Perceptual judgment and saccadic behavior in a spatial distortion with briefly presented stimuli.

When observers are asked to localize the peripheral position of a small probe with respect to the mid-position of a spatially extended comparison stimulus, they tend to judge the probe as being more peripheral than the mid-position of the comparison stimulus. This relative mislocalization seems to emerge from differences in absolute localization, that is the comparison stimulus is localized more towards the fovea than the probe. The present study compared saccadic behaviour and relative localization judgements in three experiments and determined the quantitative relationship between both measures. The results showed corresponding effects in localization errors and saccadic behaviour. Moreover, it was possible to estimate the amount of the relative mislocalization by means of the saccadic amplitude.


ed stationary
stimulus with high contrast (for overviews, see e.g., Skavenski, 1990;Westheimer, 1981).Spatial acuity is much poorer when measured with a stimulus of short duration and low contrast (see e.g., Bedell & Flom, 1983;Bocianski, Müsseler, & Erlhagen, 2008;Leibowitz, Myers, & Grant, 1955;Mateeff & Gourevich, 1983;Mateeff & Hohnsbein, 1988;O'Regan, 1984;Rose & Halpern, 1992).Moreover, localization is distorted when stimuli are briefly presented before, during, or after a saccade or during smooth pursuit eye movements (e.g., Awater & Lappe, 2006;Brenner, Smeets, & van der Berg, 2001;Rotman, Brenner, & Smeets, 2005).

Müsseler and colleagues (Müsseler & van der Heijden, 2004;Müsseler, van der Heijden, Mahmud, Deubel, & Ertsey, 1999;van der Heijden, Müs eler, & Bridgeman, 1999) also investigated spatial localization under less than optimal viewing conditions.The observers were asked to judge the peripheral position of a small probe with respect to the mid-position of a spatially extended comparison stimulus.When the two stimuli were flashed successively a systematic deviation was consistently observed: The observers perceived the probe as being more peripheral than the mid-position of the comparison stimulus.

To explain this relative mislocalization, Müsseler and colleagues (Müsseler & van der Heijden, 2004;Müsseler et al., 1999) assumed t emerged from different absolute localizations of the probe and midlocation of the comparison stimulus.From the literature it is already well-known that the absolute location of a briefly presented target is often perceived more foveally than it actually is (see e.g., Kerzel, 2002;Mateeff & Gourevich, 1983;Müsseler et al., 1999, Experiment 4;O'Regan, 1984;Osaka, 1977; van der Heijden, van der Geest, de Leeuw, Krikke, & Müsseler, 1999).In order to explain the relative mislocalization we assumed that a spatially extended stimulus is localized even more foveally than a spatially less-extended probe.Then the probe's relative position is perceived as more peripheral than the mid-position of the comparison stimulus (see Figure 1).This explanation of the relative mislocalization was successfully tested against alternative ac-counts (for details, see Müsseler & van der Heijden, 2004;Müsseler et al., 1999).

The assumptions made by Müsseler and colleagues, and especially the assumption that a spatia ly extended stimulus is localized more foveally than a spatially less extended probe, certainly need some supporting evidence.In this context it is of importance to know that comparable foveal tendencies in absolute localizations are found in saccadic eye movement studies.Firstly, saccades tend to undershoot a peripheral target by about 5-10% of its eccentricity -an error that is normally compensated with a corrective saccade (see e.g., Aitsebaomo & Bedell, 1992;Bischof & Kramer, 1968;Lemij & Collewijn, 1989).

Secondly, the saccadic undershoot seems to increase with spatially extended stimuli (so-called centre-of-gravity effect; cf.Findlay, Brogan, & Wenban-Smith, 1993; see also Vos, Bocheva, Yamimoff, & Helsper, 1993).Moreover, the size of the saccadic undershoot is in the same range as the size of the foveal mislocalization observed in a perceptual judgement task (see van der Heijden, van der Geest, et al., 1999).So, saccadic eye movement research provides support for assumptions of Müsseler et al. (1999).

The comparability between eye-movement behaviour and perceptual judgement t sks suggests an intriguing possibility: The possibility that the saccadic eye movement system is at the basis of, and provides the information for, position judgements in position-judgement tasks (see also e.g., van der Heijden, Müsseler, & Bridgeman, 1999;Wolff, 1987, for this suggestion).With regard to this possibility it is of importance to know that, in addition to the pattern of undershoot that saccades and localization judgements apparently have in common, there are further correspondences between saccadic eye movements and localization judgements.Four points are worth mentioning here.

