The role of eye movements in the Müller-Lyer illusion

The size of the illusion was found to be unaffected by reducing the exposure of the figures tachistoscopically, or by reducing the size of the figures. The illusion therefore does not seem to be due to eye movements or a tendency to make eye movements.     

The dissociation of position and extent in Müller-Lyer figures

Three experiments were designed to determine whether Müller-Lyer figures cause a misperception of the positions of their fins and, if they do, whether it is commensurate with the distortion of extent. Observers marked the visible intersection of shaft and fins either with their unseen hands or with their visible hands after the figure had been removed from view. In the former case, no systematic distortions of position were evident. In the latter case, there were small, systematic distortions of position, which were significantly smaller when the observers fixated the target vertex than when they fixated the center of the figure. These differences are discussed in terms of the probable similarities between the control of eye movements and the control of pointing responses. Of particular importance is the finding that even the largest distortions of vertex position were much smaller than the distortions of shaft extent. The results appear to provide evidence of the independence of perceived position from perceived extent in Müller-Lyer figures and to contradict all existing theories of the illusion.     

The reversed Müller-Lyer illusion in conventional and in wing-amputated Müller-Lyer figures

Summary When the wings of the conventional or four-wing Müller-Lyer figures are displaced away from the shaft, the apparent elongation of the wings-out figure decreases and the apparent contraction of the wings-in figure changes to apparent elongation. Worrall and Firth (1974) reported a different pattern of illusion change for two-wing Müller-Lyer figures containing wings at only one end of the shaft. Whereas moving the wings away from the shaft decreased the magnitude of the wings-in illusion, it changed the wings-out illusion from apparent elongation to apparent contraction. The effect of wing displacement upon the Müller-Lyer illusion was measured in three experiments. Illusion magnitude was assessed by obtaining judgments of either the length (Experiment 1) or the apparent midpoint (Experiments 2 and 3) of the shaft of four-wing (Experiment 1), two-wing (Experiments 1–3), and one-wing (Experiments 1 and 2) Müller-Lyer figures. Both measures of the illusion showed that displacement of the wings away from the shaft had similar effects on the four and two-wing Müller-Lyer figures. The results are discussed in the context of assimilation theories of the Müller-Lyer illusion, and a possible reason for the apparent inconsistency between Worrall and Firth's conclusions and the present findings is outlined.     

The effects of varying fins in Müller-Lyer and Holding illusions

Summary Five experiments were conducted to determine how distortion of spatial position induced by unidirectional Müller-Lyer fins varied as a function of angle and length of fins. Research employing Cornsweet's staircase method yielded ambiguous results, but psychophysical methods of magnitude estimation, paired comparisons, and production showed conclusively that distortions of position are affected by angle and length of fins in a manner similar to that found in distortions of length. It was concluded that similar strategies are employed in processing attributes of length and position and that a theory based on averaging of attributes within an attentional field describes the performance of real observers.Experiments 1 and 2 were reported in a Master's thesis submitted by Nancy Smith to the University of Manitoba in 1987.     

What does the implicit association test measure? A test of the convergent and discriminant validity of prejudice-related IATs

Drawing on recent criticism of the Implicit Association Test (IAT), the present study tested the convergent and discriminant validity of two prejudice-related IATs to corresponding explicit prejudice measures in a German student sample (N = 61). Confirming convergent validity, (a) an IAT designed to assess negative associations related to Turkish people was significantly related to the explicit endorsement of prejudiced beliefs about Turkish people, and (b) an IAT designed to assess negative associations related to East Asians was significantly related to explicit prejudice against East Asians. Moreover, confirming discriminant validity, (c) the Asian IAT was unrelated to the explicit endorsement of prejudiced beliefs about Turkish people, and (d) the Turkish IAT was unrelated to explicit prejudice against Asian people. These results further corroborate the assumption that the IAT is a valid method to assess the strength of evaluative associations in the domain of prejudice and stereotypes.     

The effect of the Müller-Lyer illusion on the planning and control of manual aiming movements

Two experiments used Müller-Lyer stimuli to test the predictions of the planning-control model (S. Glover, 2002) for aiming movements. In Experiment 1, participants aimed to stimuli that either remained the same or changed upon movement initiation. Experiment 2 was identical except that the duration of visual feedback for online control was manipulated. The authors found that the figures visible during movement planning and online control had additive effects on endpoint bias, even when participants had ample time to use visual feedback to modify their movements (Experiment 2). These findings are problematic not only for the planning-control model but also for A. D. Milner and M. A. Goodale's (1995) two visual system explanation of illusory bias. Although our results are consistent with the idea that a single representation is used for perception, movement planning, and online control (e.g., V. H. Franz, 2001), other work from our laboratory and elsewhere suggests that the manner in which space is coded depends on constraints associated with the specific task, such as the visual cues available to the performer.     

