University of Southern California Dissertations and Theses

The Müller-Lyer illusion: a new variant, some old and new results

(USC Thesis Other)

The Müller-Lyer illusion: a new variant, some old and new results

PDF

Download

Open document

Flip pages

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content The Miiller-Lyer Illusion: A New Variant, Some Old and New Results by Brian Roberts Nelson A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF ARTS (Psychology) May 1995 Copyright 1995 Brian Roberts Nelson UNIVERSITY O F S O U T H E R N C A LIFO R N IA T H E G R A D U A T E IC H O O L U N IV E R S IT Y P A R K L O S A N O E L E * . C A L IF O R N IA * 0 0 0 7 This thesis, written by SRIAN ROBERTS NELSON under the direction of A.!?. Thesis Committee, and approved by all its members, has been pre sented to and accepted by the Dean of The Graduate School, in partial fulfillment of the requirements for the degree of MASTER OF ARTS Dtmm Date Ap^il J8, 1995_ TABLE OF CONTENTS page LIST OF FIGURES iii ABSTRACT iv INTRODUCTION 1 METHOD OF EXPERIMENT 1 19 Subjects 19 Stimuli 19 Procedure 22 RESULTS OF EXPERIMENT 1 23 EVALUATION OF EXPERIMENT 1 2 6 METHOD OF EXPERIMENT 2 31 Subjects 31 Stimuli 31 Procedure 31 RESULTS OF EXPERIMENT 2 32 EVALUATION OF EXPERIMENT 2 3 3 DISCUSSION 39 REFERENCES 53 i i i LIST OF FIGURES Figure Page 1 Traditional Muller-Lyer 3 configurations 2 Configurations related to the 5 depth processing or size constancy approach for explaining the mechanisms of the Muller-Lyer illusion 3 Figures related to the "averaging" 8 theories of the Muller-Lyer illusion 4 Optical account for the illusion 12 5 Samples of the stimuli used 21 6 Exp. 1 fin length X fin condition 27 interaction and shaft distance X fin condition interaction 7 Exp. 1 fin length X shaft distance X 28 fin condition interaction 8 Exp. 2 fin length X fin condition 35 interaction, fin angle X fin condition interaction, and shaft distance X fin condition interaction 9 Exp. 2 fin length X shaft distance X 37 fin condition interaction 10 Exp. 2 fin angle X shaft distance X fin condition interaction 38 iv Abstract A new variant of the Muller-Lyer illusion task, in which subjects were asked to judge the distance on each side of a single set of fins, was investigated in two experiments. In Exp. 1, a centrally located fin-set was varied with respect to the distance to be judged and the length of the fins. The experiment also varied the presence or absence of a shaft. In Exp. 2, fin angle was manipulated along with the previous variables, but deleting the shaft condition. The present results support the contention that an asymmetry exists for acute versus obtuse conditions. The major finding of the present study was a difference of effect for acute and obtuse fin configurations on judgments of short and long distances. A review of theories did not find any which would predict the present results. 1 The Muller-Lyer Illusion: A New Variant, Some Old and New Results Over the years, investigative interest in the Muller-Lyer <1896) illusion has easily outpaced all other visual illusions, and a number of theories have been put forth in an attempt to explain why the illusion occurs. In general these theories fall into three broad categories. First are size constancy or depth theories such as Gregory's (1963) explanation of the Muller-Lyer illusion in terms of inappropriate constancy scaling and Fisher's (1967) attempt to relate the Muller-Lyer to the Ponzo illusion. Second are theories that propose a process which averages the spans which are contained between the fins. These include Pressey's (1967, 1970) assimilation or central tendency explanation for the effect, Erlebacher and Sekuler's (1969) confusion theory, and Coren's (1986) efferent explanation which is based on eye movements. Last, Chiang (1968) has proposed that measurement of the span is affected by the perception of a displaced vertex position inside of the fins. Since these theories capture the key concepts in describing the mechanisms of the Muller-Lyer illusion, each will be reviewed below. Paradigm and terminology A number of terms have been used to describe the components of the Muller-Lyer configuration. For example, "fins," "tails," and "wings" have all been used to depict any segment which is added to the shaft. Similarly, "inward-going," "arrowhead," "wings-in," and "tails-in" all refer to an acute condition in which the angle formed by each fin and the shaft does not exceed 90° or, for both fins, a combined 180°. Conversely, the terms "outward-going," "featherhead," "wings-out," and "tails-out" all refer to an obtuse condition in which the angle formed by each fin and the shaft is greater than 90° but less than 180°. For both fins, this angle would be greater than 180° but less than 360°. Figure 1 on page 3 depicts the traditional Muller-Lyer configuration with these angular conventions in mind. It should be noted that in the above discussion the term "fin" refers simply to a single oblique segment which is added to the shaft, whereas "fins" refers to a pair of fins which creates the appearance of an arrowhead or the tail of an arrow. "Fin-pair" describes the condition in which there are fins at each end of the shaft, as in Figure 1 (top or bottom). In discussing a given theory, it is best to use the terms provided by the author rather than forcing a translation which may not do justice to their view. However, in reporting and discussing the present experiments, the terms "acute," "obtuse," and "fins" will be used to describe the proposed new variant. 3 s o < <C) (d) (e) Figure 2. Configurations related to the depth processing or size constancy approach explaining the Miiller-Lyer illusion, (a) A vertically oriented Mviller-Lyer figure, in which the fins of the obtuse version are said to project towards the observer and the fins of the acute version project away from the observer, (b) The Brentano (1892) or composite Miiller-Lyer figure in which the segment bounded by the acute fins on the left is perceived as being shorter than the segment bounded by the obtuse fins on the right, (c) The Ponzo figure in which the the upper horizontal line segment appears to be longer than the lower horizontal segment. (d) Two Ponzo figures juxtaposed as an intermediate step in comparison with composite figure (b). (e) Four Ponzo figures juxtaposed and rotated in an attempt to emulate the composite Miiller-Lyer figure. 