The first point concerns the effect of exposure duration.It is well establish d that both saccadic eye movements and localization judgements become more precise with longer exposure durations of a target (e.g., Abrams, Meyer, & Kornblum, 1989;Aitsebaomo & Bedell, 1992;Kowler & Blaser, 1995;Lemij & Collewijn, 1989).

The second point concerns the effect of grouping within the stimulus array.It s well-known that the amplitude of saccades to targets depends on the grouping within a stimulus array; if one element is made larger (Findlay, 1982), is made more intense (Deubel, Wolf, & Hauske, 1984), or is presented with higher contrast (Deubel & Hauske, 1988), the saccade lands closer to that target.The results obtained with a relative localization experiment are in line with these findings.A salient square placed at either the inner or the outer edge of a comparison stimulus affects relative mislocalization as it affects saccadic behaviour; with the salient square at the outer position the probe is perceived as more peripheral than with the salient square at the inner position (see Müsseler et al., 1999, Experiment 7).

Third, recent studies demonstrated an effect of saccadic adaptation on pointing a d verbal localization, that is a shift in the direction of adaptation (Bruno & Morrone, 2007;Collins, Doré-Mazars, & Lappe, 2007;Georg & Lappe, 2009).On the basis of these results the authors suggested that a common mechanism might serve to recalibrate both the perceptual and the action map and that the system providing saccade metrics also contributes to the metric used for space perception.

The last -but probably not least -point concerns the effect of stimulus onset asyn hrony (SOA) between comparison stimulus and probe in a relative judgement task.The relative mislocalization emerges in an interval in which saccadic eye movements are programmed and executed, that is typically between 50 and 200 ms (Müsseler et al., 1999, Experiment 2).

Taken all together, the similarities between saccadic eye-movement behaviour and lo alization judgements are quite suggestive.So, there is evidence that the saccadic eye movement system is at the basis of and provides the information for the localization judgements.Nevertheless, there are at least three reasons to be careful about accepting this assumption.

Firstly, eye movements were not measured directly in the relative judgement tasks und r discussion.The evidence for a close correspondence between saccadic eye movement behaviour and position judgements comes from different studies designed for different purposes.

Secondly, although the correspondence seems to be obvious at first sight, other observ tions cast doubt on a too strong relationship between saccadic eye movements and spatial localization judgements.

Recently several spatial dissociations between motor behaviour (including eye movement ) and perception have been reported and are still under discussion (for an overview, see Rossetti & Pisella, 2002).

Thirdly, different brain areas with different spatial maps are involved in perception nd in the programming of saccadic eye movements.

Visual information can reach the brainstem oculomotor centres by several routes: direc ly from the retina via the superior colliculus; from a route via the corpus geniculatum laterale, the primary striate cortex, and the superior colliculus; from a route via the corpus geniculatum laterale, the visual cortex, and the frontal eye fields; and last -but probably not least -from a route via the corpus geniculatum laterale, striate, stimulus presentation and stimulus perception in the relative localization task.the greater outer localization of the single lower square (the probe) relative to the mid-position of the spatially extended row of the upper squares (the comparison stimulus) is assumed to emerge from two different foveal tendencies of the comparison stimulus (shifted to the dashed line) and the probe (shifted to the straight line).FP = fixation point.

prestriate and parietal cortices, and the frontal eye fields (cf.Deubel, 1999, p. 716).Th s multiplicity means that it is far from clear whether the spatial map used in perceptual judgement tasks corresponds metrically with the spatial map(s) involved in the programming of saccadic eye movements.

In fact, there are also studies showing a non-correspondence between a (saccadic) pointing ask and a relative judgement task (e.g., Eggert, Sailer, Ditterich, & Straube, 2002;Müsseler, Stork, & Kerzel, 2008).For example, Eggert and co-workers examined the effect of distractor presentation on the relative spatial judgement and on the width of the primary saccadic amplitude.They found no correspondence between both measures.However, their general procedure differed from the spatial illusion, on which we focus here.Therefore, the aim of the present study was to examine whether saccading to the mid-position of the spatially extended comparison stimulus and saccading to the probe revealed more absolute foveal mislocalizations for the comparison stimulus than for the probe.Moreover, our aim is to compare quantitatively the amplitude of the saccadic behaviour with the location error of the relative judgement task.

