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Grasping Weber's illusion: The effect ofreceptor density differences on grasping andmatchingHelen A. Anema a b , Vincent W. J. Wolswijk a , Carla Ruis b & H. ChrisDijkerman a ba Experimental Psychology, Helmholtz Institute, Utrecht University,Utrecht, The Netherlandsb Department of Neurology, University Medical Centre Utrecht, Utrecht,The NetherlandsVersion of record first published: 01 Dec 2010.

To cite this article: Helen A. Anema, Vincent W. J. Wolswijk, Carla Ruis & H. Chris Dijkerman (2008):Grasping Weber's illusion: The effect of receptor density differences on grasping and matching, CognitiveNeuropsychology, 25:7-8, 951-967

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Grasping Weber’s illusion: The effect of receptor densitydifferences on grasping and matching

Helen A. AnemaExperimental Psychology, Helmholtz Institute, Utrecht University, Utrecht, The Netherlands, and Department of Neurology, University

Medical Centre Utrecht, Utrecht, The Netherlands

Vincent W. J. WolswijkExperimental Psychology, Helmholtz Institute, Utrecht University, Utrecht, The Netherlands

Carla RuisDepartment of Neurology, University Medical Centre Utrecht, Utrecht, The Netherlands

H. Chris DijkermanExperimental Psychology, Helmholtz Institute, Utrecht University, Utrecht, The Netherlands, and Department of Neurology, University

Medical Centre Utrecht, Utrecht, The Netherlands

Weber found that distances between tactile stimuli on a high-receptor-density area are perceived asbeing larger than identical distances on a low-receptor-density area (Weber’s illusion). Previousstudies of visual illusions suggest that illusion effects vary with the type of response given. Here wetested a modified version of Weber’s illusion in which a solid object was placed on the forearm orhand. Blindfolded participants were required either to give a size estimation or to grasp the object.The results showed that size estimation of solid objects was consistent with Weber’s illusion,whereas grasping responses showed an opposite pattern (e.g., larger hand opening for objects on theforearm). A second experiment showed that this pattern is not due to biomechanical differencesinduced by the difference in spatial position of the target objects on the hand and arm. We suggestthat the larger grip aperture when grasping objects on the arm were due to an increase in safetymargin as a response to greater uncertainty about the object dimensions due to reduced receptor density.

Keywords: Somatosensory; Action; Perception; Weber’s illusion.

Somatosensory information is essential for manyaspects of behaviour, such as recognizing objects

that are concealed from our vision, or scratchingan itch on our back. It plays an important role in

Correspondence should be addressed to Helen A. Anema, Experimental Psychology, Helmholtz Research Institute, Utrecht

University, Heidelberglaan 2, 3584 CS Utrecht, The Netherlands (E-mail: h.a.anema@uu.nl).

We would like to thank Jeroen Smeets for the useful discussions about the possible interpretation of the data and suggestions

regarding control experiments. We are also grateful to Carola Buijtenhuijs, Mirjam Bekkenkamp, Leila Breden, and Jelle Visser

for their help with the data collection. This work was supported by a Vidi grant from the Netherlands Organization for

Scientific Research (NWO; 452–03–325 to H.C.D.).

# 2008 Psychology Press, an imprint of the Taylor & Francis Group, an Informa business 951http://www.psypress.com/cogneuropsychology DOI:10.1080/02643290802041323

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the perception of our own body and provides uswith the ability to interact with the externalworld, although in many cases vision is the moredominant sense. Within vision research, percep-tual illusions have been used to investigate differ-ential effects on implicit motor responses andconscious perceptual judgements in healthy par-ticipants (Aglioti, DeSouza, & Goodale, 1995;Haffenden & Goodale, 1998; see, e.g., Carey,2001; Franz, 2001, for reviews). These studieshave found that perceptual judgements of sizeare influenced more by a size illusion thanmaximum grip aperture during a grasping task.This differential sensitivity to the illusion hasbeen considered to be consistent with the ideathat visually guided grasping and perceptual judge-ments are based on separate representations of thesame stimulus (Milner & Goodale, 1995).However, this interpretation of these findingsremains controversial, and several authors havesuggested alternative explanations for the observeddifferences in illusion sensitivity (e.g., Franz, 2001,2003; Franz, Gegenfurtner, Bulthoff, & Fahle,2000; Pavani, Boscagli, Benvenuti, Rabuffetti, &Farne, 1999; Smeets & Brenner, 1999). Forexample, grasping responses are affected not onlyby object size, but also by other variables such asuncertainty about the perceived information.Furthermore, Franz (2003) suggested that a con-founding factor of these visual illusion studieslies in the type of response selected for testingmotor responses and perceptual judgements. Heargued that a manual size estimation response ishighly sensitive to a change in object size, illusion-ary or real, whereas traditional perceptual measuresare less sensitive. Correcting for this aspect leads insome cases to equal sensitivity for perceptual jud-gements and grasping responses. Also, it mightbe possible that the difference in illusion sensitivitydepends on whether different aspects of sensoryinformation are relevant for the task. Indeed,Smeets and Brenner (1999) showed that illusioneffects found in several tasks performed on thesame stimuli can be explained by the use of differ-ent spatial attributes. Furthermore, Bruno (2001)suggested that it depends on the reference frameused when responding to a stimulus whether the

response is sensitive to an illusion or not. Forexample, grasping a stimulus requires viewer-related coding of the stimulus whereas estimatingits size requires an object-related coding. Changingperspective rather than changing the type of res-ponse determines whether effects of the illusionare observed.

With respect to other sensory modalities,Dijkerman and de Haan (2007) recently presenteda model that specifies different somatosensory pro-cesses and their underlying neural substrates. Inline with the two visual streams model of thevisual system (Milner & Goodale, 1995), theauthors suggested that neural processing of soma-tosensory input depends not only on the type ofstimulus, but also on how this information isused. Evidence for task-dependent somatosensoryprocessing comes, for example, from dissociationsin neuropsychological patients (Paillard, 1999;Reed, Caselli, & Farah, 1996; Rossetti, Rode, &Boisson, 1995, 2001; Valenza et al., 2001) andfrom studies with healthy participants (seeDijkerman & de Haan, 2007, for a review).

Few studies have used haptic illusions to studytask-dependent differences in healthy participants.Kammers, van der Ham, and Dijkerman (2006)used a vibrotactile illusion to explore differencesbetween matching and reaching involving the pos-ition of a body part. This illusion was induced byvibration of a muscle tendon (here the bicepsmuscle), resulting in an illusory displacement ofthe stimulated arm. The effect of the illusion waslarger when participants were asked to perceptuallymatch the position of the vibrated arm with thenonvibrated arm as compared to a reachingresponse with the nonstimulated arm towards thefelt position of the vibrated arm (see also Marcel,2003, for similar findings). This suggests thatbody representations underlying perception andaction may be differentially sensitive to the illu-sion. Task-dependent effects have been observednot only regarding somatosensory input pertainingto the body, but also with respect to hapticexploration of external objects. Westwood andGoodale (2003) investigated how grasping andmatching responses were affected by a size-contrast illusion. Participants were instructed to

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manually explore with the left hand two objects: atarget and a flanker object. After touching theobjects, they had to either grasp the target objector estimate its size (right hand). The size of theflanker object was identical to, smaller than, orlarger than the target object. Consistent withseveral previous visual illusion studies (Agliotiet al., 1995; Haffenden & Goodale, 1998; Otto-de Haart, Carey, & Milne, 1999), size estimationwas affected by the illusion (albeit, for the largerflanker object only) whereas grasping was not. Alimitation of the Westwood and Goodale studyis that the size contrast illusion is likely to inducevisual imagery processes, which means that theobserved differences between matching and grasp-ing might be related to differences in visual ratherthan somatosensory processes.

A tactile illusion that originates in the differ-ence of tactile receptor densities in various skinareas was reported originally by Weber (1834/1978). It refers to the impression that a tactiledistance contracts when moved from a region ofhigh to low receptor density (e.g., from hand toforearm). In 1982, Green further explored thiseffect on various body parts, such as the palm,forearm, thigh, and so on, and found that theeffect of the illusion was dependent on the stimu-lus orientation and that the misperceptions arebased upon errors in perceived location of thestimuli. More specifically, he suggested that “per-ceived location depends on the relationship of atactile stimulus both to the body frame and tonearby stimuli” (p. 315). As a consequence, acertain distance perceived by a skin area withhigh receptor densities is perceived to be largerthan this same distance perceived by a skin areawith a lower receptor density, which was laterconfirmed by Taylor-Clarke, Jacobsen, andHaggard (2004). These authors argued that theillusion cannot be entirely explained by the differ-ences in receptor density and instead suggestedthat when judging tactile distances presented tovarious skin areas, neural signals from thesevarying receptor densities are rescaled to anobject-centred space. However, this rescalingprocess is imperfect, and thus Weber’s illusionemerges.

In the current study we sought convergingevidence for the idea that processing of tactileinput about an external target is influenced bythe type of response that is required by usingWeber’s illusion. To this purpose, we performedtwo experiments. In the first experiment, partici-pants either grasped an object or provided a sizeestimate by varying the thumb–index finger separ-ation. We hypothesized that the size estimationresponse would be consistent with Weber’s illusion(e.g., larger length estimates for objects on thehand), whereas the implicit motor graspingresponse would not. In the second experiment acontrol grasping task was studied in order to ruleout biomechanical differences between graspingconditions as a possible cause for the observeddifferences. Prior to the main two experiments,three independent pilot studies were performedto assess the feasibility of using a size-matchingresponse for measuring Weber’s illusion and toassess possible differences in sensory attributes.

EXPERIMENTS

General method

Participants were students from UtrechtUniversity or its surrounding area and receivedeither a small payment or course credits requiredas part of their studies. Written informed consentwas obtained before the start of the study. Thisstudy was approved by the local ethical medicalboard and has been conducted in according withthe declaration of Helsinki.

PILOT EXPERIMENT 1

This pilot experiment was set up in order to inves-tigate whether the method of varying thumb–index finger separation is a reliable measure ofquantifying Weber’s illusion. The illusion wasevoked by applying tactile distances to either thepalm of the hand or the forearm, in line with theparadigm used in the studies by Green (1982)and Taylor-Clarke et al. (2004).

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Method

ParticipantsA total of 4 healthy participants without history ofpsychiatric or neurological illness (3 male, 1female; mean age 25.5 years; range 22 to 29years) and who were naıve as to the purpose ofthe experiment participated in the first pilot.

ProcedureBlindfolded participants were seated in front of atable with both arms in parallel (250 mm apart)and in supine position (see Figure 1). The exper-imenter manually applied the appropriate distance(50 mm, 60 mm, or 70 mm) by using a caliper thatproduced two simple tactile stimulations. Stimuliwere applied on either of two areas, the palm ofthe hand or the ventral side of the forearm,30 mm proximally of the wrist joint. Both areasof stimulation were delineated prior to the exper-iment. During stimulation participants wererequired to indicate the perceived distancebetween the two points by adjusting the rightthumb–index finger distance. The two fingerswere always pinched together in between trials.

Participants verbally reported whenever theywere finished adjusting their fingers. The positionof the index finger and thumb was recorded sub-sequently using the Minibird magnetic movementrecording device (Ascension Technologies). Thissystem samples the 3D position of electromagneticmarkers with a frequency of 86.1 Hz. As indicatedin Figure 1, markers were attached to the nails ofthe right index finger and thumb. Each size–area combination was tested five times, and trialswere presented in a random order.

Data analyses and statisticsThe 3D position data of the markers were analysedoffline using a Matlab (Mathworks, Inc.) program-ming environment. The dependent variable ofinterest was mean grip aperture (mGA; or, meanthumb–index finger separation), which was calcu-lated by averaging the 3D difference of bothmarkers for all 86 samples recorded during onesecond.

First, we calculated the total percentage ofoverestimations across size conditions. Thus, persubject, for each distance, mean grip apertures forall arm conditions were subtracted from the meangrip apertures for hand conditions (first 50 mmobject on hand minus first 50 mm object on arm,second 50 mm object on hand minus second50 mm object on arm, etc.). This difference wasthen defined as either overestimation or underesti-mation. The number of overestimation trialswas summed, and subsequently this total wascalculated as a percentage of the total amount oftrials. Second, mean grip apertures were analysedusing a 2(area) � 3(object size) repeated measuresanalysis of variance (ANOVA) with a significancelevel of p ¼ .05. Significant main effects withmore than two levels were disentangled using posthoc Helmert contrasts. Significant interactionswere further explored by computing simple maineffects for each interacting factor. Only significanteffects are reported.

Results and discussion

As was expected (see Figure 2A), tactile distancesperceived on the palm of the hand are estimated to

Figure 1. Experimental set-up of pilot experiments and

Experiment 1 (Figure 1A). Adjustment method: Pilot

Experiment 2 (Figure 1B).

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be larger than the same distances perceived on theforearm albeit only for the larger objects. Also, thisoverestimation occurred in 78% of the trials (SD ¼

19). Submitting the aperture data to a 2(area) �

3(object size) repeated measures ANOVA revealedan significant main effect of area, F(1, 3) ¼ 12.92,p ¼ .05, and of object size, F(2, 6) ¼ 20.23, p ,

.01. Further exploration of the factor object sizemain effect revealed a significant increase in gripaperture from the 50-mm to the 60-mm object,F(1, 3) ¼ 22.16, p , .05, and from the 60-mmobject to the 70-mm object, F(1, 3) ¼ 17.73,p , .05. In addition, area interacted significantlywith object size, F(1, 3) ¼ 20.92, p , .01, anddisentangling this effect reveals significant

differences between hand and arm apertures forthe 60-mm, F(1, 3) ¼ 18.36, p , .05, and the70-mm object, F(1, 3) ¼ 15.98, p , .05, only.

In sum, Weber’s illusion reliably affected themanual estimation of tactile distances. Tactile dis-tances on the hand were overestimated as com-pared to identical distances on the arm, whichoccurred in 78% of the trials (SD ¼ 19). This per-centage is in line with what might be expectedfrom the percentages found in the study byTaylor-Clarke et al. (2004), using similar skinregions but a different direct comparison task. Intheir study, comparison of distances applied onthe index finger and the forearm resulted in anoverestimation in 77% of the trials.

Figure 2. Mean thumb–index separation for estimation response in mm as a function of object size in Pilot Experiment 1 (Figure 2A) and

Pilot Experiment 3 (Figure 2C) and of object size and response in Pilot Experiment 2 (Figure 2B). Error bars show between-participants

error of the means.

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However, overestimations did not occur for thesmallest distance, which was also observed byGreen (1982). In that study, significant differenceswere found in perceived distances between palm ofthe hand and forearm but not for the smallest dis-tance (here 20 mm, compared to 40 mm and60 mm). Also, the increase in distance estimateswas larger for the hand perceived distances as com-pared to the arm perceived distances, similar to ourresults. The differences in slope have also beenreported for visual stimuli (Newsome, 1972).Green (1982) related this finding to the differencesin peripheral receptor density and suggested thatcertain receptor areas (fovea or hand) are special-ized in extracting veridical information aboutfeatures such as size and distance. Other areasonly detect coarser differences, and when closeranalysis is desired detection can be enhanced bymoving the stimulus to an area of higher receptordensity.

Despite the observed similarities between ourfindings and those of others, the use of amanual size estimation (adjusting thumb–indexseparation) is highly debated (see Franz, 2003).Therefore a second pilot experiment was setup in order to test for differences in effectsof the illusion between a manual size estimationtask and a more traditional perceptual measure,the method of adjustment. Also, this experimenttested for similarities of the illusion effectevoked with two simple tactile stimuli (byusing the caliper) and effects induced by solidobjects.

PILOT EXPERIMENT 2

Method

ParticipantsA total of 5 participants without history ofpsychiatric or neurological illness (1 male, 4female; mean age 22 years; range 19 to 25 years)and who were naıve as to the purpose of theexperiment participated in the second pilotexperiment.

Procedure and data analysesThe procedure resembled that of Pilot Experiment1 except for the tactile stimuli and the responsegiven. In this experiment the participants werestimulated with rectangular aluminium objects(height 25 mm; width 20 mm), which varied insize, 50 mm (68 g), 60 mm (86 g), and 70 mm(92 g). Since aluminium conducts heat quicklyand is perceived as being cold, objects were pre-heated in order to prevent participants fromusing perceived coldness as a cue. Objects placedon the arm were always located 30 mm from thewrist joint, and objects on the palm of the handwere always positioned centrally. Both objectswere positioned in a longitudinal (or proximal todistal) orientation. By varying the location of thestimulus somewhat (a few mm) in lateral andmedial direction between trials, adaptation of theskin receptors to the stimulus was prevented. Intwo separate blocks blindfolded participants wererequired either to estimate the size of the objectby adjusting thumb and index finger separationor to adjust a linear scale (see Figure 1B). Thiswooden scale was equipped with a fixed part,which was used as a reference point, and an adjus-table part. Participants were required to adjust themoving part so that the distance between the refer-ence point and the adjustable part resembled theperceived distance of the object. Participants verb-ally reported whenever they had finished adjustingthe scale, and prior to the data recording partici-pants placed the thumb on the reference partand the index finger on the adjustable part.Subsequently, the position of the index fingerand thumb was recorded by the Minibird. EachObject Size � Area combination was tested fivetimes, which resulted in 30 trials per block con-dition. Within each block trials were presentedin a randomized order.

