figures 1 through 5. The term "standard line” refers to the fact that one line for each illusion was the same length on all cards whereas the ”variable line" was varied in length over the series .uaaauao was» ad weed muwas..p. m sows one mucus Ouauwwu> can vuovauuu 0:9 .xca macaw wage a“ about own squad manoeug> was chansons 0:9 .uwcwzuuv Museum oau :« muOOnnsm use so vaucomoue as case one one coauuucoauo Huuxa was swam .:Oam:~HH onsom one .A MMDUHM manmaus> . vuuvcuum Standard —D variable FIGURE 2. The Modified Ponzo Illusion. Size and axial orientation are as presented to the subjects. In the actual drawings, the variable and standard lines are drawn in blue india ink. The standard and variable lines are 8 ”d" units long in this example. 10 Variable Standard FIGURE 3. The Horizontal-Vertical with Intersect Illusion. Size and axial orientation are as presented to the subjects. In the actual drawings, the variable line is drawn in blue india ink. The standard and variable lines are each 16 "d” units long in this example. 11 12 goes one mocafl manaaum> was vumvcuum 05H onu .mwcasmuv Havana onu :H one coHumucowuo asqxw can swam .oHnEuxo masu cw wcoH mafia: :v: ea .xca mecca asap aw :3muv ma scan o~nwauu> .muoofinSm onu cu vauaomoua mwcasauc onu we came one .nonsHHH uoumumucH usonuw3 Huoauuu>nfiuucowauom osH .¢ MMDUHm osmsaaum «asussos 13 .oHameo masu cw waoH mafia: :c: m sumo mum mocHH oHnmwuw> can unmeasum one .xc« macaw mean cw asmup one monga pumpcmum was udnwaum> osu .mwca3mup Hmsuus one :H .mDOOnnsm onu cu poucmmoua mm mama one one acaumucowuo Hwaxm can swam .cowm:~HH ushqnuoHaaz use .m Maboam manmwum> cumccmum l4 and served the same function as the differing heights of the dynamite cap example. The range of "variable line" values for each illusion was great enough to accommodate all responses. The number of cards and the interval between cards of the same illusion were not the same for all illusions. The interval, number of cards, range, and length of standard for each illusion series appear in Table 1. TABLE 1. The interval between cards in the series used, the number of cards, the range of the variable line, and the length of the standard for each illusion. All lengths are in inches. Interval Number of Length of Illusion ,(d)¥, Cards Range Standard Ponzo .125 6 .875-l.50 1.00 Modified Ponzo .125 7 .75-1.50 1.00 H-V w/Intersect .25 8 2.50-4.25 4.00 H-V w/out Intersect .125 8 1.75-2.625 2.00 Muller-Lyer .25 7 1.75-3.25 2.00 All lines were drawn with a Speed-Ball C-S lettering nib, except for the wide horizon line in the Mbdified Ponzo. This line was drawn with a Speed-Ball C-l nib. Two colors of ink were used to facilitate the subject's identification of the lines to be compared. The Ponzo, Modified Ponzo, and Mbller-Lyer illusions had the standard and variable lines drawn in blue with the rest of the illusion in black. The two Horizontal-Vertical illusions had the standard line black and the variable line blue. This use of color was especially advantageous during the testing of the younger subjects for they could readily identify the comparison lines by color. 15 All cards were presented in clear plastic frames. Two frames, one for horizontal and one for vertical presentation, were constructed of l/8-inch clear plastic stock. Two pieces of plastic, 6" x 9”, were separated by l/l6-inch plastic strips forming a 5-1/2" x 8-1/2“ x 1/16” pocket between them. For presentation, each stimulus card was slipped into the appropriate frame. This limited the bow of the cards from edge to edge at l/l6-inch and E1 insured equally flat viewing of all cards for all subjects. A l" x 1" thumb hold was cut from the top of the back piece of each frame to allow removal of the cards after presentation. Each frame was held in an upright position by wood stands at 5 degrees frdm vertical, tilted away from the subject. A 100- watt lamp was placed