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Choosing Optimal Causal Backgrounds for Causal Discovery

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In two experiments, we studied the strategies that people use to discover causal relationships. According to inferential approaches to causal discovery, if people attempt to discover the power of a cause, then they should naturally select the most informative and unambiguous context. For generative causes this would be a context with a low base rate of effects generated by other causes and for preventive causes a context with a high base rate. In the following experiments, we used probabilistic and/or deterministic target causes and contexts. In each experiment, participants observed several contexts in which the effect occurred with different probabilities. After this training, the participants were presented with different target causes whose causal status was unknown. In order to discover the influence of each cause, participants were allowed, on each trial, to choose the context in which the cause would be tested. As expected by inferential theories, the participants preferred to test generative causes in low base rate contexts and preventative causes in high base rate contexts. The participants, however, persisted in choosing the less informative contexts on a substantial minority of trials long after they had discovered the power of the cause. We discuss the matching law from operant conditioning as an alternative explanation of the findings.
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Choosing optimal causal backgrounds for causal discovery
Itxaso Barberiaa; Irina Baetub; Joan Sansaac; Andy G. Bakerb
a Universitat de Barcelona, Barcelona, Spain b McGill University, Montréal, Canada c Institute for
Brain, Cognition and Behavior (IR3C), Barcelona, Spain
First published on: 01 June 2010
To cite this Article Barberia, Itxaso , Baetu, Irina , Sansa, Joan and Baker, Andy G.(2010) 'Choosing optimal causal
backgrounds for causal discovery', The Quarterly Journal of Experimental Psychology, 63: 12, 2413 — 2431, First
published on: 01 June 2010 (iFirst)
To link to this Article: DOI: 10.1080/17470211003770904
URL: http://dx.doi.org/10.1080/17470211003770904
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Choosing optimal causal backgrounds for
causal discovery
Itxaso Barberia
Universitat de Barcelona, Barcelona, Spain
Irina Baetu
McGill University, Montre
´al, Canada
Joan Sansa
Universitat de Barcelona, Barcelona, Spain, and Institute for Brain, Cognition and Behavior (IR3C), Barcelona, Spain
Andy G. Baker
McGill University, Montre
´al, Canada
In two experiments, we studied the strategies that people use to discover causal relationships.
According to inferential approaches to causal discovery, if people attempt to discover the power of
a cause, then they should naturally select the most informative and unambiguous context. For genera-
tive causes this would be a context with a low base rate of effects generated by other causes and for
preventive causes a context with a high base rate. In the following experiments, we used probabilistic
and/or deterministic target causes and contexts. In each experiment, participants observed several
contexts in which the effect occurred with different probabilities. After this training, the participants
were presented with different target causes whose causal status was unknown. In order to discover the
influence of each cause, participants were allowed, on each trial, to choose the context in which the
cause would be tested. As expected by inferential theories, the participants preferred to test generative
causes in low base rate contexts and preventative causes in high base rate contexts. The participants,
however, persisted in choosing the less informative contexts on a substantial minority of trials long
after they had discovered the power of the cause. We discuss the matching law from operant con-
ditioning as an alternative explanation of the findings.
Keywords: Causal learning; Intervention; Power; Associative theories; Inferential models.
People may discover a causal relationship or even a
causal mechanism from empirical cues such as
covariation and temporal or spatial contiguity.
It has been suggested that, although people can
learn about specific causal relations through
empirical cues, they come to each problem with
Correspondence should be addressed to Itxaso Barberia, Universitat de Barcelona, Facultat de Psicologia, Departament de
Psicologia Ba
`sica, Passeig de la Vall d’Hebron, 171, 08035. Barcelona, Spain. E-mail: itsasobarberia@ub.edu
This work was supported by a grant awarded to Itxaso Barberı
´a by Generalitat de Catalunya (with the support of the Comissionat
per a Universitats i Recerca del Departament d’Innovacio
´, Universitats i Empresa de la Generalitat de Catalunya and the Fons Social
Europeu), a postgraduate fellowship awarded to Irina Baetu by the Natural Sciences and Engineering Research Council of Canada
(NSERC), a grant from the Spanish Ministerio de Educacio
´n y Ciencia (SEJ200767409– C02 01), a grant awarded to Andy
Baker by Generalitat de Catalunya (2004PIV200013), and an NSERC Discovery Grant awarded to Andy Baker.
#2010 The Experimental Psychology Society 2413
http://www.psypress.com/qjep DOI:10.1080/17470211003770904
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a priori assumptions about how to test causal
relations (e.g., Lagnado & Sloman, 2006; Lagnado,
Waldmann, Hagmayer, & Sloman, 2007). The
main goal of the present research was to investigate
the strategies that people use to discover the strength
or power of a novel cause. Specifically, we were inter-
ested in studying whether people have a preference
for some causal contexts over others in order to dis-
cover the strength and polarity of a putative cause.
Causes might be either positive and generate
the effect, or they might be negative and prevent
it. A generative cause can increase the likelihood
of an effect whereas a preventive cause reduces it.
The relationship between these causes and effects
can be either deterministic or probabilistic. A
deterministic cause always generates or prevents
its effect when it is present, whereas a probabilistic
cause influences the probability of an effect.
In addition to the relationship between the
target cause and the effect, it is also possible that
other alternative causes might influence the likeli-
hood of the effect. For the sake of simplicity we
assume that these alternative causes (if they are
independent of the target cause) do not need to
be considered individually: only their net effect
needs to be considered (e.g., Cheng, 1997). We
simply refer to this net effect of the alternative
causes as the power of the causal context.
In order to quickly and efficiently discover the
power of a cause, people should choose the most
informative causal context available. For a positive,
generative, cause the most informative context is
one in which the alternative causes have relatively
little effectiveness. In such contexts the effective-
ness of the target is not confounded by the
power of the context. If an effect occurs it is
likely to be a consequence of the target and not
the alternatives. In probabilistic contexts the
strength of the cause can be assessed, but this is
more difficult the higher the base rate of the
effect. In the extreme case in which an effect
always occurs in the absence of the cause, genera-
tive power cannot be assessed. For a preventive
cause to be assessed, there must be events available
for it to prevent. Therefore, it would be appro-
priate to investigate the effectiveness of a possible
preventive cause in a context with a high base rate
of the effect. The power of a negative cause cannot
be assessed in a context in which effects never
occur in the absence of the cause.
With the proliferation of inferential and stat-
istical theories of causal reasoning (e.g., Cheng,
1997; De Houwer & Beckers, 2003; De Houwer,
Beckers, & Vandorpe, 2005; Lovibond, Been,
Mitchell, Bouton, & Frohardt, 2003; Waldmann
& Holyoak, 1992), one would think that this
issue would have been studied intensively.
Surprisingly it has not. Wu and Cheng (1999)
did report an experiment in which participants
had to review choices made by a hypothetical
researcher and found data consistent with the
rational choice of contexts as mentioned above.
In Wu and Cheng’s experiment, however, partici-
pants did not actively choose a causal context in
order to observe the influence of the target cause;
instead, they merely reported how informative was
a choice that had already been made. Moreover,
in their experiments the power of the target cause
was either zero or, because of ceiling or floor
effects on the base rate of the outcome, impossible
to compute. Thus, they only explored situations in
which the cause tested had no influence over the
effect or its influence could not be observed. In
addition, rather than presenting their participants
with raw causal data, they summarized this infor-
mation in the form of propositions.