Amplitude and phase in the Müller-Lyer illusion

It has previously been claimed that the Müller-Lyer illusion is the result of low-pass spatial filtering. One way to understand this would be that the distribution of amplitudes is what generates this illusion. This possibility was investigated by computing the 2-D Fourier transforms of the two Müller-Lyer stimuli and extracting their phase and amplitude spectra. These spectra were combined to create hybrid spectra having the phase of one Müller-Lyer figure and the amplitudes of the other. Images were then created by computing the inverse Fourier transform of the hybrid spectra. Except in cases where the analysis was performed patchwise on very small patches, the figures generated with the phase spectrum of the stimuli having outward-pointing fins appear the longer. This was also the case when stimuli were generated with flat amplitude spectra. Because they show that the Müller-Lyer illusion does not depend on any particular distribution of amplitudes, these demonstrations do not support the theory that the Müller-Lyer illusion is the result of low-frequency filtering.     

Why do pictures produce priming on the word-fragment completion test? A study of encoding and retrieval factors

Three experiments examined why pictures produce priming on the word-fragment completion test, despite the fact that there is no match between the physical features of the picture and the word fragment. Pictures and words were presented as primes, and performance on the word-fragment completion test was measured; encoding and retrieval conditions were varied. Experi-ments 1 and 2 examined the role of picture labeling by increasing the presentation rate and by introducing a shadowing task during encoding; labeling appears to play a role in priming. In Experiment 3, the word fragments were presented for 500 msec, and subjects were required to provide a solution immediately. Word priming was unaffected, but picture priming was elimi-nated, suggesting that word fragments enable efficient recovery of perceptually similar primes (i.e., words), but slower and less direct recovery of conceptually similar but physically dissimilar     

A general scheme for the analytic decomposition of objective test scores: Illustrative demonstrations using the Rod-and-Frame test and the Müller-Lyer illusion

Objective tests of personality typically include a number of items or trials; the total score on the test is the sum of the subject's “correct” responses across all such trials. Normally, the trials are varied systematically across various facets of the test design, so that the total score represents a composite measure of accuracy averaged across these test facets. However, since only one score is computed for each subject, some potentially important kinds of individual differences—namely all those associated with each particular variation in the test design—are treated solely as measurement unreliability. Such a psychometric stance may serve to obscure more differentiated types of individual differences, with the result that composite scores from trials based on one type of experimental design may not be highly related to such scores from trials using a somewhat different design. The present paper presents a general procedure for scoring objective tests more analytically. To illustrate this general rationale, and to demonstrate its potential utility, data have been reanalyzed from two previous studies, one using the Rod-and-Frame test, the other the Müller-Lyer illusion. In both cases, the traditional global accuracy score did not correlate significantly with other theoretically related variables, while a number of component scores were quite highly related.     

The persistence of the fluency–confidence association in problem solving

Confidence in answers is known to be sensitive to the fluency with which answers come to mind. One aspect of fluency is response latency. Latency is often a valid cue for accuracy, showing an inverse relationship with both accuracy rates and confidence. The present study examined the independent latency–confidence association in problem-solving tasks. The tasks were ecologically valid situations in which latency showed no validity, moderate validity, and high validity as a predictor of accuracy. In Experiment 1, misleading problems, which often elicit initial wrong solutions, were answered in open-ended and multiple-choice test formats. Under the open-ended test format, latency was absolutely not valid in predicting accuracy: Quickly and slowly provided solutions had a similar chance of being correct. Under the multiple-choice test format, latency predicted accuracy better. In Experiment 2, nonmisleading problems were used; here, latency was highly valid in predicting accuracy. A breakdown into correct and incorrect solutions allowed examination of the independent latency–confidence relationship when latency necessarily had no validity in predicting accuracy. In all conditions, regardless of latency’s validity in predicting accuracy, confidence was persistently sensitive to latency: The participants were more confident in solutions provided quickly than in those that involved lengthy thinking. The study suggests that the reliability of the latency–confidence association in problem solving depends on the strength of the inverse relationship between latency and accuracy in the particular task.     

Discriminability in length of lines in the Müller-Lyer figure

Receiver-operating characteristics for the discriminability in the length of the lines of the Müller-Lyer figure were obtained by the rating method of detection theory. Six observers judged the shaft length of the lines of the figure with reference to the same standard line. Maximum-likelihood estimates of the index of (discriminability,d’, were a linear function of the difference in the length of the lines, but the functions did not pass through the origin because of a constant error of judgment. Because discriminability was determined by ROC analysis, the constant error could not be attributed solely to changes in criterion placement; instead, it showed that the Müller-Lyer figure induced a change in the discriminability of the lines.     

Selective attention and asymmetry in the Müller-Lyer illusion

Two experiments reexamined the effect of selective spatial attention on the magnitudes of the wings- in and wings-out forms of the Müller-Lyer (M-L) illusion and a version of the illusion in which the two forms are superimposed to produce a figure (XX) flanked at both ends by an X. For the XX figure, ignoring the outer wings produced significant underestimation of shaft length, whereas ignoring the inner wings had no significant effect. For the M-L figures, ignoring the wings was more effective in attenuating the magnitude of the wings-out than of the wings-in illusion. The results are discussed with reference to space-based approaches to visual attention and to claims that attentional modulation of illusion magnitudes implicates high-level or cognitive factors in the formation of the M-L illusion.     