between the subject and the frame to reduce any glare or reflection on the surface of the frames from surrounding light sources. A lamp shade shielded the bulb from the direct line of the subject's viewing. When the subject pointed to his choice of line, a shadow was cast on the surface of the frame. This shadow was observable through the frame and enabled the experimenter to quickly identify the subject's choice. fisbiesfi All elementary school subjects were recruited from public schools in Ingham County. The adult samples were obtained at Fall 1962 registration at Michigan State university. The adult subjects were individually asked their ages. The range of ages for the adult samples was kept constant across l6 sexes (17-27). Since the age of each adult was available, the mean and the median ages for these samples are presented (Table 2). The ages of the elementary school samples are presented as age ranges. The maximum and minimum age for each sample and sex is given. Although there is some overlap, these groups differ by roughly one year (See Table 2). TABLE 2. Age ranges for each sample. (The superscript in the elementary school samples represents months.) ~ Age Range i Sample Males Females " Kindergarten 55-67 54-611 - Grade 1 64-75 64-75 '- Grade 2 71-89 74-88 Grade 3 82-94 82-95 Grade 4 93-108 92-107 Grade 5 103-1110 103-118 Adults 17-27 17-27 Adult Median 19 19 Adult Mean 19.47 19.06 The only restriction placed on the elementary school samples was that no child who had been retained in grade was included in the study. Elementary school classes were tested as units. Prior to the testing of the class, the teacher provided: (1) the age range for both sexes excluding retainees, and (2) the names of the retainees. The maximum and minimum age over all classes for a given grade and sex defines the age range for that grade. '17 While samples of approximately 100 subjects of each sex at each age level were obtained, the effective sample sizes are approximately one-half of this number for each group. The effective sample size for each group appears in Table 3 of the Results section. Procedure The Experimenter entered the classroom, introduced himself and told the class that they were to see a series of line drawings and answer a few questions about them. Then, a group of four or five like-sexed class members were taken to the testing room. All but one of this group were seated outside the testing room. The remaining subject was brought into the room and seated in front of the plastic frames. The distance between the subject's head and the frames varied between 2-1/2 to 4 feet. All subjects were asked to sit upright to control this distance, though no other restriction was imposed. Subjects who tilted their heads or attempted to use their fingers to measure the lines were asked to refrain from doing so. As each subject finished, he returned to his classroom and another subject entered from those waiting outside. The waiting group was constantly replenished in small groups of twos or threes from the class being tested. In this way, a fairly rapid rate was maintained until the total class had been tested. At this point, the Experimenter entered another class and the whole cycle was repeated. Prior to testing each individual, the Experimenter asked the subject his name. If it appeared on the list of retainees for that g, 18 class, his responses were not recorded. Barring this, all other treatment was the same as any other member of the class. The second step in testing was to present the subject with two different-sized weights. The subject was told: ”Pick up these weights, one in each hand, and tell me which one feels heaviest to you." Systematic collection of data for the Size-Weight Illusion was originally planned and collected over the first 200 subjects. After these first subjects, systematic collection was stOpped but a pair