Presenting data as propositions (that is,
working with verbal descriptions of causal situ-
ations) not only eliminates the data processing
part of causal induction but also has theoretical
implications. There is a general split in theorizing
about causal learning (Pinen
˜o & Miller, 2007;
Shanks, Holyoak, & Medin, 1996). Associative
models argue that associative strength drives the
behaviour at the time of choice with little other
“thought”. In contrast, what we call here inferen-
tial models posit some kind of active decision
and/or computational process that occurs at the
time of making a choice. At least some inferential
models assume that, as part of natural causal
induction, people reason by using a cognitive
structure very similar to the logical structure of
the scientific method (Cheng, 1997; Nisbett,
Krantz, Jepson, & Kunda, 1983; Peterson &
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Beach, 1967). Clearly propositions, but possibly
not verbal ones or linguistic ones, are an appropri-
ate datum for such a cognitive structure if this is
the structure for naı
¨ve or natural causal discovery.
However, in western societies people have at least
some experience with verbal inferential reasoning
in school and other societal institutions. Thus, pre-
senting data as propositions might simply recruit
these learned verbal cognitive strategies and
bypass a possible natural causal induction mechan-
ism that must start with the raw and episodic
experience with the events in a causal scenario.
Therefore, it is valuable to study people’s choices
in a situation in which they must discover the
causal structure from raw experience and not just
reason about verbal descriptions of causal situations.
We are interested here in how people develop a
representation or model of a causal relationship
and not how they reason about it once it has been
given to them or they have inferred it themselves
(e.g., Goldvarg & Johnson-Laird, 2001).
The purpose of the two experiments we report
here was to investigate whether people preferred
to investigate the strength and polarity of a potential
cause in the most informative context available. To
do so, they were first given experience with either
two or three contexts so they could learn the likeli-
hood of the effect in each context. They were then
asked on each trial to choose the context in which
they wished to test the target cause.
EXPERIMENT 1
The scenario in this experiment involved assessing
the action of folk medicines or potions that had
been brought back from the Amazon by some
explorers. The participants were asked to determine
whether a given substance increased or decreased
the probability of having a stroke in various geneti-
cally different populations. The different genetic
types represented different causal contexts with
different base rates, the substances represented
target causes, and the strokes were the effects. The
participants first observed a number of members of
each population to determine the likelihood that a
person of that genetic type would have a stroke in
the absence of the causal substance. This was the
base rate or power of that population. After that,
they were given the opportunity to assess the
power of the various potions by testing them in
the genetic population of their choice.
In order to investigate how people choose a
context in a causal discovery task, we needed a
basic causal structure to impose on a given
context so participants could discover it. The
causal structure we chose was a simple one in
which a binary target cause and the cumulative
effects of unobserved binary alternative causes (for-
malized as a single unobservable binary alternative
cause—the context) act independently. That is to
say, they do not interact. This requirement of inde-
pendence is critical for a simple, direct test of the
notion that people prefer the most informative
context because if the cause interacts with—that
is, acts differently in—the different contexts, then
participants would need to continue monitoring
all contexts to assess this interaction.
The power of a generative cause, p
(gen)
,isthe
likelihood that that cause will generate an effect
(E) in a context with no effective alternative
causes. The power of any context, p
(cont)
,isthe
probability of an effect in that context in the
absence of the target. On any trial either or both
causes may be in a state to generate an effect.
If both causes are active only one effect occurs.
The conditional probability of an effect given a
generative target cause of a given power, p
(gen)
,in
a context of a given power, p
(cont)
,issimplythe
probability from elementary probability theory that
either or both of two independent events will occur:
P(E|Cont, GenTarget)
=p(cont) +p(gen) −[p(cont) p(gen)]
This is equivalent to getting one or two heads
(heads are analogous to the effect occurring) if two
biased or unbiased coins are tossed. The power of
a preventive cause, p
(prev)
, is simply the likelihood
that that cause would prevent an outcome in a
context whose power is one, p
(cont)
¼1—that is,
in a context in which effects always occur in the
absence of the preventive target. Again elementary
probability theory can be used to describe the
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probability of an effect given the presence of a target
preventive cause in a context of any power:
P(E|Cont, PrevTarget)=p(cont)
−[p(cont) p(prev)]
As a convention, we place a negative sign before
all preventive powers—for example, for a determi-
nistic preventive cause p
(prev)
¼21—in order to
distinguish them from generative causes. The
traditional measure of contingency DP (Allan,
1980; Jenkins & Ward, 1965) describes the
action of the generative or preventive target in
any context and is the difference between the con-
ditional probability of the effect in that context in
the presence and absence of the target cause, here:
DP=P(E|Cont, Target)−p(cont)
It should be mentioned that this causal model was
used in Cheng’s Power-PC model of causal reason-
ing (Cheng, 1997). Moreover, a statistic similar to
Cheng’s phas been derived by Pearl (Pearl, 1988;
see also Good, 1961) and is used in many Bayesian
models. However, the independent cause model is
not the critical point of Cheng’s theories; rather, it
is that participants assess a range of causal models
including those with interactions involving the
context (e.g., Novick & Cheng, 2004).
The design of Experiment 1 is shown in
Table 1. This table also shows the power and DP
of the target causes. The two deterministic target
causes were either perfectly generative or preven-
tive (i.e., had powers of 1 and 1). The causes
could be tested in either of two contexts, one
with low and the other with a high base rate of
the effect (henceforth, weak and strong contexts,
respectively). Participants were assigned to one of
two conditions that differed in the base rate
probability of the effect. Participants in Group
Deterministic were exposed to two deterministic
contexts, with base rates of the effect of 0 (i.e.,
weak context) and 1 (i.e., strong context),
whereas Group Probabilistic was presented with
two probabilistic contexts, with base rates of the
effect of .2 (i.e., weak context) and .8 (i.e., strong
context). It is clear from the discussion above
that for contexts with base rates of either 1 or 0
inferential theories make the unequivocal predic-
tion that participants should quickly come to test
generative causes in the 0 context and preventive
ones in the 1 context because the effect of these
causes is completely masked in the other context.
Moreover, although there is room for both preven-
tive and generative causes to demonstrate their
effectiveness in any probabilistic context—that is,
those with base rates 0 ,P(E|Cont, Target)
,1—choosing the more informative context
(i.e., weak context for the generative cause and
Table 1. Conditional probabilities of the effect in the presence and absence of the two causes in both contexts from Experiment 1 and their
D
P
value
Group deterministic Group probabilistic
Context
Generative cause
p
(gen)
¼1
Preventive cause
p
(prev)
¼–1
Generative cause
p
(gen)
¼1
Preventive cause
p
(prev)
¼–1
Weak P(E|Cont, Target) 1 0 1 0
P(E|Cont, Target) 0 0 .2 .2
DP10.8.2
Strong P(E|Cont, Target) 1 0 1 0
P(E|Cont, Target) 1 1 .8 .8
DP 0 –1 .2 –.8
Note: p
(gen)
and p
(prev)
refer to the power of the generative and preventive causes, respectively. P(E|Cont, Target) is the programmed
probability of the effect when the target cause is present, and P(E|Cont, Target) is the programmed probability of the effect
when the target cause is absent.
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strong context for the preventive one) is more
efficient, because the effects of the two types of
causes are differentially masked by the base rate.