6 the composite version) of the Miiller-Lyer illusion, in which the portion of the horizontal line bounded by ingoing fins appears to be much shorter than the portion which is bounded by outgoing fins. He continues with Figure 2c (the traditional Ponzo illusion), in which the upper horizontal line appears to be longer than the lower horizontal line. In essence, the oblique lines of the Ponzo figure provide linear perspective cues which, in turn, cause the figure to be perceived in depth. It is this depth analysis that makes the upper horizontal line appear longer than the lower horizontal line. By juxtaposing elements of the Miiller-Lyer and Ponzo figures (Figure 2d) one can see the relationship between the Muller-Lyer and Ponzo illusions. Through additional orientation inversion of the Ponzo figure (Figure 2e) one can fully appreciate the similarities in the two figures. Rather than rely solely on the angles of the arrow-heads as the lone contributor to the Miiller-Lyer illusion, the distortion gradient principle points to the lateral relationship between the oblique lines in describing the illusion. For example, in Figure 2e the center line bounded by ingoing fins appears shorter than the outer two lines, whereas the center line bounded by outgoing fins appears longer than the outer two lines which are associated with it. Therefore, the left-side center line appears to be shorter in relation to the right-side center line, thus accounting for the illusion. 7 AVERAGING THEORIES Pressey (1967, 1970) outlined a "central tendency effect" or assimilation theory of the Miiller-Lyer illusion in which judgments of short distances are overestimated and judgments of long distances are underestimated. The crux of this position holds that the observer evaluates not only the shaft between the apices of the ingoing and outgoing finned figures, but also includes in the judgment all possible contextually parallel lengths that are bounded by the fins. For example, in Figure 3a (top) the judgement includes not only the length of shaft AB but also all of the horizontal distances which lie between EF and E'F' (see Figure 3 on page 8). Since AB is evaluated in this overall context of EF to E'F' and since AB is the shortest length in this context, the tendency will be to overestimate the length of AB and perceive it as being longer than it actually is. Similarly, in Figure 3a (bottom) shaft length CD is judged in the overall context ranging from GH to G'H'. Since CD is the longest length in this context, the tendency will be to underestimate the length of CD and to perceive it as being shorter than it actually is. Pressey and Bross (1973) have gone on to outline additional postulates of assimilation theory which includes the calculation of ratios among the components of the configuration. Specifically, they propose that the (a) (b> > < > < Q H H (c) Figure 3. Figures related to the "averaging" theories of the Miiller-Lyer illusion, (a) Assimilation model for the illusion in which shaft lenghts are compared to all other contextually parallel lengths bounded by the fins. The top figure is said to be overestimated because shaft length AB is the shortest length in the context of EF to E'F'; similarly, shaft length CD is underestimated because it is the longest length in the context of GH to G'H'. (b) Confusion theory model in which the shaft length 'd' (lower figure) gets confused with respect to inter-fin tip distance ' c.' This results in an underestimation of shaft length ' d.' Comparable overestimation occurs in the upper figure and illusion magnitude is greatest when perpendicular distance ' e ’ is reduced, (c) The efferent model for the illusion proposes a role for saccadic eye movements. The eye is shifted to a position on each fin marked here by a bullseye, and thus accounts for the overestimation (upper figure) or underestimation (lower figure) of the particular configuration being judged. magnitude of the illusion varies as the ratio of shaft length in relation to all contextual lengths. If this ratio is small, the illusion magnitude also will be small, and if the ratio is large, illusion magnitude will be large. Pressey (1974) also postulates the concept of an attentive field, defined as the midpoint between the two most extreme elements to be judged. Put simply, he suggests that illusion magnitude will either increase or decrease as a function of the relative proximity of stimulus elements. Small changes in illusion magnitude will occur when these elements are located at remote positions relative to the center of the configuration. Large changes in illusion magnitude will occur when the configuration is more compact. Similar to Pressey (1967, 1970), Erlebacher and Sekuler (1969) propose a confusion theory account for the Muller-Lyer illusion whereby the observer judges not only the shaft of a given configuration but also the length of the entire figure, including the fins. What gets confused, then, is the relationship of the inter-fin tip distance in comparison to the shaft length. For example, in Figure 3b (bottom) when shaft length 'd' is to be evaluated, the subject also considers the inter-fin tip distance 'c.' These different lengths become confused and a type of "regression towards the mean” occurs, leading shaft length 'd' to be underestimated. Additionally, if perpendicular distance 'e' (see bottom of Figure 3b) is manipulated, while 10 holding inter-fin tip distance constant, the illusion is greatest when the tips of the fins are nearer the shaft to be judged. Unfortunately, Sekuler and Erlebacher (1971) found that confusion theory only explained the ingoing fin-pair figure after they tested the comparable outgoing fin-pair figure and found no effect as a function of inter-fin tip distance on that figure. In essence, greater confusion is more likely to occur when the configuration to be judged is more compact, especially for the ingoing fins figure. Coren (1986) has proposed an efferent component in the visual perception of the Muller-Lyer illusion in which motor activity, namely voluntary eye movements or saccades, are modified on the basis of the configuration being judged. In general, the fins of the figure have the effect of shifting or directing eye movements to an area in the configuration which is centered between the end of the shaft and the tip of the fin. It is the efferent readiness of this saccadic eye movement towards this center of gravity which is responsible for the illusion. In other words, Coren (1986) is presuming a system for measuring span which uses fixation-to-fixation distance. This idea can be seen in Figure 3c in which the figure is either overestimated (top) or underestimated (bottom) based on this over-shooting or under-shooting of saccadic eye movements. An important