of weights similar to those used with the first 200 subjects was used to keep the test sequence identical for all subjects. When the weights had been returned to the Experimenter, the Kindergarten, grade 1, and grade 2 subjects were shown two test cards (Figures 6 and 7) to determine their ability to dis- tinguish between the colors used and to ascertain if they understood the concept of "longest“. The presentation order and axial orientation of these cards was alternated for each subject. One card had a black and a blue line; the other, two blue lines. Regardless of which card was presented, subjects were asked: "Do you see the two lines on this card? Which one looks longest to you? Point to that line for me." All instructions requesting the comparison of two lines asked for the identification of the "longest" rather than the "longer" of the two. The youngest subjects seemed to understand the instructions better with this usage, therefore, it was retained for all subjects. 19 After the subject had chosen one of the lines, he was asked: ”What is the color of that line? What is the color of the other line?" The same process was repeated with the second test card. For his responses to be recorded, each subject had to identify the longest line on both cards and be able to discriminate between the two colors, black and blue. Correct naming Of the F“ colors was not required although discriminating between them was. E It is of interest to note that several boys at the Kindergarten and first grade levels did not correctly name the blue line. When [thin m- l”£\M£-f.: this occurred, the name the subject had applied to that color was used through the rest of the session. For example, if the subject called the blue line "purple", he was later asked, "Do you see the two purple (instead Of blue) lines?" No such problem was found with girls. At this point, the first illusion was placed in the appropriate plastic frame. The length of the variable line of each illusion was determined in advance by the choice of the pre- ceding subject. If the preceding subject had chosen the variable line, the card shown to the present subject had the variable one “d” unit smaller. If the preceding subject had chosen the standard line, the present subject was shown the card with the variable one "d" unit larger. The illusion shown to the first subject of a sample was one .I ..‘W. nil. \) 20 Fliitlthl -... w .Eahflc- MUTE. HULL— .GOAumucOmoum some um newsman mu: puma menu mo acaumucoauo amwxu may .vumu awsuum one as made onu ma swam 0:9 .vuuu away Husuom one no humans mesa an own tonnagccfl muoHoo one .H .02 cums umoe .0 MMDUHM 03H” xdaam 21 .:o«umu:omoue none as mundane was once menu mo coauuucowuo Haaxu any .vuuo Husuou ecu no case one ma cage was .vuau unou Ausuoo onu :0 Museum henu as one vauuoavaa muoHoo any .u .92 muse away .5 mMDUHm 03am 09am rill! 22 representing the middle of the illusional series. The sequence of presentation and axial placement of the cards was the same for all subjects. This sequence was: 1. Modified Ponzo (Vertical) 2. Horizontal-Vertical with Intersect (Vertical) 3. Muller-Lyer (Horizontal) 4. Ponzo (Horizontal) 5. Horizontal-Vertical without Intersect (Horizontal) The cards were placed vertically (5" side parallel to table top) or horizontally (8" side parallel to table top) in the apprOpriate frame. With the Mbdified Ponzo before him, the subject was asked: ”Do you see the two blue lines? Which one looks longest to you? Point to that line for me." These same questions were asked upon presentation of the Muller-Lyer and Ponzo illusions. After the subject had pointed to his choice, it was recorded, the illusion removed, and the next illusion in the sequence placed in its apprOpriate frame. For the two horizontal- vertical illusions, subjects were asked: "Do you see the black and blue lines?' Which line, black or blue, looks