This means that in Group Probabilistic the
power of the target cause could be discovered
even in the less informative context (i.e., the
strong context for generative causes and the weak
context for preventive causes). Nevertheless, the
generative cause would have more room for
action in the weak context, and the preventative
one would have more room in the strong context.
Thus, it is interesting to test whether participants
might have a preference for the most informative
context in Group Probabilistic, in which
neither context is entirely uninformative. Group
Probabilistic might be more ecologically valid
because people often observe probabilistic, rather
than deterministic, base rates.
Method
Participants
A total of 48 students from the University of
Barcelona participated in this experiment for
extra credit.
Apparatus
Four PC computers were used, and the experiment
was programmed in REALbasic.
Procedure
Participants received verbal and written instruc-
tions in Spanish, and all of the phrases that
appeared on the computer screens were in
Spanish. Up to 4 participants were tested at a
time. An English translation of the instructions
appears in the Appendix.
In the first phase of the experiment the partici-
pants were given experience with the causal con-
texts that were called genetic types X and Z. For
each observation participants observed a black
screen with the words “Genetic Type X” or
“Genetic Type Z” written in white at the top
and a picture of a chromosome below it.
Immediately below the picture were written the
words “Do you think the patient will have a
stroke?”. Beneath this were “Yes” and “No”
buttons that could be clicked. Once a button had
been clicked, a feedback screen followed, which
told the participant whether that patient had had
a stroke and whether the prediction had been
correct. The participants were exposed to a block
of 20 trials of genetic type X (i.e., weak context).
The probability of a stroke was .2, P(E|Cont,
Target) ¼.2, in Group Probabilistic and 0,
P(E|Cont, Target) ¼0, in Group Deterministic.
They were then asked to predict the likelihood of
a stroke in a sample of 100 new patients of
genetic type X using the following question: “Out
of 100 new patients with genetic type X, how
many do you think will have a stroke?”. Below
this was a sliding scale with 0 at one end and 100
at the other. Following this test, the participants
observed patients with genetic type Z—that is, the
strong context, P(E|Cont, Target) ¼.8 or 1—
andthenmadeapredictionusingthesameprotocol
as for genetic type X (half the participants observed
patients with genetic type Z first).
Following the 20 training observations of each
context the participants were given 60 opportu-
nities to test one substance. During the sub-
stance-testing phase, each observation began with
a screen with the words “Red (or Blue) substance”
at the top of the screen. Below this was a picture of
the substance pouring out of a container. Beneath
were the words “Please choose a genetic type to
try it on”. Below these words were pictures of the
two genetic types with their names (genetic type
X or Z) printed above them. Once the participant
had chosen a genetic type by clicking on it, a new
screen appeared showing the substance, the
chosen genetic type, the words “Do you think the
patient will have a stroke?”, and “Yes” or “No”
buttons below them. Once the participants had
chosen “Yes” or “No”, they were shown another
screen that informed them whether a stroke had
occurred and whether they had been correct.
Following every 10 trials, the participants were
asked to assess the strength of the substance by
answering the question: “What is the overall
effectiveness of the Red (or Blue) substance?”.
They did this by sliding a pointer on a scale with
phrases “This substance always prevents strokes”
and “This substance always causes strokes” at the
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ends, and the phrase “This substance has no effect”
at the midpoint. There were no numbers associ-
ated with the scale although the response was ana-
lysed using a scale from 1 to 1 in increments of .1
to map on the power scale. After 60 trials had been
completed (and six ratings had been given), the
participants were given 10 reminder observations
of each genetic type (i.e., second block of context
training trials), using the same procedure as that
for the first one. After the 10 training observations
of each context, participants were asked to predict,
again, the likelihood of a stroke in a sample of 100
new patients of each genetic type. Then they were
allowed to discover the causal power of the other
substance using a protocol identical to that used
for the first cause (half of the participants experi-
enced the generative cause first and the other
half the preventive one first).
Results
Rating of the context base rate
Following the initial context training and again
after the 10 reminder trials between the two
blocks of context choices, the participants esti-
mated the frequency of effects (over 100 hypothe-
tical trials) in each context. These ratings very
closely mapped onto what would be expected
from the conditional effect probabilities. In the
deterministic group with conditional probabilities
of 1 and 0 the initial estimates for strong and
weak contexts were 98.67 and 13.04 (SEM ¼
0.60 and 6.79, respectively), and the final estimates
after the reminder trials were 99.33 and 0.63
(SEM ¼0.40 and 0.38, respectively). The first
estimates for the probabilistic group with prob-
abilities of .8 and .2 were 75.38 and 28.63 (SEM
¼3.04 and 4.22), and the reminder estimates were
78.13 and 29.42 (SEM ¼2.82 and 5.03). An
analysis of variance (ANOVA) on these data
with group (deterministic probabilistic) as a
between-participants factor and context (weak
strong) and rating period (firstsecond) as
within-participants factors revealed a significant
main effect of context, F(1, 46) ¼797.05, MSE
¼294.65, p,.001, h2
p=.95, and a significant
Context ×Group interaction, F(1, 46) ¼80.42,
MSE ¼294.65, p,.001, h2
p=.64. No other
main effects or interactions were significant,
maximum F(1, 46) ¼2.61, MSE ¼268.38, p¼
.11, h2
p=.05. Estimates for Group Probabilistic
differed from those for Group Deterministic at
both high and low probability levels, minimum
t(46) ¼4.35, p,.001. Thus, we can be confident
that the participants could discriminate the two
weak contexts (0 and .2) and the two strong con-
texts (1 and .8).
Causal judgements
The participants in both the deterministic and the
probabilistic groups learned the deterministic con-
tingencies very rapidly and certainly within the
first 20 trials. The absolute value of the first of
the six estimates (absolute value range ¼.86
.92, range SEMs¼.05.07) was slightly lower
than the range of the remaining five estimates
(absolute value range ¼.90– .99, range SEMs¼
.01.08), showing that these estimates increased
slightly in strength from the first to the second
block of trials, at which point they seemed to
have reached asymptote. The difference between
the estimates of the target causes with 1 and 1
powers was, of course, reliable F(1, 46) ¼
4,109.80, MSE ¼0.12, p,.001, h2
p=.99.
Evidence for a slight learning curve was provided
by a marginally reliable cause by rating period
interaction, F(5, 230) ¼2.26, MSE ¼0.03, p¼
.05, h2
p=.05. However, none of the individual
analyses of learning curves for each of the two
causes was reliable, maximum F(5, 230) ¼1.40,
MSE ¼0.03, p¼.23, h2
p=.03. No other main
effect or interaction was significant, all Fs,1.
Context choices
The data in which we were most interested were
the context choices for the generative and the
preventive cause. Figure 1 shows the number of
times each cause was tested in the weak context
for groups probabilistic and deterministic.
Because context choices are a binary variable, we
report the data in 20 trial blocks to better approxi-
mate a continuous variable. Because of the
constraints on the degrees of freedom imposed
by the fact that each participant made exactly 20
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choices per block, choices of the strong context are
the exact mirror image of the choices of the weak
context so are not shown here. It is clear that the
participants chose to test the generative cause in
the weak context more frequently than they did
the negative cause and, consequently, chose to
test the preventive cause more frequently in the
strong context. This is the pattern expected if
they preferred testing the causes in the more infor-
mative context. Moreover, the context choices were
very similar in the probabilistic and deterministic
groups and did not vary much over the blocks of
trials. This conclusion was supported by an
ANOVA with group (deterministic probabilistic)
as a between-subjects factor and cause (generative –
preventive) and block (first to third) as within-
subjects factors, which revealed that the difference
between the generative and the preventive cause
was the only reliable effect, F(1, 46) ¼30.45,
MSE ¼45.55, p,.001, h2
p=.40. All other
main effects or interactions were not significant,
maximum F(2, 92) ¼1.18, MSE ¼9.33, p¼
.31, h2
p=.03. An analysis using all six 10-trial
blocks generated the same conclusions.
