Do Smart People Have Better Intuitions?

Abstract

There is much evidence that high-capacity reasoners perform better on a variety of reasoning tasks (Stanovich, 1999), a phenomenon that is normally attributed to differences in either the efficacy or the probability of deliberate (Type II) engagement (Evans, 2007). In contrast, we hypothesized that intuitive (Type I) processes may differentiate high- and low-capacity reasoners. To test this hypothesis, reasoners were given a reasoning task modeled on the logic of the Stroop Task, in which they had to ignore one dimension of a problem when instructed to give an answer based on the other dimension (Handley, Newstead, & Trippas, 2011). Specifically, in Experiment 1, 112 reasoners were asked to give judgments consistent with beliefs or validity for 2 different types of deductive reasoning problems. In Experiment 2, 224 reasoners gave judgments consistent with beliefs (i.e., stereotypes) or statistics (i.e., base-rates) on a base rate task; half responded under a strict deadline. For all 3 problem types and regardless of the deadline, high-capacity reasoners performed better for logic/statistics than did belief judgments when the 2 conflicted, whereas the reverse was true for low-capacity reasoners. In other words, for high-capacity reasoners, statistical information interfered with their ability to make belief-based judgments, suggesting that, for them, probabilities may be more intuitive than stereotypes. Thus, at least part of the accuracy–capacity relationship observed in reasoning may be because of intuitive (Type I) processes.

Full text

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In press Journal of Experimental Psychology: General
Do Smart People Have Better Intuitions?
Valerie A Thompson,
University of Saskatchewan, Canada
Gordon Pennycook,
Yale University, USA
Dries Trippas,
Max Planck Institute for Human Development, Germany
Jonathan St. B. T. Evans,
University of Plymouth, UK
This work was funded by the Natural Sciences and Engineering Research Council of Canada.
We would like to thank Jamie Campbell, Wim De Neys, and an anonymous reviewer for
comments provided on an earlier draft. Correspondence to be addressed to: Valerie
Thompson, University of Saskatchewan, 9 Campus Drive, Saskatoon, SK. Canada:
valerie.thompson@usask.ca
Word count: 10,418

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Abstract
There is much evidence that high capacity reasoners perform better on a variety of reasoning
tasks (Stanovich, 1999), a phenomenon that is normally attributed to differences in either the
efficacy or the probability of deliberate (Type 2) engagement (Evans, 2007). In contrast, we
hypothesized that intuitive (Type 1) processes may differentiate high and low-capacity
reasoners. To test this hypothesis, reasoners were given a reasoning task modelled on the
logic of the Stroop Task, in which they had to ignore one dimension of a problem when
instructed to give an answer based on the other dimension (Handley, Trippas, & Newstead,
2011). Specifically, in Experiment 1, 112 reasoners were asked to give judgments consistent
with beliefs or validity for two different types of deductive reasoning problems. In
Experiment 2, 224 reasoners gave judgments consistent with beliefs (i.e., stereotypes) or
statistics (i.e., base-rates) on a base rate task; half responded under a strict deadline. For all
three problem types and regardless of the deadline, high-capacity reasoners performed better
for logic/statistics than belief judgments when the two conflicted, whereas the reverse was
true for low-capacity reasoners. In other words, for high-capacity reasoners, statistical
information interfered with their ability to make belief-based judgments; suggesting that, for
them, probabilities may be more intuitive than stereotypes. Thus, at least part of the
accuracy-capacity relationship observed in reasoning may be due to intuitive (Type 1)
processes.

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Dual process theories of reasoning assume that reasoning and decision making are
accomplished by two qualitatively different sets of processes (Evans & Stanovich, 2013).
Type 1 processes are autonomous, require little cognitive capacity and are generally executed
quicker than Type 2 processes. Type 2 processes, by contrast, require working memory and
tend to unfold more slowly. These models have traditionally been used to explain biases
arising from Type 1 intuitions which may or may not be corrected by subsequent Type 2
analysis. For example, prior beliefs may lead to erroneous judgements of the validity of
logical arguments; instructions to reason logically increases accuracy, but only amongst high-
capacity reasoners (Evans, Handley, Neilens, & Over, 2010). Indeed, the relationship
between cognitive capacity and reasoning performance is a critical pillar supporting dual
process frameworks. The purpose of the current paper is to provide a direct test of the basis
of this relationship.
Numerous studies have demonstrated that there is a robust relationship between
performance on many reasoning tasks and measures of cognitive capacity, such as IQ
(Stanovich, 1999; 2009). These tasks are novel from the perspective of most reasoners, such
that they cannot rely on past experience to solve them and must, instead, engage Type 2
thinking. Moreover, in cases where Type 1 processes produce an initial answer that is based
on beliefs or other heuristic processes, Type 2 processes are needed to overturn the initial
answer. Consequently, the capacity- reasoning relationship is thought to reflect the need for
cognitive capacity to overturn Type 1 outputs in favour of Type 2 reasoning: namely, to
inhibit the Type 1 answer, to create an alternative representation of the problem, and to
engage the requisite logical or numerical operations needed to produce the correct answer. In
addition to capacity, reasoners also require the motivation or disposition to implement the
override, so that measures of thinking dispositions also correlate with performance on many

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reasoning tasks (e.g., Stanovich and West, 1998; 2000; ; Toplak, Stanovich, & West, 2011).
Implicit in this explanation, and indeed, in the dual-process explanation for many
phenomena, is the temporal asymmetry of Type 1 and Type 2 processes: Autonomous (Type
1) processes are normally faster, so that they form a default response, which requires
intervention by slower, Type 2 processes.
Several challenges to this straightforward interpretation have recently arisen. For
example, on a variety of tasks, De Neys and colleagues have shown that reasoners are
sensitive to the conflict between validity/probability and beliefs, even when they give
responses based on belief (for reviews, see De Neys, 2012; 2014). The challenge is that
responses based on validity/ probability should not be generated quickly enough to interfere
with the presumably fast, autonomous, belief-based ones. More recently, Newman, Gibb,
and Thompson (2017) have demonstrated that reasoners are able to give responses consistent
with logical validity and probability on conditional inference and base rate tasks, even when
required to respond under a very challenging deadline (see also Bago & De Neys, 2017).
Again, this pattern would not be expected if belief-based judgments were faster and more
intuitive than those based on probability.
These findings challenge the pervasive assumption that belief-based responses
necessarily reflect Type 1 processing and logical/ probability-based responses reflect Type 2
responding. Indeed, more recent arguments emphasise that there is no linkage of this kind
that necessarily applies regardless of task and instructions (see Evans & Stanovich, 2013).
Nonetheless, because many of the dual process-based explanations for phenomena appeal to
speed of processing, data showing that both belief-based and validity-based reasoning can
happen quickly is a challenge. Regardless, a perhaps more direct challenge is posed by
methods that demonstrate that reasoners may generate responses based on validity or

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probability, even when those responses are goal-inconsistent (Morsanyi & Handley, 2012;
though see Klauer & Singmann, 2013 and Trippas, Handley, Verde, & Morsanyi, 2016, for a
debate).
To this end, Handley, Newstead, and Trippas (2011) developed a novel version of a
logical reasoning task, who underpinning logic is akin to that of the Stroop task (MacLeod,
1991). Reasoners were asked to solve simple logical reasoning problems with instructions to
respond on the basis of believability or validity. If belief-based processes form an initial,
default answer, then belief-based judgments should interfere with judgments based on
validity more than vice versa. The logic is similar to that underlying a Stroop task, namely
that the process of reading the word gives rise to a prepotent response that interferes with the
process of colour-naming to a greater extent than the reverse. Instead, Handley et al. observed
that in cases where the two responses conflicted (i.e., valid-unbelievable conclusions and
invalid-believable conclusions), the validity of the conclusion interfered with the ability to
make belief-based judgements at least as much as the reverse. This is an unexpected
phenomenon given the assumption that judgments of validity can be made only after a
default, belief-based response has been inhibited; by analogy, it would be surprising to find
that naming colours interfered with reading as much as reading interfered with colour
naming.
Handley et al.’s (2011) finding were replicated using a base-rate task, based on
Kahneman and Tversky’s (1973) lawyer and engineer problem (see Appendix B): The value
of the base rates interfered with making belief-based judgments, even under time pressure
(Pennycook, Trippas, Handley, & Thompson, 2014), which again challenges the assumption
that belief-based responses are more likely to form initial, Type 1 responses to problems. A
more nuanced view of these findings is that belief-based and validity-based responses exist

