Risk Analysis
DOI: 10.1111/j.1539-6924.2011.01644.x
Affective and Cognitive Factors Influencing Sensitivity
to Probabilistic Information
Tadeusz Tyszka and Przemyslaw Sawicki∗
In study 1 different groups of female students were randomly assigned to one of four probabilistic information formats. Five different levels of probability of a genetic disease in an
unborn child were presented to participants (within-subject factor). After the presentation
of the probability level, participants were requested to indicate the acceptable level of pain
they would tolerate to avoid the disease (in their unborn child), their subjective evaluation
of the disease risk, and their subjective evaluation of being worried by this risk. The results
of study 1 confirmed the hypothesis that an experience-based probability format decreases
the subjective sense of worry about the disease, thus, presumably, weakening the tendency to
overrate the probability of rare events. Study 2 showed that for the emotionally laden stimuli,
the experience-based probability format resulted in higher sensitivity to probability variations
than other formats of probabilistic information. These advantages of the experience-based
probability format are interpreted in terms of two systems of information processing: the
rational deliberative versus the affective experiential and the principle of stimulus-response
compatibility.
KEY WORDS: Communicating probabilistic information; experience-based decisions; genetic disease;
risk; sensitivity to probabilistic information
likelihood of having a child with a genetic disease,
power plant accident, etc. These problems concern
(1) people’s overrating small probabilities, and (2) insensitivity to changes in the magnitude of these probabilities.
There have been a lot of findings about the
phenomenon of overrating small probabilities. In
the 1950s, Attneave(1) found that the estimations
of English letters were highly correlated with actual frequencies of these letters in English. However,
his subjects overestimated frequencies of infrequent
letters and underestimated frequencies of frequent
letters. Similarly, Lichtenstein, Slovic, Fischhoff,
Layman, and Combs(2) in their study on judgments
of frequency of various causes of death found that
rare causes of death were overestimated and common causes were underestimated. Finally, as shown
in Fig. 1, one of the central assumptions of prospect
1. INTRODUCTION
In many domains, there is the problem of how
to present information on the likelihood of various
events against which people have to choose an appropriate (commensurate) level of protection. Examples
are informing people about the likelihood of accidents associated with various technologies. In a medical context, there is the question of informing patients about the probability of various diseases, etc.
Generally, people who are not trained in statistics
and the concepts of probability are not particularly
good at understanding and evaluating probabilistic
information. In particular, people have serious problems with estimating small probabilities, such as the
Kozminski University, Warsaw, Poland.
∗ Address correspondence to Przemyslaw Sawicki, Jagiellonska 59,
Warsaw 03-301, Poland; [email protected].
1
C 2011 Society for Risk Analysis
0272-4332/11/0100-0001$22.00/1 2
Fig. 1. Hypothetical probability weighting function.
theory is that in risky situations people underweight
moderate and large probabilities but overweight rare
events. Several empirical studies(3−5) confirmed these
properties of the prospect theory probability weighting function. Most likely, such a probability weighting function is related to people’s overrating small
probabilities.
The problem of insensitivity to changes in magnitude of small probabilities was extensively studied
by Kunreuther et al.(6) They tried various ways to
improve people’s sensitivity to very low probabilities (e.g., of hypothetical discharge of toxic chemicals
by a plant). The authors found that the best way of
communicating probabilities to ordinary people is to
make available comparison stories (scenarios), which
allow them to judge differences between probabilities.
A somewhat similar result was obtained by
Siegrist et al.(7) They compared the effectiveness of
four different formats (both graphical and numerical) of risk communication. The authors found that
only the paling perspective scale resulted in the subject discriminating between two different levels of
risk of having a newborn with Down’s syndrome. In
this format (similar to that used by Kunreuther(6) ),
the subject could compare communicated risk with
other risks, such as any chromosomal anomaly or
major congenital anomaly. Thus, again the availability of comparisons allowed one to judge differences
between probabilities. Still, as shown by Ancker,
Weber, and Kukafka,(8) even different arrangement
of stick figures representing health risks may have an
impact on perception of the risk.
