Difficulty Affects Perception Running head: DIFFICULTY AFFECTS PERCEPTION

The Effect of Task Difficulty on the Perception of Size and Distance John M. Franchak New York University Jeanine K. Stefanucci The College of William and Mary Dennis R. Proffitt University of Virginia

Author Contact: John M. Franchak Psychology Department New York University 6 Washington Place, 8th Floor New York, NY 10003 [email protected] (732) 762-5121

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Abstract The difficulty of a throwing task was found to affect the perception of the size of and the distance to a rectangular target in three experiments. Participants attempted to slide beanbags into targets of different sizes and at different distances under normal or difficult conditions. In the difficult condition, participants slid the beanbag with their nondominant hand while their eyes were closed; those in the normal condition slid the beanbag with their dominant hand and their eyes open. After attempting to hit the target, participants were blindfolded and were asked to walk to the location of the target or to walk the distance to the target in the opposite direction. Participants in the difficult condition walked significantly farther than participants in the normal condition. A visual matching task measured participants’ perception of the width of the target. Participants in the difficult condition estimated the target to be narrower than those in the normal condition. The results suggest that the ease with which the observer acts on a target influences the perceived location, distance, and size of the target.

KEYWORDS: task difficulty, distance perception, size perception, effort and perception, efficacy and perception

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The Effect of Task Difficulty on the Perception of Size and Distance This year, an autistic high school senior, Jason McElwain, made national news by scoring 20 points in the last few minutes of his first-ever basketball game. The team's coach let Jason, who is normally the team manager, suit up and play for the final minutes of the game as a "senior gift." When asked how he felt during his record-breaking performance, Jason replied, "Well, I was just hot as a pistol. The bucket was just bigger than anything. It was like free throws. I was shooting three-pointers like it was free throws! It was like a big old used bucket." (American Morning, Feb 24, 2006) Although Jason’s remarks about the perceived size of the hoop sound like an exaggeration, there may be some truth to his statements. Our aim in this paper is to provide evidence that the difficulty of a task influences the perception of the sizes and distances to objects that are part of the task. Skill-level, or efficacy is one of many factors that can influence the amount of difficulty associated with performing a task. Continuing with our basketball example, Jason exhibited a high degree of efficacy while playing basketball by skillfully making a number of shots. Other factors that can affect the difficulty of a task are the amount of energy it takes to perform the task and the precision with which the task must be performed to be successful. The power with which Jason shoots the ball determines whether or not the ball will reach the basket. Shooting from behind the three-point line requires more power than shooting a lay-up. Precision is also important because the trajectory of the shot determines whether or not the ball will go through the hoop. These factors are not mutually exclusive. When Jason made his three-pointers, he had to shoot with power, precision and skill. Previous research has shown that both efficacy and

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physiological effort can influence the perception of size and distance in a task (Proffitt, Stefanucci, Banton, & Epstein, 2003; Wesp, Cichello, Gracia, & Davis, 2004; Witt, Proffitt, & Epstein, 2004; Witt & Proffitt, 2005). In this paper, we will review these findings and present evidence indicating that the difficulty associated specifically with the precision needed to successfully complete a task also influences size and distance perception.

Efficacy and the Perception of Size Research has shown that performance efficacy, or the capacity of the actor to produce a desired effect, is related to the actor’s perception of the environment. For example, Witt and Proffitt (2005) investigated the relationship between a softball player’s batting performance and his or her estimate of the size of the softball. The researchers attended a number of intramural softball games and surveyed the players about their batting performance. The players also estimated the size of a softball by choosing the closest matching circle (in diameter) from an array of circles of varying sizes. Batting average correlated positively with the perceived size of the ball; players who had performed well (or were efficacious) remembered seeing a larger softball than players who hit poorly during the game. The estimates made in the Witt et al. (2005) study were from memory. But a similar pattern of results emerges in estimates made when the target is in full view. In a similarly designed experiment, participants attempted to drop darts onto a small, circular target until they succeeded in hitting the target (Wesp, Cichello, Gracia, & Davis, 2004). Half of the participants estimated the size of the target before dropping the darts, and the

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other half made estimates afterwards. There was a strong negative correlation found between the number of darts needed to hit the target and the estimated size of the target. However, this relationship was observed only in the group that made estimates after dropping darts. Wesp et al. concluded that the participants’ success or failure at the task affected the way that they saw the target. If they succeeded at the task (as measured by hitting the target after few attempts), the target appeared large. If they performed poorly at the task (as measured by needing many attempts to hit the target), the target appeared small. Both studies indicate that one’s success at performing a task can affect one’s perception of the size of the objects involved in the task. These results are intuitive – the object targeted by our actions, either the circle on which we drop darts or the ball at which we swing the bat, appears larger when we perform well. In the next section, we will present evidence that shows a similar influence of physiological effort on the perception of distance.

