THINKING & REASONING, 2006, 12 (4), 353 – 378
Temporal delays can facilitate causal attribution:
Towards a general timeframe bias in causal
induction
Marc J. Buehner and Stuart McGregor
Cardiff University, Wales, UK
Two variables are usually recognised as determinants of human causal
learning: the contingency between a candidate cause and effect, and the
temporal and/or spatial contiguity between them. A common finding is that
reductions in temporal contiguity produce concomitant decrements in
causal judgement. This finding had previously (Shanks & Dickinson, 1987)
been interpreted as evidence that causal induction is based on associative
learning processes. Buehner and May (2002, 2003, 2004) have challenged this
notion by demonstrating that the impact of temporal delay depends on
expectations about the timeframe between cause and effect. A corollary of this
knowledge-mediation account is that in certain situations longer delays
could facilitate, while shorter delays should impair, causal learning. Here we
present two experiments involving a physical apparatus that demonstrate a
detrimental effect of contiguity under certain conditions. In contrast to all
previous studies, delays universally promoted causal learning. This evidence is
clearly at variance with the notion of a bottom-up contiguity bias in causal
induction. A new, more general timeframe bias is discussed.
Causal learning refers to the ability to detect regularities between events in
the world around us, and to distinguish genuine causal relations from mere
spurious associations (Lien & Cheng, 2000). Cognitive science approaches
to causal learning have largely adopted Hume’s (1739/1888) premise that
causality itself cannot be observed directly (see also Young, 1995). Instead,
causal relations are inferred from observable evidence. According to Hume,
Correspondence should be addressed to Marc J. Buehner, School of Psychology, Cardiff
University, Tower Building, Park Place, Cardiff, CF10 3AT, Wales, UK.
Email: buehnerm@Cardiff.ac.uk
We would like to thank Dennis Simmonds and Howard Thomas for constructing the
apparatus, and Lorraine Woods for depicting it in Figures 1 and 2. We are also grateful to John
Culling for advice on muffling the sound, and for suggesting the use of pink noise. This research
has been funded by the Cardiff Young Researchers Initiative.
Ó 2006 Psychology Press, an imprint of the Taylor & Francis Group, an informa business
http://www.psypress.com/tar
DOI: 10.1080/13546780500368965
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this inference is constrained by two relevant environmental cues: regular
succession, and temporal and spatial contiguity between candidate causes
and effects. The majority of recent empirical studies on causal inference have
concentrated on the former cue, which is commonly referred to as
contingency, and a plethora of computational and process models have
been proposed as to how contingency constrains causal inference (for
overviews see Cheng, 1993, 1997; De Houwer & Beckers, 2002; Shanks,
Holyoak, & Medin, 1996).
Comparatively little work has investigated the role of temporal
contiguity. Until recently, results from a range of studies converged to
point out the importance of temporal contiguity, by showing that cause –
effect delays nearly always impair causal learning, in certain cases to such a
large extent that otherwise strongly rated causal relations are subjectively
rendered non-causal if implemented with a cause – effect delay of more than
2 seconds (Michotte, 1946/1963; Shanks, Pearson, & Dickinson, 1989).
Taken together, these findings have been interpreted to support a Humean
(Young, 1995) stance on causal induction, whereby cause – effect contingency and contiguity are the two fundamental principles underlying every
causal relation; unless these two principles are apparent to the reasoner, a
causal relation cannot be discovered.
THE BASIS OF THE TEMPORAL CONTIGUITY ADVANTAGE
IN CAUSAL INDUCTION: ASSOCIATIVE PRINCIPLES OR
MISMATCHES BETWEEN EXPECTATION
AND EXPERIENCE?
Buehner and May (2002, 2003, 2004) have challenged the hitherto assumed
universal importance of contiguity by showing that delayed relations can be
adequately assessed if participants are made aware that the timeframe of the
relation involves a delay. Buehner and May (2002) reinterpreted previous
data (Michotte, 1946/1963; Shanks et al., 1989) in light of Einhorn and
Hogarth’s (1986; see also Young, 1995) knowledge-mediation hypothesis.
They concluded that these studies were consistently limited to situations
where participants expected an immediate succession of cause and effect: In
Michotte’s studies of perceptual causality, for example, naı̈ve physics
informs reasoners that if the force of impact of one object onto another is
sufficiently large to set the second object in motion, this should happen
immediately. Likewise, in Shanks et al.’s experiments, participants had
‘‘considerable experience of the immediacy of cause – effect relations in such
electrical devices as computers’’ (Shanks et al., 1989, p. 155). Consequently,
delayed event pairings in these studies violated participants’ expectations of
an immediate timeframe. Buehner and May argued that this violation of
a specific expectation, rather than a general detrimental effect of delay, led to
TEMPORAL DELAY AND CAUSALITY
355
the observed decrements in estimated causal strength for delayed
causal events.
In order to test whether previously reported poor causal learning from
delayed contingencies reflects the universal necessity of contiguity (as
suggested by an associative learning account), or a rejection of the relation
as causal based on a mismatch between timeframe expectations and
empirical evidence, Buehner and May (2002, 2003, 2004) presented participants with constant contingencies and varied the amount of cause – effect
delay, analogously to Shanks et al. (1989). In addition, Buehner and May
also implicitly (2002), or explicitly (2003, 2004) manipulated participants’
expectations about the timeframe of the to-be-evaluated causal relation.
They found that the detrimental influence of delay could be significantly
reduced (2002, 2003) or even completely abolished (2004) by changing
participants’ expectations of the timeframe.
A SIMPLE TAXONOMY OF POSSIBLE COMBINATIONS OF
EXPECTED AND EXPERIENCED TIMEFRAME
In its most simplified form, the timeframe of a causal relation can be
described either as immediate (i.e., contiguous), or delayed. Naturally,
there is a continuum between what constitutes ‘‘immediately’’ and
‘‘delayed’’, and the scale and granularity of these two categories is highly
context dependent. A temporal interval of 1 second may seem immediate
when one presses a button to call a lift; that same interval may appear as a
significant delay when one considers physical collision events. In fact,
Michotte (1946/1963) reported that intervals exceeding 200 ms reliably
destroyed impressions of causal ‘‘launching’’. This threshold is clearly
context dependent and highly specific to the situations used by Michotte,
and must not be interpreted to imply that intervals exceeding 200 ms are
always perceived as ‘‘delayed’’, or render causal interpretation impossible.