Tyszka and Sawicki
In the present article, we focus on how to improve judgments of low probabilities in the context of
medical diagnosis. More specifically, we deal with the
question of how to improve in communicating information about the probability of Down’s syndrome—
a genetic condition caused by extra genes from the
21st chromosome that result in certain characteristics including some degree of mental retardation, or
cognitive disability, and other developmental delays.
Two types of factors that potentially improve differentiation between low probabilities are considered
cognitive and affective factors.
There is evidence that different ways of communicating the same information about probability can
change its perception. Gigerenzer and his collaborators(9,10) claim that frequencies are better understood
by people than probabilities or percentages. For example, people can easily understand the meaning of
the statement that 3 people in 100 have a certain disease, while some may have problems with adequately
understanding the statement that 3% of persons have
this disease. Gigerenzer and his collaborators,(9,10) as
well as Cosmides and Tooby,(11) claim that in the natural environment, people encounter frequencies of
actual events and that they store and operate on this
information.
However, Denes-Raj and Epstein(12) showed
that when offered a choice between two bowls with
one containing 9 in 100 winning beans and another one containing 1 winner in 10, many participants preferred the first bowl. Thus, participants
preferred a greater absolute number rather than a
better proportion of winning beans. Similarly, when
Yamagishi(13) asked respondents to evaluate a risk
of death in the population due to different causes,
he found that the judged degree of riskiness was
affected by the number of deaths but not by the
proportion of fatal cases caused by a given disease. It turned out that people perceived the risk
as higher when a given number of fatal cases was
greater, irrespective of the total number possible.
For example, the judged degree of riskiness was perceived higher when the proportion of fatal cases was
given in reference to 10,000 (e.g., 1,286 cases out of
10,000) than in reference to 100 (e.g., 12.86 cases out
of 100). Thus, frequencies can be misperceived as
well.
It is interesting that both proponents of “natural” frequencies(9) as well as proponents of comparison stories(6) used numbers when presenting people information about the probability (or frequency),
and also when asking them to evaluate the risk.
Sensitivity to Probabilistic Information
Contrary to this, and in line with Cosmides and
Tooby,(11) one can think that during their evolution,
humans made their decisions using no numbers at
all, but based on frequencies encoded and stored in
memory from their trial-by-trial experience.
As already mentioned, there is a somewhat forgotten series of experiments started in the 1950s (see,
e.g., Attneave(1) ) that shows that when people are
presented with sequential displays of binary events
(such as letters, words, lights, etc.), without mentioning any numbers, their estimations of frequency of
occurrence are remarkably accurate. For example,
Hintzman(14) presented to his subjects a list of short
words in which some words were repeated. Following the presentation, subjects were tested to estimate
frequencies of occurrence of different words. The
respondents turned out to be very sensitive to actual frequencies of occurrence of the words (for an
overview of some early research, see Peterson and
Beach(15) ).
Most recently Hertwig, Barron et al.(16) made a
differentiation between decisions from descriptions
and decisions from experience. People make decisions from descriptions when the outcome of each
option and the probabilities of this outcome are provided, and the information is conveyed visually (e.g.,
using a pie chart or frequency distribution). People
make decisions from experience when they rely on
personal experience, without a description of possible outcomes (e.g., whether to back up a computer’s
hard drive, cross a busy street, or go out on a date).
Hertwig et al.(16) claim that decisions from experience
and decisions from description can lead to dramatically different choice behavior. In the case of decisions from description, people make choices as if
they overrated the probability of rare events, as described by prospect theory. On the other hand, in the
case of decisions from experience, people make decisions as if they underrated the probability of rare
events.
From the above findings and the claim of
Cosmides and Tooby(11) that in their natural environment humans are accustomed to making decisions based upon experience, i.e., on naturally
encountered frequencies, one could suppose, that
with the experience-based probability format, people would be more accurate in their assessments
than with any numerical format. On the basis
of this general assumption, we formulated two
hypotheses.