Physiological Effort Influences Distance Perception Effort and distance are invariantly related; it is always more effortful to throw a ball or walk a greater distance. Manipulated differences in the effort required to walk a prescribed distance has been shown to affect distance perception (Proffitt, Stefanucci, Banton, & Epstein, 2003). An observer wearing a heavy backpack sees distances as farther than an observer who is unencumbered. Increasing the physical effort required to traverse a distance increased the perception of the extent of the distance. Similarly, Witt, Proffitt, and Epstein (2004) had participants throw either a heavy ball or a light ball to a

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cone in a field. Estimates of the cone’s distance were greater for participants who threw a heavy ball to the target, indicating that increasing the physical effort needed to throw the ball to the cone also increased the perceived distance to the cone. Wearing a heavy backpack and throwing a heavier ball are both manipulations that altered the physiological state of the observer and affected the perception of distance.

Can Precision Influence Perception? Physiological effort can make completing a task difficult. Lifting a concrete block is difficult because of the energy it takes to pick it up. However, a task can also be difficult if precision is required to complete the task successfully. Threading a needle is also a difficult task, but for different reasons than lifting a concrete block. To our knowledge, the influence of precision (as an instance of task difficulty) on perception has not been directly manipulated. The previously mentioned studies correlated performance efficacy or physiological effort with the perception of size and distance, but did not systematically vary the need for precision in the task. Varying the difficulty of a task with regards to precision may be sufficient to produce differences in perception, even in the absence of a correlation with efficacy or energetic demands. There is reason to believe that systematic manipulations in precision could affect perception. Being precise is invariantly related to the size and distance of a target, just as physiological effort is invariantly related to size and distance. It is more difficult to hit a smaller target or a target at a greater distance. The current studies will investigate how differences in difficulty due to precision affect the perception of size and distance. Though there are similarities between physical effort and task difficulty, there is a major

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difference between the two concepts. Physiological effort is a factor that ultimately represents the status of the internal environment of the observer. If you are wearing a heavy backpack, it will be more effortful to walk anywhere in the environment. Perception should be affected regardless of the specific target distance. In contrast, task precision is related to a specific external environment and situation. If you are facing a very skilled pitcher and struggling at bat, the ball will appear smaller. The first aim of the current set of studies is to determine if systematic manipulations of precision will affect perception in the same manner as the correlational investigations that related efficacy and size perception (Wesp et al., 2004; Witt & Proffitt, 2005). The second aim of these experiments is to assess the degree to which task precision affects perception in the same manner as physical effort. Egocentric distance perception is modulated by the amount of physical effort that the observer needs to traverse a distance, regardless of whether or not the requisite of effort is due to existing conditions such as old age and poor health (Bhalla & Proffitt, 1999) or experimentally controlled conditions such as wearing a heavy backpack (Proffitt et al., 2003) or throwing a heavy ball (Witt et al., 2004). Testing the perception of egocentric distance under varied conditions of precision, in which physical effort is held constant, will clarify the relationship between task difficulties related to precision rather than physiological effort. In our experiments, the participants’ ability to perform a task with precision is manipulated by requiring them to act with their non-dominant hands while their eyes are closed. Increasing the need for precision – or the difficulty – associated with performing the task should increase the perceived distance to a target while decreasing the perceived size of the target.

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Experiment 1: Size estimates are influenced by task difficulty The purpose of this experiment was to test whether participants’ visually matched estimates of the size of a target would be influenced by differences in the ease with which they could slide a beanbag to the target. Participants viewed targets (four cones that marked a square) on either end of a hallway and slid a beanbag to a target placed in the hallway either with their dominant hand and their eyes open (the NORMAL condition) or with their non-dominant hand and their eyes closed (the DIFFICULT condition). Results showed that the level of difficulty associated with sliding the beanbag to the target affected the perception of the size of the target. Participants who were in the DIFFICULT condition estimated the size of the target to be smaller than participants in the NORMAL condition, which replicates the findings of Wesp et al. (2003) and Witt et al. (2005).