longest to you? Point to that line for me." Verbal identification of the line was not accepted in the illusions where the standard and variable lines were the same color. Subjects were allowed to identify their choice by color in the two Horizontal- Vertical illusions. Each subject saw just one drawing of each illusion. [Pig‘- mum “mu-Lu] fl 23 Scoring Responses were recorded on special scoring sheets (see appendix). If the subject chose the variable line as longest, a 7 (plus) was entered in the apprOpriate place. If the standard was chosen, a 0 (zero) was entered. When a / was entered for a subject, the next subject saw a card on which the variable was one "d" unit smaller. If a zero was entered for the subject, the next subject saw a card with the variable one "d” unit larger. 2,1,. mfi.= 24 RESULTS Fourteen groups, both sexes for each of seven age levels, were defined by the experimental procedure for each Of five illusions. The normality of the distribution of the variable in all seventy groups was checked by plotting each distribution on normal probability graph paper. With one exception, all plots yielded straight or nearly straight lines of three or more points. The exception is the kinder- “—3 garten Ponzo female group which had only two points on the graph. The n, E, and SD for each group was determined by i techniques apprOpriate to the Up-and-Down Method. All is, and SDs were originally determined by the method in Dixon and Massey (1957, pp 318-327). The kindergarten and grade 2 Ponzo female groups yielded d/SD ratios greater than 2.00, necessitating the use Of the alternative technique (Dixon and Mood, 1948). Dixon and Mbod also point out that in comparisons of is, the standard error of the mean determined must be corrected by a factor "G" which is related to the size of the d/SD ratio. This correction is listed in tabular form in their article. The correction, G x SD, is less than i 5 per cent in most cases. All SDs used were so corrected for use in analysis of variance. Table 3 shows the E, corrected SD, and effective n, for each group. Figures 8 through 12 graphically show the means in terms of ”d“ units by sex and grade level for each of the five illusions. 25 TABLE 3. The mean, standard deviation (corrected according to the d/SD ratio), and effective sample size for each grade and sex of each illusion. Means and standard deviations are in terms of "d” units. Grade Level Illusion K 1 2 3 4 5 A PONZO _ Males X 8.956 9.066 9.231 9.229 9.100 9.347 9.180 SD .6188 .6239 .6079 .6877 .7902 .5730 .7048 n 57 53 52 48 50 52 50 Females H 8.885 9.198 9.265 9.420 9.324 , 9.352 9 180 SD .6307 .6291 .6273 .7869 .5955 .6603 .6474 n 52 53 51 50 51 54 50 MODIFIED_PONZO Males X 9.710 9.944 9.577 9.542 9.520 9 519 9.340 SD 1.0147 .8311 .7067 .7551 .7090 .7357 .8066 n 57 54 52 48 50 52 50 Females 2' 10.019 10.085 10.029 9.680 9.637 9.783 9.342 SD .9940 .6736 .8483 .7151 .8912 1.0376 .7009 n 52 53 51 50 51 53 50 HORIZONTAL-VERTICAL WITH INTERSECT Phles X 13.219 13.593 13.443 13.542 13.700 13.519 12.420 SD 1.4355 1.0128 1.1492 1.3384 1.4137 1.5326 1.2298 n 57 54 53 48 50 52 50 Females 2 13.538 13.934 13.637 13.378 13.657 13.310 13.280 SD 1.1915 1.1550 1.1560 1.1239 1.2394 1.0285 1.3073 n 52 53 51 49 ‘ 51 53 50 HORIZONTAL-VERTICAL WITHOUT INTERSECT Males X 17.607 17.462 17.231 17.543 17.745 17.615 18.235 SD 1.0591 1.4253 .9887 1.0193 .8929 .8520 1.1215 n 56 54 52 48 49 52 49 Females i 17.365 17.613 17.637 17.420 18.186 18.037 17.800 SD 1.3626 1.1712 1.0541 .7794 .9130 .8870 1.0890 n 52 53 51 50 51 54 50 MULLER-LXER Males x 10.589 11.037 11.104 10.646 10.720 10.673 10.700 SD .9402 .8872 .7698 .8125 .6426 .6984 .7826 n 56 54 53 48 50 52 50 Females E 10.692 11.123 11.010 10.940 10.892 10.821 10.820 SD .8210 .7142 .7926 .6853 .7284 .7406 .7048 n 52 53 51 50 51 53 50 26 Separate analyses were performed on each illusion. The general sequence of steps follow: 1. F-max test over all fourteen groups of each illusion to determine homeogeneity of variance (walker and Lev, 1953). 