Hypothesis 1 is based on the following reasoning: with a numerical format, people tend to overrate
3
the probabilities of rare events. On the other hand,
with the experience-based probability format, people
should be more accurate in evaluating the probability
of rare events than with numerical formats. Assuming that the evaluation of riskiness is based on the
perceived probability of the events, we predict the
following:
Hypothesis 1: Under the experience-based probability format, evaluations of riskiness
associated with rare events will be
lower than those under other formats of probabilistic information (e.g.,
percentages, frequency).
Hypothesis 2: Compared to other formats of probabilistic information (e.g., percentages,
frequency), in their perception, people will be most sensitive to probability
variations when observing a sequence
of events (experience-based probability).
Recent research shows that when outcomes of
risky choices are heavily emotionally laden, subjects become insensitive to probability variations. Indeed, Hsee and Rottenstreich(17) showed that the
shape of prospect theory’s S-shaped weighting function changes, depending on the affective reactions associated with the potential outcomes of risky choices.
They demonstrated that affect-rich outcomes (those
evoking strong emotional reactions), as opposed to
affect-poor ones, resulted in lower sensitivity to intermediate probability variations. In other words,
the S-shaped weighting function becomes flatter for
affect-rich outcomes (see Fig. 2).
In line with such findings, Loewenstein et al.(18)
proposed the “risk-as-feelings” model, according
to which, affect, experienced at the moment of
decision making, influences risk assessments. Following this line of research, we decided to test
whether the insensitivity to probability variations
for emotionally laden stimuli concerns not only the
weighting function, but also the perception (estimation) of probability. We formulated the following
hypothesis:
Hypothesis 3: In their perception of risk, people are
more sensitive to probability variations when the event is less emotionally laden.
4
Fig. 2. Hypothetical S-shape probability weighting function for
affect-poor and affect-rich stimuli.
2. STUDY 1
2.1. Method
2.1.1. Participants and Procedure
Female students (N = 161) enrolled at Warsaw
Agricultural University participated in the study. The
women’s age ranged between 20 and 25 years.1 Participants were requested to read the following instruction:
“Please imagine, that you plan to have a child.
You go for genetic consulting and during the visit the
doctor informs you that there is a risk of a genetic
disease in your child.”
After that, participants were given probabilistic information of a genetic disease in a newborn
child. Depending on experimental conditions, probabilistic information was communicated via different
formats.
As one can see in Table I, the participants were
randomly assigned to one of five experimental conditions. Conditions differed in respect to the format
in which the probabilistic information was presented.
In conditions 1 and 2, we used the same communication format. The only difference between them was
the photo of a child with a genetic disease. In addition to mental retardation and other developmen-
Tyszka and Sawicki
tal delays, some common physical traits of Down’s
syndrome are an upward slant of the eyes, flattened
bridge of the nose, and decreased muscle tone. Consequently, our two photos of a child with Down’s
syndrome differed with respect to some of these
physical traits. In condition 1 the moderate form of
genetic disease was presented (in this way evoking
low affective stimuli), whereas in condition 2 the severe one was presented (in this way evoking high
affective stimuli). The outcomes of the events were
randomized for each of the five probability levels.
Photographs were presented repeatedly for 0.7 seconds each, with 0.2 seconds interval between them.
Thus, the total presentation lasted less than two
minutes.
In the frequency format, the number of occurrences of a child with Down’s syndrome out of 100
was presented. In the scenario format, the number of black balls (representing a child with Down’s
syndrome) in the urn containing 100 balls was presented. In the graphical representation format, a
chart with 100 (graphic) images—some of which were
red and some of which were green—representing
the proportion of healthy to unhealthy children was
presented.
Using the formats five different types of probabilistic information were communicated. After each
one, participants were requested to indicate in the
specially created questionnaire: (1) the acceptable
level of pain they would tolerate to avoid the disease,2 (2) subjective evaluation of the disease risk,
and (3) subjective evaluation of being worried by
this risk. Participants answered on a visual analog
scale. As for the declared acceptable level of pain,
participants indicated the most intense pain level
they would tolerate suffering as mothers to prevent
a given risk of the genetic disease in their child.