Consequently, in three experiments two tasks are compared: In the relative judgement tasks, part cipants were asked to judge the perceived position of a probe relative to the mid-position of a comparison stimulus.This task matches the procedure used by Müsseler and colleagues (1999; see also Müsseler & van der Heijden, 2004).In the saccade task, participants were asked to execute a saccade to the probe or the mid-position of the comparison stimulus.In Experiment 1, relative judgements and saccadic amplitudes to the stimuli were compared.

Experiments 2 and 3 were run in order to check whether different effects of eccentricity could be observed with both tasks.


EXPERIMENT 1

Empirical evidence and theoretical considerations allow us to suggest that the rela

ve mislocaliz
tion under consideration originated from localizing a spatially extended stimulus more towards the fovea than a spatially less-extended probe.This assumption was already successfully examined by an experiment with absolute mouse pointing, in which both stimuli were presented blockwise as single targets (Müsseler et al., 1999, Experiment 4).Additionally, if our assumption is correct that saccadic eye movements are at the basis of the mislocalization, we expect corresponding results in a saccadic eye-movement task.Therefore, Experiment 1 aims to compare the findings of the relative judgement task with the findings on saccadic behaviour in similar experimental situations.

The relative judgement task was basically identical to the procedure introduced by Müsseler et al. (1 99).The probe and comparison stimulus were presented with an SOA of 0 and 120 ms.When both stimuli are flashed simultaneously, they can be processed in one spatial map as a single stimulus configuration.Therefore, with simultaneous presentation the position judgement of the probe relative to the comparison stimulus is expected to be more or less error-free.When the two stimuli are separated by an SOA, however, two successive con-figurations with different spatial information have to be superimposed.

Then relative mislocalizations are expected to emerge (see Müsseler et al., 1999;Mü seler & van der Heijden, 2004).

The saccadic eye-movement task was basically identical to the procedure used in single-stimulus studies in basic saccadic eye-movement research.The comparison stimulus and probe were presented as single stimuli in a blocked sequence.If the relative judgement task and the saccade task correspond, a more pronounced eye-movement undershoot to the spatially extended comparison stimulus than to the less extended probe is expected.Eye-movement studies already indicated comparable tendencies, that is larger undershoots with a spatially extended stimulus than with a less extended stimulus (see e.g., Findlay et al., 1993).The relevant experiments were, however, designed for different purposes and used in different experimental situations.


Method


AppArAtus And stimuli

The experiment was carried out i

it room.The experiment
was controlled by a Macintosh computer and the stimuli were presented on a 17" colour monitor with black-on-white projection ( 832x 624 pixels).The monitor had a refresh rate of 75 Hz and a luminan e of approximately 40 cd/m 2 .The participant's head was placed on a chin and forehead rest 500 mm in front of the monitor.

The stimuli appeared either to the left or to the right of a fixation cross.A square of 0.33° x 0.33° visual angle was used as the probe.A spatially more extended stimulus of 3° consisting of five squares, each separated from the next by 0.33°, was used as the comparison stimulus (see Figure 2).Stimuli were presented for only one frame of the monitor (13 ms).

In the relative judgement task, the comparison stimulus appeared 1.4° ab ve the probe and its position was held constant at 5° (mid- stimulus presentation in the experiments.Participants fixated a cross in the middle of the screen.A single lower square (probe) and a spatially extended row of upper squares (comparison stimulus) appeared to the left or to the right of the fixation cross (here, 5° to the left).Participants were asked to judge the probe position (presented at 3.8°-6.2°)relative to the comparison stimulus's mid-position.FP = fixation point.

position of the central square).The position of the probe was varied with res ect to the mid-position of the comparison stimulus by ± 0.2°, ±0.7°, and ±1.2°; thus, it was presented at 3.8°, 4.3°, 4.8°, 5.2°, 5.7°, and 6.2° eccentricity.

In the saccade task either the comparison stimulus or the probe was presented.
hese stimuli appeared horizontally in line with the fixation cross.The stimuli were presented at the same positions as in the relative judgement task, that is between 3.8° and 6.2° eccentricity.


design

The relative judgement task and saccadic eye-movement task were present

in sep
rate blocks.The sequence of the blocks was counterbalanced over participants.

In the judgement task, the probe and comparison stimulus were presented in either the left or the right hemifield.They either appeared simultaneously or the comparison stimulus preceded the probe stimulus by an SOA of 120 ms.All combinations of hemifield (left, right), probe position (3.8 to 6.2°), and SOA (0, 120 ms) were presented in a randomized sequence.In total, participants were confronted with 192 trials in the judgement task.