The haptic Müller-Lyer illusion in sighted and blind people

We examined the effect of visual experience on the haptic Müller-Lyer illusion. Subjects made size estimates of raised lines by using a sliding haptic ruler. Independent groups of blind-folded-sighted, late-blind, congenitally blind, and low-vision subjects judged the sizes of wings-in and wings-out stimuli, plain lines, and lines with short vertical ends. An illusion was found, since the wings-in stimuli were judged as shorter than the wings-out patterns and all of the other stimuli. Subjects generally underestimated the lengths of lines. In a second experiment we found a nonsignificant difference between length judgments of raised lines as opposed to smooth wooden dowels. The strength of the haptic illusion depends upon the angles of the wings, with a much stronger illusion for more acute angles. The effect of visual status was nonsignificant, suggesting that spatial distortion in the haptic Müller-Lyer illusion does not depend upon visual imagery or visual experience.     

The effect of the Müller-Lyer illusion on map reading

One important reason for studying visual illusions is that they can influence real-world perception as people interact with human-made displays. Three experiments examined how the Müller-Lyer illusion affects distance judgments and decision-making in the complex graphical context of a map by having subjects estimate the lengths of road segment lines framed by inward-going or outward-going wings in actual maps, in control displays that had the map context removed, and in simulated maps. The experiments showed that (1) outward-going wings led to higher distance estimates than did inward-going wings to the same extent both with and without the map context, (2) decisions based on distances determined from maps were affected by Müller-Lyer elements in the maps, and (3) map readers’ measurement behavior influenced the effect of the Müller-Lyer elements in maps. The discussion focuses on how certain display manipulations and task manipulations affect the Müller-Lyer illusion. In addition, the discussion addresses the instances in which using a map might be affected by misestimation due to Müller-Lyer elements.     

Distribution of practice and the Müller-Lyer illusion1

Two experiments were conducted to determine the influence of distribution of practice on the decrement of the Muller-Lyer illusion. In the first experiment, Ss judged the illusion figure 100 times per session in five sessions separated by intervals of seven days. In the second, Ss judged the figure 200 limes in a single session. The data were compared with those from an earlier experiment (Dewar, 1967) in which Ss judged the figure 100 times per session in five sessions separated by 24 h. In all three experiments two configurations of the illusion were used-one with a 60° angle between the obI ique lines and one with a 120° ang Ie. The distribution of practice did not influence the decrement of the illusion for the 120° figure. The only effect of this variable was to produce a more rapid practice decrement for the 60° figure when sessions of 100 trials were separated by a 24-h intewal.     

Geometrical haptic illusions: The role of exploration in the Müller-Lyer,vertical-horizontal,and Delboeuf illusions

This article surveys studies of the occurrence, in the haptic modality, of three geometrical illusions well known in vision, and it discusses the nature of the processes underlying these haptic illusions.We argue that the apparently contradictory results found in the literature concerning them may be explained, at least partially, by the characteristics of manual exploratory movements. The Müller-Lyer illusion is present in vision and in haptics and seems to be the result of similar processes in the two modalities. The vertical-horizontal illusion also exists in vision and haptics but is due partly to similar processes (bisection) and partly to processes specific to each modality (anisotropy of the visual field and overestimation of radial vs. tangential manual exploratory movements). The Delboeuf illusion seems to occur only in vision, probably because exploration by the index finger may exclude the misleading context from tactile perception. The role of these haptic exploratory movements may explain why haptics is as sensitive as vision to certain illusions and less sensitive to others.     

Decrement of the Müller-Lyer and Poggendorff illusions: the effects of inspection and practice

Five experiments assessed the decline or decrement in illusion magnitude for the wings-out form and the combined or Brentano form of the Müller-Lyer illusion, and for the Poggendorff illusion. Judgments were obtained under conditions of either continuous or intermittent inspection of the illusion figure. In the continuous-inspection conditions observers scanned the illusion figure during the inter-trial intervals whereas in the intermittent-inspection conditions they did not. Substantial illusion decrement was found in all continuous-inspection conditions and in intermittent conditions with short inter-trial intervals (upto 20 s) but not with longer inter-trial intervals. However, intermittent-inspection with a long inter-trial interval (40 s) produced illusion decrement but only when observers were instructed during the decrement session to ignore the wings, and pay attention to the shaft, of the Müller-Lyer figure. Taken together, the pattern of results does not support the claim that illusion decrement is primarily a product of practice or repeated trials.     

The science of language and the evolution of mind: Max Müller's quarrel with Darwinism

For Darwinism to succeed as a general theory of the development of life, it had to account for at least the rudiments of all human characteristics. Thus Darwin and his colleague G. J. Romanes had to make "mental evolution" the basis for scientific psychology. F. Max Müller, Oxford's professor of comparative philology, drew on Kant's work, Romantic Naturphilosophie, and his views on the history of language and the relation of language to thought to maintain that language showed a difference not in degree but in kind between man and the lower primates. In his debate with Romanes, he argued that the study of language, not Darwinist natural history, should be the basis for a science of human psychology. However, the two authors had such different definitions of the key terms in their discussion that their differences were not only unresolved but irresolvable.