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Psychological Science
21(11) 1724 –1730
© The Author(s) 2010
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DOI: 10.1177/0956797610387440
http://pss.sagepub.com
For most of humans’ evolutionary history, detecting potential
prey and predators in the environment was crucial for survival.
Ancestors that failed to find the protein-rich food sources sup-
plied by animals, or became that food source for other ani-
mals, would cease to be part of the family tree. Indeed, if one
assumes that the ability to rapidly detect animals in the visual
field is advantageous to survival, modern humans should be
extremely good at detecting animals even though most people
have little reason to fear predation and most likely find their
prey in decidedly un-animal-like forms in highly structured
supermarkets. Moreover, the modern world still has potential
dangers from animate creatures (certain insects and animals,
vehicles operated animatedly by humans), and detecting ani-
mate objects has always had an important social function in
enabling observers to find people in complex visual scenes. In
the study reported here, we looked for evidence of this evolu-
tionary imperative by asking the following question: Does
the motion associated with animate objects capture visual
attention?
Three distinct lines of research provide indirect evidence
supporting the possibility that animate motion capture visual
attention. First, research utilizing static images has shown that
humans prioritize the visual processing of animate objects
over inanimate ones. For example, Kirchner and Thorpe
(2006) found that people initiate saccades more quickly to
pictures of animals than to pictures of other objects, and New,
Cosmides, and Tooby (2007) used a change-detection para-
digm to show that changes in animals are detected more rap-
idly than changes in inanimate objects. Second, another line of
research has shown that people are capable of extracting a
great deal of information from very sparse displays of moving
humans known as point-light walkers (e.g., Johansson, 1973).
Even infants can extract surprising amounts of information
about the actors in extremely degraded perceptual displays
(Kuhlmeier, Troje, & Lee, in press), revealing an exquisite
sensitivity to animate motion. Third, research has shown that
the onset of motion captures attention better than objects that
are static, that are continuously moving, or that have stopped
suddenly (Abrams & Christ, 2003). Moreover, this attentional
capture by motion onset is not due to low-level luminance-
based motion detectors (Guo, Abrams, Moscovitch, & Pratt,
in press) and is not modulated by attentional control settings
(Al-Aidroos, Guo, & Pratt, 2010). Abrams and Christ specu-
lated that the reason motion onsets capture attention is that
they may signal a biologically significant event because
Corresponding Author:
Jay Pratt, Department of Psychology, University of Toronto, 100 St. George
St., Toronto, Ontario, Canada M5S 3G3
E-mail: pratt@psych.utoronto.ca
It’s Alive! Animate Motion
Captures Visual Attention
Jay Pratt1, Petre V. Radulescu1, Ruo Mu Guo2, and Richard A. Abrams3
1University of Toronto, 2University of Waterloo, and 3Washington University in St. Louis
Abstract
Across humans’ evolutionary history, detecting animate entities in the visual field (such as prey and predators) has been critical
for survival. One of the defining features of animals is their motion—self-propelled and self-directed. Does such animate
motion capture visual attention? To answer this question, we compared the time to detect targets involving objects that were
moving predictably as a result of collisions (inanimate motion) with the time to detect targets involving objects that were
moving unpredictably, having been in no such collisions (animate motion). Across six experiments, we consistently found that
targets involving objects that underwent animate motion were responded to more quickly than targets involving objects that
underwent inanimate motion. Moreover, these speeded responses appeared to be due to the perceived animacy of the objects,
rather than due to their uniqueness in the display or involvement of a top-down strategy. We conclude that animate motion
does indeed capture visual attention.
Keywords
attention, animacy, attentional capture, motion
Received 3/25/10; Revision accepted 5/26/10
Research Article
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Animate Motion Captures Attention 1725
objects that undergo a motion onset must have their own inter-
nal energy source.