The data analyses resembled those of PilotExperiment 1.

Results and discussion

As was observed in Pilot Experiment 1, we found apattern of overestimations of hand responses ascompared to arm responses for both types of

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response (see Figure 2B) Overestimationsoccurred in 81% (SD ¼ 0.09) of the trials for themanual size estimates and in 53% (SD ¼ 20) ofthe trials for the method of adjustment. A2(response) � 2(area) � 3(object size) ANOVAshows a main effect of the factor object size, indi-cating that responses increased reliably with size,F(1, 4) ¼ 12.23, p , .01. Also, Weber’s illusionreliably affected the size estimation of solidobjects: overall main effect of area, F(1, 4) ¼

36.22, p , .01. Further exploration of this effectrevealed significant increases between the 50-mmand the 60-mm object, F(1, 4) ¼ 11.54, p , .05,and between the 60-mm and the 70-mm object,F(1, 4) ¼ 16.60, p , .05. With respect to themethod used to indicate the size of the objects, nosignificant difference was found between theadjustment method and the manual size esti-mation: overall main effect of response, F(1, 4) ,1, and consequently the effect of area did not sig-nificantly differ between both responses: inter-action, F(1, 4) , 1) .

The results of this pilot study suggest that it ispossible to induce Weber’s illusion by stimulatingthe palm of the hand and the ventral side of theforearm with solid objects. Second, an overalleffect of Weber’s illusion was found, and no differ-ence between methods used was observed. Visualinspection of the results (see Figure 2B) suggeststhat Weber’s illusion was more pronounced forthe manual estimation method than for themethod of adjustment, although this differencedid not reach significance (possibly due to thesmall number of participants in this pilot). Thisdifference in effect of the illusion betweenmanual size estimation and method of adjustmenthas been reported previously by Franz (2003) for avisual size illusion. In the current study, it mightbe explained additionally by the influence of exter-nal reference information provided by the fixedpart of the device, which subsequently led to reca-libration of the position of the thumb and indexfinger with respect to the manipulated device.This type of feedback information is not availableduring the grasping response in the main exper-iment. Because of this potentially confoundingfactor and because we aimed to induce a robust

Weber’s illusion, we decided that index–finger–thumb separation may be the most suitableresponse to use as a size estimation measure inthe main experiment.

As mentioned earlier in the introduction, amanual size estimation response is aimed atobject rather than spatial features, while thelatter may be more important for the graspingresponses (Smeets & Brenner, 1999). Therefore,we conducted a third pilot experiment in whichwe changed the manual size estimation responseso that it was aimed explicitly at the end pointsof the object.

PILOT EXPERIMENT 3

Method

ParticipantsA total of 9 healthy female participants withouthistory of psychiatric or neurological illness(mean age 21.5 years; range 19 to 24 years) andwho were naıve as to the purpose of the experimentparticipated in the second pilot experiment.

Procedure and data analysesThe procedure resembled that of Pilot Experiment2 except for the type of response. After stimulusplacement, participants were required to aligntheir thumb and index finger as precise as possiblewith the perceived object’s end points. To keep allother factors equal, it was decided to keep the pos-ition of the response hand similar to that in thefirst pilot experiment (see Figure 1). Each size–area combination was tested eight times, andtrials were presented in random order. Data ana-lyses and statistics were similar to those of PilotExperiment 1.

Results and discussion

As is shown by Figure 2C, area of stimulationshowed a significant main effect, F(1, 8) ¼

16.19, p , .01. In addition, the factor object sizewas significant as well, F(1, 8) ¼ 99.11, p , .01,and post hoc contrasts revealed increases from

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the 50-mm to the 60-mm object as well as fromthe 60-mm to the 70-mm object to be significant,F(1, 8) ¼ 286.5, p , .01; F(1, 8) ¼ 25.12, p , .01.

Summing up, modifying the size estimationresponse into a response aimed at spatial ratherthan object attributes did not interfere with theeffect of Weber’s illusion. Also, the percentage ofoverestimated trials appeared to be similar tothat found in Pilot Experiment 1 (74.5%, SD ¼

15.4). Overall, these findings suggest thatWeber’s illusion affected judgements of theobject end points similar to distance judgements.One possibility that we cannot exclude entirely isthat participants might have used object size infor-mation to solve the task. However, this was neverreported by any of the participants.

The data from these three pilot experimentssuggest that the effect of Weber’s illusion onmanual size estimation responses appears to bequite robust, and the results are very similar toearlier findings (Green, 1982; Taylor-Clarkeet al., 2004). As there are possible confoundswith alternative measures of perceptual estimates,we decided to adopt it as our perceptual measureof size in our main experiment.

EXPERIMENT 1

Method

ParticipantsA total of 18 right-handed undergraduate students(3 male, 15 female; mean age 22 years; range 19 to26 years) without history of psychiatric or neuro-logical illness and who were naıve as to thepurpose of the experiment participated inExperiment 1.

Experimental set-up and procedureThe experimental set-up was similar to that of thesecond pilot study with two differences. First, inthis experiment we added an extra object of80 mm (95 g). Second, besides a size-matchingresponse (similar to Pilot Experiment 2), partici-pants were additionally asked to reach out and

grasp the object. Both responses were tested inseparate blocks.

A grasping trial started when the object waspositioned on the participant’s forearm or hand,after which participants were instructed to graspthe object immediately by its long axis (seeFigure 1), without actually lifting it. The stimu-lus remained on the skin during the response andwas removed after the response arm was back inthe starting position. Data recording duringgrasping trials started just before the stimuluswas placed and ended after 4 s. Prior to theexperiment, all participants practised both taskswith novel stimuli and were blind to thenumber and shape of the objects used in theexperiment.