The preceding analyses show that the weak
context was chosen more with the generative
target cause and the strong context was chosen
more for the preventive cause. However, in spite
of the fact that participants chose the more
informative context more than 50% of the time
in each instance, the analyses do not allow us to
conclude that the participants preferred the weak
context for the generative cause and preferred
the strong context for the preventive cause. Only
a comparison against chance would unequivocally
allow this. We compared the combined context
choices of the deterministic and the probabilistic
groups for the preventive and for the generative
causes against chance on each of the three blocks
of 20 trials (six comparisons). In all six compari-
sons the participants chose the more informative
context at greater than chance level, minimum
t(47) ¼2.93, p¼.005. Thus, we can be confident
that the participants preferred the appropriate
contexts for each cause. In spite of the fact that,
once the cause’s polarity is known, for the Group
Deterministic one of the contexts provides no
information about the cause and for the Group
Probabilistic very little information, the partici-
pants still continued to choose the less informative
context throughout the experiment on a substan-
tial proportion of trials. This tendency to choose
the less informative context was reliable; six
comparisons against 100% choices of the informa-
tive context were each reliable, minimum t(47) ¼
9.77, p,.001.
To investigate whether there were any initial
biases in context choices, we analysed the first
context choice made by each participant. A x
2
analysis on the context choices on the first trial con-
firmed that choices of both contexts did not differ
from chance nor did they differ from one target
cause to another, maximum x
2
(1) ¼0.33, p¼.56.
Figure 1. The number of choices of the weak context (in blocks of 20
trials) for each of the target causes in Experiment 1 for Group
Deterministic and Group Probabilistic. p
(gen)
and p
(prev)
refer to
the power of the generative and preventive causes, respectively.
Error bars represent standard errors.
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Discussion
The participants preferred to test the causes in the
most informative contexts just as inferential theories
predict. However, it is also clear that, in spite of
preferring the more informative context, they
continued to choose the other context a substantial
proportion of times over all 60 observations. This
is a problem because, given the assumption of
independent binary causes, these choices are less
informative (for Group Probabilistic) or entirely
uninformative (for Group Deterministic). We
discuss this issue later once we have described the
data from our other experiment.
Experiment 1 used perfect causes that always
generated or prevented the effect. It is possible
that making judgements of deterministic events
is easier than for probabilistic events. Indeed,
detecting a probabilistic cause requires integrating
frequency information about all four possible com-
binations of two binary events (i.e., all four cells in
a two-by-two contingency table). This is because,
for example, a probabilistic generative target
cause might not always be effective in generating
an effect. A deterministic cause, however, has the
power to generate an effect on each of its occur-
rences. Hence, evaluating the probability of the
effect in the presence of the cause requires little
effort. Thus, learning about a probabilistic cause
rather than a deterministic one might be a more
demanding task. There is some evidence
suggesting that as tasks become more complex par-
ticipants may switch from using propositional
information processing to a more associative
mode (e.g., Le Pelley, Oakeshott, & McLaren,
2005). Because choosing the most informative
context might be a consequence of a rational,
effortful, decision process, this effect might disap-
pear when participants are faced with a more
complex task that involves probabilistic causes.
Moreover, most real-life situations involve asses-
sing the effectiveness of probabilistic causes
rather than deterministic ones. Testing whether
people still choose the most informative context
to discover the effect of a probabilistic cause
would, therefore, add considerable weight to the
argument that this effect generalizes beyond the
laboratory situation. Experiment 2 explored
causal discovery with probabilistic causes.
EXPERIMENT 2
In this experiment, participants were presented
with a generative cause that did not always
produce the effect, p
(gen)
¼.5, and a preventive
cause that did not always prevent the effect,
p
(prev)
¼.5. Instead, their influence over the
effect was probabilistic. In addition, we introduced
a cause with zero power, p
(neut)
¼0. Zero causes
do not change the probability of the effect above
and beyond the effect of the alternative causes. It
is interesting to see whether participants have a
context preference when the cause they are asses-
sing has no effect in any context. A preference
for a high or a low base rate context in this case
might reflect a general preference for such con-
texts, or perhaps a bias caused by our scenario.
Moreover, we added a third possible context, a
medium context, where p
(cont)
¼.5. Participants
were again divided in two groups (i.e., Group
Deterministic and Group Probabilistic). As in
Experiment 1, in the strong context the effect
occurred with a probability of 1 for Group
Deterministic and with a probability of .8 for
Group Probabilistic. In the medium context the
effect occurred with a probability of .5 for both
groups. In the weak context the effect occurred
with a probability of 0 for Group Deterministic
and with a probability of .8 for Group
Probabilistic. Thus, both groups were presented
with a probabilistic context of .5 (but because the
other two available contexts were either determi-
nistic or probabilistic, we chose to keep the same
labels for the two groups in order to be consistent
with the group labels in Experiment 1). Following
the context training, we introduced the three
causes for both groups: a generative cause with a
power of .5; a neutral cause with a power of zero,
p
(neut)
¼0; and a preventive cause with a power
of .5. Analogous to Experiment 1, participants
had to discover the influence of these causes over
the effect by testing them in the previously
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trained contexts. However, the situation in
Experiment 2 was slightly different from that of
Experiment 1 because one of the available contexts
had a base rate of .5. This is a context in which a
potential cause would have equal room to increase
or decrease the probability of the effect. From one
reasoning perspective, this context might be the
best choice to test a cause, as the effects of genera-
tive and preventive causes might be equally visible
in this context. This demonstrates that there might
be several rational choices depending on the argu-
ment that is put forward. Nonetheless, using
Cheng’s (1997) argument, we expected partici-
pants to test the generative cause in the lowest
base rate context available (i.e., weak context) and
the preventive cause in the highest base rate
context (i.e., strong context). As for the zero
cause, Cheng’s theory is silent regarding which
context would be preferable. We, however,
expected that either participants might prefer the
medium context since both potential generative
and preventive powers would have a clear, visible,
effect on this context, or they might test the zero
cause in all three contexts equally to make sure
that it has no effect in all of them.
Method
Participants
A total of 48 students from McGill University
participated in this experiment for extra credit.
Apparatus
The experiment was programmed in REALbasic
using Mac Mini computers with 17-inch monitors.
Procedure
The procedure was similar to that of Experiment
1. In this case, an English version of the previous
instructions was used, and the participants were
tested individually. Three causes (red, yellow, and
blue substances) and three contexts (X, Y, and Z
genetic types) were presented. As in Experiment
1, participants first discovered the base rate of
each context in 20 trials and were then allowed to
test each substance 60 times. A total of 10 remin-
der context-training trials for each context were
again administered between training with each
substance (since we trained three substances, two
reminder context-training sessions were adminis-
tered). The order of presentation of contexts and
causes was balanced among participants. Table 2
shows, for each of the groups, the programmed
probabilities of effects in the presence and in the
absence of the cause and the DP for each cause in
each context. In this experiment, the participants’
choices could influence the actual conditional
probabilities that they observed because of the
stochastic operation of the powers of the target
causes. In these cases we also include the actual
conditional probabilities received and their stan-
dard errors in parentheses. The nominal pro-
grammed and actual probabilities were very similar.