In the saccade task, the comparison stimulus and the probe were presented blockwise n a counterbalanced order.Again, all participants were confronted with 192 presentations of the stimuli in the left and right hemifields.


procedure

In the judgement task, participants initiated the stimulus presentation by simultaneously pressing the upper and lower key of a horizontally arranged computer mouse.Each trial began with an auditory signal and a central fixation cross that appeared for 1 s.The stimuli were presented for one frame (13 ms) 200 ms after the fixation point had vanished (this interval was introduced in order to facilitate the generation of eye movements in the saccade task, cf.Kingstone & Klein, 1993).

The instruction for the judgement task stressed that the participant should fixate the fixation cross when it appeared and not move the eyes after the cross had vanished.As the presentation of comparison stimulus and target was much too short to execute eye movements successfully and as keep ng fixation was much more convenient for the observers than moving their eyes, eye movements were not recorded in the judgement task. 1 After the presentation of the stimuli the observers had to answer the question "Which stimulus was more peripheral?The upper or lower?" by pressing the upper or lower mouse key.Following


Results

As the dependent variable in the judgement task, the point of subjective equality (PSE, 50% threshold) between the probe and the midposition of the comparison stimulus was computed by a probit analysis for every participant and condit

n (cf.Finney, 1971;Lieberman,
1983).As dependent variable in the saccade task the mean deviation between the eye's first landing position and the real target position was calculated for every participant and condition.Three participants were


Discussion

The results of the relative judgement task successfully replicated previous findings (Müssele

et al.,
999;Müsseler & van der Heijden, 2004):

The probe is localized as being more peripheral than the midpoint of the comparison stimulus.This tendency is present with an SOA, but also with a simultaneous presentation of both stimuli.Up to now, more outer judgements for the probe were mainly observed with an SOA, but slight tendencies with simultaneous presentation were also ob-  served and reported by Müsseler et al. (1999).In line with the previous research, the outer judgements were clearly more pronounced with an SOA between stimuli than with an SOA of 0 ms.

The eye-movement data showed that the first saccade undershot both targets.This is in accordance with previous eye-movement studies (e.g., Aitsebaomo & Bedell, 1992;Becker, 1 72;Deubel et al., 1984;Henson, 1978).Of special importance in the present context is the (nearly significant) difference between the und

shoots to t
e comparison stimulus and the probe.As expected, a stronger undershoot occurred with saccades to the mid-position of the comparison stimulus than with saccades to the probe (see also Findlay et al., 1993).

A recent model of saccadic programming by Godijn and Theeuwes (2002) can account for the more pronounced undershoot observed with the extended comparison stimulus.It basically suggests that saccades are programmed in a common salience map, in which activity at a specific location spreads to neighbouring locations but inhibits distant locations.The integration of activation might take place in the intermediate layer o the superior colliculus, which receives input from the frontal eye fields, supplementary eye fields, and posterior parietal cortex (cf.Trappenberg, Dorris, Munoz, & Klein, 2001).The preference of the inner squares can be assumed to originate from an increased sensitivity within the saccadic map as a function of eccentricity (Findlay & Walker, 1999).As a consequence, the inner edge of the comparison stimulus receives higher activation to the mean of integrated activation than the outer edge.Accordingly, the eyes could be capture more often by the inner squares.

In the present context it is important to note that the amount of eyes' undershoot was similar to the foveal mislocalization with the absolute cursor pointing task used by Müsseler et al. (1999, Experiment 4, where it was -0.4° for the probe and -0.52° for the comparison stimulus).Moreover, the difference between the mean undershoots to the probe and the comparison stimulus is in the same range of magnitude as the differen e between PSE values with and without SOA;

(-0.55) -(-0.80)= 0.25°

ersus (-0.15)
-(-0.44)= 0.29°.This could be interpreted as a hint for a correspondence between the perceptual judgement task and the oculomotor task.However, since the difference between probe and comparison stimulus is only marginally significant in the saccadic behaviour, this conclusion needs further evidence from subsequent experiments.


EXPERIMENT 2

Experiment 1 provided support for the assumption of Müsseler et al.


Method stimuli, design, And procedure

These were the same as in Experiment 1, except for the following changes.In the judgement task all stimuli were presented with an SOA of 120 ms.The mid-position of the comparison stimulus was presented at an eccentricity of either 3.5° or 6.5°.Accordingly, the probe was presented at 2.3°, 2.8°, 3.3°, 3.7°, 4.2°, or 4.7° with a mid-position of the comparison stimulus at 3.5° or was presented at 5.3°, 5.8°, 6.3°, 6.7°, 7.2°, or 7.7° with a mid-position of the comparison stimulus at 6.5°.