DesignThe experiment had a 2 (area; palm of the handor forearm) � 2 (response; grasping or estimat-ing) � 4 (object size; 50, 60, 70 or 80 mm)within-subjects design. A total of 128 grasping(A) and matching (B) trials were tested inABBA order, and within each block of 32 trialsthe order of stimulus area and object size wasrandomized.

Data analyses and statisticsThe 3D position data of the markers were analysedoffline using a Matlab (Mathworks Inc.) program-ming environment as was done in the pilot exper-iments. Here the dependent variables of interestwere mean grip aperture (mGA) responses forthe size matching and peak grip aperture (PGA)for grasping movements. Also, the average stan-dard deviation of these values was calculated persubject within a condition in order to determinevariability in grip aperture. The analyses of theestimation trials were similar to those of PilotExperiment 1 whereas the analyses of graspingtrials differed to a certain extent. For graspingtrials, raw data were filtered with a polynomialfilter (Press, Teukolsky, Vetterling, & Flannery,1994). Secondly, movement onset was defined asthe first sample after velocity exceeded 50 mm/swhereas movement offset was defined as the firstsample after velocity dropped below 50 mm/s.

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In order to define maximum grip aperture, 3Ddifferences in x, y, and z values between Markers1 and 2 were calculated. Other kinematic par-ameters, such as peak velocity (PV), time to peakvelocity as a percentage of total movement time(TPV%), time to peak grip aperture as a percen-tage of total movement time (TPGA%), andmovement time (MT), were calculated from thedata within the same temporal boundaries.

Mean and peak grip aperture values as wellas average standard deviation values (variabilityin grip aperture within a condition for each partici-pant) were analysed using a 2(area) � 2(response)� 4(object size) repeated measures ANOVA witha significance level of p ¼ .05 for Experiment1. Significant main effects with more than twolevels were disentangled using post hoc Helmertcontrasts. Significant interactions were furtherexplored by computing simple main effects foreach interacting factor. A second set of analyseswas conducted in order to explore the above-mentioned kinematic variables of grasping move-ments. These values were analysed with separate

2(area) � 4(object size) repeated measuresANOVAs (Experiment 1). Again, significantinteractions were further analysed by calculatingsimple main effects for each interacting factor.Only significant effects are reported.

Results

Grip aperture valuesAs can be observed from Figure 3 and Table 1, amain effect of response was found, reflecting theoverall larger grip aperture in grasp responses(112.2 mm; SEM ¼ 2.5) than in estimationresponses (92.8 mm; SEM ¼ 3.1). In addition,there was a main effect of object size, implyingthat the smallest object generated the smallestgrip aperture, and the largest object generatedthe largest grip aperture (size 50 mm: 93.2 mm,SEM ¼ 1.8; size 60 mm: 99.9 mm, SEM ¼ 2.1;size 70 mm: 105.2 mm, SEM ¼ 2.3; size 80 mm:111.5 mm, SEM ¼ 2.3), irrespective of thearea of stimulation or which response wasrequired.

Figure 3. Mean grip aperture for estimation responses and peak grip aperture for grasping responses in Experiment 1. Aperture in mm. Error

bars show between-participants error of the means.

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Most relevant for our hypotheses, area inter-acted significantly with response (see Table 1).Further exploration of this effect revealed thatmean grip aperture during estimation responseswas consistent with Weber’s illusion (hand:97.6 mm, SEM ¼ 3.2; arm: 88.0 mm, SEM ¼

3.4). In contrast, when grasping the stimulus, theparticipant responded with larger grip aperturevalues for stimuli located on the arm (115.3 mm;SEM ¼ 2.8) than for stimuli located on the hand(108.9 mm; SEM ¼ 2.4). A significant interactionbetween object size and response (see Table 1)suggested that scaling was more evident in themanual estimation condition (size 50 mm:82.2 mm, SEM ¼ 2.9; size 60 mm: 89.0 mm,SEM ¼ 3.1; size 70 mm: 96.2 mm, SEM ¼ 3.1;size 80 mm: 103.9 mm, SEM ¼ 3.2), than inthe grasping condition (size 50 mm: 104.3 mm,SEM ¼ 2.3; size 60 mm: 110.8 mm, SEM ¼ 2.7;size 70 mm: 1,14.3 mm, SEM ¼ 2.6; size80 mm: 119.1 mm, SEM ¼ 2.7). Also, thisobject size effect is present both for objectslocated on the arm and for objects located on

the hand, although the significant interactionbetween object size and area (see Table 1) indi-cated that this scaling effect is more pronouncedon the hand (size 50 mm: 90.1 mm, SEM ¼ 1.9;size 60 mm: 99.5 mm, SEM ¼ 2.1; size 70 mm:107.2 mm, SEM ¼ 2.4; size 80 mm: 116.5, SEM¼ 2.3) than on the arm (size 50 mm: 96.4 mm,SEM ¼ 2.0; size 60 mm: 100.3 mm, SEM ¼ 2.7;size 70 mm: 103.3 mm, SEM ¼ 2.3; size 80 mm:106.5 mm, SEM ¼ 2.5).

Analysis of performance variability (average SDwithin a condition for each participant) revealed amain effect of response. Grasping responses(8.5 mm) are less variable than estimationresponses (10.2 mm). Also, a main effect of areawas found, which shows that hand-directedresponses (8.53 mm) are less variable than arm-directed responses (10.25 mm).

Other kinematic variablesNo significant effects of area of stimulation orobject size or an interaction of both were foundconcerning movement time (see Table 1). Peak

Table 1. The results of repeated measures ANOVA performed on the data of Experiment 1

F

Factor Level Factor GA SD TPGA% MT PV TPV%

Response 26.80�� 8.584�� — — — —

Area ns 14.04�� 4.516� ns 42.63�� 8.780�

Object size 251.9�� ns 11.38�� ns ns ns

Area � Response 55.95�� ns — ns ns ns

Area � Size 53.88�� ns ns — — —

Response � Size 11.03�� ns — — — —

Area � Response � Size ns ns — — —

Contrast Object size 50 vs. 60 mm 31.12�� — 19.33�� — — —

60 vs. 70 mm 22.84�� — 7.285� — — —

70 vs. 80 mm 13.62�� — ns — — —

Interaction effects Response � Area Estimate Area 15.71�� — — — — —

Grasp Area 29.16�� — — — — —

Area � Size Hand Size 24.78�� — — — — —

Arm Size 44.35�� — — — — —

Response � Size Grasp Size 83.52�� — — — — —

Estimate Size 17.27�� — — — — —

Note: ANOVA ¼ analysis of variance. GA ¼ grip aperture. SD¼standard deviation of the grip aperture. TPGA% ¼ time to peak

grip aperture as a percentage of total movement time. MT ¼ movement time. PV ¼ peak velocity. TPV% ¼ time to peak velocity

as a percentage of total movement time.�p , .05. ��p , .01.

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velocity appeared to be significantly higher whengrasping movements were directed to theforearm (hand: 644 mm/s; arm: 756 mm/s).Also, it emerged significantly later in time forthe arm- than for the hand-directed responses(hand: 28%; arm: 31%). PGA was reachedapproximately at two thirds of the movement. Inthis experiment PGA was reached significantlylater in grasping movements directed to objectslocated on the hand (67%), than objects locatedon the arm (66%; see Table 1).

In sum, the results showed that the manual sizeestimations of solid objects were consistent withWeber’s illusion. In contrast, the graspingresponses appeared to show the opposite patternof that observed for estimation responses: largerPGA towards objects located on the arm thantowards objects on the hand.

An important confounding factor that couldhave caused the observed opposite pattern ofresults is the influence of tactile feedback that par-ticipants received when grasping the objects.Participants received haptic feedback during thegrasping blocks whereas during the estimation

blocks this was not the case. As such, the righthand received size information that was not avail-able to the right hand in the matching condition.Therefore, participants may have been affectedinitially by Weber’s illusion but then, followingfeedback, learned that the somatosensory infor-mation from the arm leads to size underestima-tion. As a consequence, participants might havecorrected for this by purposely increasing theirgrip apertures for objects on the arm as comparedto objects on the hand. This might have resulted inan opposite effect of the illusion as is found in thematching task. To test this hypothesis, peak gripaperture data of the original experiment’s firsttrial per object size were submitted to the samerepeated measures ANOVA as that in the mainanalysis. This is described in the following section.

First-trial analysesAgain, a 2(area) � 2(response) � 4(object size)repeated measures ANOVA revealed significantmain effects of response (grasping: 110 mm,SEM ¼ 2.9; estimating: 92 mm, SEM ¼ 3.4),F(1, 17) ¼ 17.61, p , .01, and object size

Figure 4. Mean grip aperture for estimation responses and peak grip aperture for grasping responses of all first trials for each Response � Area

� Object Size condition, in Experiment 1. Aperture in mm. Error bars show between-participants error of the means.

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(50 mm: 92 mm, SEM ¼ 2.4; 60 mm: 99 mm,SEM ¼ 2.1; 70 mm 103 mm, SEM ¼ 2.9; and80 mm: 111 mm, SEM ¼ 3.0); F(1, 17) ¼ 28.90,p , .01. When exploring differences in objectsize we found significant increases in PGAbetween 50 mm and 60 mm, F(1, 17) ¼ 26.39,p , .01, between 60 mm and 70 mm, F(1, 17) ¼26.41, p , .01, and between 60 and 70 mm, F(1,17) ¼ 51.65, p , .01. Most interesting, area inter-acted significantly with response, F(1, 17) ¼

21.863, p , .01, as was found when analysing allthe trials (see Figure 4). Also, this interactioneffect yielded a similar effect of Weber’s illusionfor estimation responses, F(1, 17) ¼ 15.77, p ,

.01, versus an opposite pattern of results for grasp-ing responses, F(1, 17) ¼ 9.175, p , .01.

Discussion

Experiment 1 assessed the effect of Weber’s illu-sion on a manual size estimation response and atactually guided grasping response. As wasobserved in our pilot experiments, the pattern ofresponses revealed an effect of Weber’s illusionon the manual size estimations of solid objects:larger mGA for objects located on the hand thanfor objects on the arm.

In contrast, the grasping responses appeared toshow the opposite pattern to that observed for esti-mation responses, a finding that was not predictedprior to running this experiment.

However, this opposite pattern of results forgrasping movements existed only for the smallerobjects. The increase in peak grip aperture wasonly significant between the smaller (50 mm and60 mm), and not between the larger objects (70and 80 mm). A straightforward explanation forthis lack in increase in thumb and index separationmay be that participants had reached their maximalgrip opening (the biomechanical constraint in thejoints) when grasping the 70-mm-wide object. Afurther increase in PGA for the 80-mm-wideobject could therefore not be achieved.

Furthermore, differences in tactile feedbackbetween the matching and grasping conditionsmay have caused the opposite patterns to occur.However, additional analysis of each first trial

per condition suggests that the presence of tactilefeedback in the grasping condition is unlikely tobe the sole reason for the difference in the observedresults.

Another important potentially confoundingfactor causing the observed larger peak grip aper-tures for arm-directed grasping responses is thedifference in biomechanics in arm- versus hand-directed movements. Hand-directed graspingmovements were always aimed at a more distallocation whereas arm-directed movements wereaimed more proximally. Also, peak velocity covar-ied significantly with location, which in itself couldhave caused the larger arm-directed peak gripaperture data. Therefore we ran a second exper-iment in which we tested whether the differencein spatial location could have caused the observedlarger peak grip aperture values for graspingresponses directed towards the arm. This wasassessed by keeping the grasping movementsaimed at one location in external space, buttowards different positions on the body (forearmvs. hand). It was expected that peak velocitywould not differ between arm- and hand-directedmovements, but that the difference in peak gripaperture remained.