Each of these lines of research (prioritization of animal pic-
tures, sensitivity to point-light walkers, and capture of atten-
tion by motion onset) provides one piece of evidence
supporting the prediction that motion characteristic of animate
entities will capture attention. Such a finding would provide a
bridge from the evolutionary past to the processes that drive
the allocation of attention in modern humans. In order to
directly test the prediction that animate motion per se captures
attention, it is necessary to create a situation in which the ani-
macy of motion can be directly manipulated and in which
other factors related to animacy, such as the depiction of actual
animals (as in Kirchner & Thorpe, 2006) and the presence of
motion onsets (as in Abrams & Christ, 2003), can be elimi-
nated. One of the defining attributes of animate motion is that
it involves movement that appears to be self-produced, as ani-
mate objects move without requiring external forces and the
motion can vary in predictability. Furthermore, it has been
shown that even simple geometric figures can be perceived as
animate by virtue of their motion, a phenomenon known as
perceptual animacy (Scholl & Tremoulet, 2000). The advan-
tage of such simple displays is that they permit the study of
perceptual animacy without contamination from other factors
that might come into play with images of animals or objects
undergoing motion onsets.
To test the notion that perceptual animacy per se can cap-
ture attention, we had participants view scenes in which sim-
ple geometric objects changed in the direction or speed of their
motion (or both), either because of collisions with other
objects (inanimate motion) or because of a hidden, presum-
ably internal, source of power (animate motion). We found
that it is indeed the case that motion changes that imply an
internal energy source also attract attention.
Experiments 1a and 1b
In the first two experiments, each trial presented four objects
that moved pseudorandomly around the display, periodically
colliding with themselves and with a surrounding frame, and
rebounding in predictable ways (inanimate motion). At some
point, one of the objects suddenly changed direction without
any visible collision (animate motion). Soon after this event, a
target that involved one of the objects was presented. If percep-
tual animacy captures attention, participants should respond
more quickly to targets that involve an animate-motion object
than to targets that involve inanimate-motion objects.
Subjects and apparatus
Twelve University of Toronto undergraduates (mean age =
19.6 years; 8 women, 4 men) participated in Experiment 1a,
and 14 others (mean age = 19.3 years; 11 women, 3 men)
participated in Experiment 1b. Subjects received course
credit for their participation. All subjects reported normal or
corrected-to-normal vision, and none were aware of the
hypotheses being tested.
The experiment was conducted in a dimly lit, sound-
attenuated testing room. Visual stimuli were presented on a
CRT with a refresh rate of 85 Hz. A chin and head rest main-
tained a viewing distance of 48 cm. Eye movements were
monitored using a closed-circuit TV camera to ensure compli-
ance with the instructions.
Procedure and design
The display was black with a white border, and contained a
fixation cross (0.5° × 0.5°) in the center. Subjects were
instructed to remain fixated on the cross during the experiment
and to allocate attention evenly across the display.
In Experiment 1a, each trial began with four solid white
squares (3° × 3°) positioned randomly on the screen, each
moving with a constant speed of 0.2 pixels per millisecond in
a random direction. Occasionally a square would collide with
the border of the screen, at which point it would rebound with-
out any change in speed. Two squares would also sometimes
collide. In that case, not only did the squares rebound (i.e.,
change direction), but the velocity of each square changed ran-
domly, with the combined velocities remaining constant. The
display thus represented an environment with constant energy.
The squares always moved along straight-line paths, and
bounces against other objects were specular (the angle of inci-
dence before the collision was equal to the angle of reflection
after the collision), so that the motion was highly predictable.
After 6.0, 6.5, 7.0, or 7.5 s, a randomly selected square under-
went animate motion—that is, an unanticipated change in
direction and speed that did not follow a collision with any
object or the screen border. The changes consisted of a 50%
increase in speed and a reversal of the sign of the horizontal or
vertical component of the square’s motion vector, whichever
was larger. In other words, these changes were exactly the
same kind that occurred when an object collided with another
object or the border, but for this animate motion, no such col-
lision took place.
After the animate motion, the four squares continued mov-
ing for another 200 ms, and then a randomly selected square
vanished from the screen. Subjects were instructed to press the
space bar on a keyboard as soon as they noticed one of the
squares vanish. After the selected square vanished, the remain-
ing objects kept moving for another 2,000 ms or until the sub-
ject responded, whichever occurred first. If the subject did not
respond within 2,000 ms of the square vanishing, or if a differ-
ent key was pressed, a brief error tone was sounded. After an
intertrial interval of 750 ms, the next trial began.
Experiment 1b used the same apparatus and procedure
except that (a) the objects were four circles with a diameter of
3°, (b) the target was the appearance of either “X” or “+” in
one of the circles, and (c) subjects were instructed to identify
the target (by pressing one of two designated keys) as quickly
as possible.
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1726 Pratt et al.