consideration, though, regarding these eye movements is the 11 concept of a "functional fovea," defined as a 2 - 4° circle around the center of the anatomical fovea, where visual acuity is the best. In an effort to process the relationship between the length of the fins and the ends of the shaft, the functional fovea is shifted to an intermediate position between the two. Therefore, for the acute version of the figure, underestimation will occur as eye fixations are shifted to an interior position of the distance to be judged. Conversely, for the obtuse version of the figure, overestimation will occur as eye fixations are shifted to an exterior position of the distance to be judged. CENTROID DISPLACEMENT THEORY Chiang's (1968) optical theory for the Muller-Lyer (as well as many other visual illusions) posits that as lines intersect there is a peak of excitation in the visual system such that the subjective location of this intersection is displaced to a position somewhere between the lines. Therefore, as two lines meet at an apex (see Figure 4 on page 12), the peak of excitation and subsequent subjective location of that apex is perceived to lie on the inside (the acute side) of the intersecting lines. Additionally, the optical theory holds that the subjective movement of the fin apex away from its objective position will increase if the 12 Figure 4. Optical acount for the illusion whereby the apex of each set of fins is perceptually displaced to an interior position, i,e,, within the concave region which is bounded by the fins. Underestimation in the upper figure occurs because the apices are perceived as being closer than they actually are. Conversely, overestimation of the bottom figure occurs because the apices are perceived as being farther apart than they actually are. (NOTE: shafts are absent here so the subjective relocation of the fins can be shown with a dot, not because optical theory demands that shafts be absent.) 13 angle between the lines becomes more acute. In general all of the above theories propose an explanation for the Muller-Lyer illusion which rely on the presence of a pair of fins. In other words, there appears to be a dependence on contained figures in order to explain the illusion. It should be apparent, however, that all of the theories presented would predict underestimation for any acute variant and overestimation for any obtuse variant of the illusion. Beyond this any extension of the above theories is much less clear. More may be said, though, regarding configurational aspects of the illusion. A typical finding throughout the literature is an asymmetry in illusion magnitude between the acute and obtuse forms of the illusion. That is, an absolute difference is normally observed when comparing acute configuration underestimation to obtuse configuration overestimation. More often than not, acute variations are found to be weaker in magnitude than their obtuse counterparts (Adam & Bateman, 1983; Bross, Blair, & Longtin, 1978; Butchard & Pressey, 1971; Christie, 1975; Cooper & Runyon, 1970; Day & Dickinson, 1976; Erlebacher & Sekuler, 1974; Greist-Bousquet & Schiffman, 1981a; and Sekuler & Erlebacher, 1971). Though this finding is reasonably robust, there have been instances when this relationship has been reversed, i.e., finding acute configurations to be stronger than the obtuse ones (Coren & Porac, 1983), Also, some investigators have found 14 little or no asymmetry between acute and obtuse variations (Jordan £> Uhlarik, 1986; Worrall & Firth, 1974). It is possible that asymmetry depends not only on which variant is being tested, but on how it is tested. Another area of debate involving differences between acute and obtuse forms of the illusion is the fin length at which maximal illusion occurs. For example, Heymans (cited in Restle & Decker, 1977) used the Brentano (1892) version of the Muller-Lyer illusion and found that illusion magnitude was greatest when fin length was approximately 30 - 40% of shaft length. However, when Day (cited in Day & Dickinson, 1976) tested a truncated version of the classical Miiller-Lyer illusion (which had only one fin attached to the shaft), he found that maximal illusion occurred when fin length was 10 - 30% of shaft length. This finding supports Erlebacher and Sekuler's (1969) claim that relatively short fins elicit the greatest perceptual error. Finally, Restle and Decker (1977) used a single-fin symmetrical variation of the Miiller-Lyer illusion and found that for all acute angles and up to 120°, maximal illusion occurred when fin length was equal to shaft length. Additionally, with more obtuse angles, maximal illusion occurred as fin length was steadily reduced when compared to shaft length. Once again, the fin to shaft length which elicits maximal illusion is dependent on which variation of the Miiller-Lyer one is using. In general, there appears to be three primary variables 15 which control the strength of the Miiller-Lyer illusion: shaft length, fin length, and the angle at which the shaft and fins meet. Most often configurations are tested in which these variables are made explicit. That is, the parts of the configurations can be seen. Many investigators, though, have tested variants in which these variables are only implied. For example, Coren (1970) and Greist-Bousquet and Schiffman (1981a) tested a stripped-down variant of the traditional Miiller-Lyer configuration in which the location of the vertices (target ends of the shaft) and the wing tips were replaced by dots. Though the overall magnitude of the illusion was reduced using this dot variation, typical underestimation for wings-in and overestimation for wings-out was still found. Amazingly, removal of the contour lines of the fins and shaft did not abolish illusory effects. Beagley (1985) compared shaft and no-shaft variations of the Miiller-Lyer illusion and found that removal of the shaft made both the wings-in and wings-out configurations appear shorter than their shaft-included counterparts. However, the traditional direction of illusion magnitude for each no-shaft variant still remained. Similarly, Greist-Bousquet and Schiffman (1981b) also manipulated shaft versus no-shaft configurations and found that removing the shaft of the wings-out Miiller-Lyer illusion resulted in an overestimation of the linear extent of the configuration. This overestimation, though, was weaker than its shaft-included counterpart. Additionally, removing the shaft of the wings-in figure resulted in an underestimation of the linear extent of the configuration, and this underestimation was greater than its shaft included