Results
Ratings of the context base rate
Following the initial context base rate training and
the two reminder blocks between the context
choice treatments, the participants made quite
accurate predictions of the expected frequencies
of the effects in the absence of a cause in each
context for both groups. Judgements of the
middle density context were very close to the
expected frequency of 50 (range of means ¼
48.9252.38, range of SEM ¼0.37 1.05). The
judgements of the low-density deterministic and
probabilistic contexts were close to their expected
values of 0 and 20 (range of means ¼2.755.50
and 19.5423.83, respectively; range of SEM ¼
0.834.09). Judgements of the high-density con-
texts also approximated their expected values of
100 and 80 (range of means ¼95.25 97.21 and
75.4681.33, respectively; range of SEM ¼
0.843.55). All the appropriate differences were
reliable. The ANOVA on these predictions with
the between-subjects factor group (deterministic
probabilistic) and the within-subjects factors
context (weak, medium, strong) and rating period
(first to third) showed a reliable main effect of
context, F(2, 92) ¼1,121.76, MSE ¼175.64, p
,.001, h2
p=.96 (all pairwise comparisons ps,
.001), and a significant context by group inter-
action, F(2, 92) ¼63.96, MSE ¼175.64, p,
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.001, h2
p=.58. This interaction occurred because
the estimates of the identical medium contexts
did not differ, F,1, but those of the determinis-
tic and probabilistic strong and weak contexts did,
minimum F(1, 46) ¼40.40, MSE ¼264.28, p,
.001, h2
p=.47. The main effect of rating period
and all the other interactions were not reliable,
maximum F(2, 92) ¼1.86, MSE ¼110.73, p¼
.16, h2
p=.04.
Causal judgements
The mean estimates of causal strength are shown in
Figure 2. Much like the previous experiment, the
causal ratings mapped very closely onto the pro-
grammed power values (p¼.5, 0, .5) and did
so very early on. While the preventive cause and
the zero cause showed little evidence of a learning
curve and were very similar in both contexts, with
the positive cause there was evidence of a slight
learning curve, and it appears that judgements in
the probabilistic group were slightly higher than
those in the deterministic group. The statistical
analysis was consistent with this impression.
Following a marginally reliable cause by rating
period interaction in the omnibus ANOVA
carried out on all six curves in Figure 2, F(10,
460) ¼1.83, MSE ¼0.05, p¼.05, h2
p=.04, we
carried out two-way analyses on each level of the
cause. For the generative cause the main effect
for rating period was reliable, implying a learning
curve, F(5, 230) ¼3.11, MSE ¼0.05, p¼.01,
h2
p=.06, and judgements in the two groups also
differed, F(1, 46) ¼4.07, MSE ¼0.20, p¼.05,
h2
p=.08. The interaction was not reliable,
implying that the curves were parallel in the two
groups, F,1. None of the analyses of the curves
for the other causes approached significance,
maximum F(5, 230) ¼1.02, MSE ¼0.05, p¼
.40, h2
p=.02.
Context choices
Figure 3 shows the frequency of choices of each
context for the three causes, in blocks of 20
trials. The upper panel shows choices made by
Group Deterministic, and the lower panel shows
choices made by Group Probabilistic. Unlike
Experiment 1, the pattern of judgements in the
two groups differed; however, by the end of
training, in both Group Probabilistic and Group
Deterministic the participants chose the weakest
Table 2. Conditional probabilities of the effect in the presence and absence of the three causes in the three contexts from Experiment 2 and their
D
P value
Group deterministic Group probabilistic
Context
Generative
cause
p
(gen)
¼.5
Neutral
cause
p
(neut)
¼0
Preventive
cause
p
(prev)
¼–.5
Generative
cause
p
(gen)
¼.5
Neutral
cause
p
(neut)
¼0
Preventive
cause
p
(prev)
¼–.5
Weak P(E|Cont, Target) .5 (.50, .01) 0 0 .6 (.59, .02) .2 (.18, .02) .1 (.08, .01)
P(E|Cont, Target) 0 0 0 .2 .2 .2
DP .500 .40.1
Medium P(E|Cont, Target) .75 (.75, .03) .5 (.49, .02) .25 (.26, .03) .75 (.76, .02) .5 (.51, .02) .25 (.26, .02)
P(E|Cont, Target) .5 .5 .5 .5 .5 .5
DP .25 0 –.25 .25 0 –.25
Strong P(E|Cont, Target) 1 1 .5 (.50, .02) .9 (.91, .02) .8 (.82, .02) .4 (.41, .02)
P(E|Cont, Target) 1 1 1 .8 .8 .8
DP 0 0 – .5 .1 0 –.4
Note: p
(gen)
,p
(neut)
, and p
(prev)
refer to the power of the generative, neutral, and preventive causes, respectively. P(E|Cont, Target) is
the programmed probability of the effect when the target cause is present, and P(E|Cont, Target) is the programmed probability
of the effect when the target cause is absent. The average actual P(E|Cont, Target) experienced by participants and their standard
errors are shown in parentheses in those cases in which the programmed probability is not deterministic.
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context to test the generative cause and the stron-
gest context to test the preventive cause. This
pattern only emerged in the last block in Group
Probabilistic, but was present on all three blocks
in Group Deterministic. Moreover, there is an
interesting pattern of results for context choices
with the zero contingency cause. In Group
Deterministic the participants seemed to prefer to
test the zero contingency in the medium context,
but those in Group Probabilistic showed no prefer-
ence for the medium context. This is interesting
because, when investigating a zero contingency,
people might be uncertain whether it is generative
or preventive. Testing a possibly generative cause
in a strong deterministic context, where p
(cont)
is
1, is uninformative. Similarly, testing a possibly
preventive cause in a zero context leaves no room
to detect its preventive action. A medium, p
(cont)
5.5, context provides the most efficient context
to determine simultaneously whether the cause is
positive or negative. As we have mentioned, in
Group Deterministic people preferred to test the
zero cause in the medium context. In Group
Probabilistic, although the moderate context may
be most informative for detecting causal polarity,
there is still some room to determine the polarity
of the cause in all three contexts, and no pattern
of preference for the medium context emerged.
The statistical analysis supports these conten-
tions. Because of the limitation of the degrees of
Figure 2. Causal ratings given to each of the target causes in
Experiment 2 for Group Probabilistic and Group Deterministic.
There were six estimations for each of the causes, given every
10 trials. p
(gen)
,p
(neut)
, and p
(prev)
refer to the power of the
generative, neutral, and preventive causes, respectively. Error bars
represent standard errors.
Figure 3. The number of times each target cause was tested in each
context (in blocks of 20 trials) for Experiment 2. Left, middle, and
right panels represent the number of times each cause was tested in
the weak, medium, and strong contexts, respectively. Upper panels
correspond to Group Deterministic and lower panels to Group
Probabilistic. p
(gen)
,p
(neut)
, and p
(prev)
refer to the power of the
generative, neutral, and preventive causes, respectively. Error bars
represent standard errors.
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freedom imposed by the fact that each block was
composed of exactly 20 choices, we carried out
separate ANOVAs in each context. An omnibus
ANOVA is not possible here because, on each
block of 20 choices, once the number of choices
of two contexts is known, the third is determined.