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on a continuum of complexity (Handley & Trippas, 2015), so that when logical judgments are
simple, as in the case of Handley et al. (2011), validity will interfere more with belief than
vice versa. However, as the relative difficulty of the logical inferences increases, this
relationship reverses, such that on the most difficult problems, beliefs interfere more with
judgments of validity than vice versa (Trippas, Thompson, & Handley, 2017). It is this latter
pattern (but not the former) that is predicted by past Dual Process Theories (Evans &
Stanovich, 2013).
These data have also led to the development of a number of alternative Dual Process
formulations, in which reasoning problems may elicit more than one Type 1 response (De
Neys, 2012, 2014; Handley & Trippas, 2015; Pennycook et al., 2015; Pennycook &
Thompson, 2012; Trippas & Handley, 2018). One of these outputs will form a default
response, either because it is more fluent than the other (Pennycook et al., 2015), or because
it requires less complex processing than the other (Handley & Trippas, 2015). As in
traditional Dual Process Theories, Type 2 processes may or may not be engaged to overturn
this initial response; however, the clear implication is that answers that were previously
attributed to Type 2 processes under the “received view” (Evans & Stanovich, 2013) may
have been generated, instead, by Type 1 processes.
In the current paper, we extend this reasoning to the capacity-reasoning relationship.
As described above, the relationship between IQ and reasoning is largely thought to rest on
the asymmetry between fast, autonomous Type 1 processes and slower, WM-dependent Type
2 processes. On this view, it is assumed that high IQ reasoners have the WM capacity to
override the default response and provide an alternative based on logic or probability (Evans
& Stanovich, 2013); an assumption justified by the high correlation between measures of IQ
and WM (e.g., Colom, Rebollo, Palacios, Juan-Espinosa, & Kyllonen, 2004; Kane,

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Hambrick, & Conway, 2005). That is, the relationship between IQ and reasoning is usually
attributed to Type 2 processes. High IQ people are assumed to either have greater capacity or
greater disposition to overcome a pre-potent Type 1 response (Evans, 2007). The goal of the
current paper is to provide a direct test of that hypothesis.
There is already preliminary data to challenge the role of Type 2 thinking in the IQ-
reasoning relationship (Thompson and Johnson, 2014). Reasoners were asked to give two
responses to each of four types of reasoning problems: a quick, intuitive one and a slower,
deliberative one (Thompson, Prowse Turner, & Pennycook, 2011). The correlation between
IQ and reasoning performance was observed on both the first and second response, which is
difficult to explain under the assumption that the accuracy-capacity relationship emerges only
when Type 2 processing is cued. Instead, high capacity reasoners can quickly give responses
based on logic or probability, suggesting that at least part of the accuracy-capacity
relationship may be due to Type 1 processing. This hypothesis is also consistent with
suggestions that numerate reasoners may have better numerical intuitions than less numerate
ones (Peters, 2012; Peters, Slovic, Västfjäll, & Mertz, 2008). The goal of the current
experiments was to test this hypothesis using a variant of the instructional manipulation
developed by Handley et al. (2011).
Participants solved three-term syllogisms (Experiment 1; see Appendix A) and base-
rate problems (Experiment 2; see Appendix B). For the syllogisms, participants were
instructed to respond on the basis of logic or beliefs (Handley et al., 2011) and for the base
rate problems, we used Pennycook et al.’s (2014) instructional manipulation to respond either
according to ‘statistics’ (prior probabilities or base-rates) ‘beliefs’ (knowledge of real-world
stereotypes). On congruent problems, responding on the basis of either beliefs or validity/
probability yielded the same response, as illustrated below; in contrast, on incongruent

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problems, responses based on probability/ validity conflicted with those based on belief (see
below). Participants also completed a set of measures designed to measure analytic thinking
disposition and cognitive capacity. In each experiment we built in a replication. For
Experiment 1, we included two different types of problems, and, in Experiment 2, we
included a deadline condition to minimize the influence of Type 2 processing (Evans &
Curtis-Holmes, 2005).
Congruent (Believable and valid):
All firters are vegetables.
Some carrots are firters.
Therefore, some vegetables are carrots.
Incongruent (Believable and invalid):
All cannons are pooblings.
No pooblings are weapons.
Therefore, some cannons are weapons.
The critical prediction is as follows: If responses based on logic and probability are
relatively more accessible for high-capacity reasoners (Thompson & Johnson, 2014), it
follows that we should observe different patterns of interference as a function of capacity:
high capacity reasoners should have relatively more difficulty resolving conflict in favour of
beliefs than probabilities/ validity, whereas low-capacity reasoners should have relatively
more difficulty resolving conflict in favour of probabilities/validity than beliefs. That is, if
judgements of probability/ validity are relatively more intuitive for high capacity reasoners,
then they should interfere with that group’s ability to make judgments based on belief and
they should perform more poorly on incongruent problems under belief than logic
instructions. In contrast, in cases where there is no conflict, reasoners should perform equally

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well under the two types of instructions. This would manifest as a three-way interaction
between capacity, instructions, and conflict.
Three additional hypotheses were also considered. First, the traditional dual-process
interpretation is that high-capacity reasoners will be better than low-capacity reasoners in
resolving conflict in favour of probability/validity. This hypothesis is based on the
assumption that judgments of belief form a default response, and that capacity is needed to
overturn that response to make one based on probability or validity. In contrast, both groups
should be able to resolve conflict in favour of beliefs, such that performance should be
comparable for high- and low-capacity reasoners, and the groups should do equally well on
congruent problems.
The second hypothesis is that reasoners with strong analytic thinking dispositions may
not experience a conflict between beliefs and logic at all (as suggested by Svedholm-
Häkkinen, 2015). Using a priming paradigm, Svedholm-Häkkinen (2015) found that
incongruent problems primed subsequent answers for low, but not high ability reasoners,
suggesting that the latter did not experience conflict. However, the evidence was
inconsistent, in that many of the critical interaction effects were not significant. Our
experiments provided a second opportunity to test this hypothesis, which predicts a two-way
interaction between capacity and congruence, such that low, but not high capacity reasoners
will perform more poorly for incongruent than congruent problems.
The third possibility is an instructional set hypothesis (Engle, Carullo, & Collins,
1991), in which cognitive capacity predicts the ability to maintain an instructional set and
would therefore correlate with performance regardless of instructions or conflict. That is,
high capacity reasoners would be expected to perform better than low capacity reasoners
regardless of how they were instructed to respond.