counterpart. In essence, when the shaft of either Miiller-Lyer configuration is eliminated, a decrease in apparent linear extent occurs. A practical matter involving any Miiller-Lyer configuration includes the method employed to measure the perceptual error that is produced by the illusion. For example, the method of adjustment typically involves both an ascending and descending order of presentation in which subjects are asked to adjust the length of a comparison line to match the length of the shaft in the test figure. Similarly, the method of limits includes an experimenter generated presentation in which a comparison line is adjusted from one extreme and continued until the subject reverses their response from shorter to longer (or vice versa) than the test figure. Lastly, the method of reproduction may involve either drawing the length of the shaft provided or placing a slash through a response line such that the length marked matches the shaft length represented in the test figure. All of these methods allow acute and obtuse effects to be determined independently but a comparison across configurations which lie at different points in space may introduce covert measurement strategies. In other words, having the response segment above or below 17 the finned configuration may allow vertical alignment of end points. Placing the response segment next to the finned configuration requires that the encoded distance be remembered, and it is not clear that judgment would be immune to the influence of the fins which are present at the end of the adjacent figure. In general, each method for specifying the distance which is perceived has some potential for bias. Requiring the subject to mark a point on a line, as in the method of reproduction, presumes that the metric system for judging segment lengths is not affected by the continuous extent of the line being marked. It is well known that metric judgments of divided versus undivided space are different (Piaget, 1969), and it would not be surprising if this applied for comparisons of discrete versus extended segments. Also, having a mechanism for adjusting segment length, as in the methods of adjustment and limits, may introduce bias from dynamic (motion) factors. Lastly, it is not clear whether the illusion is dependent on the presence of fins at each end of the segment to be judged. Given these considerations, and recognizing that any choice would likely be a compromise among potential sources of bias, a decision was made to study the influence of a single set of fins, positioned at the center of the two spans to be judged. This is similar to the Brentano (1892) version in which the end-sets have been eliminated. With 18 this configuration the spaces to be judged are immediately adjacent, reducing any requirement that the distance be encoded, preserved in memory, and then used for comparison at a more remote location. This method allowed the perceived span to be indicated by the simple operant of marking a point, similar to the method of reproduction. Of primary interest in the following experiments was the question of whether or not traditional Muller-Lyer underestimation and overestimation would occur using this configuration in conjunction with a simplified judgment task. It seemed at the outset that the method would not provide a difference in illusory effects as a function of acute versus obtuse configurations, but as will be seen subsequently, this difference is manifested nonetheless. For Experiment 1, a stimulus configuration was constructed in which the fin condition (acute or obtuse) was held at a constant angle and fin length and shaft distance were manipulated. The shaft distance was indicated by the location of two dots. The first dot was located at the apex of the fins. The second dot was located on the same axis as the first dot at a position some distance from the apex. These two dots together may properly be referred to as "stimulus distance" as this was the span to be judged. The point marked by subjects in the task was designated as "response distance." It was hypothesized that the acute configuration would be underestimated and weaker in magnitude relative to the obtuse configuration. The obtuse configuration was expected to be overestimated. The results indicated that appropriate underestimation and overestimation did occur with this new variant and that shaft distance played an important role in this overall effect. Experiment 2, therefore, manipulated all three variables: fin length, shaft distance, and fin angle. The results of Experiment 2 indicated that fin angle contributed to the magnitude of the illusion. Experiment 1 Method Subjects. Eight U.S.C. undergraduates served as paid subjects in Experiment 1. All subjects were naive with respect to the phenomenon under investigation and each had normal (20/20) visual acuity with each eye, some having the benefit of contact lenses. Stimuli. All stimulus configurations were plotted on 8.5 X 11 in. paper with an Apple LaserWriter with the axis of the shaft oriented along the horizontal (long) axis of the page. Line thickness was measured with a dissecting microscope, which contained a calibrated reticule, and was found to be 4 min. of visual angle. The diameter of the dots which specified the distance to be judged were 8 min. of visual angle. The stimulus variables used in Experiment 20 1 were fin length, shaft distance, fin condition, response side, and shaft condition. Figure 5 on page 21 shows some examples of the stimuli used in Experiment 1. Two oblique segments which met to form a vertex or an intersection represented the fins of the configuration. Fin length was measured from the vertex of the fins and subtended 1, 2, 4, or 8 degrees of visual angle (abbreviated deg. to avoid confusion with angular measures in the plane of the page). Shaft distance was specified by the positioning of two stimulus dots, both of which were 8 min. in diameter. One stimulus dot was located at the vertex of the fins and centered in the middle of the page. A second dot was placed either 1, 2, 4, or 8 deg. away from the vertex along the horizontal axis of the page. Fin condition referred to either an acute or obtuse configuration (see Figure 1). For the acute condition, the angle formed by the shaft axis and one fin was held constant at 45°. The angle i formed by the shaft axis and one fin of the obtuse condition was held constant at 135°. It should be noted here that although these fin angles represent two fin conditions, the fin conditions are simply the result of one angle which is defined as acute or obtuse depending on other aspects of the configuration to be judged. For example, a configuration was defined as acute when the dot representing shaft distance was located to the inside of the vertex, whether the fins were pointing to the left or to the right (see 21 («> (b) (c) ( < J ) Figure 5. Sample of the stimuli used. "X" represents the response side of the configuration - a location which might be chosen by the subject. In the stimulus configuration this side would be blank. (removed from the fins apex) represents the stimulus side or shaft distance of the configuration being judged. Figures (a) and (d) are acute configurations and (b) and (c) are obtuse configurations. Thus it should be clear that the status of a configuration as acute or obtuse relates to the position of the stimulus dot, not whether it is pointing to the left or right. Additionally, one half of all stimuli tested in Exp. 1 included an extended shaft (see (a) or (b)) on which subjects were instructed to mark their response. 