These 2 ×3×3 ANOVAs had group as a
between-participants factor (deterministic prob-
abilistic) and causal power (p¼.5, 0, .5) and
the three 20-trial blocks as within-subjects
factors. In all three analyses the cause effects,
minimum F(2, 92) ¼6.69, MSE ¼15.14, p,
.01, h2
p=.13, as well as the cause by group inter-
actions, minimum F(2, 92) ¼4.26, MSE ¼
15.14, p¼.02, h2
p=.08, were reliable. The
cause by block interaction was also reliable for
the strong context, F(4, 184) ¼3.44, MSE ¼
18.67, p¼.01, h2
p=.07.
To investigate the reliable interactions we did a
series of six 2-factor ANOVAs, one for each level of
context strength (weak, medium, and strong) in
each group (probabilistic and deterministic) with
the target causal strength (p¼.5, 0, and –.5) and
20-trial block (3 levels) as factors. In each
ANOVA in Group Deterministic only the main
effect of cause was reliable, minimum reliable F(2,
46) ¼6.85, MSE ¼21.10, p,.01, h2
p=.23.
We report a number of comparisons of means
following reliable effects in our ANOVAs.
Generally these contrasts are preplanned with sys-
tematic replication so we report the conventional
noncorrected pvalues for two-tailed tests.
However, we did use the Bonferroni correction
on all comparisons, usually based on the two or
three contrasts reported. The pvalue is marked by
an asterisk for those comparisons that are not
reliable by this standard (e.g., p¼.03). Simple
comparisons showed that participants chose to test
the positive cause in the weak context more often
than either the zero or the negative cause,
minimum F(1, 23) ¼16.93, MSE ¼30.12, p,
.001, h2
p=.42. The participants chose to test the
negative cause more often in the strong context
than either of the other causes, minimum F(1, 23)
¼50.00, MSE ¼11.68, p,.001, h2
p=.68.
Finally, although the effect was weaker, they chose
to test the zero rather than either of the other two
causes more often in the medium context, F(1, 23)
¼18.65, MSE ¼14.89, p,.001, h2
p=.45 for the
neutral versus the preventive cause and F(1, 23) ¼
4.18, MSE ¼30.26, p¼.05,h2
p=.15 for the
neutral versus the generative one.
In Group Probabilistic the results were not quite
so straightforward. In the weak context there was
only a reliable cause effect, F(2, 46) ¼6.99, MSE
¼14.74, p,.01, h2
p=.23, and similar to Group
Deterministic the participants did choose to test
the generative cause in the weak context more
than the other causes, F(1, 23) ¼9.18, MSE ¼
22.39, p,.01, h2
p=.29, for the comparison of
the generative and the preventive causes, and F(1,
23) ¼4.18, MSE ¼14.38, p¼.05,h2
p=.15
for the comparison of the generative and the
neutral causes. No cause was preferred in the
medium context, F(2, 46) ¼2.30, MSE ¼9.18,
p¼.11, h2
p=.09. Differential preferences for
the strong context only emerged on the second
and third blocks in Group Probabilistic. This is
supported by a reliable cause by block interaction,
F(4, 92) ¼2.56, MSE ¼20.21, p¼.04,
h2
p=.10. One-way ANOVAs comparing the
three causal strengths carried out on each block
were reliable on the second and third blocks, F(2,
46) ¼3.43, MSE ¼20.74, p¼.04, h2
p=.13 for
the second block and F(2, 46) ¼8.86, MSE ¼
25.50, p¼.001, h2
p=.28 for the third. On both
of these blocks, participants chose to test the nega-
tive cause more than the positive one, F(1, 23) ¼
5.38, MSE ¼20.63, p¼.03,h2
p=.19 for the
second block and F(1, 23) ¼14.20, MSE ¼
31.71, p¼.001, h2
p=.38 for the third. The
preference for the negative cause over the zero
cause was not quite reliable on either block,
maximum F(1, 23) ¼3.93, MSE ¼26.00, p¼
.06, h2
p=.15. However, if the two blocks were
combined the difference was reliable, F(1, 23) ¼
6.70, MSE ¼14.38, p¼.02, h2
p=.23.
In Experiment 1 the constraints on degrees of
freedom imposed by the fact that 20 choices must
be shared among the two options made it
difficult to directly test the hypothesis that the
participants preferred to choose the weak context
with a generative cause and preferred the strong
context with a preventive cause. But because in
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this experiment there was a medium context, we
were able to test preferences for the weak or
strong context for both the generative and preven-
tive causes by simply doing an ANOVA on the
weak and strong contexts. We could do this
because, while there is still a ceiling effect of 20
choices, none of the means was particularly close
to this so it is a reasonable approximation of inde-
pendence. Accordingly, we did a three-factor
ANOVA on the context choices of the weak and
strong contexts on the third block of trials for
the generative and preventive causes. The three
factors were group (deterministic vs. probabilistic),
context (weak vs. strong), and cause (p¼.5 or
.5). If the participants preferred the appropriate
context in all cases, then the cause by context inter-
action, but none of the other interactions, should be
reliable. As predicted, the cause by context inter-
action was reliable, F(1, 46) ¼40.38, MSE ¼
43.39, p,.001, h2
p=.47, and none of the other
interactions was, Fs,1. The only main effect
that was reliable was the main effect for cause,
F(1, 46) ¼8.21, MSE ¼8.83, p,.01, h2
p=.15,
other Fs,1. This occurred because the partici-
pants made more total choices of the weak and
strong contexts (i.e., fewer choices of the medium
context) with the preventive cause. This latter
result implies that the ceiling of 20 total choices
did not constrain choices of the two contexts.
Thus we can be more confident with the claim
that participants prefer the weak context to test
the generative cause and the strong context to test
the preventive cause. As in the previous experiment,
we carried out simple comparison of choices of the
most informative context against 100% choice
levels for the generative and preventive causes. All
these comparisons were reliable, minimum t(23)
¼8.46, p,.001. However, because there were
two alternative less informative contexts, we also
compared the least informative context against a
choice rate of zero. Each of these comparisons was
also reliable, minimum t(23) ¼3.89, p¼.001.
This confirms that participants did not always
choose the most informative context nor reject the
least informative one.
We again carried out a complementary analysis on
the very firstcontext choice made by the participants.
Chi-square tests showed that this first choice was
similar for the three causes, x
2
(4) ¼0.84, p¼.93,
but that there was an initial general preference for
the weak context over the strong one, x
2
(1) ¼
9.35, p,.01, and for the strong context over the
medium one, x
2
(1) ¼20.08, p,.001.
Discussion
With probabilistic causes there was again a prefer-
ence to test both generative and preventative causes
in their most informative contexts (i.e., the genera-
tive cause in the weak context and the preventative
cause in the strong context). Thus, despite the
fact that the medium context with a base rate of
.5 was available, participants still chose the most
informative context. It is worth noting that partici-
pants did not prefer the medium context even
when the power of the cause was still unknown
to them—that is, on the first few trials. This
would have been the best time to use the
medium context, since any type of cause could
reveal its effect in this context.
The participants tested the zero cause, p
(neut)
¼
0, in the medium context more than they tested
the generative or preventive ones when the
other two contexts were deterministic, but they
tested all three causes equally in this context
when they were probabilistic. In fact, for Group
Deterministic, this medium context was the only
one that allowed participants to test both the gen-
erative and the preventative power of a cause at the
same time, so it is possibly the most informative
intervention for a neutral cause. For Group
Probabilistic, on the other hand, all three available
contexts were probabilistic, and the effect of gen-
erative and preventive causes would be visible in
all three of them (although to different extents).