There were eight repetitions (8 blocks with 24 trials) per participant per cell.In total, the participants received 192 trials.

In the saccade task, the comparison stimulus and the probe were presented in separate blocks.The stimuli could appear either at 3.5°

or at 6.5° to the left or to the right of the fixations cross.Sixteen repetitions were gathered for each cell of the design, yielding a total of 128 trials per participant.If no saccade was detected or the latency of the saccade was above 250 ms, an error message appeared.If those errors exceeded 8 trials, one block of 16 trials was added to the experiment.

Eye-movement calibration was repeated after two blocks.


Results

Mean relative mislocalization and mean saccadic amplitude were computed separately per participant and eccentricity.Two observers were excluded from the analysis, because their mean values exceeded the criterion of ±2 standard deviations between participants.The mean saccade latency was 172 ms (SE = 4) for the comparison stimulus and 171 ms (SE = 4) for the probe.

In the judgement task PSE values indicated a more pronounced tendency to outer judgements at the eccentricity of 6.5° than at the eccentricity of 3.5°, t(32) = 5.01, p < .001(cf. Figure 5, left part).At 6.5°

the PSE value indicates a significant difference from the objective mid-  position, -0.59°, SE = 0.13, t(32) = 4.51, p < .001.At 3.5° this result was only marginally significant, -0.12°, SE = 0.08 , t(32) = 1.49, p = .15.

Figure 6 shows the frequency plots of the eyes' horizontal landing positions.For the saccad

deviations in saccadic amplitud
from the objective positions were entered in a 2 (comparison stimulus vs. probe) x 2 (3.5° vs. 6.5°eccentricity) analysis of variance (ANOVA).

The analysis revealed a significant effect of type of stimulus, comparison stimulus, and probe, F(1, 32) = 6.1, MSE = 0.83 , p < .05; the saccadic undershoot to the comparison stimulus is more pronounced than the undershoot to the probe (cf.


Discussion

In the judgement task, the results again replicated the basic finding of In the saccade task ndershoots were observed with the probe and with the comparison stimulus.Moreover, the amount of undershoot was significantly lar er with the comparison stimulus than with the probe.This finding replicates and thereby substantiates the marginally significant result obtained in Experiment 1.

The size of the saccadic undershoot increased with increasing eccentricity.The interaction between type of stimulus and eccentricity was, however, not significant; an additive effect of eccentricity for comparison stimulus and probe was found.This additivity is in line with the results reported by basic eye movement research: The un ershoot is a fixed percentage of target eccentricity (se e.g., Deubel, 1999; see also the Introduction section).Of course, this outcome does not come as a surprise.In the saccadic eye movement task, exposure conditions were used that were virtually identical to those used in basic singletarget saccadic eye movement

esearch
see e.g., Deubel, 1999).

Note, however, that the additivity of the factors stimulus type and eccentricity is not in accordance with the assumption that absolute position judgements are at the basis of the phenomena observed in the relative judgement task.In the relative judgement task an eccentricity effect is observed: Relative mislocalization increases with increa ing eccentricity.This eccentricity effect is not apparent in the saccadic eye movement behaviour: Contrary to our predictions the difference between undershoots to comparison stimulus and probe remains the same with increasing eccentricity.Possibly the absence of the interaction indic

ed a disso
iation between saccadic behaviour and relative judgement, but it may be worthwhile to re-analyse our conditions.

So far, our considerations were based on the assumption that in the relative judgement task the probe and the compar

size of a
accadic eye movement.That is why in the saccadic eye movement task we used the single-item exposure conditions used in basic eye movement re-search.However, it cannot be excluded that in the relative judgement task, where a probe and a comparison stimulus are presented in close temporal proximity, the spatial codes of comparison stimulus and the probe modulate each other.If that is true, the additional presentation of the context stimulus could also affect the saccad c behaviour.This is tested in the subsequent experiment.


EXPERIMENT 3

The results obtained in the saccadic eye-movement task in Experiment 2 are in accord with those reported by basic saccadic eye movement research: No interaction is found between stimulus type and eccentricity.The results are, however, not compatible with Müsseler et al. 's explanation (1999) of the phenomena observed in the relative judgement task.For the eccentricity effect observed in the relative judgement task that explanation requires an interaction between stimulus type and eccentricity in the eye-movement task.