22 Figures 5a and 5d). The configuration was considered obtuse when the dot representing shaft distance was located outside the vertex (see Figures 5b and 5c). Response side, then, was to the left or to the right, on the opposite side of the vertex in relation to the stimulus dot representing shaft distance. Lastly, shaft condition was defined by the presence or absence of a shaft. When a shaft was present (see Figures 5a and 5b), it extended across the entire length of the page and passed through the vertex of the fins and the stimulus dots. A shaft was present in one half of all the materials tested in Experiment 1. In all there were 4 levels of fin length, 4 levels of shaft distance, 2 fin conditions (though just one fin angle), 2 levels of shaft condition (present or absent), and 2 levels of response side (left or right) for a total of 64 pages. This set was doubled and randomized throughout for a test set of 128 pages. Procedure. Each subject was provided with a random order of stimuli and a viewing stand, following the methods of Weintraub and Brown (1986). The stand included a mask in which the horizontally aligned eye slots were positioned at a distance of 46 cm above a viewing and marking surface. This surface was inclined at 15° to the table and was orthogonal to the line of sight of the observer. The stand also included edge-stops to aid in the alignment of the stimulus pages. The horizontal alignment of the eye slots 23 discouraged head movement and thus served to enhance a consistent orientation of the head in relation to the stimulus display. Subjects were told that this was a test of their ability to evaluate distances between points or dots. They were instructed to place one stimulus page squarely on the stand one at a time and to pencil a dot on the opposite side of the displayed dot that matched the distance between the displayed dot and the vertex of the fins. When a shaft was present, subjects were asked to mark their dot on this line and when the shaft was absent, subjects were asked to mark their response along the horizontal axis which passed through the displayed and vertex dots. No additional effort was made to constrain the response. Additionally, subjects were told that they could erase and change their response if they were not satisfied with their initial judgment (though this option was seldom used). They were then allowed to proceed through the entire stimulus set at their own pace. All subjects completed the task in under 1 hr. Results In comparing responses to acute and obtuse variants of the Mtiller-Lyer illusion, there are several methods one must choose from. For example, a difference score may be used which provides a "point of objective equality" (POE) of a 24 provided shaft length being subtracted from the subject's "point of subjective equality" (PSE) for that same length. The absolute values that have been derived from acute and obtuse configurations then may be used (or not used) depending on whether symmetry in the strength of effect is of interest. Alternatively, the POE may be calculated from a control or baseline stimulus which has been tested, or a percentage of error may be calculated based on a ratio of the PSE to the POE. Because the new variant bears a resemblance to the Brentano (1892) version of the Muller-Lyer illusion, it was not clear from the outset whether a difference would exist between acute and obtuse configurations regarding illusion magnitude. In other words, there was no reason to expect asymmetrical effects. Once it was established, however, that these configurations showed the "classic" pattern of reverse action with respect to (acute) underestimation and (obtuse) overestimation, a more direct comparison of the results became warranted. Therefore, in order to permit a more direct comparison of the errors made under the experimental treatments, acute configuration judgments were reversed in sign relative to their obtuse configuration counterparts. In this regard, acute and obtuse configurations were compared on the same scale. For each stimulus page the distance marked by the subjects was measured to the nearest .5 mm. After reversing the sign of the acute configuration responses, all values were then converted to a proportional error using the formula: (Response distance - Stimulus distance) / Stimulus distance. The stimulus distance was the shaft distance specified by the position of the dot. For the sake of clarity in all figures to be presented, and since acute configuration responses were reversed in sign, positive proportions for acute and obtuse configurations are indicative of underestimation and overestimation, respectively. Negative proportions, on the other hand, are indicative of overestimation for acute configurations and underestimation for obtuse configurations. If acute and obtuse effects were symmetrical for each of the other factors tested, one would just use absolute distance and combine them into a percentage effect. However, asymmetry was found with respect to "fin length" and "shaft distance," the span being judged. Therefore, except for one main effect comparison, the acute and obtuse distinction will be maintained. The data for the 8 subjects were analyzed with a five-way within-subjects analysis of variance (ANOVA). There were 4 levels of fin length, 2 levels of response side, 2 levels of fin condition, 4 levels of shaft distance, and 2 levels of shaft condition. This analysis indicated that response side (F(l,7) = 0.18) and shaft condition (F(l,7) = 2.45) were nonsignificant at the .05 level. Also, 26 an effect of shaft condition or response side was not