Similarly, subjective evaluation of the risk that the
disease will occur was measured on a visual analog
scale ranging from “complete lack of risk” to “extremely high risk.” Finally, subjective evaluation of
being worried by the possibility of the disease was
also measured on a visual analog scale ranging from
“extremely calm” to “extremely anxious.”
Between each evaluation of probability, participants had a three-minute break during which they
1 Generally,
the chance of having a Down’s syndrome birth is related to the mother’s age. The odds of having a child with Down’s
syndrome at age 35 are much higher than under age 25. Thus, the
young women answering our survey were not at high risk of having a Down’s syndrome child. Still, most of them were presumably concerned with our experimental task.
2 The
scale of pain could be associated with the Chorionic Villus
Sampling (CVS) procedure, being a diagnostic prenatal test, considered by most women as a painful procedure that causes considerable discomfort and psychological distress.
Sensitivity to Probabilistic Information
5
Table I. Characteristics of Five Experimental Conditions (Four Formats of Communicating Probabilistic Information, with One Being
Subdivided into Two Variants) of Representation of Five Probability Levels
Communication Format
(Between Subjects)
Condition
1
Experience based with weaker affective
stimuli
2
Experience based with stronger affective
stimuli
3
Frequency
4
Scenario
5
Graphical representation
Specification
A sequence of 100 binary events represented by two
photos—one of a healthy child and the other of a
child with a moderate form of Down’s syndrome
A sequence of 100 binary events represented by
two photos—one of a healthy child and the other
of a child with a severe form of Down’s syndrome
Explicitly expressed frequency (e.g., three in one
hundred)
“Balls in the urn” scenario (e.g., 3 black balls and
97 white balls)
A chart with 100 (graphic) images, representing the
proportion of healthy to unhealthy children
were listening to a fragment of a poem (as an experimental filler).
2.2. Results
We did not find any differences between less and
more affectively laden groups under the experiencebased probability format. Therefore, in the analyses below we put together the data from these two
groups. Since one of our three dependent measures,
that of subjective evaluation of riskiness, revealed a
different pattern of results than the two other measures, first we present analyses on the scale of pain
and the scale of worry, and separately for the evaluation of riskiness. Figs. 3 and 4 represent average
evaluations of the five risk levels on the scales of
pain and worry in the four probability formats. As
can be seen, in comparison with other communication formats, under the experience-based probability
format, participants were less worried by the risk of
the disease, and accepted a lower level of pain that
they would tolerate to avoid the disease. One-way
ANOVA for four information formats, with five risk
levels as a repeated factor performed on evaluations
on the scale of pain and worry, revealed significant
effects of both level of risk (F[4;157] = 25.71; p <
0.001 for the scale of pain, and F[4;157] = 73.28; p <
0.001 for the scale of worry) and information format
(F[3;157] = 5.24; p < 0.01 for the scale of pain, and
F[3;157] = 3.98; p < 0.01 for the scale of worry).
Thus, our results confirm hypothesis 1 that under
the experience-based probability format evaluations
of riskiness associated with rare events were lower
Five Probability Levels
(Within Subjects)
0.01
0.03
0.06
0.12
0.20
than under any other format of probabilistic information. Assuming that evaluations on both scales are
based on perceived probability of the disease, our results imply that under the experience-based probability format, people’s evaluations of rare events were
less overrated than under any other format of probabilistic information.
Regarding the evaluation of riskiness, the oneway ANOVA for four information formats, with five
risk levels as a repeated factor, revealed significant
effects of information format (F[3;157] = 3.08; p <
0.05). However, in this case evaluations of riskiness
associated with rare events were lowest for the frequency format of probability. As we will see in study
2, this effect was not replicated; therefore, we tend to
attribute this to the vagueness of the notion of “risk”
in ordinary people’s cognition.
In accordance with our hypothesis 2, one should
also expect an interaction effect of the information format and the level of risk. However, one-way
ANOVA for four information formats, with five risk
levels as a repeated factor, performed on evaluations
on the scale of pain and worry, revealed no significant
interaction effects. Thus, the data did not support hypothesis 2 that, compared to other formats of probabilistic information (e.g., percentages, frequency),
in their perception people will be most sensitive to
probability variations when they observe a sequence
of events (experience-based probability).
As already mentioned, we also did not confirm
hypothesis 3 that under the experience-based probability format, people are more sensitive to probabilistic information when it is less affectively laden.
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100
Evaluations of risk level on the scale of pain
90
80
70
Fig. 3. Average evaluations of the five
risk levels on the scale of pain in the four
formats of communicating probabilistic
information.
60
50
40
30
0.01
0.03
0.06
0.12
0.20
Probabilities of adverse state
Experience-based
Chart
Scenario
Frequency
100
Evaluations of risk level on the scale of worry
90
80
70
60
Fig. 4. Average evaluations of the five
risk levels on the scale of worry in the
four formats of communicating
probabilistic information.
50
40
30
20
10
0.01
0.03
0.06
0.12
0.20
Probabilities of adverse state
2.3. Discussion
We confirmed the hypothesis that under the
experience-based probability format, evaluation of
worry and other reactions to riskiness associated with
rare events were lower than under numerical formats of probabilistic information. This may imply
that under the experience-based probability format,
people’s evaluations of small probabilities were less
overrated than under any other format. However,
Experience-based
Chart
Scenario
Frequency
our procedure did not allow us to directly test this
claim. Still, our result is in agreement with findings
by Hertwig et al.,(16) who showed that people overestimated the probabilities of rare events when they
were taken from descriptions and underestimated
these probabilities when they came from participants’ direct experience. Although we did not study
how people weigh the probability of rare events in
making decisions, and instead studied subjectively
perceived probabilities, we think that our finding is
Sensitivity to Probabilistic Information
pertinent to the problem raised by Hertwig et al.(16)
These authors explain the underweighting of rare
events probability learned from experience by the
fact that respondents tended to draw too few samples (median draws per problem = 15), which led
to skewed distributions and to less frequent occurrences of the rare event than in reality. Our results
demonstrate that Hertwig’s(16) explanation is not sufficient. In our study, participants did not choose how
many draws they would take to learn the distribution; instead, each participant experienced the same
sequence of 100 events with a specified number of
minority events (1%, 3%, etc.).
Thus, people’s underweighting of a rare event
probability under its numerical format must be an
effect of more basic cognitive processes than limited search effort and the resulting skewed observed
distributions. We believe it may be related to how
probabilistic information expressed in different formats is processed. As is well known, human cognition works through two distinct processes: system 1,
which corresponds to intuitive thought, and system
2, which corresponds to rational thought.(18−21) In
Kahneman’s(20) words: The operations of system 1
are fast, automatic, effortless, associative, and often emotionally charged . . . The operations of system
2 are slower, serial, effortful, and deliberately controlled . . . .
Following this distinction, we can assume that
when the experience-based format (where no numbers are involved) is used, it originates in operations
of system 1, which generates automatic, effortless impressions. On the other hand, processing of numbers
concerns the deliberative mode of thinking. It requires the individual to have specific knowledge and
abilities. Indeed, as shown by Peters et al.,(15) in these
type of tasks high-numeracy people have an advantage over those with low numeracy. Still, both groups
of people have problems with mental arithmetic.(22)
Now, the question remains which of the two
systems facilitates processing of probabilistic information? As research shows, information processing
is strongly affected by stimulus-response compatibility.(23,24) As shown by Fischer and Hawkins(25)
one of the categories of compatibility is scale compatibility (see also Hawkins(26) ), i.e., the similarity between input and output. Generally speaking, stimulus-response compatibility facilitates performance (in both judgments and decision making).
One can assume that in our case, where individuals were faced with the tasks of assessment regarding being worried by the possibility of the disease,
7
or accepting pain to avoid the child’s possible disease, system 1 is activated. Thus, we can expect the
experience-based format of probability to be more
compatible with such output, compared to numerical formats of probability presentation. This inputoutput compatibility should result in more accurate
evaluations.
Naturally, when looking at participants’ levels of
worry and willingness to tolerate pain, there is no
way to directly assess the accuracy of the evaluation of risk levels. Neither are we able to directly
test whether people’s evaluations of rare events were
over- or underrated. However, we found that when
the experience-based format was used, people’s assessments of worry, etc. were lower than when numerical formats were used. From earlier research, we
know that when using numerical formats people tend
to overrate the probabilities of rare events. From this
we can infer that people’s evaluations of the probabilities of rare events when using the experiencebased format are perhaps less overrated than when
using numerical formats. In this sense one can claim
that when using the experience-based probability
format, people’s evaluations of risk levels are more
accurate than when using numerical formats.
However, our study did not support the hypothesis that people would be more sensitive to probabilistic information with the experience-based probability format, as compared to the numerical formats
of probabilistic information. Neither did we find that
people were less sensitive to probabilistic information when the stimulus was affectively laden.
The question remains how probabilistic information is represented under graphical representation.
On the one hand, in this format, probabilities are
not expressed in numbers. Yet on the other hand,
upon seeing a graphical representation consisting of
two kinds of elements, the observer can easily translate the observed proportions into numbers. In any
case, this format is not the equivalent to sequentially
learned experienced frequencies. Our results suggest
that the graphical representation format is closer to
the numerical formats than to the experience-based
format.
Of course, it is possible that the strength of
our experimental manipulation was inadequate. The
two photos of a child with a genetic disease possibly did not differ enough to evoke lower versus
higher affective reactions. However, the lack of a
difference in sensitivity to probability variations between groups, in response to more versus less emotionally loaded stimuli, could be characteristic of the
8
experience-based probability format, whereas not of
the other formats. We decided to test this conjecture
in the next experiment.
3. STUDY 2
The purpose of study 2 was to test the difference in sensitivity to probability variations, under
different probability formats, for emotionally laden
stimuli. It is well known that emotionally loaded
stimuli often deteriorate performance. Indeed, Hsee
and Rottenstreich(17) showed that when stimuli were
strongly emotionally loaded, individuals were insensitive to probability variations. Moreover, one can
speculate that emotionally loaded stimuli deteriorate
performance when they require a sufficiently substantial cognitive effort, while they need not deteriorate performance if the task does not require such
an effort. For this very reason, in some judgmental
tasks, stimulus-response compatibility facilitates performance, while in other tasks it does not. It does so
when the task requires substantial cognitive effort. In
such tasks, the stimulus-response compatibility simply reduces cognitive effort.
Similarly, stimulus-response compatibility may
be an important factor in the assessment of worry, or
other feelings of riskiness. The assessment of worry
seems to be more compatible with the direct experience of the frequency of dangerous events in system 1, than with deliberate reasoning about the probability of dangerous events when this is presented in
a numerical format in system 2. Therefore, the assessment of worry, etc. when it originates in system 1
should be less affected by emotional distortion than
assessment of worry when it originates in system 2.
In line with the above reasoning, we formulated the
following hypothesis:
Hypothesis 4: For the emotionally laden stimuli, the
experience-based probability format
will result in higher sensitivity to probability variations than other formats of
probabilistic information.
3.1. Method
3.1.1. Participants and Procedure
Female students (N = 176) enrolled at two
Warsaw universities were randomly assigned to one
of the six experimental conditions. The instruction
and procedure of study 2 were similar to those of
study 1. However, three formats of communicating
Tyszka and Sawicki
probabilistic information (experienced-based, frequency, scenario) were employed, instead of the four
in study 1.
Each of the three formats was employed in two
variants. In variant 1 participants were informed
about the probability without seeing a photo of a
child, whereas in variant 2 in addition to information
on probability, participants were shown a photo of a
child with a severe case of Down’s syndrome.
Thus, in the case of the experience-based format,
participants were presented with a sequence of 100
labels “healthy child” and “unhealthy child” in variant 1, or a sequence of 100 photos of a child without Down’s syndrome and with Down’s syndrome in
variant 2. In the frequency and in the scenario formats, in the case of the emotionally laden stimuli,
a photo of a child with Down’s syndrome was presented in addition to the corresponding numerical information.
After learning the probabilistic information
about a genetic disease, the participant was asked to
fill in a questionnaire—similar to the procedure in
the first study. Also, as in the first study, between
each evaluation of probability, participants had a
three-minute break during which they listened to a
fragment of a poem (as an experimental filler).
3.2. Results
Figs. 5, 6 and 7 represent the mean evaluations
of risk levels (averaged over five risk levels) on the
scales of pain, worry, and risk in the three probability formats, for the affect-poor (without photo) and
affect-rich stimuli (being shown a photo of child with
a severe form of Down’s syndrome). As is visible,
evaluations on pain, worry, and risk are higher for
the affect-rich than for the affect-poor stimuli. Performing two-way ANOVA (two levels of emotionally laden stimuli × three formats of communicating probabilistic information, with five risk levels as
repeated factor) on the scores on the scale of pain,
worry, and risk revealed significant effects of affect
for the scale of pain (F[1;170] = 11.27; p < 0.001),
for the scale of worry (F[1;170] = 12.00; p < 0.001),
and for the scale of risk (F[1;170] = 12.27; p < 0.001).
Similarly, the analysis revealed significant effects of
format for the scale of pain (F[2;170] = 13.90; p <
0.001), for the scale of worry (F[2;170] = 9.46; p <
0.001), and for the scale of risk (F[2,170] = 6.93; p
< 0.001). As can be seen, compared to other communication formats, evaluations of risk are generally
lowest under the experience-based probability format. Finally, for both scales, the analysis revealed
Sensitivity to Probabilistic Information
9
100
Evaluations of risk level on the scale of pain
90
80
70
60
50
40
30
20
10
0.01
0.03
0.06
0.12
0.20
0.01
Affect-rich stimuli
0.03
0.06
0.12
0.20
Frequency
Scenario
Experience-based
Aff ect-poor stimuli
Fig. 5. Mean evaluation scores (averaged over five risk levels) on the scale of pain in the three formats of communicating probabilistic
information for the affect-poor (without picture) and affect-rich stimuli (with picture).
F(8, 680)=2.6463, p=.00731
100
Evaluations of risk level on the scale of worry
90
80
70
60
50
40
30
20
10
0.01
0.03
0.06
0.12
Affect-rich stimuli
0.20
0.01
0.03
0.06
0.12
0.20
Frequnecy
Scenario
Experience-based
Affect-poor stimuli
Fig. 6. Mean evaluation scores (averaged over five risk levels) on the scale of worry in the three formats of communicating probabilistic
information for the affect-poor (without picture) and affect-rich stimuli (with picture).
10
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80
Evaluations of risk level on the scale of risk
70
60
50
40
30
20
10
0
-10
0.01
0.03
0.06
0.12
0.20
Affect-rich stimuli
0.01
0.03
0.06
0.12
0.20
Frequency
Scenario
Experience-based
Affect-poor stimuli
Fig. 7. Mean evaluation scores (averaged over five risk levels) on the scale of risk in the three formats of communicating probabilistic
information for the affect-poor (without picture) and affect-rich stimuli (with picture).
significant affect–format interaction effects (for the
scale of pain F[2;170] = 4.16; p < 0.05, for the scale of
worry F[2;170) = 5.67; p < 0.01), and for the scale of
risk (F[2,170] = 5.39; p < 0.01). For pain, worry, and
risk the differences in evaluations between affectrich and affect-poor stimuli were higher under both
numerical formats than for the experience-based
probability format.
To further test the hypothesis concerning people’s sensitivity to probability variations, we analyzed
the differences between evaluations of the highest
(0.20) and lowest (0.01) risk levels, on each of the
scales separately. Figs. 8, 9, and 10 show these differences. As can be seen, for both numerical probability formats—frequency and scenario—participants
were much less sensitive to changes in probability
60
Difference in evaluations on the scale of pain
50
40
Fig. 8. The difference between
evaluations of the highest (0.20) and
lowest (0.01) risk levels on the scale of
pain for affect-rich and affect-poor
stimuli.