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Experiment 1: Logical Reasoning
Method
Participants. We recruited 112 University of Saskatchewan students (69% females,
mean age = 21.4 years), who received partial course credit or CAN$7. Our goal was to test
100 participants, but to maintain parity with Experiment 2, where multiples of 16 were
required to counterbalance the stimuli, we tested to the next highest multiple of 16, giving
112 participants. This number gave us good (.8) statistical power to detect moderate effects
(ηp2 = .07) for all main effects and interactions involving our two-level factors and good (.8)
power to detect a slightly larger interaction with ability (ηp2 = .09). All power calculations
were computed using the MorePower calculator (Campbell & Thompson, 2012).
1
We note that prior approval for the research was obtained from the University of
Saskatchewan Research Behavioural Research Ethics Board.
Materials and procedure.
Reasoning Problems. Each participant was presented with 64 syllogistic reasoning
problems of moderate complexity (for examples, see Appendix A; the complete problem set
is available in the supplementary materials). Half of the problems were three-term categorical
syllogisms (e.g., all A are B; all B are C; therefore, all A are C). All of these arguments,
could, in principle, be solved by constructing a single mental model (e.g., Johnson-Laird,
2001); the invalid arguments featured determinately invalid conclusions. The remaining
problems were disjunctive syllogisms. Within the set of disjunctive syllogisms half featured
an affirmation inference (e.g., either A or B but not both; A; therefore not B) and the other
half featured a denial inference (e.g., either A or B but not both; not A; therefore B).
1
Freely available at: https://wiki.usask.ca/pages/viewpageattachments.action?pageId=420413544

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We crossed logical validity with the believability of the arguments resulting in two
types of congruent problems (valid-believable and invalid-unbelievable) and two types of
incongruent problems (valid-unbelievable and invalid-believable). We randomly assigned
problem contents to argument structures for each participant independently to ensure that any
observed effects of logical validity could not be attributed to incidental confounds between
the logical structure and the believability of the argument (cf, Clark, 1973; Trippas, Handley,
& Verde, 2013; 2014; Trippas, Pennycook, Verde, & Handley, 2015). Examples of the
arguments for each cell of the design can be found in Appendix A.
Individual Differences (ID) measures. We used four widely used measures to assess
cognitive ability and analytic cognitive style: 1) The Shipley-2, a standardized intelligence
test that includes verbal and abstract reasoning components (Shipley, Christian, Martin, &
Klein, 2009); 2) A three item test of numeracy (Schwartz, Woloshin, Black, & Welch, 1997;
Lipkus, Samsa, & Rimer, 2001); 3) The Cognitive Reflection Test (CRT; Frederick, 2005), a
set of 3 word problems that cue intuitive but incorrect responses and that measures the
willingness to engage analytic reasoning to question a misleading intuition (e.g., Toplak,
West, & Stanovich, 2011), plus an additional 4 CRT items from Toplak, West, & Stanovich
(2014); and 4) A thinking disposition questionnaire that included the 41 items from the
actively open-minded thinking questionnaire (Stanovich & West, 2006).
Procedure. The participants were tested on individual computers in small groups.
Upon entering the laboratory each participant was briefed about the study and requested to
answer a short demographic questionnaire. The Shipley-2 was administered first, followed by
the logical reasoning problems, the AOT, Numeracy, and CRT in that order. The instructions
for the logical reasoning task were displayed on the computer screen and read:

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In this experiment, we are interested in your ability to make two types of judgments:
judgments on the basis of LOGIC, and judgments on the basis of BELIEFS
When the word "LOGIC" appears in red at the top of the screen, you should assume
all the information ABOVE the line is true (even if it's not, or if it doesn't appear to
make much sense).
After a short amount of time, a conclusion sentence BELOW the line will appear
which you will be asked about. If you judge that the conclusion necessarily follows
from the premises, you should answer "Valid" by pressing the "s"-key, otherwise you
should answer "Invalid" by pressing the "k"-key.
For example:
All cars are blurbs
All blurbs are cheap
All cars are cheap
Given the instruction to respond on the basis of LOGIC, you should respond "Valid",
because the sentence "All cars are cheap" necessarily follows from the premises
above the line (if you assume they are true).
When the word "BELIEF" appears in red at the top of the screen, you should focus on
whether the information is in line with your beliefs about what is true in the world. If
you think the information BELOW the line is in line with you knowledge of the world,
you should respond "Believable" by pressing the "s"-key. Otherwise, please respond
"Unbelievable" by pressing the "k"-key
For example:
All cars are blurbs
All blurbs are cheap
------------------------------------
All cars are cheap
Given the instruction to respond on the basis of BELIEF, you should respond
"Unbelievable", because you presumably know from your experience of the world that
the sentence "All cars are cheap" is false (consider, for instance, the cost of a Ferrari
or a Porsche).
After reading the instructions, each participant was presented with 64 syllogistic reasoning
problems. At the onset of a trial, the premises were presented. After three seconds, the
conclusion followed. On half the trials the participant was cued with the word “LOGIC” at
the top of the screen to signal that they had to respond according to the logical validity of the
syllogism. On the remaining half of the trials the word “BELIEF” appeared at the top of the

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screen, cueing the participant to produce a response on the basis of their knowledge of what
is true in the world. The stimuli were presented in a fully randomized order. Importantly, the
instructional manipulation was crossed with problem type and conflict to eliminate any
potential confounds. On each trial we measured whether the participant responded
affirmatively or negatively. After all trials were completed, the participants were thanked and
debriefed.
Results
Principal components analysis of individual difference measures and acceptance
rates. We adopted two strategies to test our hypotheses. Our first was a multivariate approach
in which we subjected our eight dependent variables and four predictor variables (all
normalized) to a principal component analysis. This served two functions. The first was as a
preliminary test of our hypotheses. As argued above, there is more than one way that
individuals could differ. For example, some may comply better with instructions on all tasks,
but others might do better on probabilistic judgments and worse on belief judgments and so
on. The PCA will enable us to see if there is more than one factor of individual differences, as
well as to interpret what each factor represents. Secondly, we were able to examine the
correlations amongst our predictor variables in order to determine whether we could simplify
the next set of analyses by replacing them with a composite variable.
Three components with eigenvalues greater than one were extracted, explaining 60%
of the variance; see Table 1. We first note that the categorical syllogisms and disjunctive
syllogisms loaded together on the same components, suggesting that the effect of congruency
and instructions were similar for the two problem types. In addition, the fact that all of our
individual differences measures load on the same factor indicates that producing a composite
score based on the four measures is a suitable option.

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A more detailed look at the component structure indicated that the component loading
for Components A and B are consistent with our hypothesis that high-capacity reasoners
would be relatively better at resolving conflict in favour of validity than beliefs: As is clear
in Table 1, Component A reflects high capacity and analytic thinking dispositions. It also
reflects good performance on three of the four problem types; the exception is for problems
that require conclusion validity to be inhibited in favour of belief (Incongruent-Belief), which
were strongly associated with Component B. Clearly, these problems capture something
unique about reasoning performance that is distinct from both the other types of problems and
from cognitive capacity.
Components B and C offer a view of less successful reasoning. Component B is
shows a low correlation with cognitive ability and thinking dispositions. This component
reflects poor performance under logic instructions, at least when conflict is involved and
good performance under belief instructions, again when conflict was involved. The pattern
for Component C is slightly more complex, showing modest, positive correlations with both
analytic thinking dispositions and capacity. Performance on the congruent problems, which
do not require conflict resolution, load negatively onto this component. In sum, the data
suggest that high capacity as well as a disposition to think analytically is conducive to
successful reasoning, except when belief-based responses must be inhibited in favour of
logical ones. There were two distinct patterns of less successful performance: one that
showed opposite patterns for resolving conflict under logic and belief instructions, and
another showing poor performance on congruent items.
Factorial analysis of response accuracy. The preceding analysis indicated that
computing a composite score for our individual differences measures would be justified. We
did this by normalizing each of the four measures and computing their mean. For ease of

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illustration, the composite ability score was divided into quartiles and the data were then
analysed with a 4 (Ability Group) X 2 (Problem Type) X 2 (Instruction Condition) x 2
(Congruency) mixed ANOVA. These data are plotted in Figure 1. To ensure that none of our
results were artifacts of the way that we chose to divide up the groups, the crucial tests were
repeated with the individual differences composite entered as a covariate in an ANCOVA.
As is clear from Figure 1, performance for the highest ability group is at ceiling,
which means that the data from this group could artifactually create or suppress interaction
effects. For this reason, the crucial interaction tests were repeated, using only the data from
the first three groups. As would be expected, performance increased with ability, F(3,108) =
17.94, p < .001, ηp2 = .33. The main effects of instruction, congruency, and problem type
were all significant, F(1,108) > 7.45, p < .007, ηp2 > .065 such that performance was better
under logic than belief instructions (.85 vs .80), for congruent than incongruent problems (.90
vs .74) and for disjunctive than categorical syllogisms (.84 vs .80). These main effects were
qualified by several higher-order interactions. We will proceed by decomposing the highest-
order interaction, which was the predicted three-way interaction between ability, instructions
and congruency, F(3,108) = 4.71, p = .027, ηp2 = .12. This interaction was significant when
the disjunctions and syllogisms were analysed separately, meaning that it replicated across
problem types, F(3,108) > 3.55, p < .017, ηp2 > .09, and when the highest ability group was
removed from the analyses, meaning that it was not an artifact of the ceiling effect in that
group, F(2,81) > 4.57, p < .013, ηp2 > .10. We also note that this interaction was reliable
when the ability composite was entered into an ANCOVA as a continuous covariate,
F(1,110) = 4.68, p = .033, ηp2 = .04 and when the highest ability group was removed from
that analysis, F(1,82) = 10.77, p = .002, ηp2 = .12.

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The form of the interaction is apparent in Figure 1 : it is clear that the pattern of
interference is quite different for the high and low ability groups. For the incongruent
problems, there were main effects of instruction, F(1,108) = 6.84, p = .010, ηp2 = .06 and
ability, F(3,108) = 15.46, p < .001, ηp2 = .30. More importantly, there was a cross-over
interaction between ability and instruction, F(3, 108) = 5.50, p = .001, ηp2 = .13, such that the
lowest ability group performed better under belief than logic instructions, whereas the reverse
was true for the higher ability groups.. As is also clear from the Figure, the increase in
performance as a function of ability was more marked for logic than belief instructions. For
the congruent problems, there was only a main effect of ability, such that performance
increased with ability, F(3,108) = 8.11, p < .001, ηp2 = .18. Finally, we note that performance
on incongruent problems was worse than congruent problems in each of the four ability
quartiles; smallest F(1,27) = 12.89, p = .001, ηp2 = .32.
Before we discuss the implications of these findings, there were two significant
interactions with problem type to report from the omnibus analysis: Problem type interacted
with both instruction and congruency, F(1,108) > 5.0, p < .028, ηp2 > .04. The effect of
congruency was larger for syllogisms than disjunctions (.19 vs .13), as was the effect of
instructions (.07 vs .03).
Discussion
These data provide a clear discrimination amongst the four hypotheses outlined
earlier. The data are consistent with the hypothesis that the relative accessibility of logical
intuitions varies as a function of ability (Thompson & Johnson, 2014). For higher-ability
reasoners, logical validity interfered with their ability to make judgments based on belief,
suggesting that the former was the dominant default response for this group. In contrast, for
the lower-ability group, we noted that conclusion believability interfered more with

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judgments of validity than the reverse, suggesting that belief judgments form the default
response for this group. By extension, the data support the conclusion that at least some of
the relationship between measures of capacity and reasoning performance can be accounted
for by differences in Type 1 processes.
Some of the findings are also consistent with a traditional dual process interpretation.
As predicted by that view, higher capacity reasoners were better at resolving conflict in
favour of logical validity than lower capacity reasoners. More difficult to explain is the fact
that, overall, reasoners were better at responding on the basis of validity than belief. Given
that belief-based responses should be available via autonomous Type 1 processes, all groups
should quickly have access to belief-based responses, and all groups should therefore have
fared well under belief-instructions, regardless of congruency. Instead, our data are
consistent with recent evidence showing that logical judgments can happen very quickly
(Newman, et al., 2017); that even on complex logical reasoning tasks, logical validity
interferes with belief-based judgments (Trippas, et al., 2017); and with recent proposals that
both logical and belief-based judgments can arise from Type 1 processes (De Neys, 2012;
Pennycook, Koehler, & Fugelsang, 2015; Pennycook & Thompson, 2012; Trippas et al.,
2016).
These data are not consistent with the hypothesis that high-capacity reasoners perform
better than low-capacity reasoners because they do not experience conflict (as suggested by
Svedholm-Häkkinen, 2015). Instead, performance in all groups was lower for incongruent
than congruent problems. Finally, there was evidence to suggest that high-capacity reasoners
performed better in all conditions, including the congruent problems, suggesting that part of
the capacity-reasoning relationship may arise because high capacity reasoners are better at
maintaining an instructional set (Engle, Carullo, & Collins, 1991).

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Experiment 2: Base Rates
The goal of Experiment 2 was to replicate Experiment 1 using a different task. Here,
reasoners solved base-rate problems with instructions to respond using statistics or beliefs.
As before, half of the problems were incongruent and half were congruent problems. Our
built-in replication was to add an additional group of participants who responded under a
deadline in order to minimize the role of Type 2 processes. Strictly speaking, the logic of the
Stroop task does not require a deadline to allow one to conclude that reading interferes with
colour-naming more than the reverse; however, given that our methodology is relatively new
to the psychology of reasoning, we thought it prudent to replicate our main finding under
conditions that maximize the probability that reasoners would rely on Type 1 processes. We
also gathered confidence measures as an additional means to measure the effect of conflict on
reasoning (De Neys, Cromheeke, & Osman, 2011; Shynkaruk & Thompson, 2006;
Thompson & Johnson, 2014; Thompson, Prowse-Turner, & Pennycook, 2011; Thompson et
al., 2013).
We note that prior approval for the research was obtained from the University of
Saskatchewan Behavioural Research Ethics Board.
Method
Participants. We recruited 224 University of Saskatchewan students (69% females),
who received partial course credit or CAN$7. Our goal was to test 100 participants per group,
but because multiples of 16 were required to counterbalance the stimuli, we tested to the next
highest multiple of 16, giving 112 participants per group. This number gave us good (.8)
statistical power to detect small (ηp2 = .035) for all main effects and interactions involving our
two-level factors and good (.8) power to detect a slightly larger three-way interaction with
ability (ηp2 = .05).

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19
Materials and procedure.
Base-rate problems. The materials and procedure were those used by Pennycook et al.
(2014). Participants were given 24 base-rate problems (12 incongruent, 12 congruent; see
Appendix B for examples), each providing the prior or base-rate probability of two categories
of people as well as a personality sketch that contained stereotypes typical of one of the
categories (the complete set of materials is available in the supplementary materials). These
items had been pretested to ensure that the description was a good fit to the intended
stereotype and was non-diagnostic of the complementary category (Pennycook et al., 2014).
The three elements of the problem were previewed to the participants prior to the
presentation of the instruction to respond according to beliefs or statistics (see Figure 2). The
goal was to familiarize participants with the information but minimize the amount of time
they had to integrate it: Participants saw a fixation cross, followed by the presentation of the
sample information (e.g., In a study 1000 people were tested. Jack is a randomly chosen
participant of this study) for four seconds. This was followed by the description of the
stereotype for seven seconds, and the base rate information for four seconds. The order of
these latter two pieces of information was randomized across trials. The entire problem then
appeared on the screen until the participant entered a response. Participants were cued to
respond on the basis of belief half the time and on the basis of statistics half the time via a
“BELIEF” or “STATISTICS” prompt that appeared at the bottom of the screen; instructions
were counterbalanced across all other factors. In the deadline condition, the screen turned red
after five seconds indicating that an immediate response was required. Prior work showed
that this deadline was challenging, but not impossible for participants to meet (Pennycook et
al., 2014). We also asked for a rating of confidence on a seven-point Likert scale on each trial
(after participants gave their response), with “1” marked as “not at all confident” and 7

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20
marked as “extremely confident”.
Three base-rate probability ratios were presented equally often; 995/5, 996/4, 997/3.
Participants were asked to estimate the probability that the person described belonged to one
of the categories. Each description was presented to each participant in one of four equally
occurring combinations, defined by whether the description and the base-rate were congruent
(i.e., indicated the same response), and whether the smaller or larger of the categories was
queried (see Appendix B). Problem order was randomized for each participant.
Participants were instructed to indicate the likelihood that a randomly chosen
participant belonged to one of the two groups. They were instructed that answering
according to their beliefs meant answering according to their knowledge of what is true in the
world. They were given an example concerning a person who is on the street and dressed in
ragged clothing, asking for money. Answering on the basis of beliefs would mean that it is
probable that the person is homeless. In contrast, they were told that when answering
according to statistics, their prior beliefs about the world weren’t necessarily relevant and to
concentrate on the actual probability that something will happen. In the case of the street-
person, they were told that because only a small percentage of people in a city are homeless,
they would give a low probability to the person being homeless.
Individual difference measures. The numeracy, IQ, and thinking disposition measures
were the same as in Experiment 1. For the CRT, the original three items were used, rather
than the extended test used in Experiment 1. The tasks were administered in the same order
as in Experiment 1.
Results
Scoring. Responses that did not meet the deadline were coded as missing (27.1% of
responses in the speeded condition); consequently, 15 participants were excluded who did not

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21
have observations in each of the congruency by instruction cells. We note that the fact that so
many responses occurred outside the deadline means that it was challenging to meet and
supports our goal to minimize the role of Type 2 processes in this condition. Three
participants did not complete all of the individual differences measures. This still left us with
good (.8) power to detect small effects (ηp2 = .038) involving our 2-level factors.
When the category asked about was the smaller one (cells 2 and 4 in Appendix B),
responses were subtracted from 100 so that high estimates always indicated compliance with
the instructions (see Pennycook et al., 2014). For example, in cell 4 of Appendix B, the
correct response under both belief and statistics instructions would be a low probability; to
make it comparable to responses in cell 1, the former were subtracted from 100. Overall,
probability estimates were high (M = 73), indicating that, in general, participants were able to
respond according to the instructions.
Principal components analysis of individual difference measures and probability
estimates. As in Experiment 1, we adopted two strategies to test our hypotheses. Our first
was a multivariate approach in which we subjected our four dependent variables and four
predictor variables to a principal component analysis (PCA). As was the case in Experiment
1, three components with eigenvalues greater than one were extracted, which were very
similar in nature to those we observed in Experiment 1 (See Table 2). Once again, the fact
that all of our individual differences measures load on the same factor indicates that
producing a composite score based on the four measures is a suitable option.
As in Experiment 1, the component loading for Component A reflects high capacity
and analytic thinking dispositions. It also reflects good performance on three of the four
problem types; the exception is for problems that require statistical information to be
inhibited in favour of belief (Incongruent-Belief), which shows null or negative loadings onto

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22
this component. Instead, performance under the incongruent-belief instructions was strongly
associated with Component B, which reflects relatively low to moderate capacity/ thinking
dispositions. These data replicate the findings from Experiment 1, and show that probelms
requiring reasoners to resolve conflict in favour of beliefs appear to tap processes that are
distinct from both cognitive ability and the other problem types.
Components B and C offer a view of less successful reasoning that shows some
similaries to that observed in Experiment 1. Component B shows low to modest correlations
with cognitive ability and thinking dispositions. This component is negatively correlated with
reasoning under statistics instructions and positively correlated with reasoning under belief
instructions, particularly for the incongruent problems. This component might be labelled
“base-rate averse”, as it seems to reflect a particular difficulty in reasoning under statistics
instructions. Finally, Component C shows a similar pattern to Experiment 1, with opposite
loadings for cognitive ability and performance on congruent problems. This factor suggests
that motivation and ability are not required for success on problems that do not require
conflict resolution, as would be expected if low ability participants do not attempt to reason
statistically and rely on belief-based intuitions throughout. In sum, the data suggest that high
capacity as well as a disposition to analytic thinking is conducive to successful reasoning,
except when inhibition of statistical information is required. There were two distinct patterns
of less successful performance: one reflects an inability to follow instructions to use the base
rates, and another that reflects an inability to deal with conflict.
Factorial analysis of probability estimates. For our second set of analyses, we
computed a composite score from the four individual differences measures (which was
justified by the previous analysis, showing that all four loaded onto the same principal
component). For this, each of the four measures was normalized separately for each deadline

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23
condition. As before, we divided the participants in each condition into quartiles, and as
before, we repeated the critical tests with the individual differences composite entered as a
continuous covariate in an ANCOVA. Our first analysis in this series was 2 (Instructions) x
2 (Congruency) x 2 (Deadline Condition) x 4 (Ability Group) mixed ANOVA of the
probability estimates. The data are plotted in Figure 3. None of the higher-order interactions
with the deadline factor were reliable, largest F = 1.46, p = .24 [recall that there was adequate
(.8) power to detect small effects (ηp2 > .038) involving this variable]. The main effects of
congruency and deadline condition were significant, F(1,201) > 8.00, p < .005, ηp2 > .04, with
higher accuracy in the congruent (M = 83) than incongruent (M = 64) conditions and higher
accuracy for the standard (M = 75) than speeded (M = 71) conditions. The main effect of
ability group was also reliable, F(3,201) = 10.12, p < .001, ηp2 = .13, meaning that accuracy
was higher overall for those with high ability and analytic thinking dispositions.
The instructions variable interacted with ability group, F(3,201) = 5.30, p = .002, ηp2
= .07; most critically, however, the predicted three-way interaction between congruency,
instructions, and cognitive capacity was significant, F(3,201) = 8.18, p < .001, ηp2 = .11. This
interaction was reliable when the composite cognitive ability measure was entered as a
continuous covariate, F(1,206) = 7.86, p = .006, ηp2 = .04. The fact that the deadline variable
did not interact with any of the other variables indicates that the patterns were similar in both
the speeded and standard conditions; however, because it was critical to demonstrate that the
effect held under time pressure, we computed the interaction for the speeded and unspeeded
conditions separately; speeded: F(3,93) = 3.23, p = .026, ηp2 = .09, unspeeded: F(3,108) =
5.33, p = .002, ηp2 = .13.
2
2
We also ran the preceding analyses including those observations that did not meet the deadline in the Deadline
condition. The three-way interaction was observed in first two analyses (p < .001), and it was marginally
significant when the deadline condition was analysed separately (p = .059).

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24
The data plotted in Figure 3 reinforced the conclusions drawn both from the PCA as
well as from the data in Experiment 1 in favour of our hypothesis that for high capacity
reasoners, responses based on probability are relatively more accessible than those based on
beliefs. Statistical analysis verified the visual pattern, and replicated the pattern reported in
Experiment 1. An additional 2 (Instructions) x 2 (Deadline Condition) x 4 (Ability Group)
ANOVA revealed that for Incongruent problems, there was a cross-over interaction between
ability and instructions, F(3,205) = 7.41, p < .001, ηp2 = .10. For the lowest ability group,
performance was better under belief than ability instructions, whereas the reverse was true for
the high ability group. The fact that statistical information was available quickly enough to
interfere with belief-based judgements for our high-capacity group suggests that for these
reasoners, statistical responses may be more intuitive than belief-based ones, whereas the
opposite pattern held for the lower-capacity reasoners.
A similar ANOVA for the congruent problems indicated that neither the effect of
instructions nor the interaction was reliable, p > .12. Once again, none of the interactions
with the deadline condition were significant in either this or the previous analysis, largest
F(3,205) = 1.39, p > .25, ηp2 < .02, suggesting that the effects replicated even under
conditions meant to minimize Type 2 processes. As was the case in Experiment 1, the main
effect of ability was reliable for both congruent and incongruent problems F(3,205) > 4.48, p
< .004, ηp2 > .06. Finally, when data from the top and bottom quartiles was analysed
separately, we note that the effect of congruency was reliable in both cases, F(1, 50) > 51.24,
p < .001, ηp2 > .51, meaning that both high- and low-ability reasoners experienced conflict.
Confirmatory analysis of confidence measures. As is clear from the Figure 4, the
effects of our variables are less dramatic for confidence than for probability estimates. As
such, the critical three-way interaction between congruency, instructions, and ability was