EXPERIMENT 2

Method

ParticipantsA total of 13 right-handed participants (4 male, 9female; mean age 27 years; range 20 to 34 years)with no history of psychiatric or neurologicalillness and who were naıve as to the purpose ofthe experiment participated in Experiment 2.

Procedure and designIn this experiment only grasping responses wereperformed by the participants. Keeping graspingresponses aimed at the same location in externalspace (see Figure 5) was achieved by varying theposition of the arm on the table in between trials(prior to the placement of the object). The objectof 80-mm length was removed from the experiment

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since the results of Experiment 1 suggested influ-ences of biomechanical constraints when graspingobjects of 80 mm. The rest of the procedure andthe experimental set-up were identical to those ofthe grasping condition of Experiment 1.

The experiment had a 2 (area; palm of the handor forearm) � 3 (object size; 50, 60, or 70 mm)within-subjects design. A total of 48 graspingtrials were tested in randomized order.

Results

All preprocessing procedures and statistics weresimilar to those of Experiment 1. In this exper-iment PGA data were submitted to a 2 (area:palm of the hand or forearm) � 3 (object size;50, 60, or 70 mm) repeated measures ANOVA.

As expected, the analyses of the peak grip aper-ture data revealed similar main effects of area(hand: 103 mm, SEM ¼ 2.2; arm: 110 mm,SEM ¼ 2.2) and of size (50 mm: 103 mm, SEM¼ 2.1; 60 mm: 107 mm, SEM ¼ 2.2; 70 mm:110 mm, SEM ¼ 2.2; see Table 2). Both 50-mmand 60-mm objects differed significantly in gripaperture, as did 60-mm and 70-mm objects.Finally, area interacted significantly with objectsize (see Figure 6). Further analysis of this effectrevealed significant effects of object size, both inthe hand condition and in the arm condition;however, the increase in PGA in the latter con-dition was less pronounced, similar to the observedArea � Object size interaction in Experiment 1.

Other kinematic variablesA significant main effect emerges for object size (seeTable 2 for F and p values) when analysing the rela-tive time to PGA (TPGA%). The smallest andmiddle objects cause the TPGA% to occur signifi-cantly earlier in time than does the largest objectsize (50 mm: 67.0%; 60 mm: 67.7%; 70 mm:69.9%). Also, a significant main effect of objectsize was found for peak velocity (50 mm:722 mm/s, SEM ¼ 52; 60 mm: 749 mm/s,SEM ¼ 54; 70 mm: 744 mm/s, SEM ¼ 54; seeTable 2). This implies that grasping movementstowards the smallest object resulted in significantlyslower movements than did those to the largerobjects. Most importantly, the difference in peakvelocity values between arm- and hand-directedgrasping responses observed in Experiment 1 dis-appeared, F(1, 12) , 1. However, with respect

Figure 5. Experimental set-up of Experiment 2. Note: Objects are now located in the same spatial location.

Figure 6. Peak grip aperture for grasping responses, in Experiment

2. Aperture in mm. Error bars show between-participants error of

the means.

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to the relative time to peak velocity (TPV%), an inter-action effect of area and object size was found.Further exploration of this effect revealed only atrend towards significance for object size on thehand, F(1, 12) ¼ 3.345, p ¼ .052. This impliesthat the larger the object, the earlier the peak in vel-ocity emerges (50 mm: 33%; 60 mm: 32%; and70 mm: 30%), although post hoc contrasts did notreveal any significant differences. No significanteffects were found when analysing movement time.

First-trial analysesTo test the hypothesis of tactile feedback causingthe observed grasping pattern, which is oppositeto that of Weber’s illusion, an additional analysisof the aperture data of the first trial per object sizewas submitted to the same repeated measuresANOVA as that in the main analysis. Again, a 2(area: palm of the hand or forearm) � 3 (objectsize; 50, 60, or 70 mm) repeated measuresANOVA revealed a significant main effect of area(hand: 103 mm, SEM ¼ 2.8; arm ¼ 112 mm,SEM ¼ 2.7); F(1, 12) ¼ 22.26, p , .01. No signifi-cant effects were found for object size, F(1, 12) ¼1.710, or Area � Size, F(1, 12) ¼ 1.056 .

Discussion

The results of Experiment 2 suggest that biome-chanical differences between grasping responses

directed to different spatial locations cannotaccount for the observed larger peak gripaperture, but did produce the higher peak velocityvalues for arm-directed responses in Experiment1. However, some new significant effects of otherkinematic variables, which did not occur in thefirst experiment, require some discussion.

First, the time at which PGA occurred wasrelated to object size. Similarly, peak velocitywas related to object size as well. Both findingsare consistent with the idea of more time foronline adjustment for the smaller object. Thiseffect might be consistent with higher spatialaccuracy demands (a more precise grip) for grasp-ing smaller objects, which is also observed invisuomotor grasping (Gentilucci et al., 1991).Then why was this effect not observed in ourfirst experiment in which grasping movementsto the arm were just as uncertain? A simplereason may be that in Experiment 2 the positionof the arm was changed in between trials, and thisnew position had to be recurrently updated inorder to accurately perceive the spatial locationof the object to grasp. It could be that theseupdates generate noise leading to uncertaintyabout location of the arm and therefore uncer-tainty about the location of the object. Togetherwith the higher spatial demands of the smallerobjects, this might have caused the need formore online adjustments.

Table 2. The results of repeated measures ANOVA performed on the data of Experiment 2

F

Factor Level Factor GA TPGA% MT PV TPV%

Area 35.69�� ns ns ns ns

Object size 25.09�� 5.864� ns 5.927� ns

Area � Size 17.96�� ns ns ns 4.160�

Contrast Object size 50 vs. 60 mm 35.80�� ns — 23.60�� —

60 vs. 70 mm 10.05�� 14.41�� — ns —

Interaction effects Area � Size Hand Size 42.85�� — — — ns

Arm Size 8.130�� — — — ns

Note: ANOVA ¼ analysis of variance. GA ¼ grip aperture. SD ¼ standard deviation of the grip aperture. TPGA% ¼ time to peak

grip aperture as a percentage of total movement time. MT ¼ movement time. PV ¼ peak velocity. TPV% ¼ time to peak velocity

as a percentage of total movement time.�p , .05. ��p , .01.