2. A two-way analysis of variance using sex and age level. (Linquist, 1953). Since the Up-and-Down ram Method yields only is and SDs, the following re- 7 lationships were used to obtain the needed sums ; of squares: g :Efix 3 ‘E n E 2x2 502 (n-1)I(ZX)2/n Any error incurred due to the slightly unequal sample sizes is Type II error (Dixon and Massey, 1957, pp 181-182). 3. If the Analysis of variance did not indicate significant sex or interaction effects, the sexes at each age level were pooled, leaving seven age groups. These combined groups were then tested for homeogeneity of variance using the F-max procedure. Finally, all possible comparisons were made between these seven age groups using a range or critical difference technique (Dixon and Phssey, 1957, pp 152-153). This technique does not increase the Type I error level and, if anything, is conservative. 27 4. If the Analysis of variance did indicate sex and/or interaction effects, the sex groups at age levels were not combined. First, an F-max was calculated over age levels for each sex separately. Then all comparisons between like-sexed age groups were made using the critical difference technique. Lastly, differences between sexes at each age level were tested using t-tests. Ponzo The F-max test over the fourteen groups of the Ponzo illusion is not significant (P:> .05) indicating homeogeneity "in; I. Séiiéli-L‘m—h—J of variance. Table 4 shows the Analysis of variance for the Ponzo data. TABLE 4. Analysis of Variance for the Ponzo Illusion Source SS df MS F Age 13.1024 6 2.1837 5.0479** Sex 1.0624 1 1.0624 2.4558 Age x Sex 1.7265 6 .2878 .6653 Within 306.6931 709 .4326 - Total 322.5844 722 - - **Significant at the .01 level Since no sex and/or interaction effects appear in Table 4, sexes at each age level were pooled. The means for these combined groups appear in Table A, in the Appendix. An F-max test over these seven combined groups indicates homeogeneity of variance (P) .05). All possible comparisons between these combined groups, listed in 28 Table B of the Appendix, show that the amount of illusion dis- played by the kindergarten group is less than that shown by the grade 2, 3, 4, and 5 age levels. There is also a decrease in the magnitude of the illusion at the adult level (Figure 8) but this difference is not statistically significant. Medified Ponzo The F-max test over the fourteen groups of the Medified Ponzo indicates homeogeneity of variance (F:) .05). The Analysis of Variance for this illusion (Table 5) shows sex differences, pre- cluding pooling of sexes at each age level. TABLE 5. Analysis of Variance for the MOdified Ponzo Illusion Source . SS df MS F Age 29.7140 6 4.9523 7.2254** Sex . 7.2904 1 7.2904 10.6367** Age x Sex 3.7394 6 .6232 .9093 Within 485.9325 709 .6854 - Total 526.6763 722 - **Significant at the .01 level. F-max tests over the seven age levels of each sex are not significant, indicating homeogeneity of variance (E>>.05). All possible comparisons between the age levels of each sex separately appear in Tables C and D in the Appendix. Table C indicates that adult males have less illusion than kindergarten level males. Table D indicates that female adults have less illusion than kindergarten, grade 1, and grade 2 females. Differences between sexes at each age level show that kindergarten, grade 2, and grade 5 females see more illusion than males at the same ages (Appendix, Table E). -‘I"'?.!J§L wk. 19'! In“ ‘1‘ 29 Percent Illusion .wcoa agar: :6: w aa ddaa addendum are .Aadrdda om.uv eNH ou Aadrdda mnw.v ch soda «can magnum mafia o~nmwuu> onu .oncom use now .mvumo ammo coosuoa Hm>uou:a ecu .muacs :v: mo mEu0u cw commouaxo one memos HH< .:0amsHHH owcom onu how memos ona .w MMDUHm . AM>MA MQ .uuaas :v: we now 338 2:. .m mmDUHm G.m m.® m.~ w.wH 0.0N m.HNI m.NN7 w.n~ O.mN n.0N1 m.hN —l I 1 @ _ _ 3:: Q “1&5 N.o m.o ¢.¢ m.m c.a .n.a m.o m.a o.cH ~.oH ~.oH 13A1°3ul ”Pu 31 Horizontal-Vertical with Intersect The F-max test over the fourteen groups of this illusion is not significant, indicating homeogeneity of variance (P) .05). The Analysis of variance (Table 6) shows both sex and interaction effects at the .05 level, precluding combining sexes. TABLE 6. Analysis of variance for the Horizontal-vertical with Intersect Illusion F“2 Source SS df MS F 2 Age 53.2572 6 8.8762 5.7251“ Sex 6.3292 1 6.3292 4.0823* A Age x Sex 20.8619 6 3.4770 2.2426* A; Within 1099.2350 709 1.5504 - Total 1179.6833 722 - - *Significant at the .05 level **Significant at the .01 level F-max tests over the seven age levels of each sex are not significant (P) .05). All possible comparisons between male groups show the adults displaying a greater magnitude of illusion than the children in grades 1 through 5. (Appendix, Table F). No significant differences occur between female groups (Appendix, Table G). Differences between sexes at each age level show males to have a greater amount of illusion than females at grade 1 and adult levels (Appendix, Table H). ‘Horizontal-Vertical without Intersect The F-max test over all fourteen groups of this illusion is not significant (P) .05), indicating homeogeneity of variance. 32 Percent Illusion SS mam a.: SS 6.8 0.8 «.3 9S TS fl: AS «.3 6.2 o.S «.3 9S S.S TS .wdoa adads :6: 6S aa dead unaudada are .Aadrdca n~.av 65a 66 Aadauda om.~v uoH Eoum mean nuance mafia o~nuaum> one .uOOmuoDca new: kuwuuo>nauuconwuo:. ago you .mmumo ammo coo3uon am>u0uaa osu .muacs :0: mo menu» :« vommounxo one mouse ~H< .cofimsaaH ooowuouaH now: Hwowuuo>uamucowauom may you muses use .oH manon AM>MA mn use .uoomHOuoH usosuaa Hmoauuo>uamuconauo= one uom .mcumo umou cooauop Hw>woucw onu .muacs :v: mo mshmu ow commouaxo one mCQOE ~H< .COHflflHHH UUQMHOUCH ufiOfiuwsv dQUHHHO>IHSGONHHOS Or—u HOW MCGQE 05H. In." MMDUHh am>ma wears < m e n N a M A _ . _ n q _ A . r . 1 m a 4 L ~.m T o L we I C 4‘ ¢.m l W 1 4‘ 0.2.. 4 4 1 6.3.. 1 4 m.:.. 0 .. TS- L 52.. C adaaefi O 1 Honda-l . I. 9S- 0 1 AV moan: q.¢~l AV 1 N.n~ m.na ¢.- n.5H c.n~ n.n~ w.na 0.5H o.mH H.wH N.wH m.mH snlun H pll 35 Muller-Lyer The F—max test over the fourteen groups of this illusion is not significant (P) .05) indicating homeogeneity of variance. The Analysis of variance (Table 8) shows significant sex differences, precluding the combining of sexes at age levels. TABLE 8. Analysis of variance for the Muller-Lyer Illusion r“. 1.: :3. q E Source - SS df MS F i Age 17.2949 6 2.8825 4.8429** Sex 2.4451 1 2.4451 4.1080* Age x Sex 2.0670 6 .3445 .5788 .Within 422.0132 .709 .5952 - ._.4 Total 443.8202 722 - - *Significant at the .05 level **Significant at the .01 level F-max tests over the seven age-level groups of each sex indicate homeogeneity of variance (P): .05). All possible comparisons between males show that the grade 2 males have a greater illusion than the kindergarten level males (Appendix, Table L). No significant differences are found between female groups (Appendix, Table M). Comparisons between sexes at each age level find the grade 3 females with a larger illusion than the grade 3 males (Appendix, Table N). All Possible Comparisons The use of the All Possible Comparisons technique for testing differences between individual groups seems to find very few such differences significant. This seems especially contradictory considering that all Analysis of Variance tests indicate differences 36 Percent Illusion 65. Fig-...”. \ 4.21. onu .uo%41quH:z onu Mom .n... 16.1.1» MO $50..“ CH UGmmUHQunO 0H0 mSGO—fl HH< .wcoH moan: :v: w m« mafia unoccuum .Amonoca m~.mv va cu Amazon“ mn.Hv on Baum mash weapon saga manuaus> .mvuao ammo cooauon Hm>nouca one .muaan :v: £033: nomquuozg as... How 239: can... 4m>mq ma