In the saccadic eye-movement task of Experiment 1 (and 2), single stimuli, either the probe or the comparison, were used as targets.In the relative judgement ta k, however, the two stimuli were presented in close temporal contiguity.The probe is presented in the context of the comparison stimulus and context effects are well known in saccadic eye-movement research.For example, saccades tend to land at an intermediate position between a target and a distractor (Findlay, 1982).It can therefore not be excluded that the context modulates the saccadic eye movements to comparison stimulus and probe.

Experiment 3 was conducted to examine this possibility.Like in the judgement task, both stimuli were now presented in each trial of the saccade task with the saccadic target determined blockwise as either the comparison stimulus or the probe.If the saccades show the predicte

non-additive
attern of undershoots, there is again a correspondence between saccadic behaviour and perceptual relative judgements.

Additionally, the number of squares of the comparison stimulus were increased from five to seven to stress the different spatial extension of the stimuli.The relative mislocalization was shown to increase with the spatial extension of the comparison stimulus (Müsseler et al., 1999, Experiment 5).Measuring the saccadic amplitudes under these conditions offers the possibility to test our assumptions over a wider spatial range.


Method stimuli, design, And procedure

The stimuli, design, and procedure were the same as in Experiment 1 except for the following changes.In both tasks, the comparison stimulus now consisted of seven squares instead of five squares, that is, the extension changed from 3° to 4.3°.The most important change was introduced in the saccade task: As in the judgement task in both conditions -saccade to the probe and saccade to the comparison -both the comparison stimulus and the probe were presented separated by an SOA of 120 ms.

In the saccade task, two different instructions wer given in two blocks of trials with the order of instruction counterbalanced over par-ticipants.In one block the participants were asked to make a saccade to the mid-position of the comparison stimulus, and in the other block to make a saccade to the probe and to ignore the other stimulus.

The midpoint of the comparison stimulus was at an eccentricity of either 3.5° or 6.5° (the position of the probe was va ied as in Experiments 1 and 2 with steps of ± 0.5°).In total, the participants received 320 trials in both tasks.The experiment lasted approximately 45 min.


pArticipAnts

Twenty-one female and 9 male individuals who ranged in age from 20 to 39 years (mean age of 25 years) were paid to participate in the experiment.


Results

Mean relative mislocalizations and mean saccadic amplitudes were computed per participant and conditi

icipants were excluded because
heir mean PSE values or saccadic amplitudes deviated more than ±2 standard deviations from the other participants.

The mean saccade latency was 248 ms (SE = 7) for the comparison stimulus and 122 ms (SE = 7) for the probe.This obvious latency difference might originate from the tendency to initiate the saccade to the comparison stimulus not before both stimuli were presented and/or from the tendency to use the comparison stimulus as a temporal cue to initiate the saccade to the target.

target
nd eccentricity, F(1, 27) = 6.8,MSE = 0.05, p = .02(cf. Figure 7, right part).The saccadic undershoot to the comparison stimulus is more pronounced than the undershoot to the probe; the undershoot increases with eccentricity, and this increase is more pronounc d for the comparison stimulus than for the probe.


Discussion

In the judgement task the probe was again localized as being more peripheral than the comparison stimulus and the amount of mislocalization increased when the eccentricity of presentation was increased.

These results replicate the finding reported by Müsseler et al. (1999, Experiment 3).Moreover, with the present comparison stimulus of seven squares the amount of mislocalization was clearly larger than in Experiment 2, where the comparison stimulus consisted of five squares.The mean PSE values were -0.355° (Experiment 2) and -0.765° (Experiment 3), respectively, S

= 0.132, t(
9) = 3.15, p = .003.

This outcome replicates the result reported by Müsseler et al. (1999, Experiment 5).

The saccade task revealed the most important finding.With the additional presentation of the co text stimulus, the saccadic undershoots showed the predicted non-additive interaction.The difference between the undershoots for comparison stimulus and probe was larger at 6.5° than at 3.5° eccentricity.In contrast, in Experiment 2 with a singletarget presentation no comparable difference occurred.Apparently, the presentation of the task-irrelevant context stimulus leads to a pattern of saccadic undershoots that matches with the observed eccentricity effect in the perceptual judgement task.The context stimuli appear to modulate the saccadic eye movements to the targets, thus producing the pattern of results required for the explanation (given by Müsseler et al., 1999) of the eccentricity effect observed in the relative judgement task.http://www.ac-psych.org2010 • volume 6 • 1-14 10 GENERAL DISCUSSION Müsseler et al. (1999) investigated spatial localization with a relative judgement task.The observers were asked to judge the peripheral position of a small probe with respect to the mid-position of a spatially extended comparison stimulus.When the two stimuli were flashed successively, the observers perceived the small probe as being more peripheral than the mid-position of the comparison stimulus.In the present study this outcome, plus a number of additional related

henomena reported b
Müsseler et al. (such as the extension effect and the eccentricity effect), was replicated.