indicated by any higher order interactions involving acute versus obtuse configurations. Because of this lack of significance the data were collapsed across these two variables and the three-way within-subjects ANOVA was rerun. The main effect for fin condition was nonsignificant at the .05 level, F{1,7) = 1.48. The two two-way interactions of interest were both significant: for fin length X fin condition, the values were: F(3,21) = 4.71, jd < .05; and for shaft distance X fin condition, the values were: F (3,21) = 30.15, £ < .001. The three-way interaction of fin length X shaft distance X fin condition was also significant, F(9,63) = 3.00, £ < .01. Figure 6 on page 27 shows the fin length X fin condition and the shaft distance X fin condition interactions. Figure 7 on page 28 shows the three-way interaction as a function of fin length in four separate panels. Evaluation of Experiment 1 The first question to be raised by the results of Experiment 1 is the issue of acute and obtuse angle symmetry. Though the main effect for this variable did not reach significance, there was a 5% difference in the overall size of acute and obtuse effects. Additionally, this difference occurred in the traditional direction with the 27 QC UJ 15 10 5 0 1 2 4 8 ACUTE OBTUSE FIN LENGTH (DEG) (a) 30 n 2 5 - 20- cr § o c UJ 1 0 - 0- 1 2 4 8 SHAFT DISTANCE (DEG) (b) Figure 6. (a) Exp. 1 fin length X fin condition interaction As can be seen , illusion magnitude was little changed for the obtuse configuration as fin length was increased. Conversely, illusion magnitude decreased with the acute configuration as fin length was increased, (b) Exp. 1 shaft distance X fin condition interaction . Here, the acute and obtuse configurations were differentially affected as a function of increasing shaft distance. For the acute configuration, underestimation increased as shaft distance increased. For the obtuse configuration, overestimation decreased as shaft distance increased. 28 (a) < b ) ACUTE OBTUSE 35-i FIN - t DEG 3 0 - 20- 1 5 - UJ / 1 0- 0- 2 4 SHAFT DISTANCE (DEO) 1 25-, FIN - 2 DEG 20- 15 - IU 5 - 2 4 SHAFT DISTANCE (DEG) 8 1 (C) (d> 25-1 FIN - 4 DEG 20- 10- UJ 0- 2 4 SHAFT DISTANCE (DEO) 1 a 30-n FIN - B DEG 20- 1 5 - 1 0 - 8 2 4 SHAFT DISTANCE (DEG) 1 Figure 7. Exp. 1 fin length X shaft distance X fin condition interaction. Here it is shown that the "X" pattern observed in Fig 6b hold across each of four fin lengths. Once again, as shaft distance increased, acute configuration underestimation increased and obtuse configuration overestimaton decreased. 29 obtuse effect being relatively stronger in magnitude than the acute effect (Adam & Bateman, 1983; Bross, Blair, & Longtin, 1978; Butchard & Pressey, 1971; Christie, 1975; Cooper & Runyon, 1970; Day & Dickinson, 1976; Erlebacher & Sekuler, 1974; Greist-Bousquet & Schiffman, 1981a; and Sekuler & Erlebacher, 1971) . As can be seen from Figure 6a, acute and obtuse angle variants behaved differently when paired with different fin lengths. The obtuse angle effect provided an average overestimation of 15.5% and did not change much regardless of which fin length was used. The acute angle effect, in stark contrast, was greatly affected by the length of the fins. An increase in fin length produced a decrease in the magnitude of the underestimation. In this regard, for the acute angle variant, as fin length increased subjects became more accurate in judging the shaft distance which was presented to them. In Figure 6b, acute and obtuse variations differ considerably when paired with shaft distance. For the acute angle, underestimation increased as shaft distance became longer. That is, when judging longer spans for the acute variant, subjects made greater errors associated with contraction. Conversely, for the obtuse angle, overestimation decreased as shaft distance increased. In other words illusion effects declined as shaft distance increased. 30 Figure 7 is an expanded version of figure 6b. Figure 7 shows that the relationship between fin condition and shaft distance holds up for all four fin lengths even though there is a slight variation in the patterns observed. This variation may account for the significant three-way interaction. Underestimation of the acute variant monotonically increased as shaft distance was increased and overestimation of the obtuse variant monotonica11y decreased as shaft distance increased. It is also noteworthy in both Figure 6b and Figure 7 that, for the shortest shaft distance, subjects actually averaged an overestimation for the acute angle when an underestimation would be expected. Just as interesting is the fact that, for the obtuse angle and at the maximal shaft distance, subjects were nearly perfectly accurate in judging this distance. For the obtuse angle, it is difficult to explain why subjects actually underestimate the longest shaft distance when it is paired with the shortest fin length. Because of the interesting and unusual results of Experiment 1, an additional experiment was conducted in which fin angle was manipulated in conjunction with most of the variables used in Experiment 1. This was done to ensure that the results obtained in Experiment 1 were reproducible and in the interest of determining if a difference existed between acute and obtuse configurations on this variable. 31 Experiment 2 Method Subjects. An additional eight U.S.C. undergraduates served in Experiment 2. All subjects had 20/20 binocular vision, some having the use of contact lenses. All subjects were paid for their participation and were naive with respect to the phenomenon under investigation. Stimu1i. Unless specifically stated, all stimuli used were identical to those in Experiment 1. The stimulus variables for Experiment 2 were fin length (2 or 8 deg.), shaft distance (1, 2, 4, or 8 deg.), fin condition (acute or obtuse), fin angle (acute: 15, 30, 45, 60, or 75°; obtuse: 105, 120, 135, 150, or 165°), and response side (left or right) for a total of 160 pages. Though response side did not reach significance in Experiment 1, it was included here to provide counterbalancing in order to avoid the potential development of a response bias. Shaft condition did not reach significance in Experiment 1 and it was not included as a factor in the second experiment. In addition to the acute and obtuse angles which were used, a 90° fin angle was tested under all combinations of fin length, shaft distance, and response side for an additional 16 pages of material. Each subject received a different random order of the entire set of 176 pages. Procedure. Unless stated otherwise, the procedure used 32 in Experiment 