In each experiment, there were 256 trials, including 64 in
which the target (offset or symbol) occurred in the object that
underwent animate motion.
Results and discussion
Trials with reaction times (RTs) less than 100 ms or greater
than 1,500 ms and trials on which the wrong key was pressed
were removed prior to analysis (less than 2% of the trials in
Experiment 1a and less than 3% in Experiment 1b). The RTs
for both experiments (see Fig. 1) were analyzed with t tests
comparing targets involving animate-motion objects with tar-
gets involving inanimate-motion objects). In Experiment 1a,
offsets were detected 45 ms faster for animate-motion objects
than for inanimate-motion objects, t(11) = 6.15, p < .001. In
Experiment 1b, targets were identified 21 ms faster in animate-
motion objects than in inanimate-motion objects, t(13) = 5.10,
p < .001.
In both experiments, subjects were faster to respond to tar-
gets (offset or symbol) involving objects that underwent a
change in motion consistent with the movement of an animate
object. These experiments are the first empirical demonstra-
tion that perceptual animacy (i.e., the appearance of motion
not due to an external event) can capture attention. Moreover,
the attentional capture was not dependent on the judgment
required: It occurred for both the detection of offset and the
discrimination of symbols. Finally, in interviews following
the experiments, none of the subjects reported having noticed
the animate motion; that is, no one was aware that on each trial
one of the objects changed speed and direction without hitting
another object or the screen border.
Experiments 2a and 2b
Experiments 1a and 1b strongly supported the conclusion that
perceptual animacy can capture attention, but we also consid-
ered two potential alternative explanations of the results. One
alternative explanation was that because only one animate-
motion event occurred amid a multitude of nonanimate-motion
events in each trial, the animate-motion event captured atten-
tion because it was unique—a perceptual singleton—and not
because it signaled animacy per se. Indeed, other types of per-
ceptual singletons have long been known to capture attention
(e.g., Treisman & Gelade, 1980). To examine this possibility,
in Experiment 2a we used the same stimuli as in Experiment 1a
but inverted the motion probabilities: All four objects per-
formed animate motion as their default motion, and 200 ms
before one of them disappeared, an inanimate-motion event
occurred (making the inanimate motion the singleton). If
uniqueness drove the effect in the initial experiments, then the
inanimate-motion event in Experiment 2a would be expected
to produce attentional capture.
The other alternative explanation arose from the fact that
the occurrence of the offset or appearance of the target symbol
was always 200 ms after the animate-motion event in the ini-
tial two experiments. Subjects may have learned that animate
motion always predicted the arrival of the target, and they may
have attended to that motion in a strategic, top-down manner.
Experiment 2a provided a test of this possibility, as in this
experiment the inanimate-motion event could be used to pre-
dict the arrival of the upcoming target. We further examined
the possibility of a top-down-driven allocation of attention in
Experiment 2b, by making the animate-motion event nonpre-
dictive of the occurrence of the target. To accomplish this, we
used three types of trials with different probabilities of occur-
rence. On neutral trials (25%), no animate-motion event ever
occurred, and after some time, one of the objects disappeared.
On delayed trials (50%), an animate-motion event did occur in
one object, but the offset occurred (in any of the four objects)
after two to seven intervening inanimate-motion events
involving the animate-motion object. Only on immediate trials
(25%) did the target offset immediately follow (200 ms) the
occurrence of an animate-motion event. In this experiment, it
would not be strategic to attend to the animate-motion event,
as it predicted the timing of a target offset on only one quarter
of the trials overall and one third of the trials containing ani-
mate motion.
Subjects
Sixteen University of Toronto undergraduates (mean age =
18.6 years; 9 women, 7 men) participated in Experiment 2a,
and 15 new undergraduate subjects (mean age = 18.9 years;
7 women, 8 men) participated in Experiment 2b. All subjects
reported normal or corrected-to-normal vision, and all were
naive to the purpose of the study and had not participated in
any previous experiments in this study.
Target
Inanimate Animate
RT (ms)
380
400
420
440
460
580
600
620
640
660
Experiment 1a Experiment 1b
Fig. 1. Mean reaction times (RTs) for detecting the offset of an object
(Experiment 1a) and identifying a symbol in an object (Experiment 1b) as
a function of whether the object had undergone animate motion or only
inanimate motion. Error bars represent 95% confidence intervals.