Our concern in this paper is not with contiguity in a Michottean sense of
perceptual causality (i.e., contiguous ¼ instantaneous). Instead, ‘‘contiguity
bias’’ here refers to the finding that, everything else being equal, shorter
event sequences will never produce lower causal ratings than delayed
sequences, even when prior knowledge suggests a cause – effect delay. As we
will explain later, our experiments refer to cause – effect sequences
separated by 1500 ms as contiguous, in contrast to 3150 ms, which will
constitute a delayed sequence.
A reasoner’s expectation about the timeframe of a causal relation
analogously can be contiguous or delayed, resulting in a 2 6 2 table of
Expectation 6 Experience as depicted in Table 1. This arrangement affords
two ways in which experience and expectation can match (Immediate/
Immediate, Delayed/Delayed), and two ways in which they can mismatch
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TABLE 1
Possible combinations of expected and experienced timeframe of
causal relations
Experience
Expectation
Immediate
Delay
Immediate
Match
Mismatch
Delay
Mismatch
Match
Immediate and Delay are used in relative, task-dependent sense. See text for
further discussion.
(Immediate/Delayed, Delayed/Immediate). According to a knowledgebased account, contingencies should only be evaluated as indicative of a
causal relation in the first two, but not the latter two situations. Buehner and
May’s (2004) evidence satisfied three of these four criteria required by a
knowledge-mediation account:
1. Immediate relations were judged as causal when participants expected
an immediate mechanism. This is the simplest of all cases, and
replicates findings from no-delay conditions of previous work (e.g.,
Shanks et al., 1989).
2. Delayed relations were judged as causal when participants expected a
delayed mechanism: A 4-second delay had no discernible detrimental
influence on causal ratings, compared to no delay. This finding
contrasts with earlier findings from Shanks et al.
3. Delayed relations were not judged as causal when participants expected
an immediate mechanism. This finding corresponds to the delay conditions in Shanks et al., where the absence of delay instructions effectively implied that participants expected the relation to be immediate.
However, Buehner and May failed to obtain the critical fourth piece of
evidence necessary to fully endorse a knowledge-driven account of causal
induction:
4. Immediate relations should not be judged as causal when participants
expect a delayed mechanism.
Participants in Buehner and May (2004) always judged immediate relations
as causal, regardless of whether they were instructed that the relation was
TEMPORAL DELAY AND CAUSALITY
357
immediate or involved a delay. Buehner and May attributed this finding to
the artificial nature of the experimental apparatus. Participants were well
aware that the scheduling of effects was controlled by a computer. Since
their actions (clicking a button labelled ‘‘Lightswitch’’) indeed produced the
effect (illumination of a computer drawing of an energy-saving lightbulb), it
would in fact have been irrational for participants not to report the causal
efficacy of their actions. While this explanation is plausible, it is also posthoc. The failure to obtain evidence of participants rejecting an immediate
relation as non-causal, rather than being a methodological artifact, might
reflect a fundamental contiguity bias in covariation assessment.
THE CONTIGUITY BIAS IN COVARIATION ASSESSMENT
Schlottmann (1999) reported evidence suggesting a contiguity bias. In her
study, children and adults learned about two possible causal mechanisms
that could both bring about an identical effect (the ringing of a bell). One
mechanism would do so immediately after the cause occurred (a ball being
dropped in one of two holes in a ‘‘mystery box’’), the other only after a
delay. Both children and adults successfully learned the implications of both
mechanisms: Based on the timing between cause and effect they could
correctly infer which mechanism was inside the box; when told that a certain
mechanism was inside the box, they could correctly predict whether the
effect would occur immediately, or after a delay.
In a crucial test case, however, Schlottmann (1999) cleverly pitted
contiguity against knowledge of mechanism: Participants were shown which
mechanism was inside the box (slow or fast), but they did not know under
which of the two holes the mechanism was placed. To make sure that young
children would not forget which mechanism was inside the box, a sticker
with a picture of the relevant toy (slow runway or fast seesaw) was also
attached to the box. The experimenter then dropped one ball into one hole,
paused, dropped a second ball into the other hole, and then the bell rang.
Participants were asked which of the two balls had made the bell ring. The
correct answer of course depended on which toy was inside the box: if the
fast seesaw was in the box, then the second, contiguous, ball would have
made the bell ring, but if the slow runway was in the box, the first, delayed,
ball would have made the bell ring. Older children and adults appreciated
this distinction. However, 5- to 7-year-olds, failed to integrate their
knowledge of mechanism with their experience of contiguity: they
consistently claimed that the second, contiguous, ball had made the bell
ring, even when they knew perfectly well that the slow toy was inside the
box. Evidently, for these children, experienced contiguity provided such a
powerful cue to causality that well-engrained knowledge of the causal
mechanism that brought about the effect was disregarded.
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Schlottmann’s (1999) study differed from Buehner and May’s (2002,
2003, 2004) in a number of important ways. Most importantly, Schlottmann
employed deterministic causal relations, while Buehner and May used
probabilistic schedules. The developmental trajectory of Schlottmann’s
results suggests that the integration of mechanistic knowledge and temporal
contiguity involves effortful processing. The assessment of probabilistic data
likewise requires processing power. While adults might be capable of
successfully integrating knowledge and relative contiguity with respect to a
simple, deterministic causal relation, they might fail to do so with respect to
processing intensive, probabilistic causal relations.
Another difference between Buehner and May’s (2002, 2003, 2004)
studies and other studies assessing the influence of delay on causal learning
(including Schlottmann, 1999; but also Allan, Tangen, Wood, & Shah, 2003)
concerns the structure of the learning experience. Buehner and May
employed a Free Operant Procedure (FOP), in which participants could
execute (potentially) causal actions as little or as often as they wanted. Each
action produced a concomitant outcome according to the programmed
probability, after the programmed delay. Crucially, the event stream was
not segmented into individual learning trials. In other words, the decision of
whether a given outcome covaried with a preceding action (or occurred due
to alternative causes) was a fundamental component of the inductive
process. Schlottmann, on the other hand, structured the learning phase into
clearly defined learning episodes. The additional cognitive effort of parsing
an unsegmented event stream into meaningful causal and non-causal
episodes in Buehner and May’s studies may likewise have hindered a
successful integration of prior knowledge and experienced contiguity.