Thus, it might be that participants in this group
did not prefer the medium context because it was
not the only probabilistic context available.
GENERAL DISCUSSION
These experiments showed that participants prefer
to test target causes in the most informative causal
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contexts. This tendency was observed in both
experiments, where we combined probabilistic
and deterministic causal contexts and/or target
causes. Therefore, in general, our results indicate
that the participants acted as rational learners
seeking causal information in a way that could effi-
ciently assess the existence of causal mechanisms.
This finding is consistent with Cheng’s analysis
from both her probabilistic contrast model
(Cheng & Novick, 1990, 1992) and the later
Power-PC model (Cheng, 1997) that describes
why participants should prefer more informative
contexts. In the same way, there are other
models that do not explicitly discuss the predic-
tions tested here but that can implicitly account
for the present data. These models share the
notion of a rational learner and thus could be
easily adapted to explain the preference for con-
texts that give more information about the causal
mechanism (e.g., De Houwer & Beckers, 2003;
Lovibond et al., 2003; Steyvers, Tenenbaum,
Wagenmakers, & Blum, 2003; Waldmann &
Holyoak, 1992).
There have been previous attempts in Bayesian
tradition to study how people intervene in a causal
discovery situation (e.g., Lagnado & Sloman,
2004, 2006; Steyvers et al., 2003). However, that
research has focused on interventions that help
the observer discover the underlying causal struc-
ture. Contrary to this, the present work focuses
on interventions that reveal the effectiveness of a
potential cause over the effect, when the causal
structure or possible causal links are already
known (i.e., events are already defined as potential
causes or effects). Nevertheless, the Bayesian
approach can be applied to our participants’ inter-
ventions as well. In our experiments, the causal
model was explicitly stated as one in which the
context and the cause could influence the effect.
Instead of discovering the causal structure, partici-
pants had to discover the effectiveness of the cause,
which always occurred in the presence of an
alternative context. When attempting to discover
the effectiveness of a cause, one logical interven-
tion is to eliminate alternative causes or keep
them constant (Cheng, 1997; Lagnado et al.,
2007). Although participants could not entirely
eliminate the context, they could nonetheless
diminish the strength of the link between the
context and the effect by changing the base rate.
For a generative cause, the most logical intervention
is to decrease the base rate and thus weaken the
generative effect of the alternative context. For a
preventive cause, the most logical intervention is
to increase the base rate of the context, which
means decreasing its preventive power. Given the
assumption that people attempt to remove alterna-
tive causes of the same effect when testing a target
cause, a Bayesian or a causal model approach might
predict this type of intervention.
However, even though the participants showed
a tendency to choose the most informative con-
texts, they still frequently chose the less informa-
tive (in Group Probabilistic of both experiments)
or entirely uninformative context (in Group
Deterministic of both experiments). This tendency
continued throughout training, long after accurate
causal assessments had been made. For Group
Probabilistic, even though the base rates were
greater than zero or less than one, some contexts
allowed less room for the target cause to act than
others. For Group Deterministic, in which the
strong and weak contexts were deterministic (i.e.,
with base rates of one or zero), some interventions
were completely uninformative. When, for
example, participants in this group tested a genera-
tive cause, selecting the context that generates
the effect with a probability of 1 gave them no
information about the generative strength of the
cause because the context always produced the
effect. Thus, if participants were acting rationally,
we would have expected to see the tendency to pick
the less informative context to decline as the
experiment progressed. Contrary to this, we
found that the uninformative context was chosen
quite frequently throughout. If we assume people
make rational interventions, how can we explain
this continuing tendency to choose contexts that
give little or no information about the cause as
a crucial mechanism for causal discovery or
induction?
One possibility is that participants were not
convinced that the causes were independent.
Cheng’s theory assumes independence of the
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target cause with respect to alternative causes (i.e.,
the context). If this independence is assumed, the
observer has no need to test the causes in all con-
texts. Thus, it is more efficient to carry out the
test only in the context where the room for
action of the target cause is greatest. However, if
the target cause and alternative causes interact,
then it becomes necessary to test how the cause
acts in each context. An interaction would occur
when the actual causal mechanism of a cause was
influenced by the context in which it was tested.
For example, the causal mechanism might
depend on some resource that varies between con-
texts. Since we did not give explicit instructions
about the independence of the causes, it could be
that the participants continued to look for possible
interactions and thus chose the less informative or
the uninformative context. It has been shown that
people report that there are interactions between a
cause and different contexts when the cause
appears to have a different causal power in every
context, but not when the cause has an identical
power in every context (Liljeholm & Cheng,
2007). Because the causes had the same power in
every context (in those contexts in which the
power of the cause could be assessed), our partici-
pants might have eventually discovered that each
cause’s effect was independent of the contexts.
Another possibility concerns the trial-by-trial
predictions the participants had to make about
the presence or absence of the effect. When the
target causes are probabilistic (Experiment 2),
testing a cause in the most informative context
makes it harder to correctly guess what the effect
will be. For example, in Group Probabilistic of
Experiment 2, with a generative cause of power
.5, the effect occurs 60% of the time in the weak
context whereas the effect occurs 90% of the time
in the strong context. Thus, if participants choose
to maximize the probability of making a correct
prediction, it is better to test this cause in a high
base rate context, even though this context gives
them less information about the power of the
cause. Thus, although a low-density context is
more informative for discovering the generative
power of the cause, it is less informative for
predicting the effect on every trial. Therefore, the
tendency to continue choosing the less informative
contexts could be due to the fact that in these
contexts the effect was easier to predict. In spite
of our instructions encouraging the participants
to discover the power of the causes, they may
have chosen to make the most accurate predictions
of the effect.
While the latter argument is attractive for
Experiment 2, it is not so attractive for
Experiment 1 because Experiment 1 used determi-
nistic causes so there was no difference in outcome
regardless of which context participants chose. For
example, if the generative cause was tested in the
deterministic positive context, there would be an
outcome on 100% of the trials (presumably, and
ambiguously, caused by both the context and the
target). If the generative cause was tested in the
weak (0%) context, then there were still 100%
outcomes because the cause was perfectly effective.
In spite of this, participants still chose the less
informative context about a third of the time.
Thus, there was no advantage (in terms of
outcome control) to choosing the weak context as
there was in probabilistic experiments. Therefore,
it is probably more realistic not to ascribe a single
mechanism for the continuing choices of the less
informative contexts, rather it is probably a combi-
nation of several sources of variation including
hypothesis testing for interactions as listed above,
looking for changes in contingency over the long
task, looking for possible reinforcement patterns,
or simply believing the demands of the task
required continued inspection of all contexts.
What is unequivocal is that participants main-
tained their preferences for the more informative
context even when this preference gave them no
advantage predicting or generating outcomes. In
any case, further research is needed to understand
why participants continued choosing the less infor-
mative or uninformative contexts for their inter-
ventions throughout the experiment.
Our experimental design illustrates an advan-
tage of the notion of power and other theories
based on an internal model of cause over other
computational theories. Because power is a prop-
erty of the cause and thus is constant across
contexts, people can easily transfer a cause’s
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power to another context (Baker, Murphy, Mehta,
& Baetu, 2005; Buehner, Cheng, & Clifford,
2003), but they can also easily integrate infor-
mation from different contexts to assess power.