Method Participants. Twenty-four University of Virginia students (10 male and 14 female) participated. All participants had normal or corrected-to-normal vision. The participants were naïve to the purpose of the experiment, and were paid $5 for their involvement in the study. Apparatus & Stimuli. The experiment was conducted in a hallway (38.07 meters long x 1.82 meters wide) of the psychology building of the University of Virginia. Two small sports cones placed across the width of the hallway created a “home base” where the participants stood during the experiment. Two cones could be placed, centered in the

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hallway, 5.5m from the home base with a space measuring either .38m, .51m, .64m, .76m, or 1.01m. These targets were used for pretest trials. In the other direction of the hallway, four cones could be placed to create squares (.51m x .51m, .64m x .64m, .76m x .76m) that were 5.5m from the home base and centered in the hallway (see Figure 1a). These square targets were used in the posttest trials. Three small beanbags were used in the experiment. Each beanbag was 10cm by 10cm and weighed about 125 grams. Design. Participants were assigned in alternating order to either the DIFFICULT or NORMAL condition. Due to an experimenter error, there were 11 participants in the NORMAL condition and 13 in the DIFFICULT condition. Target size served as a within-subjects variable. Each participant completed five pretest trials, sliding practice, and then three posttest trials. The pretest target sizes were .38m, .51m, .64m, .76m, and 1.01m (the distances between the two cones). The .38m and 1.01m targets were used as distracters and were presented to minimize the participants’ expectations of a pattern in the target sizes. The posttest target sizes were .51m, .64m, and .76m (the distances between the front cones of the square target). Thus, the targets in the pretest and posttest were the same size and the same distance from the observer. The orders of the sizes used for the pretest and posttest trials were counterbalanced. Procedure. Pretest Trials. Each participant made five pretest trial estimates. Before each estimate was made, the experimenter placed two cones on the floor of the hallway while the participant’s eyes were closed. After the cones were placed on the floor, the experimenter would stand 1m from the participant on the side of the hallway, and instruct the participant to open his or her eyes. The participant would then tell the experimenter to open or close a tape measure (with the numbers facing away from the

Difficulty Affects Perception 10 participant) until the length of the tape measure matched the distance between the two cones. This process was repeated for all five target sizes. Sliding Practice. After the pretest, all participants completed a sliding practice. This practice helped the participants to understand the task and get a sense of its difficulty. The practice target was always 3m from the home base in the same direction as the pretest, and was a rectangular target 1m wide and 1m long created by placing four small cones on the floor. Each participant threw six times to the target. Their goal was to slide the beanbag along the floor so that it would stop within the area of the target. An attempt was considered a “hit” if (a) the beanbag stopped within the outer boundary created by the four cones, (b) the beanbag did not touch any of the cones or the walls, and (c) the beanbag came in contact with the ground before entering the target. All other attempts were considered misses. After each attempt, the experimenter told the participant if it was a hit or a miss. All participants completed the sliding practice with their eyes open and using their dominant hands. Posttest Trials. After the practice, the participants completed three posttest trials, one for each target size. Before each trial, the experimenter placed four cones on the floor while the participant’s eyes were closed. Each trial consisted of two phases – sliding and visual matching. During the sliding phase, the participant attempted to slide the beanbag to the target six times. The number of hits the participant managed for the target was recorded as a measure of task difficulty. The experimenter told the participant after each attempt if it was a hit or a miss. After the sixth attempt, the participant completed the visual matching phase of the trial. The participant tried to estimate the distance between the front two cones of the target using the same visual matching

Difficulty Affects Perception 11 procedure used in the pretest. The participant told the experimenter to open or close a tape measure until the length of the tape measure matched the distance between the front cones. This process was repeated for all three target sizes. Participants in the NORMAL condition completed the procedure exactly as described. Participants in the DIFFICULT condition completed the throwing phase differently in two ways. First, participants in the DIFFICULT condition threw with their non-dominant hands. Second, instead of throwing with their eyes open, the participants closed their eyes before throwing and counted 2 full seconds before throwing the beanbag. The participants were instructed to open their eyes as soon as the beanbag left their hands. This enabled the participants in both conditions to receive nearly the same amount of throwing feedback. After completing the throwing phase, participants in the DIFFICULT condition viewed the target for the same amount of time as the participants in the NORMAL condition prior to making their estimates.

Results Sliding Accuracy. A 2 (sex) x 2 (condition) x 3 (target distance) repeated measures analysis of variance was performed for the number of hits made at each target, with target size as a within-subjects factor and sex and condition as between-subjects factors. As predicted, the analysis showed an effect of condition on sliding accuracy, F(1,22) = 11.048, p = .003. It comes as no surprise that participants in the DIFFICULT condition, who slid the beanbags to the target with their eyes closed and using their nondominant hands, hit the target fewer times than participants in the NORMAL condition. This finding validates our claim that there is indeed a difference in difficulty between the

Difficulty Affects Perception 12 NORMAL and DIFFICULT conditions. There was no significant effect of sex (p = .260), and the Sex x Condition interaction was also not significant (p = .974). Size Estimation. Ratios were calculated between the posttest and pretest estimates made by each participant for each target size. This ratio indicated the degree of change in a participant’s perception of the target’s size following the sliding task, where a ratio of 1 would specify no change from pretest to posttest. A 2 (sex) x 2 (condition) x 3 (target distance) repeated measures analysis of variance was performed for the ratio of the posttest estimate to the pretest estimate. Target size was the within-subjects factor and sex and condition were the between-subjects factors. The analysis yielded an effect of condition on the ratio between posttest and pretest estimates, F(1,22) = 6.737, p = .017. (See Figure 2). This indicates that sliding the beanbag to the target under difficult circumstances led participants to underestimate the target size relative to their previous estimates. There was no significant effect of sex (p = .283), nor was there a significant interaction of Sex x Condition (p = .457). Participants in the NORMAL condition saw the target as larger relative to their previous estimates than participants in the DIFFICULT condition, suggesting that the difference in the difficulty of the beanbag sliding task produced a change in the perceived size of the target.

Discussion In this task, participants were asked to slide a beanbag into a target by sliding the bag with their eyes open, using their dominant hand (the NORMAL condition), or by sliding the bag with their non-dominant hand and their eyes closed (the DIFFICULT condition). Importantly, we found that participants in the DIFFICULT condition did not

Difficulty Affects Perception 13 “hit” the target as often, suggesting that the task was harder for them. We believe that because the task was harder for participants in the DIFFICULT condition, they saw the target as being smaller. Their estimates of the size of the target were less than estimates made by participants in the NORMAL condition. This result suggests that the perception of size can be influenced by the difficulty associated with performing a task.

Experiment 2: Task difficulty affects blindwalked estimates of a target’s location In this experiment, we were interested in whether difficulty associated with performing a task would also affect the perception of the distance to a target. Again, participants viewed targets on either end of a hallway and slid a beanbag to the target in the NORMAL condition or the DIFFICULT condition. After sliding the beanbag, all participants were asked to don a blindfold and walk without vision until they believed they were standing in the center of the target. Results showed that participants who were in the DIFFICULT condition estimated the distance to the target to be greater than participants in the NORMAL condition. These findings suggest that difficulty associated with a task can modulate the perception of distance to the target as well as its size.

Method Participants. Forty University of Virginia students (20 male and 20 female) participated. All participants had normal or corrected-to-normal vision. Participants were either paid $5 or were recruited in order to fulfill a requirement for an introductory psychology course. Participants were naïve to the purpose of the experiment.

Difficulty Affects Perception 14 Apparatus & Stimuli. The experiment was conducted in a hallway (65.12 meters long x 1.84 meters wide) of the psychology building of the University of Virginia. Two small sports cones placed across the width of the hallway created a home base where participants stood during the experiment. Tape markers along the side of the hallway marked 4m, 5.5m, 7m, and 8.5m in both directions from the home base and were not visible to the participants. At each of these distances, two small marks were made on the floor 1m apart and centered in the hallway. These marks allowed four small orange cones to be placed on the floor creating rectangular targets 1m wide and 1.5m long at three distances (4m, 5.5m, and 7m). During each trial, only four cones were placed on the floor to create a single target (see Figure 1b). These three targets served as the perceptual stimuli in this experiment. The same three beanbags from Experiment 1 were used. Design. Participants were assigned in alternating order to either the NORMAL or DIFFICULT conditions. Each participant completed one practice trial at 3m followed by three test trials, one for each of the three target distances: 4m, 5.5m, and 7m. Target distance served as a within-subjects variable in this experiment. In the practice trial, all participants completed the trial according to the procedure for the NORMAL condition from Experiment 1 (eyes open, using the dominant hand). The order of the presentation of test trials was counterbalanced. The direction the participant faced in the hallway for the first trial was also counterbalanced for each target distance. Procedure. Participants in both conditions completed three test trials. Each trial consisted of a sliding phase and a blindwalking phase. After each test trial, the participant turned to the other direction in the hallway and completed the next trial in that

Difficulty Affects Perception 15 direction; this measure was taken to minimize the participants’ potential use of comparisons between trials that might aid in distance judgment. The sliding phase of each trial was identical in procedure to the sliding phase in Experiment 1. Participants attempted to slide the beanbag into the target six times with their eyes closed and using their non-dominant hands (DIFFICULT condition), or with their eyes open and using their dominant hands (NORMAL condition). After the sixth sliding attempt, the participants completed the blindwalking phase of the trial. The participants were given a blindfold and then received instructions. Participants were told to walk to the center of the target and then tell the experimenter when they were finished walking. After hearing the instructions, the participants put on the blindfold and tried to walk to the target. Once the blindfold was on, the experimenter removed the target cones from the floor and kept silent. When the participant indicated that he or she was done walking, the experimenter marked the distance for measurement. Still blindfolded, the participants were led directly back to the home base so that they received no visual feedback about the distance walked. A second experimenter was present to follow the participant while he or she wore the blindfold, and was also responsible for leading the participant back to home base.

Results Sliding Accuracy. A 2 (sex) x 2 (condition) x 3 (target distance) repeated measures analysis of variance was performed for the number of hits made at each target, with target distance as the within-subjects factor and sex and condition as betweensubjects factors. As expected, the analysis showed an effect of condition on sliding accuracy, F(1,38) = 30.005, p < .001. As in Experiment 1, the eyes closed/non-dominant

Difficulty Affects Perception 16 hand manipulation decreased the participants’ ability to successfully slide the beanbag into the target, suggesting that there was a significant difference in task difficulty between the two conditions. There was no significant effect of sex (p = .796), and the Sex x Condition interaction was not significant (p = .642). Distance Estimation. A 2 (sex) x 2 (condition) x 3 (target distance) repeated measures analysis of variance was performed for blindwalking distance. Target distance was a within-subjects factor and sex and condition were between-subjects factors. As predicted, the analysis yielded an effect of condition on blindwalking distance, F(1,38) = 6.681, p = .014. (See Figure 3). Participants who were confronted with the difficult task of sliding the beanbag into the target with their eyes closed and using their non-dominant hands walked farther than participants who completed the same task under easier circumstances. This indicates that participants in the DIFFICULT condition perceived the target to be farther away than participants in the NORMAL condition. There was no significant effect of sex (p = .131), nor was there a significant interaction of Sex x Condition (p = .244).

Discussion In this experiment, participants were asked to slide a beanbag into a target with their eyes open, using their dominant hand (the NORMAL condition) or with their eyes closed, using their non-dominant hand (the DIFFICULT condition). As expected, participants in the DIFFICULT condition were less likely to slide the beanbag into the target area, suggesting that the manipulation made the task more difficult for them. Because the task was more difficult for these participants, they blindwalked farther than

Difficulty Affects Perception 17 the participants in the NORMAL condition. These results suggest that the difficulty associated with performing a task influences the perception of the location or distance to objects involved in the task.

Experiment 3: Task difficulty influences the perceived distance to a target In the previous experiment, participants may have estimated the distance to the target by representing only its location rather than the ground distance to the target. Whereas location is a single point that could be perceived in terms of angular elevation, the distance to a target requires that the extent between the observer and target be perceived. In this experiment, we tested whether manipulating the difficulty associated with performing a task affected the perceived distance to the target, without confounding that distance with the perceived location of the target in the hallway. Previous research has shown dissociations between estimates of perceived location and perceived distance (Philbeck et al., 1997; Witt et al., in press). In this experiment, participants slid the beanbag to the target in either the NORMAL or the DIFFICULT condition, but then turned and blindwalked the perceived distance to the target in the opposite direction to prevent them from using the location of the target as a cue. As in Experiment 2, increased task difficulty led to increases in the perceived distance of the target.

Method Participants. Twenty-eight University of Virginia students (13 male and 15 female) participated. All participants had normal or corrected-to-normal vision.

Difficulty Affects Perception 18 Participants were paid $5 for their completion of the study. Participants were naïve to the purpose of the study. Apparatus & Stimuli. The apparatus and stimuli were identical to that of Experiment 2, except the study was conducted in a different hallway in the psychology building. The hallway used was the same as that of Experiment 1. Design. Participants were assigned in alternating order to the NORMAL or DIFFICULT condition. The experimental design of this experiment was identical to that of Experiment 2. Target distance (4m, 5.5m, and 7m) served as the within-subjects variable. Each participant completed one practice trial at 3m followed by three test trials, one for each of the three target distances: 4m, 5.5m, and 7m. The order of targets and the hallway direction that the participant faced in the first trial were counterbalanced. As in Experiment 2, the participants alternated directions in the hallway for each trial. Procedure. The procedure of this experiment was the same as in Experiment 2, but with one major difference in the blindwalking phase of each test trial. Participants in this experiment viewed the target after their final sliding attempt and then faced the opposite direction in the hallway and put on a blindfold. Rather than walking to the center of the target, all participants walked in the opposite direction from the target to approximate the distance to the target’s center.

Results Sliding Accuracy. A 2 (condition) x 3 (target distance) repeated measures analysis of variance was performed for the number of hits made at each target, with target distance as the within-subjects factor and condition as the between-subjects factor. Sex

Difficulty Affects Perception 19 was not analyzed as a factor in this experiment because it was found to have no effect on either dependent measure in the first two experiments. As expected, the analysis showed an effect of condition on throwing accuracy, F(1,25) = 19.615, p < .001. Due to an experimenter’s error, the number of hits made by one participant was not recorded. Distance Estimation. A 2 (condition) x 3 (target distance) repeated measures analysis of variance was performed for blindwalking distance. Target distance was the within-subjects factor and condition was the between-subjects factor. As predicted, the analysis yielded an effect of condition on blindwalking distance, F(1,26) = 17.055, p = .028, replicating our findings from Experiment 2 (See Figure 4). Participants in the DIFFICULT condition saw the target as farther than participants in the NORMAL condition, and consequently recorded greater blindwalking distances. The difficulty of the beanbag sliding task for participants in the DIFFICULT condition caused an overestimation of distance relative to those participants in the NORMAL condition.

Discussion As in the previous experiments, participants in the DIFFICULT condition had a harder time sliding the beanbag into the target than participants in the NORMAL condition. The increase in task difficulty for participants in the DIFFICULT condition influenced the perceived distance to the target. Participants who had a harder time sliding the beanbag into the target blindwalked farther in the opposite direction of the target. Because the participants did not blindwalk to the location of the target, their blindwalked estimates were representations of the perceived ground distance to the target.

Difficulty Affects Perception 20 We believe that participants in the DIFFICULT condition saw the target as being farther, so they blindwalked farther when asked to replicate the distance in another direction.

General Discussion The results of these three experiments indicate that the perception of the size, location, and distance of a target is affected by one’s performance efficacy. In our task, the goal of the actor was to slide a beanbag into a rectangular target. The ability of the actor to slide the beanbag with precision was directly manipulated by requiring the “difficult” actors to throw with the non-dominant hand and without vision of the target. In all three experiments, participants who threw under the conditions of our difficulty manipulation hit the target with less accuracy than those participants who threw under normal conditions. Observers perceived the size and distance of the targets differently depending on the difficulty of the throwing task in which they were engaged during the experiment. In Experiment 1, observers attempted to slide beanbags to targets of different sizes and then made estimates of the width of the target using a perceptual matching task. Observers who acted under difficult conditions saw the target as smaller with respect to their baseline estimates compared to observers who acted under normal conditions. This finding is consistent with previous demonstrations that relate efficacy to the perception of the size of a ball or a circular target (Wesp et al., 2004; Witt & Proffitt, 2005). While the previous investigations looked at the existing variation in the observers’ skill-level at the tasks, the current experiment found the same pattern of results using systematic manipulation of difficulty.

Difficulty Affects Perception 21 In Experiments 2 and 3, observers attempted to slide beanbags into targets at different distances and then estimate the location (Experiment 2) or the distance (Experiment 3) to the target using a blindwalking measure. In both cases, observers who threw to the target under difficult conditions walked farther than observers who threw to the target under normal conditions. Thus, decreasing the observer’s ability to act with precision during the beanbag-sliding task increased the observer’s perceived distance to the target. These findings are similar to the demonstrations of Proffitt et al. (2003) and Witt et al. (2004), which showed that increasing the physical effort needed to walk or throw to a target extends the perceived distance to the target. The present demonstration shows that the type of difficulty that affects the perception of distance is not limited to physical effort, but also includes one’s ability to act with precision. Difficulty, in a general sense, affects distance perception in a systematic manner; increasing the difficulty required to act on a target also increases the perceived distance to the target. These studies support the argument that visual perception is influenced by the behavioral potential of the observer to act in the environment. By increasing the difficulty of a task through skill-level (Wesp et al., 2004; Witt & Proffitt, 2005) or a manipulation that affects precision (Experiment 1), perceived size of a target decreases. By increasing the difficulty of a task through physical effort (Proffitt et al., 2003; Witt et al., 2004) or a manipulation that affects precision (Experiments 2 & 3), perceived distance to a target increases. Future research should investigate the relationships between difficulty due to physical effort and size perception and between difficulty due to skill-level and distance perception. We would expect to find effects on perception in both of these cases that are consistent with the current findings: increased difficulty to act

Difficulty Affects Perception 22 on a target (due to physical difficulty or differences in skill-level) should lead to increased perception of the target’s distance and decreased perception of the target’s size. By our account, the visual system is influenced by optical information and the observer’s behavioral potential because perception controls action. In traditional views of perception, the visual system is only concerned with providing an accurate general purpose representation of spatial layout that preserves geometric consistency. However, the current data indicate that the visual system’s interpretation of the geometry of spatial layout can be inconsistent. We know from Experiment 1 that observers who participated in the difficult beanbag-sliding condition saw the target’s width as smaller with respect to baseline estimates. According to the size distance invariance hypothesis, the observer should see the distance to the target as nearer since the target’s retinal image is the same. However, the results from Experiments 2 and 3 indicate that the opposite occurs – observers in the difficult condition see the target as farther away. For example, observers in the difficult condition estimated the size of the test target to be 91% of the size of the practice target, whereas, on average, observers in the normal condition perceived the size of the target accurately. The retinal size of the two targets was identical, yet the observers in the difficult condition perceived the width of the test target to be smaller. In order for this perception of size to be consistent with estimates of distance, the observers in the difficult condition should also have perceived the distance to the target to be farther (see Figure 5 for predicted and actual estimates). However, the results of our experiments clearly show that the outcome was opposite to that predicted by size constancy. Observers in the difficult condition saw the target as

Difficulty Affects Perception 23 smaller and also more distant; this finding is a case in which size distance invariance is violated. Paradoxes in the perception of spatial layout are not without precedent. Geometrical inconsistencies have been found in earlier studies on the perception of spatial layout (Epstein, 1977; Epstein, Park & Casey, 1961; Sedgwick, 1986) and more recent studies on the perception of distances on hills (Stefanucci, Proffitt, Banton, & Epstein, 2005). These findings are inconsistent with those perceptual theories that assume that geometric relationships between percepts will be represented accurately by the visual system. However, geometrical inconsistencies involving size, distance and motion, are present in the Moon Illusion and the Trapezoidal Window S-motion demonstration (Hershenson, 1999, pp. 123-130). Geometrical inconsistencies have also been observed with natural settings. For example, Gillam (1967, 1995) reported an inconsistency involving shape, slant and binocular disparity, which is similar to the sizedistance paradox. When one of the two binocular images is magnified by the interposition of an aniseikonic lens, distortions of perceived shape in the geometrically predicted direction can be observed, while distortions to perceived slant are opposite to that predicted by geometry. That the difficulty of an action affects spatial perception at the cost of preserving geometric consistency is only surprising within a theoretical context that claims accurate representation as the sole purpose of the visual system. We believe that, above all else, perception is concerned with the planning and guidance of action. One’s ability and intention to act in a context determines what information is relevant for planning and executing an action. As such, it should not be surprising that changing the ability of an

Difficulty Affects Perception 24 individual to act with precision affects perception. The extent of our ability to interact with a target is just as important as the spatial extent to the target. Both factors determine the outcome of the action; it does not matter how far away the basket is if you are completely unable to shoot a basketball with accuracy. On one special night, Jason McElwain shot a basketball with almost perfect accuracy. He said, following his performance, that the basket looked like a “big old bucket.” Our findings suggest that Jason did, indeed, perceive the size of the basket to be larger than usual. Spatial layout is perceived in terms of people’s ability to achieve their goals within the environment. The ease with which people can effectively perform intended actions related to spatial layout is reflected in their perceptions of its size and distance.

Difficulty Affects Perception 25 References American Morning, Feb 24, 2006. Cable News Network. Retrieved from http://transcripts.cnn.com/TRANSCRIPTS/0602/24/ltm.06.html. Bhalla, M., & Proffitt, D. R. (1999). Visual-motor recalibration in geographical slant perception. Journal of Experimental Psychology: Human Perception & Performance, 25, 1076-1096. Epstein, W. (1977). Stability and constancy in visual perception: Mechanisms and processes. New York: Wiley. Epstein, W., Park, J., & Casey, A. (1961). The current status of the size-distance hypotheses, Psychological Bulletin, 58, 491-514. Gillam, B. (1967). Changes in the direction of induced aniseikonic slant as a function of distance. Vision Research, 7, 777-783. Gillam, B. (1995). The perception of spatial layout from static optical information. In W. Epstein & S. Rogers (Eds.), Perception of space and motion (pp. 23-67). San Diego: Academic Press. Hershenson, M. (1999). Visual space perception: A primer. Cambridge, MA: MIT Press. Philbeck, J. W., Loomis, J. M., & Beall, A. C. (1997). Visually perceived location is an invariant in the control of action. Perception & Psychophysics, 59, 601-612. Proffitt, D. R., Stefanucci, J., Banton, T., & Epstein, W. (2003). The role of effort in perceiving distance. Psychological Science, 14, 106-112. Sedgwick, H. A. (1986). Space Perception. In K. R. Boff, L. Kaufmann, & J. P. Thomas (Eds.), Handbook of perception and human performance, Vol. 1. Sensory processes and perception (pp.21.1 to 21.57). New York: Wiley.

Difficulty Affects Perception 26 Stefanucci, J. K., Proffitt, D. R., Banton, T., & Epstein, W. (2005). Distances appear different on hills. Perception & Psychophysics, 67(6), 1052-1060. Wesp, R., Cichello, P., Gracia, E. B., & Davis, K. (2004). Observing and engaging in purposeful actions with objects influences estimates of their size. Perception & Psychophysics, 66, 1261-1267. Witt, J. K., & Proffitt, D. R. (2005). See the ball, hit the ball: Apparent ball size is correlated with batting average. Psychological Science, 16(12), 937-938. Witt, J. K., Proffitt, D. R., & Epstein, W. (2004). Perceiving distance: A role of effort and intent. Perception, 33, 577-590. Witt, J. K., Stefanucci, J. K., Riener, C. R., & Proffitt, D. R. (in press). Seeing beyond the target: An effect of environmental context on distance perception. Perception.

Difficulty Affects Perception 27 Author Note John M. Franchak, Department of Psychology, New York University; Jeanine K. Stefanucci, Department of Psychology, The College of William & Mary; Dennis R. Proffitt, Department of Psychology, University of Virginia. The experiments reported in this article were part of John Franchak’s senior thesis research conducted at the University of Virginia. This research was supported in part by NSF ITR/Carnegie Mellon Grant 0121629 and ONR Grant N000140110060, to the third author. The authors wish to thank Blair Hopkins and Daniel Partin for their help collecting and entering the data. Correspondence concerning this article should be addressed to John M. Franchak, Department of Psychology, New York University, 6 Washington Place 8th Floor, New York, NY 10003.

Difficulty Affects Perception 28 Figure Captions Figure 1. (a) Experiment 1 overhead view, showing possible locations of cones for pretest or posttest trials. Two cones were placed on the floor during pretest trials, and four cones were placed on the floor during posttest trials. (b) Experiments 2 and 3 overhead views, showing possible locations of cones used to create targets 1m wide and 1.5m long at 4m, 5.5m, and 7m from the home base. Only four cones were placed on the floor during a trial. Figure 2. Ratio of posttest to pretest size estimates in Experiment 1 as a function of target size and condition. Error bars show one standard error. Figure 3. Blindwalking distance in Experiment 2 as a function of target distance and condition. Error bars show one standard error. Figure 4. Blindwalking distance in Experiment 3 as a function of target distance and condition. Error bars show one standard error. Figure 5. Based on the rules of size constancy, observers in the difficult condition should perceive the target to be at a distance of 5.98m based on the perceived target width (0.69m) and visual angle. However, Experiment 3 indicates that a target at 6.25m was actually perceived to be at 6.8m by participants in the difficult manipulation. Since the size and distance results are from different samples in different experiments, we cannot be sure that this is a fair comparison, however, the pattern of results suggests that size constancy was not preserved in our experiments.

Difficulty Affects Perception 29 Figure 1 a)

Pretest Direction

.76m target

Posttest Direction

5.5m

.51m target

5.5m

Home Base

.76m x .76m target

.51m x .51m target

b)

Direction 1

8.5m

7m

5.5 m

Direction 2

4m

4m

Home Base

5.5m

7m

8.5m

Difficulty Affects Perception 30 Figure 2

Posttest Estimate / Pretest Estimate

1.10

Condition Normal Difficult

1.05

1.00

0.95

0.90

0.85

0.51

0.64

Target Size (meters)

0.76

Difficulty Affects Perception 31 Figure 3

10.00

Blindwalking Distance (meters)

Condition Normal Difficult

9.00 8.00 7.00 6.00 5.00 4.00 3.00 2.00

4.75

6.25

7.75

Actual Target Distance (meters)

Difficulty Affects Perception 32 Figure 4

10.00

Blindwalking Distance (meters)

Condition Normal Difficult

9.00 8.00 7.00 6.00 5.00 4.00 3.00 2.00

4.75

6.25

7.75

Actual Target Distance (meters)

Difficulty Affects Perception 33 Figure 5

Perceived Target Distance – 6.8m Actual Target Width Perceived Target Width

.76m

Actual Target Distance – 6.25m

.69m

Predicted Perceived Target Distance – 5.98m