2 was identical to that used in Experiment 1. Because of the size of the stimulus set tested, the task, was administered in two sessions. After completion of the first half of the stimulus set each subject was provided with a 5 minute break, which allowed them to relax and rest their eyes. After this break the second half of the stimulus set was provided. Even though the size of the stimulus set was relatively large, all subjects completed the entire task in under 1 hr. Results After reversing the sign of the acute condition responses (see Experiment 1), proportional errors were again calculated for all acute and obtuse configurations tested. Prior to performing any statistical analysis, the data were collapsed across response side as this variable was not of intrinsic interest. Having shown that response side does not produce a difference (Exp. 1), it would be a waste of statistical power to treat it as a factor in the ANOVA. Additionally, because it cannot properly be classified as a level of fin condition, i.e., acute or obtuse, the 90° fin angle condition was not included in the statistical analysis either. The data for the 8 subjects were analyzed with a four-way within-subjects ANOVA. There were 2 levels of fin 33 length, 2 levels of fin condition, 5 fin angles, and 4 levels of shaft distance. The main effect for fin condition was significant, F{1,7) = 30.98, £ < .001. All three two-way interactions involving fin condition were also significant. For fin length X fin condition, the values were: F (1,7) = 12.25, £ < .01. For fin angle X fin condition, the values were: F(4,28) = 8.44, jo < .001. Also, for shaft distance X fin condition, the values were: F(3,21) = 123.05, £ < .001. The fin length X fin angle X fin condition interaction was not significant (F (4, 2 8) = 0.80, ^ > .05), but the fin length X shaft distance X fin condition and the fin angle X shaft distance X fin condition three-way interactions were: F {3,21) = 3.44, H < .05, and F{12,84) = 4.11, £ < .001, respectively. Finally, the four-way interaction was not significant, F(12,84) = 1.30, jn > .05. Evaluation of Experiment 2 The significance of the main effect for fin condition in Experiment 2 suggests that the earlier tendencies for an asymmetry of strength of effect from acute and obtuse angle variants were real. The overall underestimation of acute angles was 4% and the overall overestimation of obtuse angles was 11%. The significance of this result may differ from that obtained in Experiment 1 because of the additional angles which were used in Experiment 2. Whereas Experiment 1 used only one angle for each of the fin conditions (45° for acute, 135° for obtuse), Experiment 2 employed ten different angles in total. The use of these additional angles resulted in more trials, and this may have provided enough reliability to find a significant effect. In any case, a main effect which is indicative of asymmetry was obtained in Experiment 2 where a weak trend was found in Experiment 1. Once again, the magnitude of the illusory effect was stronger for obtuse, rather than acute, angles. Figure 8a on page 35 shows a finding consistent with Experiment 1 (Figure 6a), that acute and obtuse angles are affected differently when paired with fin length. As before, fin length was a minor factor in the overestimation observed for obtuse angles whereas underestimation decreased as a function of increasing fin length for acute angles. The size of the stimulus set made it necessary to reduce the number of fin lengths employed in the present experiment, but by simply using two of the fin lengths which were tested in Experiment 1, all of the interactions observed in Experiment 1 involving fin length were maintained. Figure 8b shows a finding that was not investigated in Experiment 1. Here, acute and obtuse angles are affected differently depending on the angle of the fins. For acute angles there appears to be a peak underestimation at 45° and 60°. Obtuse angles, on the other hand, show a maximal 35 (a) (b) ACUTE 12 a 4 o 2 a OBTUSE 14 i s ( i e s ) 30 (ISO) 45 (135) SO (120) 75(105) FM LENGTH (DEO) FIN ANGLE (DEO) <C) 2 5 - I 10- UJ 0- 1 2 4 SHAFT DBTANCE (DEG) a Figure 8. (a) Exp. 2 fin length X fin condition interaction. Consistent with Exp. 1 (Figure 6a), illusion magnitude changed very little for the obtuse configuration when it was paired with increasing fin lengths. When fin length was increased in the acute configuration, however, illusion magnitude decreased substantially, (b) Exp. 2 fin angle X fin condition interaction. Here, maximal overestimation of the obtuse configuration occurred at an angle of 150°. On the other hand, maximal underestimation occurred at an agle of 45 - 60° for the acute configuration, (c) Exp. 2 shaft distance X fin condition interaction.Comparable to Figure 6b in Exp. 1, the acute configuration underestimation increased as shaft distance increased and obtuse configuration overestimation decreased as shaft distance increased. Also shown here is a ’ ’reverse" illusion for the acute configuration associated with the two shortest shaft distances and for the obtuse configuration associated with the longest shaft distance. 36 overestimation at 150°. Additionally, for obtuse angles, there seems to be an improvement in judgment as the obtuse angles become more orthogonal. Figure 8c is comparable to Figure 6b in Experiment 1. These results replicate the finding that acute angle configurations were perceived as being contracted to a greater extent as shaft distance was increased and that obtuse angle variations resulted in a loss of illusion effect as shaft distance was increased. Also, for the shortest two shaft distances, overestimation, rather than underestimation, occurred for acute angles; for a shaft distance of 8 deg, a slight underestimation was found for obtuse angles. Figure 9 on page 37 provides an expanded view of the data seen in Figure 8c, showing the three-way interaction between fin length, shaft distance, and fin condition. These results replicate what was found in Experiment 1 and can be compared with Figure 7. Here it can be seen that the pattern of effects on acute and obtuse angles was comparable regardless of what fin length was used. Also, the same monotonic relationships observed in Experiment 1 are witnessed here. An increase in shaft distance was associated with increased underestimation for acute angles and with decreased overestimation for obtuse angles. Figure 10 on page 38 represents the three-way interaction of fin angle, shaft distance, and fin condition. 37 (a) 30 FIN - 2 DEG 25- 20 - 10 - o- -5- -1 0 - 1 2 8 4