In the event of failure to integrate the two concepts, adults, just like
children, might resort to the most powerful cue, contiguity. Failure to
integrate knowledge and contiguity constitutes an alternative explanation of
Buehner and May’s (2002, 2003, 2004) finding that immediate relations were
always judged as highly causal, irrespective of the timeframe suggested by
the instructions. Note that whereas Buehner and May’s explanation of this
finding as a methodological artifact implies that it is specific to the nature of
the experiment involved, an extrapolation of Schlottmann’s (1999) argument implies that the contiguity bias is pervasive and should replicate across
a range of experiments.
The goal of the experiments in this paper was to test whether timeframe
expectations and timeframe experience interact to determine causal
inference according to a match/mismatch principle in realistic causal
inference tasks; that is, tasks where decisions about co-occurrence constitute
part of the inductive problem. Alternatively, the processing effort of
tracking covariation in real time might be too high to allow successful
integration of knowledge with contiguity cues. As in Schlottmann’s (1999)
TEMPORAL DELAY AND CAUSALITY
359
studies, on failing to integrate mechanistic with temporal cues, participants
might then adopt a simple contiguity heuristic, according to which
contiguous cues are always deemed causal, irrespective of the temporal
affordances of the causal mechanism. The apparatus needed for such
experiments has to allow a realistic manipulation of the plausibility of the
timeframe of the causal relation (short vs long). Our earlier work suggested
that computer-based paradigms are extremely limited on this dimension, as
participants always realise that computers can react immediately (and in fact
most often do), even when instructions suggest otherwise. We therefore
departed from a computer-based paradigm and used a real physical device,
inspired by Schlottmann’s (1999) seminal studies.
EXPERIMENT 1
An important consideration in choosing an appropriate apparatus for our
studies was that it had to be flexible enough to accommodate both immediate
and delayed relations, and that the temporal constraints towards both types
of relation would be easily perceived as necessary and binding for
participants. This, together with the need for implementing probabilistic
causal relations, led us to base the design of our apparatus on a Bernoulli
board, the probabilistic nature of which is perfectly obvious. Previous studies
on the influence of delay on causal induction always employed binary causes
and effects (i.e., causes and effects were either present or absent), so it was
necessary to adapt the Bernoulli board to give rise to such cause – effect
patterns. We achieved this by combining the board with electrical equipment,
in particular a set of microswitches mounted at the end of each chute, and a
lamp. The illumination of the lamp constituted the effect; the insertion of a
ball into the board was the candidate cause. Additional electrical equipment
was used to control and activate a connection between each microswitch and
the lamp. The probability of the lamp illuminating after a ball had been
inserted therefore was dependent on the number of active switches. Having
four equally probable routes of travel, each furnished with a switch that
could be individually activated, thus allowed us to implement the following
values for p (ejc)—the probability of the effect given the presence of the
cause: 0, 0.25, 0.50, 0.75, 1.0.
The cause – effect delay consisted of the time interval between insertion of
a ball at the top of the board and the illumination of the light, once the ball
rolled over an active switch at an exit chute. The extent of this delay could
be manipulated by changing the tilt of the board, with a tilt at low angle
affording longer delays than a tilt at a high angle. One additional constraint
was that there needed to be plausible alternative causes other than the
candidate in question. This was necessary to afford an explanation of effects
occurring after an implausible (short or long) delay: If the expectation of the
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timeframe does not match the experience, and the observed co-occurrence
between cause and effect is not interpreted as causal, then some other
alternative explanation for what produced the effect must be available. In
the absence of plausible alternative causes, reasoners would find themselves
in the very confusing situation of having to accept either a causal pairing
that does not match their timeframe expectations, or an effect that
apparently appeared without a cause. The standard solution employed in
past studies (e.g., Buehner & May, 2002; Shanks et al., 1989) was always to
instruct participants that sometimes the effect might occur ‘‘on its own’’,
even when in fact that never happened and all effects were caused by the
candidate cause in question. We followed this tradition, by telling
participants that in addition to the switches, the computer could also
control the light, and may sometimes randomly turn the light on. This
instruction was presented as an additional twist to the experiment that
would make an otherwise trivial task harder for participants.
Method
Participants. A total of 14 participants (9 female, 5 male, median
age ¼ 19) took part in the experiment. All participants were undergraduate
students from Cardiff University and received £3 for participating.
Apparatus. Figures 1 and 2 provide schematic depictions of the apparatus
and experimental set-up. The apparatus was a purpose-built wooden
‘‘Bernoulli-board’’, measuring 76.5 6 61 6 24 cm, covered with a clear
perspex lid. The board was attached to a wooden case beneath it and could
be tilted at different angles with respect to the lower board. A standard-sized
lightbulb, enclosed within an opaque red cover, was attached to the front of
the bottom case. Glass marbles, with a circumference of 10 cm, could be
inserted into an opening at the top end of the Bernoulli board. The board
contained a symmetrical system of pins and chutes that guided the marble
along one of four possible paths. Which path the marble took was random, as
in a typical Bernoulli board. Each path ended at a hole at the bottom of the
board, into which the marble fell once it reached the end of the path. The holes
fed to a slope inside the lower box (not visible from the outside). This slope
guided the marble to the back of the apparatus. The entire board and the slope
inside the lower box were covered with blue felt to minimise the noise the
marble made when traversing the apparatus.
A microswitch was mounted at the end of each of the four paths, but
before the respective holes. The four microswitches were surrounded by red
felt, to make them more visible. Whenever the marble rolled into one of the
four holes, it triggered the corresponding switch. There was also a fifth
hidden switch (concealed under the felt and thus invisible to participants) at
TEMPORAL DELAY AND CAUSALITY
361
Figure 1. The experimental set-up with the participant on the left and the experimenter on
the right.
the top end of the board, directly beneath the entry point for the marbles.
This switch was triggered every time a marble was inserted into the
apparatus; the experimenter could also trigger it without placing the ball
into the apparatus merely by touching it with his hand.