To explain the relative mislocalization, the authors assumed that it emerged from different absolute localizations of probe and comparison stimulus; the exact assumption was that both the probe and the comparison stimulus are perceived more foveally than they really are and that the spatially extended comparison stimulus is even perceived more foveally than the spatially less-extended probe.

Saccadic eye movements to a target position can be regarded as absolute judgement of the target location.A pattern of results as speci-fied in the explanatory assumption proposed by Müsseler et al. (1999) has been reported by basic saccadic eye movement research: Saccadic eye movements tend to undershoot the target (e.g., Aitsebaomo & Bedell, 1992;Bischof & Kramer, 1968;Lemij & Collewijn, 1989), and the undershoot seems to be greater with spatia ly extended stimuli than with less extended stimuli (e.g., Findlay et al., 1993).Saccadic eye movements have, however, up to now never been investigated in the experimental setting used in the relative judgement task.Therefore the aim of the present study was to examine in one experimental setup whether the target positions as indicated by the saccadic eye movements correspond with the absolute pos

ions presu
posed by the discussed explanation (Müsseler et al., 1999) of the phenomena observed in the relative judgement task.

The basic results obtained in the saccadic eye-movement tasks support the main idea of Müsseler et al.: In all three experim

rshoot bot
the comparison stimulus nd the probe.Moreove , they undershoot the com arison stimulus even more than the probe.Also the extension effect was clearly apparent in the saccadic eye movement data (see the compari-  A problem was, however, encountered with the eccentricity ef ect.This problem requires some further discussion.

The pattern of saccadic eye movements required for explaining the eccentricity effect only showed up in Experiment 3 where both comparison and probe were presented in close temporal proximity; in this experiment an interaction between type of target (probe and comparison) and eccentricity (3.5º and 6.5º) was found.This interaction was absent in Experiment 2 with isolated blockwise presentation of comparison stimulus and probe.When comparing these experiments, it is obvious that the crit cal difference between them is target selection.

In the saccadic eye movement task of Experiment 2, on each trial after the disappearance of the fixation point, a single target (the comparison stimulus or the probe) appeared in an otherwise empty field.In this exposure situation target selection is no problem at all.The situation mimics the single-stimulus situation used in basic saccadic eye movement research.That res arch consistently reports a 5-10% undershoot.

With such a fixed undershoot an additive relation between type of target and eccentricity is to be expected, independently of how the di ference between types of targets is produced.

In the saccadic eye movement task of Experiment 3, in each trial after the disappearance of the fixation point, two stimuli, the comparison stimulus and the probe, appeared in close temporal proximity.In the instruction before a block of trials it was verbally specified whether the comparison stimulus or the probe should be regarded as the target for the eye.In other words, this task requires the participant to make a top-down selection of the target and to ignore a distractor.However, it is well known that distractors affect pointing tasks and eye-movement tasks (e.g., Sheliga, Riggio, Craighero, & Rizzolatti, 1995;Tipper, Howard, & Jackson, 1997).It is likely, because of the decreasing retinal acuity, that these tendenc es increase with increasing eccentricity.Therefore, in this situation an interaction between ty e of target and eccentricity can arise.

In the present context it is of importance to see that the information processing situation in the relative judgement task is closer to the experimental situation in the saccadic eye movement task of Experiment 3 than that of Experiment 2. Just as in the saccadic eye movement task of Experiment 3, in the relevant conditions of the relative judgement tasks in each trial, both comparison stimulus and probe are presented in close temporal proximity.Moreover, just because the positions of the comparison stimulus and the probe have to be compared, top-down selection is required.

Taken all together, the main outcome of the saccadic eye-movement resea ch here reported is clearly in accord with, and therefore supports, the explanatory assumption introduced by Müsseler et al. (1999) for accounting for the main phenomena observed in the relative judgement task (see above).Also the eccentricity effect can be accounted for because the eye movement data of Experiment 3, not those of Experiment 2, are the relevant data.

As already stated in the Introduction, the fact -now further supported by the data presented here -that saccadic eye movement research supports the assumptions made by Müsseler et al. suggests an intriguing possibility: The possibility that the saccadic eye movement system is at the basis of, and provides the information for, pos tion judgements in position judgement tasks (see also, e.g., van der Heijden, Müsseler, & Bridgeman, 1999;Wolff, 1987, for this suggestion).If that is correct, the difference between the absolute localizations of the stimuli should correspond not only qualitatively but also quantitatively with the relative localizations.This is examined in the subsequent analysis.

In the present study the landing positions of the eyes to the comparison stimulus and the probe, which are used as indicators of the perceived a solute localizations, proved to be determined by various variables (above all by the eccentricity, the spatial extension, and the context).Corresp ndingly, the differences of the landing positions of the eyes determined by these variables should correspond with the SE values from the relative judgement task, which also proved to be determined by these variables.

In order to compare the correspond

ce more directly and to ensur
the generalization of the data, the subsequent analysis is based on two steps:

(1) Multiple Linear Regression is used to estimate the saccadic landing positions determined by the various variables.

(2) Then the differences of the estimated landing positions are compared with the PSE values of the present and previous experiments.


Multiple Regression analysis

Previous research revealed that saccadic amplitudes are determined by several variables.In the present context the mos relevant variables are the eccentricity of stimulus presentation (

e also Aitsebaomo & Bedell, 1992;Bischof & Kramer, 1968;Lemij & Collewijn, 1989), the spatial extension
f the stimuli (see also Findlay et al., 1993), and the context of stimuli (see also Findlay, 1982).The variables proved also to determine s ccadic amplitudes in the present Experiments 1-3.

To estimate the contribution of each variable to the saccadic amplitude, these variables are entered as predictor variables in a Multiple Linear Regression (MLR).Multiple Regression provides information on how the saccadic amplitude (the criterion variable) is determined quantitatively by the predictor variables.The measure for the relative impact of the predictors on the criterion is the respective slope ß.In its non-standardized form, ß reports the increase (or decrease) in saccadic amplitude in units of the predictor variables.

The following values of predictor variables are entered in the MLR: the eccentricity of stimulus presentation with the values of 3.5 or 6.5°, and the spati l extension of the stimuli with the values 0.165° for the probe and 1.5° (Experiment 2) or 2.11° (Experiment 3) for the comparison stimulus, 2 while the context describes the presence or absence of the second stimulus.In Experiment 2 no context stimuli were presented (context = 0), in contrast to Experiment 3, where the second stimulus serves as the context for the other stimulus (context = 1).Additionally, Experiment 3 revealed an interaction between eccentricity and extension.This interaction can be taken into account by calculating the product of the two predictor variables and entering this into the regression analysis as an additional variable (e.g., Kerlinger & Pedhazur, 1973, p. 415).

The mean saccadic amplitudes of the conditions of Experiments 2 and 3 were entered as the criterion variable in a Multiple Linear Regression. 3 The analysis yields a multiple R 2 of .994and the equation:


Comparison of estimated and observed relative mislocalizations for the present and previous experiments

The observed relative mislocalization was assumed to originate from the different absolute localizations of comparison stimulus and probe.

Thus, the difference in saccadic amplitudes to the comparison stimulus and the probe can be used as an estimation of the observed relative mislocalization.

Figure 9 shows the plot of the observed and the estimated mislocalizations of the present experiments as well as of three further experiments, which were gathered under comparable conditions (Müsseler et al., 1999, Experiments 1, 3, and 5).Linear regression revealed an R 2 of .921.This result demonstrates that the mislocalization estimated from the saccadic behaviour fits nicely with the mislocalization observed in the relative judgement task.The linear function integrates all effects of the different eccentricities and of the different spatial extensions of comparison stimuli.

However, the slope of the regression line is not 1 and the intercept is not 0. Especially the deviation of the slope indicates that the observed mislocalization is more pronounced than the estimated mislocalization derived from the landing positions of the eye movements.According to the proposed distinction between visio for perception and vision for action (Milner & Goodale, 1995), this is what to expect.Recent studies testing this distinction revealed only small effects of an illusion on action scaling as compared to its effect on perception (e.g., Bartelt & Darling, 2002;Haffenden, Schiff, & Goodale, 2001).Another explanation of the rather small slope is that it emerges from a range effect in saccades.Withi