Capacity and Conflict
25
marginally reliable when we used the grouping variable, F(3, 201) = 2.12, p = .10, ηp2 = .03,
but it was reliable when our ability composite was entered as a continuous covariate, with a
small effect size, F(1, 206) = 7.85, p = .006, ηp2 = .04. The pattern nonetheless maps onto the
pattern observed with the probability estimates. For the incongruent problems, there is a
cross-over interaction whereby lower ability participants are more confident under belief than
statistics instructions, but this difference is reversed for the higher ability group, F(3, 205) =
3.95, p = .009, ηp2 = .06. Again, this pattern is consistent with the hypothesis that for high
ability people, responses based on probability interfere with responses based on belief,
lowering confidence in belief-based responses. For the congruent problem, the interaction
was not reliable, F(1, 205) = 1.91, p = .13, ηp2 = .03, but the main effect of instructions was
reliable, F(1, 205) = 5.53, p = .02, ηp2 = .03, such that reasoners were more confident under
statistics (M = 5.72) than belief instructions (M = 5.59).
Discussion
Reasoners with strong cognitive capacity and who have an analytic thinking
disposition were better than their low capacity counterparts at resolving conflict in favour of
probabilistic information. These data support the claim that capacity and analytic cognitive
style are necessary to inhibit a prepotent belief in favour of one based on probability
(Stanovich, 1999; 2009). However, as was the case in Experiment 1, the data do not support a
straightforward Dual-Process interpretation: High capacity reasoners were relatively poorer
and less confident at resolving conflict in favour of beliefs than statistics. This finding
supports the hypothesis that for high-capacity reasoners, responses based on probability are
the default, and cause interference when they are asked to make belief-based judgments. It
also converges with other findings showing that capacity differences in reasoning may
emerge at an early stage in processing (Peters, 2012; Peters, Slovic, Västfjäll, & Mertz, 2008;

Capacity and Conflict
26
Thompson & Johnson, 2014). In sum, the data suggest that at least part of the relationship
between capacity and reasoning arises early in processing, and may be due to difference in
the nature of Type 1 outputs between higher- and lower- capacity reasoners.
Our principal component analysis suggested that failures to succeed on the task are
not unidimensional: It appears that one pattern is to perform well only on problems where
there is no conflict at all and the other is to experience difficulty following the instructions to
respond on the basis of statistics, even when there is no conflict. These patterns of
performance were associated with low to moderate capacity and analytic cognitive style and,
as above, suggest that a more nuanced approach to understanding unsuccessful, as well as
successful performance in reasoning is warranted.
An alternative interpretation of our findings might be that our instructions to reason
solely on the basis of the base rates or statistics was confusing, given that the appropriate
(Bayesian) response to the task should be to combine these sources of information. We
concur that the normative approach to these problems would be to weight the statistical
information in light of one’s degree of belief in the description. In contrast, however, the
evidence is clear that this is not how participants approach the task. For example, Pennycook
and Thompson (2012) observed that, in the absence of instructions to reason according to
beliefs or statistics, participants produce a markedly bi-modal distribution of responses to
conflict problems, with a large proportion of responses consistent with either the base rate or
the description, and very few intermediate responses. This indicates that some people can be
biased by the base rate – or, in other words, they display what might be called “stereotype
neglect” and that the phenomenon known as “base-rate neglect” is produced by averaging
over two distinct strategies. That is, rather than attempting to combine information,
participants appear to choose which of the two responses is most credible (in cases of

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27
conflict; see Pennycook & Thompson, 2012).
Finally, we note that the effect of the deadline was to lower correct responses overall
and that the deadline did not interact with any other variable or with cognitive ability. Of
course, one must exercise caution when interpreting null findings. Nonetheless, given that we
had a reasonably powered study, we can infer that the interaction effects with the deadline
are, at best, small in size. There are several conclusions that might be drawn on this basis.
First, it tells us that most (if not all) of the interference that we observed occurs due to Type 1
processing, given that it occurred under conditions designed to minimize Type 2 processing.
This finding is consistent with recent hybrid Dual-Process models (e.g., De Neys, 2012;
2014; Pennycook, et al., 2015; Handley & Trippas, 2015) that posit multiple, parallel Type 1
processes that may conflict prior to intervention by Type 2 processes. Here, however, the
crucial finding is that the ‘logical intuition’ is the default for high cognitive ability
individuals. Thus, not only are logical responses often intuitive, but for some people they are
more intuitive (they arise earlier in the reasoning process) than stereotype or belief-based
responding (canonical cases of intuitive processing). Note that the fact that high-capacity
reasoners tend to have a dominant logical/ probabilistic intuition does not imply that, for
them, belief-based responding requires Type 2 processing. Instead, the reason that the
deadline does not affect interference is likely because the competition between responses
comes before Type 2 processes are engaged (see Pennycook, Fugelsang, & Koehler, 2015 for
an extended version of this argument).
Finally, we note that our findings may have implications for interpreting reasoning
performance under dual task conditions
3
. Specifically, our data suggest that high capacity
reasoners should continue to perform well under load because they can rely on their logical or
3
We thank Wim De Neys for this observation

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28
probabilistic intuitions. Instead, moderate and low-capacity reasoners should be especially
disadvantaged by the load, because they are more likely to have to rely on WM capacity to
overturn a belief-based response in order to derive a logical or probabilistic response.
Although De Neys (2006) did not observe such differential effects, the trend was in the
posited direction, suggestion that this might be a worthwhile avenue for further exploration.
General Discussion
In two large experiments, with three different types of problems and two different
speed conditions, we have found a consistent pattern of differences between high- and low-
capacity reasoners. Our tasks were akin to the Stroop task; answers based on validity/
probability conflicted with answers based on belief, accompanied by an instructional set to
ignore one dimension and to respond based on the other. High-ability reasoners repeatedly
demonstrated more difficulty in resolving such conflicts in favour of beliefs than validity/
probability, meaning that, for them, answers based on validity/ probability produced more
interference than answers based on belief. This interference occurred despite clear
instructions to focus only on one dimension, and under conditions designed to minimize Type
2 engagement. This means that the interference likely occurred between two Type 1 outputs,
and that, for the high-capacity group, answers based on probability/ logic are likely the
default, Type 1 response. In contrast, the reverse was true for low-capacity reasoners, who
consistently behaved as expected by traditional Dual-Process Theories: belief-based
judgments interfered with judgments based on validity/ probability, consistent with the
assumption that belief-based judgments form a default, Type 1 response for this group.
Two other findings were consistent across our studies. Both high and low capacity
reasoners did better on congruent than incongruent problems, which means that the observed
superiority of high capacity reasoners is not due to the fact that they do not experience

Capacity and Conflict
29
conflict, as suggested by Svedholm-Häkkinen (2015). Second, we observed that high
capacity reasoners performed better than lower capacity reasoners, even on congruent
problems, which would not be expected if the sole role of capacity on these tasks was to
resolve conflict. Instead, it suggests that high capacity reasoners may be better at maintaining
an instructional set, meaning that they do well regardless of the task (Engle, Carullo, &
Collins, 1991).
Fundamentally, our data are challenging for the traditional Dual-Process explanation
for the relationship between capacity and reasoning, which is a cornerstone of support for that
view. A standard default-interventionist view of the relationship between capacity and
accuracy is that high-capacity reasoners have the wherewithal to inhibit a pre-potent, Type 1
response, create an alternative model of the problem, and perform the necessary computations
to reach the correct answer (e.g., Stanovich, 1999; 2009). In other words, the relationship
between capacity and reasoning is explained by Type 2 processes. Instead, our data supports
Thompson and Johnson’s (2014) contention that differences in capacity may arise, at least in
part, from Type 1 processes. Thus, one reason that high-capacity reasoners give answers
based on probability or logic may be that, for them, those are the first answers that come to
mind. As such, at least some of the relationship between cognitive capacity and accuracy
arises because high-capacity reasoners intuitively process numerical information and logical
relationships, which a) allows them to quickly resolve conflict in favour of probabilities and
validity, and b) means that they are relatively less efficient at resolving conflict in favour of
beliefs. These findings challenge the common interpretation of the role of cognitive capacity
in reasoning, which has focussed on the role of Type 2 processes to explain why high-
capacity reasoners are more successful on reasoning tests. Instead, it appears that some of that
relationship can be explained by Type 1 processes.

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We say “some” because, of course, our findings do not rule out a role for Type 2
processes in reasoning (as per Evans & Ball, 2010), nor in explaining the capacity-
performance relationship. For example, given that cognitive capacity likely plays a role in
the development of logical and probabilistic reasoning during adolescence, reasoning
according to logic and statistics may become natural and intuitive for higher capacity
individuals though extended practice (Stanovich, West, & Toplak, 2011). In addition, it is
perfectly plausible that cognitive capacity is needed to overturn a belief-based answer in
favour of logic/ probability, in the manner suggested by the traditional Dual-Process account.
That is, those high-capacity reasoners who initially generated a belief-based response , as
well as medium capacity reasoners, may have the wherewithal to overturn the initial response
in favour of logic/ probability.
In other words, it is possible that cognitive capacity plays a role in the improvement
that people show over time. In studies using a two response paradigm, where the first
response is given under pressure and the second under free time, accuracy normally increases
between the first and second responses (Bago & De Neys, 2017; Newman et al., 2017;
Shynkaruk & Thompson, 2006; Thompson et al., 2011). A reasonable hypothesis is that this
increase may be a function of cognitive capacity, that is, higher-capacity reasoners may be
able to overturn an initial, belief-based response in order to derive a response based on logic
or probability.
Our findings demonstrate that the relative impact of rule-based and belief-based
information on judgment varies as a function of cognitive capacity: Belief based-information
interferes relatively more for high-than low-capacity reasoners, whereas the reverse is true for
high-capacity reasoners. The term “relatively” in this context is important, because high-
capacity reasoners performed better overall, even on problems that did not require them to

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31
resolve conflict. However, one might have expected high ability people to do poorly under
belief-instructions, especially under time pressure, given the high degree of interference they
experienced from the statistical/ logical information contained in the problems. Instead,
performance on belief-based conflict problems was relatively constant across the ability
spectrum. A parsimonious explanation for this pattern is one that is broadly consistent with
dual-process explanations: the ability to access belief-based representations is relatively low-
cost, with little variability across individuals. Access to computations based on logical
structure or probabilities is more common to individuals with high capacity, either because
they have previously practised such computations to the point of automaticity, or because
they are able to do the computations quickly and efficiently on line.
Two other observations are important in helping us to understand the role that
cognitive capacity plays in reasoning. First, we note that the effect of the deadline in
Experiment 2 was constant across conditions. That is, performance was about 5% lower in
the deadline condition, but not selectively lower for the conflict problems. For this reason, it
appears that detecting and resolving conflict on these problems does not necessarily require
capacity, in that the conflict problems were not especially affected by the deadline. Instead,
the deadline must have affected some other aspect of reasoning performance. One possibility
is that it might have affected reasoner’s ability to comply with the instructions for all
problems. Consistent with this view, we note that in both Experiments, high capacity
reasoners performed better even on congruent problems, where there is no conflict to resolve.
Thus, it is possible that one effect of capacity is an enhanced ability (or motivation) to attend
to and carry out the task instructions.
One possible concern with our findings is that we used relatively simple reasoning
tasks. For example, the statistical information that was available in Experiment 2 was highly

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32
salient (e.g., 997 out of 1000), making it possible to be evaluated by Type 1 processes
(Pennycook, Fugelsang, & Koehler, 2012). One might also argue that the reasoning tasks in
Experiment 1 were of only moderate complexity, in that the overall rate of performance was
high (.82) and the high-capacity group performed at ceiling. We note, however, that in both
experiments, the low capacity group was at floor in one condition (incongruent,
statistics/logic-instructions), so that the tasks were not trivially easy. Nonetheless, there are
likely to be clear boundary conditions for our findings. Other types of numerical and logical
relationships will be more difficult to compute, making them poor candidates for Type 1
processes. Consequently, on more difficult reasoning tasks (e.g., three series multiple-model
syllogisms) or in situations where reasoners need to compare ratios (rather than estimate
magnitude), we would not necessarily expect even high-capacity reasoners to be able to
produce Type 1 answers based on logic or probability. In those cases, we would expect much
of the relationship between capacity and performance to derive from Type 2 processes.
Another possible interpretation of our findings is that they dilute the clarity of Dual-
Process explanations for many reasoning phenomena, allowing for Type 2 responses to be
delivered by Type 1 processes. However, this argument would be a typical example of the
“normative fallacy” that equates correct answers with Type 2 reasoning and “biased” answers
with Type 1 reasoning (Elqayam & Evans, 2011). Instead, ours and other’s data (e.g.,
Handley et al., 2011; Pennycook et al., 2014) show that this straight-forward mapping is
experimentally, as well as theoretically untenable. We do, however, agree that these data
demand a task-by-task analysis of how Type 1 and Type 2 processes may contribute to
performance (see Handley & Trippas, 2015; Thompson & Newman, 2018). In addition, our
data speak to the need for a more nuanced accounts of when individual differences are
consequential in the reasoning process (De Neys & Bonnefon, 2013), which naturally require

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33
more nuanced models of the time course of Type 1 and Type 2 processes (Pennycook,
Fugelsang, & Koehler, 2015).
It is, however, clear that our data, along with others (De Neys, 2012, 2014; Handley &
Trippas, 2015; Newman et al., 2017) are challenging for a straight-forward interpretation of
Dual-Process Theory. In fact, one might wonder at what point to draw the line and to reject
the basic Dual-Process assumptions that reasoning is best characterized by a distinction
between autonomous and WM-intensive processes. As an example of an alternative
explanation that does not depend on the autonomy-WM distinction, it is possible that the
interactions that we observed in the current experiments were between memory-based and
rule-based processes
4
: memory-based processes give rise to belief-based judgments, whereas
rule-based processes give rise to judgements of probability and logic. For low-ability
participants, memory retrieval may be relatively easier than rule-based processes, and vice
versa for high-ability participants. Although this explanation is compelling, we do not see an
a-priori reason to predict that belief-based judgments should be relatively more difficult than
logic judgments for high-ability participants. Moreover, we are uneasy about the implied
mapping of the Type 1/ Type 2 distinction onto memory vs rules, particularly given the
evidence that both rule and memory-based processes can be fast and slow (Newman et al.,
2017). Rule-based processes may arise from automated, compacted procedures, or may be
implemented sequentially, requiring WM capacity (Kruglanski & Gigerenzer, 2011).
Similarly, we can make retrievals from memory autonomously, in response to a stimulus, or
make a deliberate search of memory for information relevant to the current context.
Another interpretation might be that performance generally increases with ability, but
that performance under logic/ probability instructions increases more than performance under
4
We thank an anonymous reviewer for this suggestion

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34
belief-instructions. Whilst this explanation is consistent with the pattern observed in the
incongruent condition of Experiment 1, it does not hold overall. We note, for example, that
performance on incongruent, belief-instructions did not increase as a function of ability in
Experiment 2. Moreover, this explanation would predict an over-additive two-way
interaction between capacity and instructions, in which the effect of capacity is positive for
both belief and logic instructions, but stronger for the latter. Instead, we reliably observed a
three-way interaction, in which the effect of capacity on performance for congruent items was
similar under belief- and logic-instructions.
In sum, although the data challenge a strict, default interventionist interpretation of
Dual Process Theories (Evans & Stanovich, 2013; Stanovich, 2009), our data fit nicely with
current, parallel process models in which problems cue multiple type 1 outputs (e.g., De
Neys, 2012, 2014; Handley & Trippas, 2015; Pennycook et al., 2015). Moreover, the fact
that predictions for the current study were grounded in those theories a-priori attests to the
continuing utility of the Dual Process Framework as a generator of research questions. In
addition, as we have argued above, our data do not, in any way, rule out WM capacity as a
basis for the reasoning-capacity relationship; instead, we have demonstrated that at least part
of that relationship is likely attributable to Type 1 processes. As we have described above,
there is still research to be done to ascertain whether the distinction between autonomous and
WM based processes remains a viable basis for making experimental predictions (Thompson
& Newman, 2018).
Conclusions. In two experiments, in four different conditions, we have demonstrated
that when responses based on beliefs and logic/probability conflict, high- and low-capacity
reasoners demonstrate different patterns of interference. High-capacity reasoners show more
interference when making belief- rather than logic-based responses, suggesting that responses

Capacity and Conflict
35
based on logic/probability are the default response for this group. Low-capacity reasoners,
instead, show the pattern anticipated by the received view of Dual Process Theories, wherein
belief-based responses interfered more with logic-based judgments than vice versa. These
data challenge the Dual Process explanation of the reasoning-capacity relationship, and
suggest that it may be in part due to Type 1, rather than Type 2 processes. We also noted that
there are likely to be limits to the ability of even high-capacity reasoners for “intuitive logic”,
and that there is much work to be done to identify the boundary conditions for this effect and
to investigate the relative contributions of Type 1 and Type 2 processes in reasoning.
Context. Dual processes theories, which postulate the combination of slow, reflective
thought with faster, intuitive thinking have been influential in many areas of
psychology. However, dual process theories of reasoning have recently been challenged on a
variety of fronts. These challenges appear to undermine the commonly accepted explanation
for most reasoning biases, namely that fast, heuristic processes deliver default answers that
may not be overturned deliberate, reflective processes (e.g., Kahneman, 2011). Some of
these data come from our own laboratories, challenging us to rethink the basic assumptions of
the framework. In that context, we decided to re-examine the relationship between cognitive
capacity and reasoning biases, which is one of the evidentiary foundations of dual process
theories of reasoning. It is widely believed that higher capacity people resist cognitive biases
due to superior reasoning ability, but recent findings of our own suggest that it may instead
reflect better logical intuitions (Thompson& Johnson, 2014). On that basis, we made the
counter-intuitive prediction that high-capacity reasoners would experience relative difficulty
overcoming answers based on logic and probabilities in order to make what should be the

Capacity and Conflict
36
easier judgment of belief, and that is exactly what we observed in four separate experimental
conditions.

Capacity and Conflict
37
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Table 1
Component loadings for the principal components analysis of the syllogisms and disjunctive
problems.
Component A
Component B
Component C
Shipley (IQ)
.707
-.092
.138
Numeracy
.472
-.104
.288
Cognitive Reflection Test
.589
-.021
.442
Actively Openminded Thinking
.481
.078
.300
Percent Correct
Congruent
Logic
Syllogisms
.691
.073
-.381
Disjunctions
.648
-.134
-.286
Beliefs
Syllogisms
.592
-.044
-.416
Disjunctions
.603
.021
-.552
Incongruent
Logic
Syllogisms
.712
-.262
.246
Disjunctions
.752
-.347
.209
Beliefs
Syllogisms
.362
.860
.051
Disjunctions
.321
.860
.122

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Table 2
Component loadings for the principal components analysis of the baserate responses.
Component A
Component B
Component C
Shipley (IQ)
.707
.329
-.221
Numeracy
.528
-.056
-.116
Cognitive Reflection Test
.652
.220
-.007
Actively Openminded Thinking
.629
.074
-.572
Probability Estimates
Congruent
Statistics
.414
-.253
.621
Beliefs
.392
.347
.585
Incongruent
Statistics
.658
-.455
.118
Beliefs
-.154
.814
.184

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Figure Captions
Figure 1. Experiment 1: Proportion correct on the syllogisms and disjunction
problems as a function of congruence, instruction type, and cognitive ability.
Error bars are standard errors.
Figure 2. Sequence of events for a single trial in Experiment 2
Figure 3. Experiment 2: Mean probability estimates for the base rate task as a
function of congruence, instruction type, deadline condition, and cognitive
ability. Error bars are standard errors.
Figure 4. Experiment 2: Confidence judgments for the base rate task as a
function of congruence, instruction type, and cognitive ability. Error bars are
standard errors.

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Figure 2: Sequence of trial event for Experiment 2

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Appendix A. Examples of problems in each congruency by logic condition for Experiment 1
Logically valid
Logically invalid
[CONGRUENT: valid-believable]
Categorical syllogism:
All salmons are bunges
No bunges are fruits
Therefore, no salmons are fruits
Disjunctive syllogism (affirmation):
Either beers are boats or they are drinks
Beers are drinks
Therefore, beers are not boats
Disjunctive syllogism (denial):
Either beers are boats or they are drinks
Beers are not boats
Therefore, beers are drinks
Correct according to logic: accept
Correct according to belief: accept
[INCONGRUENT: invalid-believable]
Categorical syllogism:
All salmons are bunges
No bunges are fish
Therefore, some salmons are fish
Disjunctive syllogism (affirmation):
Either beers are boats or they are drinks
Beers are boats
Therefore, beers are drinks
Disjunctive syllogism (denial):
Either beers are boats or they are drinks
Beers are not drinks
Therefore, beers are not boats
Correct according to logic: reject
Correct according to belief: accept
[INCONGRUENT: valid-unbelievable]
Categorical syllogism:
All salmons are bunges
No bunges are fish
Therefore, no salmons are fish
Disjunctive syllogism (affirmation):
Either beers are boats or they are drinks
Beers are boats
Therefore, beers are not drinks
Disjunctive syllogism (denial):
Either beers are boats or they are drinks
Beers are not drinks
Therefore, beers are boats
Correct according to logic: accept
Correct according to belief: reject
[CONGRUENT: invalid-unbelievable]
Categorical syllogism:
All salmons are bunges
No bunges are fruits
Therefore, some salmons are fruits
Disjunctive syllogism (affirmation):
Either beers are boats or they are drinks
Beers are not boats
Therefore, beers are not drinks
Disjunctive syllogism (denial):
Either beers are boats or they are drinks
Beers are drinks
Therefore, beers are boats
Correct according to logic: reject
Correct according to belief: reject

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Note. In the actual study several other syllogistic structures were used. The examples serve
only to demonstrate the manipulations.

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Appendix B. Examples of problems in each congruency by base-rate condition for
Experiment 2
High base-rate
Low base-rate
[CONGRUENT, CELL #1]
In a study 1000 people were tested. Brannon
is a randomly chosen participant of this
study.
Among the participants there were 995
accountants and 5 street artists.
Brannon is 29 years old. He is very good
with numbers but is shy around people. He
spends much of his time working.
What is the probability that Brannon is an
accountant?
Correct according to statistics ~ 100
Correct according to beliefs ~ 100
Correct according to base-rate ~ 100
[INCONGRUENT, CELL #2]
In a study 1000 people were tested.
Brannon is a randomly chosen participant
of this study.
Among the participants there were 5
accountants and 995 street artists.
Brannon is 29 years old. He is very good
with numbers but is shy around people.
He spends much of his time working.
What is the probability that Brannon is an
accountant?
Correct according to statistics ~ 0
Correct according to beliefs ~ 100
Correct according to base-rate ~ 0
[INCONGRUENT, CELL #3]
In a study 1000 people were tested. Brannon
is a randomly chosen participant of this
study.
Among the participants there were 5
accountants and 995 street artists.
Brannon is 29 years old. He is very good
with numbers but is shy around people. He
spends much of his time working.
What is the probability that Brannon is a
street artist?
Correct according to statistics ~ 100
Correct according to beliefs ~ 0
Correct according to base-rate ~ 100
[CONGRUENT, CELL #4]
In a study 1000 people were tested.
Brannon is a randomly chosen participant
of this study.
Among the participants there were 995
accountants and 5 street artists.
Brannon is 29 years old. He is very good
with numbers but is shy around people.
He spends much of his time working.
What is the probability that Brannon is a
street artist?
Correct according to statistics ~ 0
Correct according to beliefs ~ 0
Correct according to base-rate ~ 0