This is not so clear for other computationally
based metrics such as DP (Allan, 1980), weighted
DP (e.g., Anderson & Sheu, 1995; Kao &
Wasserman, 1993; Lober & Shanks, 2000), or
the proportion of confirmatory instances (White,
2004) because their computation is based on the
context in which they are observed. There is no
rule for transferring these measures to another
context. So after calculating one of these metrics,
participants are left with two or three separate
computed values and no rule for combining them.
Associative theories (e.g., Pearce, 1987;
Rescorla & Wagner, 1972) do provide a mechan-
ism for transferring causal effects to a different
context—namely, the transfer of associative
strength. At least for the RescorlaWagner
(1972) model there is a problem with this
because associative strength in the training
context very closely maps onto DP (Chapman &
Robbins, 1990; Wasserman, Elek, Chatlosh, &
Baker, 1993). A simple transfer to another
context thus would involve adding this constant
associative strength onto the associative strength
of the context. But we know that a binary cause
has different absolute effects at different base
rates. This problem can, however, in principle, be
dealt with by a response rule that requires greater
changes in associative strength at greater base
rates to generate a constant increase, similar to
the WeberFechner law in perception (e.g.,
Cornsweet & Pinsker, 1965).
Nonetheless, although the associative theories
can describe how power is transferred to other
contexts, they do not provide a mechanism for
choosing the contexts. However, in the animal
operant conditioning literature there is an interest-
ing empirical parallel to the continuing choices
of the nonoptimal contexts we have already dis-
cussed. There has been a long tradition in animal
learning to argue that animals will respond for,
or be “reinforced” by, stimulus change and/or for
information (cf. Berlyne, 1969). Choosing a low
base rate context is more informative and generates
a much greater change from the base rate, so
should generate more choices for a generative
cause. If it is assumed that the more informative
choice is more reinforcing and that less informa-
tive contexts are less reinforcing but still somewhat
reinforcing, then a possible empirical parallel to
our finding that participants continue choosing
the less informative context can be found in
operant conditioning. Herrnstein (1961) and
many others have studied animals’ concurrent
choices when they are given choices of schedules
with different reward frequencies, densities, or
magnitudes using the general framework of the
matching law. They generally find that animals
do not end up choosing the strongest alternative
on every choice, rather they distribute their
choices between the alternatives in a proportion
determined by the relative value of the two alterna-
tives. In the matching law we have described an
empirical and not theoretical parallel. While we
favour associative explanations of classical and
instrumental conditioning, it has been argued
that animal instrumental and classical condition-
ing is inferential in nature (Blaisdell, Sawa,
Leising, & Waldmann, 2006; Holyoak, Koh, &
Nisbett, 1989; Mitchell, De Houwer, &
Lovibond, 2009). Thus, it would seem that there
is at least a precedent for our findings, and our
considerations of them, in the theories and
empirical results of classical and operant con-
ditioning. In this context, the continued choice
of the less informative context does not seem so
mysterious.
In summary, the present study investigated the
important but never fully tested assumption in
causal discovery that participants will tend to
choose those contexts that are more informative
to help discover the strength and polarity of a
cause. As far as we know, there has been only
one previous attempt to test this prediction
(Wu & Cheng, 1999). However, they used prop-
ositional information instead of the more
naturalistic trial-by trial procedure used here. As
we pointed out in the introduction, presenting
participants with propositional information could
bypass important features of causal induction
that are used to process more ecologically valid
2428 THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2010, 63 (12)
BARBERIA ET AL.
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episodic information. Here, using a trial-by-trial
procedure, we found that participants tended to
choose the most informative contexts during
causal discovery. However, participants continued
to choose less or uninformative contexts quite fre-
quently during the entire experiment. There are
interesting parallels between these results and tra-
ditional work on instrumental conditioning. This
encourages the use of associative explanations of
some of these findings as a possible alternative to
inferential models.
Original manuscript received 29 July 2008
Accepted revision received 9 February 2010
First published online 1 June 2010
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APPENDIX
Instructions
“Two years ago, a group of scientific explorers brought back
several folk remedies from the Amazon. However, these folk
culture potions need to be tested. Imagine that you received
approval to test the effects of two (three) of these folk medicines
on patients who are at different levels of risk of having a stroke.
Each of these substances might increase, decrease, or have no
effect on the likelihood of stroke.
The patients on whom you can test the two (three) sub-
stances are divided into two (three) groups according to their
genetic type: X and Z (X, Y, and Z). Patients with different
genetic types might be more or less prone to having strokes.
Hence, when you evaluate the effect of the two (three) sub-
stances it is important that you take into consideration the
fact that patients with different genetic types might differ in
their likelihood of having a stroke before they are given a
substance.
The experiment will begin by showing you the records of 20
patients with Genetic Types X and Z (X, Y, and Z) who were
not given any medicine. For each record, you will be asked to
guess whether that patient had a stroke and then you’ll be
given feedback. These records will give you an idea of how
often patients with these genetic types have a stroke. After
you see the records of the patients with each genetic type, you
will be asked to estimate the proportion of patients with that
genetic type who would have a stroke.
Then, you will have the opportunity to test each substance.
On each trial, you will be given the option of testing the sub-
stance on a patient with one of the two (three) genetic types.
Following your choice, you will be asked to guess whether
that patient will have a stroke during the year that followed
the treatment and then you’ll be given feedback. Every 10
trials, you will be asked to evaluate the overall effectiveness of
the substance. Your estimates may change as you learn more
about the effect of the substance. Also, try to choose the most
informative genetic type to test the substance. There will be a
total of 60 trials and 6 estimates for each substance. After you
finished testing the first substance, you will observe 10 more
records of patients with Genetic Types X and Z (X, Y, and
Z) who were not given a medicine to remind you how often
the patients have a stroke. Then, you will test the second
(the second and third) substance (substances) using the same
procedure as for the first one.”
Note: the phrases in parentheses are changes for Experiment
2 in which there were three substances and three genetic types.
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... In fact, Wu and Cheng (1999) have shown that people tend to report that causal conclusions are not possible in these extreme situations with effect ceilings or floors. We carried out a series of experiments designed to test if people actively choose more informative and avoid less informative interventions when they are allowed to do so (Barberia, Baetu, Sansa, & Baker, 2010). We studied the way people would intervene in order to choose the most informative context to discover a potential causal relationship. ...
... Finally, there was a neutral medicine that did not influence the probability of the strokes (p = 0). This third substance acted as a control.Figure 2 shows the results of this experiment (Barberia et al., 2010, Experiment 2 -Group Deterministic). As can be observed inFigure 2, for the neutral control substance, there was a preference for the medium base rate context, BR = 0.5, maybe because only in this population the potential increase or decrease in the probability of the effect could be simultaneously observed. ...
... As can be observed inFigure 2, for the neutral control substance, there was a preference for the medium base rate context, BR = 0.5, maybe because only in this population the potential increase or decrease in the probability of the effect could be simultaneously observed. Most importantly, and as expected, participants showed a preference for the low base rate (BR = 0) population when testing a generative substance, and a preference for the high base rate (BR = 1) population when testing a preventive substance.Figure 2. Proportion of choices of the low, medium, and high base rate contexts for the Generative, Neutral, and Preventive target causes, respectively (data from Barberia et al., 2010 , Experiment 2 - Group Deterministic). ...
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