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Meta-analysis on the misattribution of arousal

PDF

A qualitative study on the relationship of future orientation and daily occupations of adolescents in a psychiatric setting

PDF

The relationship between alcoholism and crime: autonomic and neurpsychological factors

PDF

Rationalizing risk: sexual behavior of gay male couples

PDF

Predictors of pretend play in Korean-American and Anglo-American preschool children

PDF

Children's immediate reactions to interparental conflict

PDF

How casual attribution influences behavioral actions taken by self-aware individuals

PDF

Work for the masters degree

PDF

A thesis

PDF

Fine motor skills of two- to three-year-old drug exposed children

PDF

An investigation of the pseudohomophone effect: where and when it occurs

PDF

The dream becomes a reality (?): nation building and the continued struggle of the women of the Eritrian People's Liberation Front

PDF

Diminishing worlds?: the impact of HIV/AIDS on the geography of daily life

PDF

Violent environments and their effects on children

PDF

On the limits of not being scripted: video-making and discursive prositioning in coastal southeast Sulawesi

PDF

The study of temporal variation of coda Q⁻¹ and scaling law of seismic spectrum associated with the 1992 Landers Earthquake sequence

PDF

Lateral variability in predation and taphonomic characteristics of turritelline gastropod assemblages from Middle Eocene - Lower Oligocene strata of the Gulf Coastal Plain, United States

PDF

Air terrorism and the international aviation regime: the International Civil Aviation Organization

PDF

A follow up study of adapted computer technology training at the High Tech Traning Center of Santa Monica College

PDF

The Hall Canyon pluton: implications for pluton emplacement and for the Mesozoic history of the west-central Panamint Mountains

Asset Metadata

Creator Nelson, Brian Roberts (author)

Core Title The Müller-Lyer illusion: a new variant, some old and new results

School Graduate School

Degree Master of Arts

Degree Program Psychology

Degree Conferral Date 1995-05

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag OAI-PMH Harvest,psychology, psychometrics

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Greene, Ernest G. (committee chair), [Brader, L.] (committee member), Mady, Stephen (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-6485

Unique identifier UC11357681

Identifier 1376493.pdf (filename),usctheses-c18-6485 (legacy record id)

Legacy Identifier 1376493-0.pdf

Dmrecord 6485

Document Type Thesis

Rights Nelson, Brian Roberts

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA