Manuscript in preparation: Do not cite or circulate
On Dual Nature of Uncertainty: Cues From Natural Language
Craig R. FoxUCLA Anderson School and Department of Psychology
Gülden ÜlkümenUSC Marshall School
Bertram F. MalleBrown University Department of Psychology
Address Correspondence to:Craig R. FoxUCLA Anderson School110 Westwood Plaza #D511Los Angeles, CA [email protected]/206-3403
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Abstract
Probability theorizing since its inception has come in two forms: aleatory models that
deal with the relative frequency or propensity of events in the world, and epistemic
models that are concerned with subjective degree of belief. We argue that this stubborn
bifurcation reflects dual intuitions that people carry with them concerning the nature of
uncertainty. We review past behavioral research hinting at this distinction, and then
present a series of studies in which these variants of uncertainty are reflected in natural
language use. In particular, we show that speakers and listeners distinguish “internal
mode” statements (e.g., “I am 80% sure that…” or “I am reasonably confident that…”)
that express epistemic uncertainty (in the mind of the speaker) from external mode
statements (e.g., “I think there is an 80% chance that…” or “I believe there is a high
probability that…”) that express aleatory uncertainty (chance factors). Speakers place
more weight on singular information (e.g. feeling-of-knowing) when using internal
statements and more weight on distributional information (e.g. relative frequencies) when
using external statements. Meanwhile, listeners associate internal language with singular
reasoning and uncertainty attributed to the speaker’s mind whereas they associate
external language with distributional reasoning and uncertainty in the world. Moreover,
speakers using internal (versus external) mode statements are judged to be more
deserving of credit if they are right and blame if they are wrong. We close with a
discussion of the broader implications of this work for various domains of judgment and
decision making under uncertainty.
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“Probability… is … a physical constant belonging to the experiment as a whole and comparable with all of its other physical properties. The theory of probability is only concerned with relations existing between physical quantities of this kind.” --von Mises (1957).
“All uncertainties are inherently the same kind … [and] probabilities are personal degrees of belief about uncertain outcomes.” --von Winterfeldt & Edwards (1986)
“Philosophers seem singularly unable to put asunder the aleatory and the epistimological side of probability. This suggests that we are in the grip of darker powers than are admitted into the positivist ontology. Something about the concept of probability precludes the separation…” --Hacking (1975)
Most judgments and decisions involve uncertainty. Whether we are choosing a
spouse, buying a car, assessing a budget, forecasting a job applicant’s performance, or
estimating the likelihood of rain, we cannot know in advance precisely how things will
turn out. In some situations uncertainty can be attributed entirely to gaps in our
knowledge (e.g., whether the Amazon is longer than the Nile); in other situations
uncertainty can be attributed to external causal factors that are for practical purposes
unpredictable beyond their propensities (e.g., whether a fair coin will land heads). A
voluminous behavioral literature in recent decades has explored judgment and decision
making under uncertainty (for collections of papers see, e.g., Kahneman, Slovic &
Tversky, 1982; Kahneman & Tversky, 2000; Gilovich, Griffin & Tversky 2002);
however, researchers rarely distinguish different varieties of uncertainty and generally
treat it as a unitary construct.
The history of probability theorizing, almost from its inception, is marked by a
bifurcation in the conception of uncertainty (Hacking, 1975). Probability theory is
traditionally traced to a correspondence between Blaise Pascal and Pierre de Fermat in
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1654 concerning how one ought to divide the stakes of a game of chance that has been
prematurely interrupted (see e.g., Devlin, 2008). The early calculus of chance was based
on what some have termed an aleatory conception of uncertainty involving unknowns
that can differ each time we run an experiment under similar conditions. Shortly
thereafter Pascale framed the choice of whether or not to believe in the existence of God
as a wager with an “equal risk” of gain (infinite reward if God exists and one believes) or
loss (a finite mortal cost of believing). He thus advanced what some have termed an
epistemological or epistemic conception of uncertainty involving missing knowledge
concerning an event that is in principle knowable. Disagreement concerning the nature of
uncertainty has persisted to this day in the two dominant schools of probability
theorizing, with frequentists treating probability as long run stable frequencies of events,
and Bayesians treating probability as a measure of subjective degree of belief.
While probability theorists continue to debate philosophical questions concerning
the nature of uncertainty, our focus in this paper is to better understand how people
intuitively conceive of uncertainty and the behavioral implications of these conceptions.
We assert that the bifurcation of uncertainty in probability theory reflects an inherent
ambivalence concerning uncertainty that resides within most decision makers. On one
hand, people are often charged with assessing their epistemic uncertainty that a statement
is or will be true, or that a particular scenario will transpire. For instance, when a person
says she’s pretty sure that she left her cell phone on the nightstand, she is typically
assessing her knowledge concerning a fact that may or may not be true. On the other
hand, people are often charged with assessing the propensity that a particular event may
occur, selected from a class of possible events. For instance when a person observes that
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if you send your child to daycare she’ll probably get sick in the first few months, he is
typically considering the relative frequency of a class of events (children in daycare
getting sick or not). Of course these forms of uncertainty are not mutually exclusive; in
fact, most judgments entail a mix of both forms of uncertainty. For instance, a statement
such as, “I think there is a good chance that this paper will be accepted if we submit to
the special issue, but I’m not sure” may reflect both a consideration of aleatory
uncertainty (the proportion of papers of similar quality that are accepted to this journal)
and epistemic uncertainty (degree of confidence in that assessment).
Evidence of an intuitive distinction between aleatory and epistemic uncertainty.
An intuitive distinction between aleatory and epistemic uncertainty appears to be
in evidence from an early age. In an ingenious study, Robinson et al (2006) presented
children 4-6 years old with one bag containing orange and green colored building blocks
in equal proportion and another bag containing black building blocks. On each trial the
experimenter pulled a block from one of the bags without the child seeing what was
drawn, then put the block drawn was placed on a shelf behind one of three doors (orange,
green, or black) that was cut into a cardboard screen. The child’s job on each trial was to
put trays underneath doors to make sure that the block would be caught. On
“unknowable” trials the experimenter told the children he would draw a block from the
orange-green bag and asked the participant to place trays before he did so. On the
“unknown” trials the experimenter drew a block from the orange-green bag, placed it
behind the screen (without the child seeing which color) and then asked the participant to
place trays. This minor procedural variation yielded a dramatic contrast in behavior. On
“unknowable” trials in which the experimenter was yet to engage in a chance selection
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process and uncertainty might be deemed aleatory, most children correctly placed a tray
under the orange door and one under the green door. However, on “knowable” trials in
which the experimenter had already selected a block so that the uncertainty was purely
epistemic, most children a tray under a single door, apparently making their best guess
concerning of the color that had already been determined.
The perception of epistemic uncertainty may have distinct neural correlates from
epistemic uncertainty. In a provocative set of studies Volz, Schubotz & von Cramon
(2004; 2005) presented participants with competitions between two cartoon UFOs that
varied color, shape, and pilot character, and asked them to predict which UFO would win
a virtual competition game. In one experiment participants learned that each pairing was
associated with a fixed proportion of victories for one figure over another (e.g., A beats B
70% of the time); this could be seen as a manipulation of aleatory uncertainty. In a
companion experiment participants learned a fixed set of rules that determined which
UFO would win each competition (e.g., yellow always beats blue), with participants
informed of some rules and practicing them to optimal performance, informed of other
rules but never practicing them, and never informed of or practicing other rules; this
study could be seen as manipulating the level epistemic uncertainty. Comparison of
BOLD signal using functional MRI suggests common neural correlates in a number of
areas including right posterior fronto-median cortex (Brodmann Area 8) and also
distinctive activation for the rule-based task in regions including middle frontal gyrus,
inferior frontal junction area, and inferior parietal sulcus, brain areas though to subserve
working memory functions.
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Epistemic and aleatory uncertainty have distinct behavioral influences on decision
making. Holding information constant, people find betting on events less attractive when
their epistemic uncertainty is more salient. For instance, Rothbart and Snyder (1970)
found that undergraduates were willing to bet more on the roll of a die if they were asked
before the die was rolled (in which case, the outcome was presumably seen by most as
purely aleatory) than if they were asked after the die was rolled (in which case epistemic
uncertainty was more salient). Likewise, Heath and Tversky (1991) found that
participants preferred to bet on their guess of whether a randomly chosen stock would go
up or down the next day than bet on their guess of whether a randomly chosen stock went
up or down on the previous day, despite the fact they if anything they had more
information concerning the previous day’s stock movement. More generally they found
that people prefer to bet in situations where they feel more knowledgeable or competent,
holding judged probabilities constant. Fox and Tversky (1995) found that the aversion to
bet on less familiar events is triggered by a contrast with other events about which the
decision maker is more knowledgeable or other people who are more knowledgeable.
Building on this work, Fox and Weber (2002) report that people find gambles (e.g. bets
by Americans on the outcome of the upcoming Russian presidential election) more
attractive when they are reminded of less familiar events (e.g., the upcoming presidential
election in the Dominican Republic) than when they are reminded of more familiar
events (e.g. the upcoming presidential election in America). Likewise, naïve participants
(e.g., psychology students) were less willing to bet on an unfamiliar event (e.g., the
inflation rate in Holland) after they were provided relevant information that they did not
know how to use (GDP growth, interest rates, unemployment). Similarly, Chow and
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Sarin (2002) found that people find bets less attractive when missing information (e.g.,
which of two apples has more seeds) is missing to all (they have not yet been cut) then
when they are available to someone else (an experimenter who has counted the seeds).
The increased salience of epistemic uncertainty after an outcome is realized may
also partially explain why events seem more predictable after they occurred than before
they occurred, a phenomenon known as “creeping determinism” or “hindsight bias”
(Fischhoff, 1975). Interestingly, this bias is pronounced when plausible deterministic
causes (human skill or lack of skill) are cited or when no causal attribution is provided,
but it is virtually eliminated when the outcome is attributed to aleatory factors such as an
unexpected act of nature (Wasserman, et al. 1991).
Studies of confidence in forecasts have found persistent differences in judged
probabilities of general knowledge items that entail purely epistemic uncertainty and
judged probabilities of future events that also presumably entail aleatory uncertainty. In
particular, Ronis and Yates (1987) found that participants were more confident,
overconfident, and had worse calibration scores when asked to judge probabilities
concerning general knowledge items compared with when these same participants were
asked to judge probabilities concerning which team would win each of several upcoming
professional basketball games. Interestingly, participants expressed complete certainty
for general knowledge items more than 15 times as they did for basketball games,
perhaps recognizing inherent limits to one’s ability to perfectly predict outcomes
entailing some aleatory uncertainty. Similar patterns of higher confidence and greater
willingness to express certainty for general knowledge questions than future events were
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obtained by Fischhoff and MacGregor (1982), Wright (1982) and Wright & Wisudha
(1982).
Several studies have found that while participants tend to display overconfidence
on average when assessing probabilities that their answers to general knowledge
questions are correct item-by-item, they tended toward underconfidence when they asked
to estimate the proportion of items that they had answered correctly (Sniezek, Paese &
Switzer, 1990; Gigerenzer, et al., 1991; Griffin & Tversky, 1992). This is consistent with
the notion that evaluations of epistemic uncertainty (the likelihood that I answered this
item correctly) and aleatory uncertainty (the proportion of times I answered correctly)
entail reliance on distinct information and/or weight this information in distinct ways.
However, we assert that when a particular judgmental strategy or heuristic is especially
accessible, it will be employed regardless of elicitation mode (confidence versus
frequency). For example, Brenner et al. (1996) presented participants with responses
than another group had provided to various behavior question (e.g., “Are you often late
for class? Yes/No”) and their classification on a Myers-Briggs inventory; one group
predicted responses of a target subject with a particular score then assessed their the
probability that they were correct, while a second group assessed the percentage of target
subjects of a given profile who chose a particular answer. Interestingly, responses of
these two groups closely coincided with one another—and both responses correlated very
highly with a separate group’s assessment of the which of the two responses to the
behavior question was more representative of the personality profile in question (r
= .96, .86 with confidence and frequency assessments, respectively).
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Similarly, one study showed that the planning fallacy—the tendency to
underestimate task completion times—is attenuated when participants judge the relative
frequency of tasks that will be completed on time than when participants judge the
probability of completing each task on time—but only when they judge relative
frequency after judging probability. However, the reasoning cited only showed a slight
tendency toward more of an “outside perspective” under frequency than probability
judgment (Griffin & Buehler, 1999).
There is a great deal of evidence that the conjunction fallacy—the tendency to
judge the conjunction of a plausible and implausible event as more likely than the
plausible event--is diminished when participants are asked to judge relative frequencies
rather than single event probabilities (e.g., Tversky & Kahneman, 1983; Fiedler, 1988;
Hertwig & Gigerenzer, 1994) or when they are presented frequentistic rather than case-
specific information (Reeves & Lockhart, 1993). This is consistent with the notion that
relative frequencies primes more extensional reasoning (Kahneman & Tversky, 1996).
Likewise, tendency to underweight base rates when updating based on case information
(Kahneman & Tversky, 1973) has been shown to diminish when aleatory factors are
made more salient. For instance, the use of base rate data increases when problems are
framed as repetitive rather than unique (Kahneman & Tversky, 1979 TIMS), when
presented after case information (Krosnick, Li & Lehman, 1990), varying base rates
across trials within participant (Bar-Hillel & Fischhoff, 1981), or when participants are
asked to think as “statisticians” (Schwarz, Strack, Hilton & Naderer, 1991). Likewise,
when participants were induced to make their judgments “as a scientist analyzing data”
they were more sensitive to base rates than when they are induced to “understand the
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individual’s personality, professional inclinations and interests” (Zukier & Pepitone,
1984).
When one attributes uncertainty to human causes (e.g., deception by another) this
may facilitate a more clinical mindset and when attributes uncertainty to a stochastic
process this may lead to more rule-based behavior. Indeed, Schul, May, Burnstein,
Yahalom (2007) asked participants drew matchboxes that had either blue or yellow
stickers on them and either had blue or yellow tokens inside. All participants know that
the token color matched the sticker 2/3 of the time and were asked to predict the color
based on the token. Some participants were told that the allocation of tokens was
assigned at random whereas others were told that they were assigned by another
participant who had an incentive to deceive. Participants more frequently guessed the
color matching the sticker (i.e., using the optimal decision rule) when they thought the
tokens were assigned at random compared to when they thought that another person
made the assignments, in which case they more frequently searched for patterns in the
sequence. Likewise, several recent studies have suggested that the well-documented
tendency toward probability matching (i.e., choosing options in proportion to their
relative probability of success) reflects a search for patterns in random sequences
(consistent with a model of uncertainty that is largely epistemic) whereas optimizing
(choosing the option that offers the highest probability of success) reflects a more
sensible acknowledgment that no such patterns exist in random sequences (consistent
with a purely aleatory model of uncertainty (Wolford, Newman, Miller & Wig, 2004;
Unturbe & Corominas, 2007; Volkan, 2000). Inded, Gaissmaier and Schooler (2008)
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find that probability matchers are more likely than maximizers to identify and take
advantage of predictable patterns when they encounter non-random outcome sequences.
Friedland (1997) categorized participants according to how much they attributed
outcomes in hypothetical scenarios to chance versus luck. Participants who attributed
more to luck tended to make betting decisions in a chance game that reflected a more
epistemic view of uncertainty in which “luck” was a scarce resource to be allocated: if
they had encountered a string of run of mostly unfavorable outcomes they subsequently
bet more money (i.e., expecting their luck to turn); if they had encountered a string of
mostly favorable outcomes then they subsequently bet less money (i.e., expecting their
luck to turn).
Intuitive Conceptions of Uncertainty
Several authors proposed frameworks for distinguishing between different
intuitive conceptions of uncertainty (Howell & Burnett, 1978; Kahneman & Tversky,
1982; Keren, 1991; Smith, Benson & Curley, 1991; Tiegen, 1994; Rowe, 1994;
Dequesch, 2004). Most of these were theoretical accounts with little data confirming that
participants intuitive drew similar distinctions. The central thesis of this paper is that
people
The most influential framework in the psychology literature was advanced by
Kahneman and Tversky (1982), who distinguished between internal uncertainty which is
attributed to one’s state of knowledge and external uncertainty, which is attributed to the
external world. They further distinguish internal uncertainty into reasoned mode which
is based on explicit arguments (e.g., I believe that New York is further north than Rome
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because it has a cooler climate) and introspective mode that reflects a feeling-of-known
(e.g., I believe that I have correctly spelled a word because it ‘looks right’). They further
distinguish external uncertainty into the singular mode that entails an assessment of the
case at hand (e.g., I believe that I will complete a project on time because I’ve considered
the steps of my plan and adjusted for unforeseen contingencies) and the distributional
mode in which the case at hand is seen as an instance of a class of similar events (e.g., I
believe that I will complete the project on time because most similar projects have been
completed on time). We propose that what we have called epistemic uncertainty
encompasses both internal uncertainty an external uncertainty that is evaluated using
singular representations; aleatory uncertainty maps best onto distributional
representations of external uncertainty.
Howell & Burnett (1978) develop a taxonomy of uncertain events that includes:
(1) whether the event is part of a class of repeated events (“frequentistic”) or is unique
(“nonfrequentistic”); (2) whether the decision maker feels he or she has some control
over the outcome (“internal”) or has no control (“external”). For frequentistic, external
events, they further distinguish (3) whether or not the process is attributed to a stable
process familiar to the decision maker (“known”) or not (“unknown”). These authors
argue that different tasks (frequency estimation, probability estimation, prediction and
choice) engage different “cognitive elements” (e.g., past frequencies, heuristics)
depending on the nature of the event. For our purposes we would consider
nonfrequentistic, and internal uncertainty as more epistemic; frequentistic and external as
more aleatory.
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Natural Language as a tool for probing intuitions.
The central thesis of this paper is that people intuitively distinguish epistemic and
aleatory uncertainty. Our method for examining these intuitions is natural language that
participants choose to express their uncertainty. Some statements that we call internal
mode (e.g., “I am fairly confident,” “I am 90% sure,” “I strongly believe) qualify or
quantify one’s degree of epistemic uncertainty. Other statements that we call external
mode (e.g., “I think there is a high probability,” “I’d say there is a 90% chance,” “I
believe it is fairly likely”) qualify or quantify one’s assessment of aleatory uncertainty.
Note that in the latter examples we preface the stems with words indicating subjectivity
(“I think,” “I’d say,” “I believe”) so that we do not confound subjective]ity/objectivity
statements with linguistic stems.
Some events are purely epistemic or aleatory and most naturally map onto internal
and external mode statements. For instance, it is much more natural to say that “I’m 90%
sure the Amazon is longer than the Nile” than it is to say “I think there is a 90% chance
that the Amazon is longer than the Nile.” Likewise it is much more natural to say that “I
think there is 5/6 chance that this fair die will land on a number less than 6” than it is to
say “I am 5/6 sure” of it. More often, events reflect a mixture of epistemic and aleatory
cues. For instance, the outcome of a basketball game may reflect consideration both of
how often each team tends to win and how well the teams match up on this particular
occasion. We assert that linguistic choices can both provide insight into the speaker’s
conception of uncertainty when the statement is made and that it can prime one form of
reasoning over another.
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We now turn to the presentation of data in support of our hypotheses. We first
present a number of studies in which we examine ways in which speakers systematically
differentiate between epistemic and aleatory uncertainty using internal versus external
modes. In these studies we also show that forcing people to quantify their beliefs in the
internal mode can make epistemic cues more salient whereas forcing them to quantify
their beliefs in the external mode can make aleatory cues more salient. Next, we turn to
the listener’s perspective and show that listeners draw a number of inferences about
information and cognitive process on which the speaker relies from the mode in which
the speaker chooses to express him or herself. Finally we examine the social
consequences (in particular the assignment of credit and blame) for speakers who choose
to express themselves in these modes following the resolution of uncertainty.
SPEAKER’S PERSPECTIVE
STUDY 1a: NYT STUDY
Procedure
Using the Proquest database, we screened articles that appeared in New York
Times during calendar years 2008 and 2009. We searched for terms that qualified or
quantified the uncertainty of the speaker. We included stems that communicate epistemic
uncertainty (sure, confident, certain), and aleatory uncertainty (chance, likely/likelihood,
probability). These statements were coded on speaker traits (perspective, expertise,
gender, control), characteristics of the prediction (source, backing), and characteristics of
the event (subject, negation, tense, desirability, temporality, locus). We considered five
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sentences that come before and five sentences that come after the target statement to
facilitate coding of variables that required an understanding of the context (e.g., speaker’s
expertise).
Results
General. The search described above returned 967 statements. 754 of these
statements had external stems, and 372 had internal stems. Although speakers had an
overall tendency to qualify, rather than quantify their uncertainty, internal stems (11%)
were much less likely to be quantified than external stems (24%), Pearson Chi-Square (1)
= 23.52, p = .000.
Speaker traits. Statements were much more likely to use internal stems when
communicated from the 1st person’s perspective (41%) than the 2nd or the 3rd person’s
perspective (27%; p = .000) (see table 1). Mixed speakers were more likely to use
external statements (81%) than male speakers (58%) and female speakers (56%; p
= .000). When speakers are communicating the uncertainty experienced by others, they
are more likely to use internal stems when the other person is a friend, romantic partner
or close relative (67%), but more likely to use external stems when the other person is a
stranger or an acquaintance (77%, p = .002). The amount of control speakers had over the
event had a strong influence over the choice of language, such that the speakers were
more likely to use external stems when they had no control over the event (68%), but
they were more likely to use internal stems when they had influence over the event (79%)
or when they could bring about the event (73%; p = .000).
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Characteristics of the prediction. Source of the prediction also had a strong effect
on language choice. Speakers were more likely to use an external stem when the
prediction was based on calculation or logic (94%), than when it was based on trends or
facts (79%), or intuition or no specific source (51%; p = .000). Speakers were more likely
to use external stems when the prediction involved backing (e.g., “because”) (72%) than
when it did not (60%, p = .000). Speakers were more likely to use external stems when
the prediction did not involve a negation (66%), but they were more likely to use an
internal stem when the prediction involved a negation (71%, p = .000).
Characteristics of the event. Speakers were more likely to use external stems
when prediction was about non-sentient targets (e.g., trends, facts, processes or events),
(71%) than about sentient targets (58%; p = .000). Events about sentient targets were
further categorized as behavioral (e.g., uncertainty about whether a person will speak) or
mental (e.g., uncertainty about what a person is thinking). Speakers were more likely to
use external stems when predicting behavioral events regarding a sentient target (62%),
but they were more likely to use internal stems when predicting mental events regarding a
sentient target (69%; p = .000). Speakers were more likely to use external stems when the
prediction involved hypothetical events or events that will take place in the future (71%),
but they were more likely to use internal stems for events that are currently happening
(53%) or events that happened in the past (55%; p = .000). We coded for the desirability
of the event separately from an objective perspective (a swimmer winning a medal) and
from a subjective perspective (a thief stealing a painting). External stems were much
more likely to be used for both objectively (83%) and subjectively (82%) undesirable
events than events that were desirable, or neutral (both p’s = .000). There was a very
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strong effect of the locus of the event’s uncertainty. When the uncertainty about the event
lay outside the predictor (i.e., inherently random or probabilistic events), speakers were
more likely to use external stems (74%), but when the uncertainty lay fully within the
predictor (i.e., due to lack of knowledge or evidence), speakers were more likely to use
internal stems (61%, p = .000).
STUDY 1b: SENTENCE COMPLETION STUDY
Method
One hundred forty seven participants were given roots of sentences (stems), and
were asked to complete each stem with an event such that the complete sentence sounded
natural to them. Every participant completed four such stems: two internal and two
external. For half of the participants, the internal stem was “sure” and the external stem
was “chance,” and for the other half the internal stem was “confident” and the external
stem was “probability.” For every participant, one external and one internal stem were
quantified by 60%, and the remaining stems were quantified by 80%. The order of
presentation of the internal and external stems, as well as the order of presentation of the
percentages was counterbalanced. None of these between subjects variables had an effect,
and therefore we collapsed the data across them and compared internal and external
stems. Two independent coders, blind to the condition coded the stems on speaker traits
(control over the event), and characteristics of the event (subject, timing, and locus of
uncertainty). The two coders had a 97% initial agreement, and the disagreements were
resolved by discussion.
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Results
Participants were more likely to complete internal stems with events that were
mostly controllable (74%) than events that were mixed, uncertain or those that they had
little or no control over (26%, p = .000). When completing internal stems, participants
were more likely to use a subject referring to themselves (i.e., I, me, my, we), (73%) than
to others or objects (27%, p = .000). Participants were more likely to complete external
stems with future events (90%), than present or past events (10%, p = .000). External
stems were completed such that the locus of uncertainty was more likely to be outside the
speaker (65%) than inside the speaker (35%, p = .012).
We also conducted a series of mixed binomial logit regression models with stem
type, and the two order variables as between subjects variables, and internal/external as
the within subject variable. We did not expect stem type or order variables to have a
significant effect on any of the dependent variables. As we expected, internal/external
independently and significantly predicted all of the dependent variables. Internal, as
opposed to external stems significantly and positively predicted the controllability of the
event (B = .793, p = .000), significantly and positively predicted use of first person
subject (B = .696, p = .000), negatively predicted use of future events (B = -.953, p
= .000), significantly and positively predicted the locus of uncertainty stemming from
inside the speaker’s mind (B = .399, p = .027). As expected, stem type did not have an
effect in any model, suggesting that there was no difference between sure and confident
stems in representing internal mode, and between chance and probability stems in
representing external mode. The only unexpected finding was that when predicting locus
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of uncertainty, order of presentation of the percentages had a positive and significant
effect (B = 418, p = .020).
STUDY 2a: PICK AND FILL
Method
Fifty six undergraduate students participated in the study in exchange for partial
course credit. Three participants provided incomplete responses, and were dropped. All
analyses are based on the remaining 53 participants. The participants were presented with
20 events. Half of these were about self (e.g., I will earn at least a 3.0 GPA this semester),
and half were about the world (e.g., Intelligent life exists in other planets). For each
event, participants’ task involved two parts. They were presented with a choice between
two different root phrases (e.g., “There is a ___ % chance that USC will play in the
Rose Bowl next January 1" and "I am ___ % sure that USC will play in the Rose Bowl
next January 1”). The first part of the task was to select the root phrase that sounded
most natural to them. On the next screen, they were presented with only the phrase they
selected. The second part of the task involved completing the phrase by entering a
number between 0 and 100 that best reflected their belief about the given event. The
order of presentation of these 20 events was randomized for each participant. In the
choice part of the task, for half of the participants sure phrase appeared above the chance
phrase. This order was reversed for the remaining participants.
Next, participants were asked to rate each event on five 7-point likert scales,
anchored by strongly disagree, and strongly agree. They indicated their perceived control
(I have control over the outcome), their knowledge about the topic (I know a lot about
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this event), the likelihood that the event will happen (this event will definitely occur),
singular reasoning (Earlier, when I quantified my belief about this event, I had a specific
story in mind for how or why the event will happen), and distributional reasoning
(Earlier, when I quantified my belief about this event, I was thinking about how often this
kind of event tends to happen). The order of presentation of these items was
counterbalanced. Due to a programming error, we had incomplete responses for control
and distributional reasoning. We are focusing on knowledge and likelihood judgments for
the purposes of the analysis below.
Results
Overall, participants were equally likely to choose the sure mode (51%), and the
chance mode (49%).
Events that were assigned a probability of less than or equal to 50% were more
likely to be described by the chance mode (68%), than the sure mode (32%). In contrast,
events that were assigned a probability of more than 50% were more likely to be
described by the sure mode (63%), than the chance mode (37%). For those events that the
participants picked the sure mode, the mean probability was 73%. For those events that
the participants picked the chance mode, the mean probability was 53%.
64% chose the sure mode for events about self, and 63% chose the chance mode
for world events, as a natural way of communicating their uncertainty about these events
(Pearson Chi-Square = 75.04, p < .001).
Predicting choice of sure vs. chance mode. To see which factors influence
whether participants choose the sure mode or the chance mode, we used a repeated logit
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model? (GENLIN), where the 20 events were included as the repeated factor and
knowledge and likelihood judgments were included as covariates. Therefore, this
analysis was conducted over a total of 1060 responses elicited from 53 participants. The
coefficient for knowledge (B = .036, p < .001) and likelihood (B = .059, p < .001) were
positive and significant, indicating that increases in these factors were associated with a
higher likelihood to choose the sure mode. The results were similar when a similar
analysis was conducted only for those participants who indicated probability estimates
higher 50% (637 responses elicited from 53 respondents). The coefficient for knowledge
(B = .048, p < .001) and likelihood (B = .071, p < .001) were positive and significant.
Next, we added into the model an indicator of whether the events were self-
related or not (I-statements). We used a repeated logit model? (GENLIN), where the 20
events were included as the repeated factor and knowledge and likelihood judgments
were included as covariates, and self-relevance was included as a factor. The coefficient
for likelihood (B = .060, p < .001), and self-relevance (B = .174, p < .001) were positive
and significant. However, the coefficient for knowledge was not significant anymore (B =
.012, p >.05). The results were similar when a similar analysis was conducted only for
those participants who indicated probability estimates higher 50% (637 responses elicited
from 53 respondents). The coefficient for likelihood (B = .064, p < .01), and self-
relevance (B = .169, p < .005) were positive and significant, and the coefficient for
knowledge was only marginally significant (B = .025, p =.062).
We also ran a repeated logit model? (GENLIN), where the 20 events were
included as the repeated factor and knowledge and likelihood judgments, and the
probability estimates were included as covariates. The coefficient for knowledge (B
Page 23
= .038, p < .001), and probability (B = .003, p < .001) were positive and significant.
However, the coefficient for likelihood was not significant anymore (B = .020, p >.05).
The results were similar when a similar analysis was conducted only for those
participants who indicated probability estimates higher 50% (637 responses elicited from
53 respondents). The coefficient for knowledge (B = .038, p < .005), and probability (B
= .010, p < .001) were positive and significant, but the coefficient for likelihood was not
significant (B = .025, p > .05). When we conduct this analysis for only those who
indicated probability estimates less than or equal to 50% (420 responses, 53 respondents),
the only significant factor was probability (B = -.004, p < .05), indicating that for low
probability events, as the probability decreased, participants were more likely to choose
the sure mode.
STUDY 2b: PICK AND FILL STUDY WITH LOC
Method
Forty one undergraduate students participated in the study in exchange for partial
course credit. Participants were presented with 20 events. Half of these were about self
(e.g., I will earn at least a 3.0 GPA this semester), and half were about the world (e.g.,
Intelligent life exists in other planets). For each event, participants’ task involved two
parts. They were presented with a choice between two different root phrases (e.g.,
“There is a ___ % chance that USC will play in the Rose Bowl next January 1" and
"I am ___ % sure that USC will play in the Rose Bowl next January 1”). The first part of
the task was to select the root phrase that sounded most natural to them. On the next
screen, they were presented with only the phrase they selected. The second part of the
Page 24
task involved completing the phrase by entering a number between 0 and 100 that best
reflected their belief about the given event. The order of presentation of these 20 events
was randomized for each participant. In the choice part of the task, for half of the
participants sure phrase appeared above the chance phrase. This order was reversed for
the remaining participants. Finally, participants completed the Locus of Control Scale
(Rotter 1966).
Results
For the ten "I" statements in which there could plausible be varying levels of
control (e.g. I will get at least a 3.0 GPA this term), LOC significantly correlates with the
tendency to use "sure" over chance (especially when controlling for the fill #).
There is no such correlation (nonsignificant in the opposite direction) for the ten "world"
statements for which there is little or no plausible control (e.g., there will be an
earthquake of at least 6.0 in LA in the next 5 years) (see table 2).
STUDY 3a: MANIPULATING EXTERNAL CERTAINTY
One hundred and thirty six participants took part in this study. Participants were
presented with scenarios about three different events. All scenarios comprised of one
sentence reflecting an internal cue, and one sentence reflecting an external cue about the
probability of the event. We manipulated the external certainty to be high (Suppose that
you are married and that you and your spouse are leaning toward the decision to have a
baby but have not yet made up your minds. A fertility expert tells you that you will have
Page 25
a very easy time conceiving), or low (Suppose that you are married and that you and your
spouse have nearly decided to have a baby. A fertility expert tells you that it may be a
little difficult for you to conceive).
After reading each scenario, participants indicated their belief about the event by
entering a number between 0 and 100. They did this either in a sure mode (e.g., I’m
______% sure that we will have a baby in the next year or two), or the chance mode (I’d
say there is a ______% chance that we will have a baby in the next year or two).
We counterbalanced the order of presentation of the three scenarios. I am just presenting
the results for one of the scenarios where results were strongest and significant, for the
order in which this scenario came first.
The results of a 2 (External Probability Cue: High, Low) x 2 (Communication
Mode: Sure, Chance) between subjects ANOVA revealed a main effect of external cues
(F (1, 62) = 4.07, p < .05), such that participants’ probability estimates were higher when
the external cue was high (M = 71.74%), than when it was low (M = 54.64%). The two-
way interaction was also significant (F (1, 62) = 4.07, p < .05). Planned contrasts
revealed that in the sure mode, high and low external cues did not lead to a difference in
probability estimates (Mhigh = 67.88%, Mlow = 63.88%; F (1, 66)< 1), whereas in the
chance mode, high external cues resulted in higher probability estimates than lower
external cues (Mhigh = 75.59%, Mlow = 45.39%; F (1, 66) = 10.80, p < .005). These results
show that the external cues influenced participants’ probability estimates in the chance
mode, but not in the sure mode.
STUDY 3b: FORCED MODE STUDY FULLY CROSSED
Page 26
Method
Two hundred ninety nine participants participated in the study. Participants were
presented with two sentences, one related to external sources of certainty and the other
related to internal sources of certainty. External certainty was manipulated to be either
low (Your friend Tom wears a cap a few times a week), or high (Your friend Tom wears
a cap almost every day). Similarly, internal certainty was manipulated to be either low
(You were in the same large lecture class with him yesterday and you have the vague
sense that he might have been wearing a cap), or high (You were in the same large lecture
class with him yesterday and you have the impression that he was wearing a cap). After
reading these two sentences, participants were asked to indicate the probability that Tom
was wearing a cap by completing a sentence with either a chance stem (I’d say there is a
_____% chance ), or a sure stem (I’m _____% sure).
Results
A 2 (Mode of Communication: Sure, Chance) x 2 (External Certainty: High, Low)
x 2 (Internal Certainty: High, Low) ANOVA revealed a main effect of external certainty
information (F(1,291) = 76.11, p < .001), and a main effect of internal certainty
information (F(1,291) = 17.02, p < .001), where higher levels of both types of
information lead to higher probability estimates. The mode of communication did not
have a significant main effect (F(1,291) = 2.161, p > .1). There was a significant
interaction between external certainty information and the mode of communication
(F(1,291) = 12.97, p < .001), as well as between internal certainty information and the
mode of communication (F(1,291) = 8.81, p < .005). When completing sure sentences,
Page 27
probability estimates were affected by both external and internal certainty information.
However, when completing chance sentences, probability estimates were influenced only
by external, but not by internal certainty information.
We also conducted a regression analysis predicting probability estimates from
external and internal certainty, communication mode, and the two-way interactions
between communication mode and information type. The results reveal a significant
effect of external certainty information (B = 8.71, p < .001). Although the effect of
internal certainty information is significant in a model with only main effects, it is no
longer significant in this model with the interaction terms. More importantly, there is a
significant interaction between communication mode and external information (B = -
14.82, p < .001), suggesting that the effect of external certainty information is stronger in
the chance mode than in the sure mode. Moreover, there is a significant interaction
between communication mode and internal information (B = 12.22, p < .005), suggesting
that the effect of internal certainty information is stronger in the sure mode than in the
chance mode.
STUDY 4: PICK AND FILL – NUMBERS PART
To see which factors influence probability estimates for different events, we used
a repeated logit model? (GENLIN), where the 20 events were included as the repeated
factor and knowledge and likelihood judgments were included as covariates. This
analysis was conducted over a total of 1057 responses elicited from 53 participants. The
Page 28
coefficient for likelihood (B = .11.897, p < .001) was positive and significant, but the
coefficient for knowledge was not significant (B = -.287 p > .05).
We run another analysis with the 20 events was the repeated factor, knowledge
and likelihood judgments were covariates, and the choice of communication mode (sure
vs. chance) was included as a factor. This analysis was conducted over a total of 1057
responses elicited from 53 participants. The coefficient for likelihood (B = 11.455, p
< .001), and coefficient for communication mode (B = 7.275, p < .001) were positive and
significant. However, the coefficient for knowledge was not significant (B = -.560 p > .1).
These results indicate that the probability estimates are positively associated with
likelihood judgments, and the choice of sure mode.
We added self relevance (I-statements) to the above analysis. For this analysis, the
20 events was the repeated factor, knowledge and likelihood judgments were covariates,
and the choice of communication mode (sure vs. chance), and self-relevance (I-
statements) were included as factors. This analysis was conducted over a total of 1057
responses elicited from 53 participants. The coefficient for likelihood (B = 11.389, p
< .001), and the coefficient for communication mode (B = 7.823, p < .001) were positive
and significant. The coefficient for self-relevance (B = 4.267, p < .05) was negative and
significant. The coefficient for knowledge was not significant (B = .029, p > .1). These
results indicate that the probability estimates are positively associated with likelihood
judgments, and the choice of sure mode, and negatively associated with the self-relevance
of the event.
Page 29
Next, to more clearly understand the effects of knowledge and likelihood on
probability estimates, we examined the effects of these factors separately among events
with high and low probability estimates, and the choice of sure vs. chance modes.
In summary, this analysis revealed several interesting findings about the factors
that affect probability estimates (the details can be found in the following paragraphs).
First, knowledge has a positive and significant effect only for high probabilities, whereas
likelihood judgments always have a positive and significant effect for all modes and
probability levels. Second, likelihood moderates the relationship between knowledge and
probability judgment in the high probability, sure cell. Third, in the chance mode, for
high probabilities (e.g., p >50%), participants provide more extreme probabilities, the
more knowledgeable they are. In contrast, in the chance mode, for low probabilities (e.g.,
p <=50%), participants provide more extreme probabilities, the less knowledgeable they
are. These results are consistent with an ignorance prior account in which less knowledge
leads to probabilities closer to 50%.
For events that were assigned probability estimates of 50% or less. We ran a
repeated logit model? (GENLIN), with the 20 events as the repeated factor and likelihood
judgments as covariates, only using the events that were assigned probability estimates of
50% or less. Among events that chance was chosen as the preferred mode of
communication, this analysis revealed that the coefficient of likelihood was positive and
significant (B = 3.899, p < .001). Among events that sure was chosen as the preferred
mode of communication, this analysis revealed that the coefficient of likelihood was
positive and significant (B = 5.191, p < .001).
Page 30
We ran a repeated logit model? (GENLIN), with the 20 events as the repeated
factor and knowledge judgments as a covariate, only using the events that were assigned
probability estimates of 50% or less. Among both chance and sure events, coefficient of
knowledge was not significant.
When both likelihood and knowledge were included in the model, for chance
events, coefficient of likelihood was positive and significant (B = 4.345, p < .001), and
the coefficient of knowledge was negative and significant (B = -1.179, p < .05). For sure
events, coefficient of likelihood was positive and significant (B = 5.294, p < .001), but
the coefficient of knowledge was not significant (B = -.715, p > .05).
For events that were assigned probability estimates of more than 50%. We ran a
repeated logit model? (GENLIN), with the 20 events as the repeated factor and likelihood
judgments as covariates, only using the events that were assigned probability estimates of
more than 50%. Among events that chance was chosen as the preferred mode of
communication, this analysis revealed that the coefficient of likelihood was positive and
significant (B = 3.630, p < .001). Among events that sure was chosen as the preferred
mode of communication, coefficient of likelihood was positive and significant (B =
5.746, p < .001).
We ran a repeated logit model? (GENLIN), with the 20 events as the repeated
factor and knowledge as a covariate, only using the events that were assigned probability
estimates of more than 50%. The coefficient of knowledge was significant for both
chance events (B = 2.184, p < .001), and sure events (B = 2.767, p < .001).
When both likelihood and knowledge were included in the model, for chance
events, both the coefficient of likelihood (B = 2.958, p < .001), and the coefficient of
Page 31
knowledge (B = 1.063, p < .05) were positive and significant. For sure events, coefficient
of likelihood was positive and significant (B = 5.502, p < .001), but the coefficient of
knowledge was not significant (B = .302, p > .05). These results are summarized in Table
3.
LISTENER’S PERSPECTIVE
STUDY 5: WHAT WERE THEY THINKING?
Method
One hundred and twenty eight undergraduate students participated in the study in
exchange for partial course credit. Participants were presented with 10 pairs of
statements. For each statement pair, one speaker communicated their probability
judgment about an event in the sure mode (e.g., Colin says: “I am 70% sure I’ll win the
poker tournament”), and the other speaker communicated their probability judgment
about the same event in the chance mode (e.g., Shane says: “I think there is a 70% chance
I’ll win the poker tournament”). Below these statements, participants were presented
with one or two thoughts that might have been going through the minds of these speakers
when they made their statements (e.g., ____ is thinking about his own poker skill, ____ is
thinking about the poker skill of all players in the tournament). Participants’ task was to
indicate which speaker was more likely to have relied on which thought in forming their
statement. If there were two thoughts listed, their task was to choose one thought for each
speaker.
The order of questions was randomized for each participant. Half of the
participants saw the sure mode statement at the top of the page, followed by the chance
Page 32
mode statement. For the remaining participants, this order was reversed. The order in
which the thoughts appeared on the screen was also counterbalanced.
Results
Below, we report the results for all participants (n = 128), and also for the subset
of participants (n = 105, in parentheses) who matched one speaker with one thought, and
the remaining speaker with the remaining thought. The pattern of results remains the
same.
For the first question, 62% (62%) of the participants paired the speaker who
communicated their statement in the sure mode (Doctor Ames says: “I am 80% sure that
you have Crohn’s disease”), with the diagnosticity-related thought (is thinking “This
patient has most of the signs and symptoms of Crohn’s disease”), and 61% (62%) of the
participants paired the speaker who communicated their statement in the chance mode
(Doctor Baker says: “There is an 80% chance that you have the Crohn’s disease”) , with
the thought related to the posterior probability (is thinking “Most of the patients I have
seen with these signs and symptoms have Crohn’s disease”). Table 4 summarizes the
results for all 10 questions.
Discussion
The results of this study suggest that when a speaker communicates a statement in
the sure mode, participants infer that the speaker is thinking about singular information
(questions 1-4), their direct experience with the subject (questions 5-6), self- related
thoughts (questions 7-8), and internal locus of control (questions 9-10). In contrast,
when a speaker communicates a statement in the chance mode, participants infer that the
Page 33
speaker is thinking about distributional information (questions 1-4), distributional
knowledge (questions 5-6), competition- related thoughts (questions 7-8), and external
locus of control (questions 9-10).
STUDY 6a: POETRY JOURNAL
We asked 185 participants to imagine that they would like to publish an essay in a
poetry journal. Each participant was then presented with two beliefs, expressed by two
poetry journal editors. Editor of Journal A expressed her belief in the sure mode (If you
submit to Journal A, I’m 80% sure that we’ll publish the essay), and the editor of Journal
B expressed her belief in the chance mode (If you submit to Journal B, I think there is an
80% chance we’ll publish your essay). Participants were asked to select which journal to
send their work on the basis of these statements. Half of the participants saw statements
made by journal editors, and the remaining participants saw statements made by the mail
clerks at these journals. We counterbalanced whether the sure statement or the chance
statement appeared at the top of the page.
Results
When statements were made by editors, 76% of the participants (n = 93) chose
journal of the editor who communicated her belief in the sure mode. When the
statements were made by mail clerks, 65% of the participants (n = 92) chose the journal
of the clerk who expressed her belief in the sure mode (Fischer exact, p < .05, one-sided).
These results indicate that overall, listeners infer greater belief strength when the same
Page 34
belief is expressed in the sure mode than in the chance mode. This effect is moderated by
the expertise of the speaker such that for people who are not considered to be experts, the
belief-strengthening effect of the sure-mode seems to diminish, perhaps due to lack of
credibility of the novices. Unfortunately, we do not get a reversal here.
General Discussion
In this paper we have shown that speakers and listeners distinguish “internal
mode” statements (e.g., “I am 80% sure that…” or “I am reasonably confident that…”)
that express epistemic uncertainty (in the mind of the speaker) from external mode
statements (e.g., “I think there is an 80% chance that…” or “I believe there is a high
probability that…”) that express aleatory uncertainty (chance factors). Speakers place
more weight on singular information (e.g. feeling-of-knowing) when using internal
statements and more weight on distributional information (e.g. relative frequencies) when
using external statements. Meanwhile, listeners associate internal language with singular
reasoning and uncertainty attributed to the speaker’s mind whereas they associate
external language with distributional reasoning and uncertainty in the world. Moreover,
speakers using internal (versus external) mode statements are judged to be more
deserving of credit if they are right and blame if they are wrong.
Page 35
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Table 1. Use of External and Internal Language by Characteristics of the Speaker, Prediction
and Event
Internal External p value
Speaker Perspective 1st Person 290 410 p = .0002nd or 3rd Person 70 193
Expertise Expert 195 299 p = .09Non-expert 166 307
Gender Male 249 347 p = .000Female 71 90Mixed 40 167
Relation Stranger or acquaintance 49 166 p = .002Friend, romantic partner or close relative
8 4
Control No control 262 575 p = .000Influence 70 19Can bring about event 29 11
Prediction Source None/Intuition 282 289 p = .000Trends/Facts 77 286Calculation/Logic 2 31
Backing None 294 432 p = .000Backing/Justification 67 173
Negation Non-negation 306 583 p = .000Negation 55 22
Event Subject Sentient 266 372 p = .000Facts/Things/Processes/Events
95 234
Type (if sentient) Mental event 54 24 p = .000Behavioral event 212 348
Timing Past 71 58 p = .000Present 100 88Future 190 460
Objective desirability Undesirable 55 261 p = .000Neutral/Indeterminate 155 191Desirable 151 154
Subjective desirability Undesirable 56 263 p = .000Neutral/Indeterminate 117 181Desirable 183 162
Temporality One-time 194 319 p = .000Extended 74 189Timeless 93 98
Locus Epistemic uncertainty 182 115 p = .000Aleatory uncertainty 176 491
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Table 2
Statement (I-statements) BLOC pLOC Bprobability pprobability
I will go to a party this weekend -.09 .316 .024 .009
I will earn at least a 3.0 GPA this semester -.27 .087 .113 .053
I will go to bed before 1AM tonight -.066 .518 .043 .005
I will speak to my parents at some point in the next week -.643 .021 .099 .023
I will attend my 10 year high school reunion -.217 .033 .039 .012
I will get married by the time I am 30 -.066 .55 .095 .001
I will travel out of state this summer -.096 .364 .05 .004
I will attend graduate school -.091 .36 .045 .004
I will get at least a B- in BUAD 307 this semester -.28 .074 .16 .012
I will go to the beach sometime in March -.113 .228 .029 .009
Statement (World-statements) BLOC pLOC Bprobability pprobability
President Obama will be reelected in 2012 -.132 .212 .053 .015
there will be a commercially available cure for AIDS by 2020 .088 .394 .004 .814
Intelligent life exists on other planets .242 .053 .026 .037
USC will play in the Rose Bowl next January 1 .163 .096 .054 .028
A major earthquake (at least 6.0) will hit Los Angeles in the next five years
.029 .759 .018 .327
The high temperature in Downtown LA will be at least 70 degrees next Tuesday
-.086 .395 -.005 .744
Slumdog Millionaire will win the Academy Award for Best Picture -.047 .69 .05 .04
The U.S. unemployment rate will go up in the next month .223 .058 -.002 .906
Britney Spears will go back into rehab sometime in the next five years
.064 .476 .009 .484
The Lakers will win most of their games in March .231 .019 .023 .199
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Table 3
Probability <=50% Probability > 50%Chance Mode Model: likelihood (B = 3.899, p < .001)
Model: knowledge(ns)
Model: likelihood, (B = 4.345, p < .001) knowledge (B = -1.179, p < .05)
Model: likelihood (B = 3.630, p < .001)
Model: knowledge (B = 2.184, p < .001)
Model: likelihood (B = 2.958, p < .001) Knowledge (B = 1.063, p < .05)
Sure Mode Model: likelihood (B = 5.191, p < .001)
Model: knowledge (ns)
Model: likelihood (B = 5.294, p < .001) knowledge (ns)
Model: likelihood (B = 5.746, p < .001)
Model: knowledge (B = 2.767, p < .001)
Model: likelihood (B = 5.502, p < .001) knowledge (ns)
Page 40
Table 4
Questions Statements and Inferred Thoughts Proportion of Respondents
Question 1 Doctor Ames says: “I am 80% sure that you have Crohn’s disease.”“This patient has most of the signs and symptoms of Crohn’s disease.”
62% (62%)
Doctor Baker says: “There is an 80% chance that you have the Crohn’s disease.”“Most of the patients I have seen with these signs and symptoms have Crohn’s disease.”
61% (62%)
Question 2 Dick says: “I am 70% sure that the Celtics will beat the Knicks tonight.”“The Celtics have a stronger lineup of players than the Knicks.”
72% (75%)
George says: “I think there is a 70% chance the Celtics will beat the Knicks tonight.”“The Celtics have a better win-loss record than the Knicks.”
73% (75%)
Question 3 Cade says: “I am 80% sure that I will be married within three years.”has a specific person in mind to marry.
86% (86%)
Peter says: “I think there is an 80% chance that I will be married within three years.”
Question 4 Ellen says: “I am 60% sure I will go to the beach this month.”
Sarah says: “I think there is a 60% chance I will go to the beach this month.”is thinking about how often she tends to go the beach in a typical month.
66% (66%)
Question 5 Derek says: “I am 90% sure that Chip wore a vest sometime last week.”saw Chip last week.
92% (92%)
Lyle says: “I think there is a 90% chance that Chip wore a vest sometime last week.”is thinking about how often Chip tends to wear vests.
91% (92%)
Question 6 Miguel says: “I am 80% sure the Warriors won last night.”is trying to recall the outcome of the game that he read in the newspaper.
81% (85%)
Noah says: “I think there is an 80% chance the Warriors won last night.”
Question 7 Emily says: “I’m 70% sure Brian parked his car in lot C today.”
Sabrina says: “I think there is a 70% chance Brian parked his car in lot C today.”is thinking “Brian parks in lot C on most days.”
75% (61%)
Question 8 Mr. and Mrs. Adams say: “We are 90% sure we are going to have a baby in the next few years”are uncertain about their decision to conceive.
71% (74%)
Mr. and Mrs. Bing say: “We think there is a 90% chance we will have a baby in the next few years”are uncertain about their ability to conceive.
72% (74%)
Page 41
Question 9 Suzanne says: “I am 60% sure my new restaurant will be profitable.”thinks that success depends mostly on individual effort and ability.
91% (91%)
Wendy says: “I think there is a 60% chance my new restaurant will be profitable.”thinks that success depends mostly on factors outside of one’s control.
91% (91%)
Question 10
Colin says: “I am 70% sure I’ll win the poker tournament.”is thinking about his own poker skill.
80% (83%)
Shane says: “I think there is a 70% chance I’ll win the poker tournament.”is thinking about the poker skill of all players in the tournament.
81% (83%)
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