The five microswitches and the lightbulb were connected to a PsyScope
Button-box, which was attached to an Apple G4 iMAC, running PsyScope
(Cohen, MacWhinney, Flatt, & Provost, 1993). The button-box processed
information about the status of each switch and controlled the light fitted to
the front of the apparatus. A ball could thus be placed into the top of the
apparatus, roll down the board through one of the four holes, and depress
the corresponding switch. Changing the angle of the Bernoulli board with
respect to the lower box directly affected the speed with which the marble
travelled through the board, and thus the time elapsing between a marble
being inserted into the board and depressing one of the four visible switches.
We used two fixed angles in the experiments, 14 and 32 degrees with
respect to the horizontal plane (and lower box). The average elapsed times
between releasing the marble and triggering one of the bottom switches
were approximately 2500 ms and 1300 ms for the two angles of tilt,
respectively.
The apparatus furthermore comprised a set of headphones playing pink
noise, which participants had to wear during the main experimental phase.
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Figure 2. A bird’s eye view of the Bernoulli board.
Procedure. The participant was seated approximately 1 metre in front
of the main apparatus, with a clear view of the Bernoulli board and the
light mounted at the front end of the apparatus. Initially, the basic
functionality of the apparatus was described. The experimenter explained
how the glass marbles could be placed into the top of the board, and how
they would roll down into one of the four exit holes. The switches above
each hole (but not the hidden switch) were indicated, and the participant
informed that these switches operated the light at the front of the board.
The causal relation between putting the ball into the apparatus and the
light being turned on (when the ball rolled across one of the switches) was
highlighted at this point. Participants were then informed that each of the
switches could be made inactive by the experimenter, and would thus not
turn on the light when in this state.
TEMPORAL DELAY AND CAUSALITY
363
Following these instructions, the experimenter began to demonstrate the
apparatus to the participant, first focusing on how the four switches
afforded a probabilistic relation between marble insertion and light
illumination. The precise percentages possible (0, 25, 50, 75, 100) were
explicitly explained, and participants were informed that their task would be
to estimate the extent to which inserting a ball into the board caused the
light to turn on. The experimenter then proceeded to demonstrate how the
tilt of the board altered the time it took for the marble to reach the switches
(and turn the light on), after being placed in the mechanism.
Once they were sufficiently acquainted with the constraints of the
apparatus, participants were given instructions for the main experimental
phase. They were informed that they would observe several sets of examples
and be asked to judge the extent to which dropping the ball had caused the
light to turn on for those examples. The configuration of the switches
(active/inactive) would remain constant for each set of examples, but might
well vary between sets. Next, the experimenter stated that this alone would
be too easy a task, and that he had therefore introduced some difficulty into
it: In addition to the four switches, the computer might also sometimes turn
the light on. This could happen randomly at any moment, once the
experimenter had started a random generator. How often the computer
would turn the light on would also remain constant within a set of examples,
but might well vary between sets.
The experimenter then summarised the constraints of the apparatus once
more, pointing out the five possible probabilities supported by different
configuration of switches, and reiterated the possibility of the computer
turning the light on at any time, independent of the ball rolling over any
switches. Next, he stated that this experiment would not so much be
concerned with participants’ observation, but rather their understanding of the
apparatus. Therefore, he said, he would cover up the top of the apparatus with
a piece of cloth, preventing participants from observing the ball travelling
through the board. The only visual feedback available would consist of
observing the experimenter inserting a ball into the apparatus, and whether or
not the light came on. After each set of examples the experiment would
request a rating between 0 and 100 of the extent to which inserting the ball
made the light come on. 0 would mean that the ball never caused the light to
come on and 100 would mean that the ball always caused the light to come
on—even though the constraints of the apparatus limited p (ejc) to five discrete
values, we employed a continuous scale in order to allow participants to take
their (subjective) impression of p (ejØc) into account when making their causal
judgement. The demonstration phase took approximately 5 minutes.
The experimenter covered the top of the apparatus with a sheet of fabric
in a way which ensured that the light remained clearly in view. It was
explained that on each example the experimenter would hold up the ball
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before placing it into the board, so that the participant would know when
the ball had been released. The participant was told that the ball would be
placed into the board at a regular rate, approximately every 6 seconds.
During each set of examples the participant had to wear headphones,
which played a continuous loop of pink noise. This was done to block out
any potential sound emitted from the ball travelling through the apparatus
and crashing against the walls or pins. If participants were able to hear the
sound of the ball exiting the chute, they could base their causal judgements
purely on a perceptual judgement, namely whether the light came on at the
same time as they heard the ball exiting the chute.
The experimenter proceeded through eight blocks consisting of eight
insertions of the ball per block. For each insertion, the experimenter
pretended to insert the marble into the board, but in fact only pressed the
hidden switch on top of the board with his finger. These pretend insertions
were spaced at a rate of about one every 6 seconds. Every time the
experimenter triggered the hidden switch, it sent a signal to the button-box,
and the computer program determined whether and when to turn the light
on, according to the programmed schedule.
Immediately after each block of examples, participants were asked to
take off the headphones and to provide their rating of the extent to which
they thought the ball caused the light to turn on for those examples. They
verbally provided a numerical rating between 0 and 100, which the
experimenter immediately entered into the computer running the experimental software. At the end, the experimenter engaged participants in a final
debriefing and gradually revealed the purpose of the study, and also checked
whether participants had any suspicions that the experimenter had never
actually put the ball into the apparatus. No participant indicated any
suspicion of that, and the experimenter withheld information about this
deception from participants, to ensure that participants could not reveal this
to other potential participants from the undergraduate pool.
Design. The design comprised the factors Tilt (high, low), Delay (short,
long), and Repetition (1, 2). Factorial combination of Tilt and Delay yielded
four experimental conditions: high/long, high/short, low/long, and low/
short, which respectively yielded the following pattern of expectation –
experience congruency: match, mismatch, match, mismatch. These four
conditions were manipulated within subjects. The factor Repetition meant
that each participant worked on each condition twice during the experiment,
yielding a total of eight blocks per participant. We repeated each condition
twice to avoid or minimise order effects reported in previous studies of
delayed causal induction (Buehner & May, 2002, 2003).
The eight blocks were divided into two cycles consisting of four sets each
(one from each experimental condition). The order of sets was random
TEMPORAL DELAY AND CAUSALITY
365
within each cycle, and there was no break or other signal between cycles.
Each set consisted of eight insertions of the ball into the apparatus, and the
probability that the light would turn on (after the relevant delay) given the
hidden switch was depressed was always .75. Consequently, the computer
randomly chose six trials per set on which the light was turned on. On trials
when the light was programmed to turn on, it did so either after a short
(1500 ms) or long (3150 ms) time after the top switch had been pressed.1 The
computer only turned the light on when the hidden switch had been pressed;
contrary to the instructions provided by the experimenter, the computer
never actually ‘‘spontaneously’’ turned the light on. The software running
the experimental schedule thus had a clear discrete trial structure, and each
occurrence of a candidate cause (pretend insertion of the marble) was clearly
marked. However, the absence of visual or auditory feedback from the ball
traversing the apparatus, combined with the possibility of random,
computer-generated illuminations of the light rendered this structure
impenetrable for participants. It appeared that the experimenter inserted
the marble at a regular rate, but they had to infer whether a given
illumination of the light constituted a causal pairing (i.e., marble rolled over
an active switch) or a spurious pairing (computer turned the light on
independently of the marble’s path).
Results
Preliminary analyses revealed no systematic effects of Repetition, so all
subsequent analyses are based on averages across this factor. Figure 3
displays participants’ mean causal ratings. We adopted a significance level
of .05 for all analyses. A 2 6 2 repeated measures ANOVA revealed a
significant main effect of Delay on causal ratings, F(1, 13) ¼ 11.58,
MSE ¼ 425.00; no effect of Tilt, F(1, 13) ¼ 1.28, MSE ¼ 306.19; and a
Tilt 6 Delay interaction, F(1, 13) ¼ 7.10, MSE ¼ 527.67. Planned t-tests
analysed the effect of Tilt separately for Long and Short levels of Delay. For
conditions involving the Short Delay, causal ratings were significantly
weaker if a Low compared to a High Tilt was employed, t(13) ¼ 3.12,
p ¼ .008. In contrast, conditions involving the Long Delay were unaffected
by manipulations of Tilt, t(13) ¼ 1.31, ns.
1
Based on pilot data, we decided to facilitate distinction between Short and Long Delays by
highlighting the difference in Delay between High and Low Tilt: We implemented a slightly
shorter interval for High Tilt, and a longer interval for Low Tilt than the respective average
travel times observed in the demonstration phase. It is important to point out that these times
were still well within the range of possible times afforded by the apparatus on the respective tilts.
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Figure 3. Mean causal ratings from Experiment 1.
Discussion
The Tilt 6 Delay interaction shows that expectation about and experience
of a particular timeframe jointly influence the quality of causal inferences
drawn from observational data. The significant influence of timeframe
assumptions (manipulated via Tilt) on the assessment of causal relations
involving a Short Delay furthermore clearly rules out a relative contiguity
bias: Whether a covariation associated with a short delay was interpreted as
evidence for a causal relation was determined by the temporal assumptions
participants brought to bear. Unlike in Buehner and May’s (2002, 2003,
2004) earlier studies, short delay contingencies did not universally attract
causal attribution. More specifically, participants clearly rejected the
combination of Low Tilt and Short Delay as non-causal, despite the
implemented contingency of .75. Short delay contingencies were only
interpreted as supporting a causal link when the mechanics of the apparatus
clearly afforded a short delay (i.e., when the Tilt was High). When the
constraints of the board suggested a long delay (i.e., when Tilt was Low),
relatively contiguous data apparently clashed with delayed timeframe
expectations, and consequently were dismissed as non-causal.
An unexpected finding was the absence of an analogous impact of Tilt on
causal ratings in conditions involving a Long Delay. If the match/mismatch
TEMPORAL DELAY AND CAUSALITY
367
principle is pervasive, one would expect contingencies associated with a
Long Delay to be interpreted as causal only if the mechanism implies such a
delay. Contrary to this principle, our participants consistently regarded
delayed contingencies as supportive of a causal connection, irrespective of
whether the apparatus primed delayed or immediate temporal expectations.
As far as we know, these results demonstrate for the first time an overall
advantage of temporal delay in human causal induction: with a longer
cause – effect delay, participants always judged the relation as highly causal,
even when Tilt was set to High, which—we thought—would have induced
an expectation of (relative) immediacy. The current pattern of results is
exactly opposite to what Buehner and May (2002, 2003, 2004) have
consistently reported: Whereas Buehner and May found that delayed
relations required a justification for the delay in order to appear causal, and
immediate relations were always rated as highly causal, irrespective of
timeframe expectations, participants in the current study required a
justification for (relative) contiguity in order to perceive immediate relations
as causal, whereas they always rated delayed relations as causal, irrespective
of timeframe expectations.
Why the ratings for the High Tilt/Long Delay condition remained
relatively high is an issue that requires further analysis. One explanation is
that participants might have generated hypotheses about the physical
mechanism that enabled them to rationalise why a Long Delay occurred on
some instances for the High Tilt. When the board was set to High Tilt the
ball travelled through the board considerably faster. One consequence of this
higher speed was that it also bounced back harder (and thus further) when it
hit the pins. Although the overall duration of travel was of course shorter on
High as opposed to Low Tilts—as described in the Method section the
average travel time on High Tilt was 1300 ms, compared to 2500 ms on Low
Tilt—longer cause – effect delays could have been ‘‘explained away’’ by
participants, based on observations of the rougher travel and bouncing back
on the High Tilt during the demonstration phase. Conceivably the harder
bouncing could have increased the (imagined) subjective duration of travel
on High Tilt beyond the duration actually observed.
In other words, the demonstration phase might have failed to establish
sufficiently accurate timeframe expectations associated with High and Low
Tilt in our participants. Vague timeframe expectations could have blurred
the critical distinction between high and low tilts, which in turn would have
rendered the manipulation of Tilt ineffective. More specifically, an
insufficient distinction between the timeframes of High and Low Tilt would
lower the likelihood of rejecting as non-causal (a) Long Delays resulting
from the High Tilt position and (b) Short Delays resulting from the Low Tilt
position. However, the data from the Low Tilt conditions suggest that
participants could discriminate Long from Short Delays.
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BUEHNER AND MCGREGOR
Nonetheless, the ability of participants to accurately observe and
reconstruct the time delays afforded by the mechanism is of importance to
the interpretation of the overall result of this experiment. Experiment 2
assessed this issue further by gathering data on participants’ initial ability to
judge the time delays involved, and the effect this might have on subsequent
causal judgements.
EXPERIMENT 2
Method
Participants. A total of 18 participants (13 female, 5 male, median
age ¼ 19) took part in the experiment. All participants were undergraduate
students from Cardiff University and received £3 for participating.
Apparatus and procedure. The apparatus was identical to the one used in
Experiment 1, except that the Psyscope button-box was also used to collect
participants’ time estimates. The new task of time estimation was introduced
to the demonstration phase by instructing the participant:
Now I would like you to estimate how long it takes the ball to travel down
the board and reach one of the switches. First, press the button to indicate the
point when the ball would be released into the top of the board, hold down the
button and then release it when you think the ball would have reached one of
the switches.
The participant performed this time estimation task once using the buttonbox. The experimenter then mentioned that he could alter the angle of the
board, and tilted it to a higher (or lower) angle. Whether participants began
with a high or low tilt was counterbalanced. The experiment proceeded with
the instructions:
This has the effect of either reducing or increasing the time that it takes the ball
to fall from the top to the bottom. In the higher (lower) tilted position the ball
will take less (more) time to reach the bottom and roll over the switches. In the
lower (higher) position, as you have just seen before, it will take more (less) time
to reach the bottom and roll over the switches.
The experimenter demonstrated five examples at the new board tilt. The
participants were then again asked to provide a time estimate, but this time
for the board tilted at the new angle. Participants were then told how the
switches could be made inactive, and were shown this in operation, as had
been done in Experiment 1.
TEMPORAL DELAY AND CAUSALITY
369
After this demonstration the participants were asked to provide two final
time estimates. They were asked to estimate the time once for the board
tilted at both the higher and lower angles. The order of these two estimates
was counterbalanced in line with the order with which they had observed the
two board tilts. The rest of the procedure was identical to that described in
Experiment 1.
Design. The design was identical to Experiment 1, except that it
employed an additional between subjects counterbalancing factor, which
controlled the order in which the two tilts were observed during the
demonstration phase.
Results
Time estimates. Each participant provided two time estimates for each
level of tilt during the demonstration phase. We calculated an average time
estimate for each participant and level of Tilt. Analysis of these average
estimates showed that the apparatus did induce different timeframe expectations for the Low Tilt (Mdn ¼ 2399 ms) versus High Tilt
(Mdn ¼ 1611 ms). The difference between timeframe expectations, albeit
smaller than the actual difference supported by the apparatus in the
demonstration phase (1200 ms), or the difference between delays implemented in the experimental phase (1650 ms), was significant on a Wilcoxon signed
rank test (Number of High Tilt rated shorter than Low Tilt ¼ 15, number of
High Tilt rated longer than Low Tilt ¼ 3, 0 ties, Z ¼ 7 2.156, p ¼ .03).2
Another way to analyse time estimates is to look at their variability. If
timeframe expectations are vague, one would expect considerable betweensubject variability of the estimates. The variance between estimates for the
High Tilt (SD ¼ 968.42) was larger than the variance for estimates for Low
Tilt (SD ¼ 778.263), but this difference failed to reach significance on an
Fmax-test, F(2, 17) ¼ 1.548.
Causal ratings. Preliminary analyses of causal ratings revealed no
systematic effects of Repetition, so all subsequent analyses are based on
averages across this factor. Furthermore, the counterbalancing of order also
revealed no effects, so we collapsed across this factor. Figure 4 displays
participants’ mean causal ratings. There was a significant main effect of
Delay on causal ratings, F(1, 17) ¼ 6.29, MSE ¼ 629.43; a significant effect
2
Participants’ time estimates for the Low Tilt followed a skewed distribution, rendering
interpretation of means problematic. The difference in estimates is also highly significant on a
paired t-test, however, t(17) ¼ 7.86.
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BUEHNER AND MCGREGOR
Figure 4. Mean causal ratings from Experiment 2.
of Tilt, F(1, 17) ¼ 6.06, MSE ¼ 239.32; and a significant Delay 6 Tilt
interaction F(1, 17) ¼ 15.19, MSE ¼ 281.65. Again, we employed planned
t-tests to analyse the effect of Tilt separately for Short and Long Delays. For
the Short Delay, causal ratings were weaker if a Low compared to a High
Tilt was employed, t(17) ¼ 4.74, p 5 .005. In contrast, conditions involving a
Long Delay were unaffected by manipulations of Tilt, t(17) ¼ 1.15, ns.
Visual inspection of the data from both experiments, however, suggests a
consistent difference between High and Low Tilt for the Long Delay. In
order to check whether the failure to detect a significant difference was due
to small sample size, we pooled the data from both experiments, and
recalculated the planned comparisons. The effect of Tilt was highly
significant on Short Delay problems, t(25) ¼ 5.43, p 5 .005, but not on
Long Delay problems, t(25) ¼ 1.59, ns. We conducted a power analysis
(Buchner, Faul, & Erdfelder, 1997) for the latter comparison, with effect size
d set to .25, which is the conventional value for a ‘‘medium’’ effect on a
repeated measures procedure. The power for a two-tailed test with sample
size 26 is only .23, suggesting that we ought to exercise caution in
interpreting the lack of an effect of Tilt for the Long Delay problems.
We also analysed whether participants’ timeframe expectations (measured by time estimates provided during the demonstration phase) related to
their causal ratings. In order to do so we subtracted each participant’s
average estimate of the delay in the Low Tilt from his or her estimate of
TEMPORAL DELAY AND CAUSALITY
371
delay in the High Tilt to obtain a score of timeframe distinction. A
correlational analysis between all four causal ratings and the timeframe
distinction reveals that causal ratings in the Short Delay/High Tilt condition
were highly correlated with the timeframe distinction score, r ¼ .632,
p 5 .05. Causal ratings from the other three conditions did not correlate
with the timeframe distinction (all rs 4 .25, ps 4 .3). Figure 5 displays a
scattergram of causal ratings 6 timeframe distinction.
Discussion
Experiment 2 replicated the results of Experiment 1: Participants always
judged the delayed problems as highly causal, but only judged the short
problems as causal when the apparatus supported a rationale for a short
delay. As in Experiment 1, this finding shows a general advantage of
temporal delay, and a disadvantage of relative contiguity. In order to judge
a short cause – effect pairing as causal, participants needed to be supplied
with a mechanistic explanation for why the delay might be so short. When
such an explanation was not available, the short examples were not judged
as causal.
Experiment 2 further showed that participants appreciated the different
timeframes associated with the two different levels of Tilt employed in
the experiment, even though the subjective differentiation was smaller in
magnitude than the objective difference supported by the apparatus. This
result rules out concerns that our apparatus might have failed to set up
distinctive timeframe expectations for Low and High Tilt. Participants had
very clear ideas about the possible timeframes afforded by the apparatus.
Nonetheless, it proved interesting to investigate individual differences in
timeframe distinction, and how these differences relate to patterns of causal
attributions. With the exception of the Short Delay/High Tilt condition,
causal ratings were not correlated with participants’ distinction between the
two timeframes. The positive correlation reveals that causal ratings in this
condition increased as a function of timeframe discrimination. We will
return to this point in the General Discussion.
GENERAL DISCUSSION
The goal of the work presented here was to investigate whether human
causal induction is subject to a pervasive contiguity bias or not. Our analysis
of the literature revealed two possible explanations for the persistent
contiguity bias reported in the adult literature:
(a)
Integration of (temporal) knowledge with empirical cues (contingency, contiguity) requires effortful processing. If there are
Figure 5. Experiment 2: Scattergram of causal ratings from High Tilt (A) and Low Tilt (B)
conditions. The abscissa represents the difference in participants’ time estimations for Low and
High Tilt.
372
TEMPORAL DELAY AND CAUSALITY
(b)
373
insufficient resources available or the induction task itself requires
effortful processing (e.g., involves probabilistic data, or continuous
event streams), integration fails and a contiguity bias emerges.
Adult reasoners routinely integrate knowledge with empirical cues,
as evidenced by their real-life capabilities to reason about delayed
causal relations. A contiguity bias does not exist in adults.
Previous laboratory studies reporting such a bias employed an
artificial procedure, which, together with a rational approach
towards the task, gave rise to an apparent contiguity bias.
According to the latter explanation, emergence of the contiguity bias is
determined by properties extraneous to the reasoning task itself, and is
highly task dependent. According to the former hypothesis, the bias reflects
fundamental and general constraints of the reasoning system, and should
prevail over a wide range of paradigms.
Evidence against a contiguity bias
The evidence obtained from the current experiments does not neatly fit
either of these two possibilities: Causal relations involving a short delay did
not consistently give rise to causal attribution. This clearly rules out a
relative temporal contiguity bias. Unexpectedly, manipulation of timeframe
expectations only affected the appraisal of comparatively immediate causal
relations. Although a clear trend was observable such that delayed relations
were judged stronger when the apparatus suggested a delay, compared to
when a relatively immediate relation was plausible, the difference was not
significant. Lack of statistical power for this comparison notwithstanding,
this latter result is embarrassing for a knowledge-based account, as it
suggests a failure to apply the match/mismatch principle. As we explained
earlier, there are two ways in which this principle can be violated: when
short delay relations are judged causal even though the causal mechanism
involves a longer delay, and when delayed relations are judged causal even
though the causal mechanism is immediate. Previous studies only reported
the first kind of violation, suggesting a pervasive contiguity bias. To our
knowledge, the current results demonstrate, for the first time, the second
kind of violation against the match/mismatch principle: a ‘‘delay bias’’.
Participants in our experiments evidently failed to integrate knowledge of
temporal constraints with empirical data derived from observed cause –
effect timings. However, they only failed to do so when observed evidence of
a delay was paired with an apparatus that afforded a shorter timeframe.
This clearly undermines the argument that observed contiguity overrides
prior knowledge. If anything, then, in our experiments observed delays
overrode prior knowledge.
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Towards a timeframe bias
There are two ways to present the Delay 6 Tilt interaction in our results:
either one could say that delayed causal relations consistently gave rise
to causal attribution, irrespective of prior knowledge, while relatively
contiguous relations were only deemed causal when the apparatus afforded
short delays; or one could say that the High Tilt consistently gave rise to
causal induction, irrespective of whether the implemented timeframe was
contiguous or delayed, whereas the appraisal of evidence obtained from the
Low Tilt conditions was dependent on the observed timeframe.3
The choice of presentation implies a concomitant interpretation of where
the fault of reasoning lies: According to the former, the fault is related to the
integration of temporal and mechanistic cues: mechanistic cues were only
considered when the observed timeframe was short; short relations observed
under High Tilt were correctly identified as causal, whereas short relations
observed under Low Tilt were correctly rejected as non-causal. Observation
of a delayed timeframe, on the other hand, served as such a strong cue to
causality that no integration of knowledge and experience took place, in a
matter analogous, yet opposite, to Schlottmann (1999).
The other presentation implies a fault in the methods we employed: While
the Low Tilt might have clearly implied a long cause – effect delay, the High
Tilt could have failed to evoke such clear timeframe expectations. Instead,
participants could have had vague expectations, rendering both short and
delayed sequences as highly causal. Experiment 2 was aimed at distinguishing between these two interpretations. Results showed that participants
clearly distinguished between the timeframes implied by the two levels of
Tilt, which in turn suggests that they had likewise built up concomitant
timeframe expectations once they reached the learning phase. We could
also show that between-subjects variability of time estimates was not
significantly greater for the High Tilt, a finding that further assures us
our procedure succeeded in setting up sufficiently different timeframe
expectations.
Nonetheless, the extent to which participants distinguished between the
two timeframes afforded by the apparatus of course varied between
participants. However, causal ratings in most conditions were not correlated
with this ability. Particularly, causal ratings in the High Tilt/Long Delay
condition were not negatively correlated with the extent of timeframe
distinction, as one might expect. Intriguingly, ratings for the High Tilt/
Short Delay condition were highly correlated with participants’ ability to
3
Indeed, comparing the simple effects (on data pooled from both experiments) in this way
reveals that Delay had a significant effect for Low Tilt only, t(25) ¼ 7.73, but not for High Tilt,
t(25) ¼ 0.121.
TEMPORAL DELAY AND CAUSALITY
375
distinguish between the two timeframes afforded by the apparatus. Taken
together, these correlational results suggest that the failure to reject the High
Tilt/Long Delay condition as non-causal is not associated with a failure
to discriminate between the two timeframes, or a failure to construct
appropriate timeframe expectations. Rather, it seems as if the ability to
correctly identify a causal relation in the High Tilt/Short Delay condition is
related with successful distinction of the two timeframes. It is as if a short
delay was seen as poor evidence for a causal relation, such that additional
cues (i.e., knowledge that the current state of the apparatus was at High Tilt,
coupled with successful prior acquisition of the short timeframe affordance
under High Tilt) were required to render a short delay causal. In other
words, whereas delayed relations were effortlessly (and sometimes incorrectly) interpreted as causal, short relations required effortful processing.
Interestingly, correct rejection of the Low Tilt/Short Delay condition was
not likewise correlated with the extent of timeframe distinction. It is as if this
particular combination of cues was deemed so unlikely that it was rejected
without further processing. In sum, the following sequence of reasoning
processes might have occurred in our participants:
1.
2.
3.
4.
Is the experienced timeframe delayed? If yes, then the relation is
causal.
If the experienced timeframe is immediate, then consider the status of
the apparatus.
If the status of the apparatus is Low Tilt, then the relation is noncausal.
If the status of the apparatus is High Tilt, then the relation may be
causal.
This cascade of reasoning processes suggests a hierarchy of cues similar to
Schlottmann’s (1999) original proposal: Experience of a particular timeframe is more important than and thus may override expectation of a
timeframe. Our hierarchy is more general than Schlottmann’s, however, in
that it does not assign a unique role to temporal contiguity. In our specific
case, temporal delays were privileged, and participants only engaged in
effortful processing if this cue was not available. In Schlottmann’s case
exactly the opposite was true.
In both Schlottmann’s (1999) and our experiments, participants were
perfectly aware of the mechanism and temporal affordances of the
apparatus. In Schlottmann’s studies, this was ensured by placing a sticker
representing either the fast or slow toy outside the box; in our studies the
angle of tilt was visually salient and perfectly observable during each
experimental phase. Yet if a specific, canonical, timeframe was observed,
participants ignored considerations of mechanism, and made a causal
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BUEHNER AND MCGREGOR
inference. In Schlottmann’s case, the canonical timeframe was immediate; in
our case it was delayed. We can only speculate as to why the two
apparatuses used in the respective studies induced different canonical
timeframes. One way is to consider the respective causal mechanisms at a
more abstract level. In Schlottmann’s experiments, the observed events were
the dropping of a ball into a hole of a 27 cm high box, and the ringing of a
bell. In our studies, the observed events were the insertion of a ball into a
76.5 cm long tilted board, and the illumination of a light. In the absence of
any knowledge of mechanism (i.e., at the beginning of the experiment),
children and adults alike postulated an immediate timeframe in
Schlottmann’s study—only once they were instructed of the two possible
toys could they appreciate the possibility of long timeframes. Arguably, this a
priori expectation of immediacy reflects the underlying canonical timeframe.
We did not run a similar test about a priori expectation with our participants,
because that would have been impossible given the nature of our experiment.
However, one could conceivably argue that the appearance of our apparatus
(irrespective of level of Tilt) triggered a general delayed timeframe
expectation. Balls take very little time to fall a distance of 27 cm, but they
take considerably longer time to roll down a surface of 76.5 cm, sloped at 14
or 32 degrees. In the words of one of our reviewers: ‘‘. . . balls take some time
to roll over some distance. Many natural factors might slow a ball down even
more than expected, but nothing short of external force can make it go faster
than allowed by the slope.’’
These general canonical timeframe expectations (immediate in
Schlottmann’s case, delayed in our case) appear to be persistent despite
specific knowledge of mechanism suggesting an atypical timeframe (the slow
runway toy in Schlottmann’s study, or the High Tilt in ours). It is important
to point out, however, that our results are not in conflict with a knowledgemediation account. We argue that strongly ingrained temporal expectations,
derived from life-long experience, result in a canonical timeframe bias. This
general canonical bias may override specific knowledge of atypical
mechanical constraints, if they are in conflict with it. What our results did
show, however, is that the direction of the timeframe bias need not be
restricted to a preference of short over delayed relations, but can also
comprise a preference of delayed over shorter relations. We should
acknowledge, however, that our results cannot as yet rule out an absolute
contiguity bias, as found in perceptual causality, which involves delays in
the order of 100 ms. Our studies required that we compare relatively
contiguous to comparatively delayed relations; we could not operate with
delays shorter than 1500 ms due to the constraints of our method. If
perceptual causality is a modular process, as some have suggested (for an
overview see Scholl & Tremoulet, 2000), then it may well be subject to
domain-specific biases, which are outside the scope of our more general
TEMPORAL DELAY AND CAUSALITY
377
hypothesis (although see Scholl & Nakayama, 2002 for evidence of
inferential components in perceptual causality, which are at odds with a
modular account).
Our canonical timeframe hypothesis does not discredit temporal
contiguity as an important guiding cue towards the discovery of causal
relations, in situations where learners have no prior knowledge of the
constraints (temporal, structural, or mechanical) of the target causal
relation. As we have argued elsewhere (Buehner & May, 2003), contiguous
relations are considerably easier to detect than delayed ones, due to the
lower number of potentially intervening events that need to be taken into
account, lower memory and attention load, etc. The role of contiguity as a
cue to resolve ambiguities in causal event parsing is especially salient in
novel situations, where no prior knowledge regarding the timeframe of the
putative relation can be applied, and for situations that involve longer
delays, where computational complexity is increased.
Conclusion
We propose that mental representations of causal relations are associated
with a timeframe variable. Furthermore, we argue that, in line with a
simplicity principle (Chater & Vitanyi, 2003) reasoners strive towards
assigning a single, canonical, value to this variable. Reasoning about a
relation with variable timeframes requires additional computational effort,
as multiple values need to be considered, and resources need to be allocated
towards changing the value of the variable depending on the context or
prior knowledge. When resources are limited, people might adopt a
heuristic, economical approach towards the evaluation of evidence. If an
observed relation matches the canonical timeframe it is considered causal. If
it does not match the canonical timeframe, further effortful processing is
required to consider the specifics of the context, and whether they license a
non-canonical timeframe. This approach is similar to a believability bias
found in syllogistic reasoning (e.g., Evans, Barston, & Pollard, 1983), where
plausible conclusions are endorsed irrespective of their validity, and only
implausible conclusions are subjected to detailed scrutiny.
Manuscript received 17 December 2004
Revised manuscript received 19 September 2005
First published online 13 June 2006
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