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GENERAL DISCUSSION

The current study aimed to investigate whetherWeber’s illusion differed depending on the typeof response given. Experiment 1 assessed differ-ences in grasping and manual size matching ofobjects placed on the hand and the arm. Theresults of the size-matching responses were con-sistent with Weber’s illusion. In contrast, PGAduring grasping of the objects showed an oppositepattern with larger hand openings for objectsplaced on the arm. Experiment 2 showed thatthe observed pattern was not caused by biomecha-nical differences. Overall, these findings are con-sistent with the idea that the somatosensorysystem deals differently with tactile informationdepending on whether the information will beused to provide a conscious perceptual size judge-ment response or an implicitly driven motoraction. With respect to the size estimationresponses, the current findings are consistentwith previous studies showing differences in dis-tance judgements between areas with low andhigh receptor density. As described above, thispattern has been attributed to incomplete size con-stancy judgements for which visual input about thesize of the body part is used (Taylor-Clarke et al.,2004). In contrast, the current results suggest thatdifferences in receptor density (and incompletesize constancy mechanisms) are not the mostdominant when determining the pattern of gripaperture during tactually guided grasping.Instead, other mechanisms must have caused apattern that is opposite to that expected based onWeber’s illusion. One possibility might be thatdifferences in tactile feedback between the match-ing and grasping conditions may have caused theopposite patterns to occur. However, additionalanalysis of each first trial per condition suggeststhat the presence of tactile feedback in the grasp-ing condition is unlikely to be the sole reason forthe difference in the observed results. Thus,although tactile feedback may have influenced per-formance in later trials, the pattern of larger handopening for objects placed on the arm was alreadypresent during the very first trials. Another poss-ible explanation could be that the manual size

estimation used in this experiment is not a feasibleperceptual measure. Indeed, Franz (2003)suggested that a manual size estimation responsesuch as the adjustment of the thumb–index separ-ation is highly sensitive to a change in object size,illusionary or real, whereas a more “classical”measure of size such as the method of adjustmentshows less sensitivity to an illusion. The authorshowed that when using a more traditionalmeasure of size, a frequently found differencebetween grasping and matching responses ineffect of the Titchener illusion disappeared.Results from our second pilot experiment indeedshowed that the traditional measure was less sensi-tive to Weber’s illusion; however, this differencewas not significant. Furthermore, this responsestill showed an overestimation of hand- versusarm-perceived objects, and a reversal of thispattern as observed for the grasping responsefound in Experiment 1 did not occur. Therefore,other factors might have caused the observeddifferences between matching and grasping inour experiment.

Interestingly a similar response pattern forgrasping movements was found in a visuomotorexperiment (Brown, Halpert, & Goodale, 2005).They compared grasping towards foveally and per-ipherally presented objects and found larger gripapertures in the peripheral condition. This simi-larity in response patterns suggests that whengrasping is directed towards areas with reducedreceptor density such as the skin of the forearm,or peripheral vision, the hand is opened wider. Apossible explanation for this is that when sensoryinput about the target is nonoptimal, the motorsystem responds by increasing its safety margin(Schlicht & Schrater, 2003); when grasping anobject, the participants must be aware of the possi-bility to collide with the object. The more uncer-tain they are about the size or location of theobject, the wider they would open their grip inorder to avoid collision (Jakobson & Goodale,1991). In addition to a larger grip aperture, onewould perhaps also expect increased variabilitywhen sensory input is reduced. Although Brownet al. (2005) could not find evidence for increasedvariability in their peripheral grasp condition, in

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our experiment both grasping and matchingresponses revealed a larger variability for arm-placed objects. Hence one could argue that sizeinformation for objects placed on the arm is pro-cessed with less certainty than that for theobjects located on the hand. This uncertaintyforced participants to open their thumb andindex finger wider when grasping objects locatedon the arm, in order to avoid collision. When esti-mating the size of an object, however, collisionavoidance is not necessary as there is no directcontact with the object. Therefore, a possibleunderlying mechanism responsible for theobserved differences between grasping and match-ing responses may be that in principle all incomingtactile information is affected by the (imperfect)size constancy mechanisms resulting in an under-estimation of tactile size for areas with reducedreceptor density. However, uncertainty abouttactile input causes an extra safety marginbetween thumb and index finger when graspingthe object. Consequently this could maskWeber’s illusion for the grasping trials. Based onthe current data, we cannot rule out this possi-bility, but the extra safety margin must be of a con-siderable magnitude for this pattern to emerge.

A second possible mechanism could be thatdifferences in effects of an illusion depend on whichreference frame is used to solve the task (Bruno,2001). Size judgement responses are more likely tobe based on an object-based frame of reference andtherefore are influenced by imperfect size constancymechanisms as suggested by Taylor-Clarke et al.(2004). In contrast, for grasping responses object fea-tures (e.g., size or object end points) are coded withrespect to the actor’s grasping hand, in a “hand-centred reference frame”. These are not necessarilyinfluenced by size constancy mechanisms.

However the current data do not allow us to dis-tinguish between the discussed mechanisms, andtherefore future studies should further investigatecauses of the observed pattern, for example bymanipulating sensory input about the target objectin a different way. One way to achieve this is byincreasing certainty about tactile input provided bynoninformative visual input of the arm, as wasdone by Kennett, Taylor-Clarke, and Haggard

(2001) and Taylor-Clarke et al. (2004). Finally,exposure to a visually magnified version of onesown arm might be a way of assessing whether sizeconstancy mechanisms also affect grasping responses.

First published online 17 May 2008

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