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Animate Motion Captures Attention 1727
Apparatus, procedure, and design
The apparatus and basic experimental procedure were identi-
cal to those used in Experiment 1a except that the circle objects
from Experiment 1b were used. In Experiment 2a, the four
objects moved around the display as before but did not contact
each other or the screen border. After 6.0, 6.5, 7.0, or 7.5 s, one
of the circles underwent inanimate motion after a collision
with another object or the screen border. Then, after 200 ms,
one of the four objects disappeared. As before, this experiment
had 256 trials, but in this case the sole circle that underwent
inanimate motion disappeared on 72 of those trials.
Experiment 2b used a procedure similar to that used in
Experiment 1a; indeed, on 25% of the trials, the target offset
followed the animate-motion event by 200 ms (immediate
condition), exactly as in the earlier experiment. In addition, on
another 25% of the trials, no animate motion preceded the tar-
get offset (neutral condition). Finally, on 50% of the trials, the
target offset occurred after the animate object underwent two to
seven subsequent inanimate-motion events (delayed condition).
In other words, after the animate-motion event, the animate
object collided with the screen border and other objects two to
seven times (about 1.5 to 7 s) before one of the objects disap-
peared (the three inanimate objects continued their collision-
associated trajectories during the delay period). This experiment
had 576 trials, and as before, the circle that vanished could be
any of the four objects.
Results and discussion
For Experiment 2a, the trimmed RTs (see Fig. 2) were ana-
lyzed with a t test, and no difference was found between RTs
to offsets of objects that underwent inanimate motion and RTs
to offsets of objects that did not undergo inanimate motion,
t(15) < 1. To compare these findings with those from Experi-
ment 1a, we conducted a 2 (experiment: 1a or 2a) × 2 (motion:
singleton or nonsingleton) analysis of variance (ANOVA).
Although there was a significant main effect for motion,
F(1, 26) = 35.31, p < .001 (RTs to singleton motion targets were
faster than RTs to nonsingleton motion targets), no effect of
experiment was found, F(1, 26) < 1. There was an interaction
between experiment and motion, F(1, 26) = 41.74, p < .001, as
differences in RTs between singleton and nonsingleton targets
occurred only in Experiment 1a. In other words, unique ani-
mate motion captured attention, but unique inanimate motion
did not. These results suggest that animacy, not uniqueness,
was the reason for the capture in Experiment 1a.
For Experiment 2b, the trimmed RTs (see Fig. 2) were first
analyzed with a 2 (condition: delayed or immediate) × 2
(motion: animate or inanimate) ANOVA. Although there were
definite trends, neither the main effect of condition, F(1, 14) =
3.53, p < .09, nor the main effect of motion, F(1, 14) = 3.43,
p < .09, reached significance. The critical interaction, how-
ever, was significant, F(1, 14) = 7.26, p < .02, as offsets of
animate-motion objects were detected faster than offsets of
Target
Inanimate Animate
Target
Inanimate Animate
RT (ms)
380
390
400
410
420
430
440
450
RT (ms)
400
410
420
430
440
450
460
470
Immediate Delayed
Neutral
Experiment 2bExperiment 2a
Fig. 2. Results from Experiments 2a and 2b: mean reaction times (RTs) for detecting the offset of an object as a function of the movement of that object.
In Experiment 2a (left panel), inanimate targets were offsets of an object that underwent a unique inanimate-motion event just prior to the offset, and
animate targets were offsets of an object that underwent only animate-motion events. In Experiment 2b (right panel), animate targets were offsets of an
object that underwent a unique animate-motion event prior to the offset, and inanimate targets were offsets of an object that underwent only inanimate-
motion events. On immediate trials, the target offset occurred just after the unique animate-motion event, and on delayed trials, it occurred after two to
seven intervening inanimate-motion events. On neutral trials, there was no animate-motion event. Error bars represent 95% confidence intervals.
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1728 Pratt et al.
inanimate-motion objects in the immediate condition, but not
in the delayed condition. There was an advantage for animate-
motion objects despite the fact that animate motion was not
predictive of the timing of the target offset in this experiment.
The difference between RTs to animate targets and RTs to
inanimate targets in the immediate condition was confirmed
by a t test, t(14) = 3.57, p < .005. A t test confirmed that offsets
of animate objects in the immediate condition were detected
faster than offsets in the neutral condition, t(14) = 3.82, p <
.005. Moreover, a one-way ANOVA comparing RTs in the ani-
mate delayed, inanimate delayed, inanimate immediate, and
neutral conditions found no differences, F(3, 42) < 1.
Together, these two experiments indicate that the atten-
tional capture found in Experiments 1a and 1b was not due to
singleton capture (as no such capture was found when the
inanimate motion was the singleton) nor to a top-down alloca-
tion of attention (as animate motion still captured attention
even when the event was not predictive of the timing of the
target offset). Instead, attention was captured by perceptual
animacy.
Experiments 3a and 3b
If animate motion does indeed capture attention by virtue of its
animacy, then it should be possible to modulate the magnitude
of the attentional capture by altering the extent to which the
motion is perceived to be animate. In a series of psychophysi-
cal experiments, Tremoulet and Feldman (2000, 2006) asked
observers to assess the animacy of a small moving dot that
changed its direction and speed of movement. Dots that under-
went larger direction or speed changes were perceived to be
more animate than dots that underwent smaller changes. If the
attentional effects found in our previous experiments were in
fact due to animate motion, then we should find stronger atten-
tional capture with greater changes in direction or speed
because such events are more likely to be perceived as indica-
tive of animacy.
Subjects
Twenty University of Toronto undergraduates (mean age =
20.1 years; 9 women, 11 men) participated in Experiment 3a,
and 21 new student subjects (mean age = 19.2 years; 9 women,
12 men) participated in Experiment 3b. All subjects reported
normal or corrected-to-normal vision, and all were naive to the
purpose of the study and had not participated in any previous
experiments in this study.
Apparatus, procedure, and design
The apparatus and basic experimental procedure were identi-
cal to those used in Experiment 1a except that the circle objects
from Experiment 1b were used. In Experiment 3a, the animate
motion consisted only of a change in direction of motion: 10°,
40°, or 70°. In the case of offset of an inanimate-motion object,
one of the same three direction changes occurred just prior to
the offset. In Experiment 3b, the animate motion consisted
only of a change in speed; the speed after the change was a
multiple of that before the change. The multipliers used were
1 (default speed of all objects; no change), 2 (twice the initial
speed), and 4 (quadruple the initial speed). In the case of offset
of an inanimate-motion object, one of the same three speed
changes occurred just prior to the offset. Across trials, the dif-
ferent directional changes (Experiment 2a) or speed changes
(Experiment 2b) for the animate motion were equally likely.
Each experiment consisted of 288 trials, with a short break
after every 48 trials. In 72 trials, the circle that performed the
animate motion was also the circle that vanished. Hence, the
animate-motion event was not informative.
Results and discussion
For each experiment, the RTs were analyzed with a 2 (motion:
animate vs. inanimate) × 3 (change magnitude: angular devia-
tion of 10°, 40°, or 70° in Experiment 3a; speed-change multi-
plier of 1, 2, or 4 in Experiment 3b) ANOVA. In Experiment
3a (see Fig. 3), there was a main effect of motion, F(1, 19) =
13.15, p = .002 (detection latencies were shorter for animate-
motion targets than for inanimate-motion targets), and change
magnitude, F(2, 38) = 16.98, p < .001 (RT decreased as the
angular deviation increased). There was also a significant
interaction between motion and change magnitude, F(2, 38) =
14.47, p < .001, as the magnitude of the angular change
affected offset detection only for the animate-motion objects.
In Experiment 3b (see Fig. 3), there were also significant
main effects of motion, F(1, 20) = 16.25, p = .001 (RTs were
shorter for animate-motion targets than for inanimate-motion
targets) and change magnitude, F(2, 40) = 108.42, p < .001
(RT decreased as the speed change increased). The interaction
between motion and change magnitude was also significant,
F(2, 40) = 3.73, p = .033. In this case, although both types of
motion yielded reductions in RT with increases in speed, the
effect was greater for animate-motion objects.
The findings of greater attentional capture with greater
changes in direction and speed support the notion that percep-
tual animacy captures attention, because greater changes in
direction and speed are associated with stronger perceptions of
animacy (Tremoulet & Feldman, 2000, 2006). As before, in a
postexperiment interview, the subjects gave no indication that
they were aware of the animate motion.
General Discussion
The question addressed in this study was whether or not ani-
mate motion, the motion associated with animate entities, cap-
tures attention. The six experiments provide a clear answer:
yes. In Experiments 1a and 1b, targets that involved objects
that had undergone animate motion (i.e., a change in direction
and speed not attributable to an external source) were detected
and discriminated more quickly than targets that involved
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Animate Motion Captures Attention 1729
objects that had undergone the same motion changes after col-
lisions with other objects or the surrounding frame (i.e., inani-
mate motion). In Experiments 2a and 2b, no evidence of
attentional capture was found when inanimate motion was the
unique (singleton) event, but animate motion captured atten-
tion even when that motion did not predict the timing of the
upcoming target (i.e., capture was not due to a top-down strat-
egy). In Experiments 3a and 3b, offsets of moving objects
were easier to detect the more likely the movement was to
reflect animacy. Taken together, the results demonstrate that
animate motion captures attention. Moreover, this capture
appears to have occurred without awareness of the perceptual
animacy that generated the orienting of attention.
One of the interesting aspects of this study is that although
the magnitude of the direction change in Experiment 3a
affected RTs to animate but not inanimate targets, in Experi-
ment 3b, the magnitude of the speed change affected RTs to
both animate and inanimate targets (although RTs to animate
targets were affected to a greater extent). It may be that
changes in speed are more salient events and induce a general
alerting function across the display, whereas directional
changes remain localized to the object in question. Thus, it
appears that the various aspects of animate motion differ in
saliency. In addition, there are most likely limits to when cer-
tain visual events will capture attention. For example, Cosman
and Vecera (in press) recently reported that motion onset does
not capture attention under conditions of high perceptual load.
Another interesting aspect of the study is the seemingly
unavoidable confound between predictability and animacy.
The aspect of animate motion that we focused on in this study
was the self-generated, or self-propelled, nature of the motion.
Objects that are animate can move where and when they want,
and this makes their movement unpredictable; in contrast,
inanimate objects are at the mercy of the forces acting on
them, which makes their motion much more predictable
(although, granted, some forces are not immediately obvious).
Disentangling predictability from animacy will be an impor-
tant next step in determining what it is about animate motion
that attracts attention.
The present findings add to the growing literature indicating
that the human attentional system has been finely tuned by evo-
lution. It is very likely that undergraduate students at major
universities, the population from which most research subjects
are recruited for these sorts of studies, have more experience
with automobiles than with nonhuman animals. Despite their
personal history, however, this population of subjects initiates
saccades to (Kirchner & Thorpe, 2006), and detects changes in
(New et al., 2007), static pictures more rapidly if the pictures
depict animals rather than other objects. And there still are
important reasons to attend to “biological” entities, such as cars
(operated animatedly) and people, in visually dense and com-
plex environments. The present study shows that simple geo-
metric objects whose movement is animate in nature receive
priority in the attentional system. Why should observers priori-
tize static, two-dimensional representations of animals they
have never encountered, or selectively attend to decidedly
inanimate geometric objects whose motion, ever so briefly, is
consistent with that of a biological entity? It seems that the evo-
lutionary past, during which detecting animate objects was
critical to survival, and the selection pressures exerted by mod-
ern environments have a profound impact on the way in which
people extract information from the visual field.
Speed Multiplier
1.0 2.0 4.0
RT (ms)
315
330
345
360
375
Direction Change (°)
10 40 70
RT (ms)
370
380
390
400
Inanimate Animate
Experiment 3a
Inanimate Animate
Experiment 3b
Fig. 3. Mean reaction times (RTs) for detecting the offset of an object that underwent animate or inanimate motion, as a function of the magnitude of the
object’s motion change immediately prior to its offset. In Experiment 3a (left panel), the magnitude of the object’s angular change varied across trials, and
in Experiment 3b, the magnitude of the object’s change in speed varied across trials. Error bars represent 95% confidence intervals.
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1730 Pratt et al.
Acknowledgments
We would like to thank two anonymous reviewers for suggesting the
alternative explanations tested in Experiments 2a and 2b.
Declaration of Conflicting Interests
The authors declared that they had no conflicts of interest with
respect to their authorship or the publication of this article.
Funding
This work was supported by a grant from the Natural Sciences and
Engineering Research Council (NSERC) of Canada to Jay Pratt.
Petre V. Radulescu was supported by an NSERC Undergraduate
Student Research Award.
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