30
20
10
0
Frequency
Scenario
Experience-based
Affect-rich stimuli
Affect-poor stimuli
Sensitivity to Probabilistic Information
11
Difference in evaluations on the scale of worry
60
50
40
Fig. 9. The differences between
evaluations of the highest (0.20) and the
lowest (0.01) risk levels for the scale of
worry for affect-rich and affect-poor
stimuli.
30
20
10
0
Frequency
Scenario
Experience-based
Affect-rich stimuli
Affect-poor stimuli
60
Difference in evaluations on the scale of risk
50
40
Fig. 10. The differences between
evaluations of the highest (0.20) and the
lowest (0.01) risk levels for the scale of
risk for affect-rich and affect-poor
stimuli.
30
20
10
Affect-rich stimuli
Affect-poor stimuli
0
Frequency
Scenario
Experience-based
when they were shown a photo of a child with severe Down’s syndrome versus not being shown the
photo. On the other hand, such a difference was
not observed in the case of the experienced probability format. Two-way ANOVA performed on differences between evaluations on the scale of pain
(two levels of emotionally laden stimuli × three information formats) revealed a significant affect effect (F[1;170] = 7.20; p < 0,01). At the same time,
there was a significant format–affect interaction effect (F[2;170] = 4.46; p < 0.05). Similarly we found
a significant affect effect for the scale of worry
(F[1;170] = 12.57; p < 0.001) and for the scale of
risk (F[1;170] = 8.99; p < 0.001), and significant interaction format–affect effect for the scale of worry
(F[2;170] = 9.74; p < 0.001) and for the scale of
risk (F[2;170] = 5.78; p < 0.01). Thus, while in
the case of less emotionally laden stimuli, sensitivity
12
to probabilistic information did not differ between
various formats, in the case of more emotionally
laden stimuli, the assessments were more sensitive
to probability changes under the experience-based
probability format than under the two other formats
(frequency and scenario).
3.3 Discussion
The results of our second experiment show
the advantage of the experienced probability format over other probability formats is particularly
prominent when the risk being evaluated is affectively laden. Indeed, it turned out that only with the
experience-based probability format, the subjects’
evaluations of risk were not affected by how heavily
emotionally laden the stimulus was. Our interpretation of this finding is that when the experience-based
format (where no numbers are involved) is used, it
originates in operations of system 1, which generates
automatic, effortless impressions. On the other hand,
when probabilities are presented in a numerical format, it originates in deliberate reasoning in system 2.
Some support for this claim can be found in probability learning experiments. In these tasks, participants are presented with a repeated choice between
two responses, one of which has a higher payoff probability than the other (e.g., 70% vs. 30%). The participant is required to predict which of two events will
occur in each trial. In these tasks it is commonly observed that participants match their response probabilities to the payoff probabilities. Such a probability matching strategy is obviously suboptimal.
(Optimal is a pure strategy to consistently choose the
more frequent response.) What is, however, important in the present context is that probability matching implies that subjects learn the stimuli probabilities exceptionally well. What is even more important,
probability matching behavior is also observed in experiments with animals.
We further assume that the assessment of worry,
or other feelings of riskiness, is more compatible with
the experience of frequency of dangerous events in
system 1 than with deliberate reasoning about the
probability of a dangerous event when this is presented in a numerical format in system 2. Therefore,
the assessment of worry, etc. when it originates in experience of frequency is easier than the assessment of
worry, etc. when it originates in deliberate reasoning
in system 2. As a result, the assessment of worry, etc.
when it originates in system 1 is less affected by emotional distortion than the assessment of worry, etc.
when it originates in system 2
Tyszka and Sawicki
Therefore, under the experienced probability
format, people’s evaluations could be sensitive to
frequency information, regardless of how emotionally laden the stimulus is, whereas under the numerical formats, evaluations were more affected by emotional distortion, and thus less sensitive to frequency
information.
However, it is also possible that under the
experience-based probability format, repeated presentation of the same emotionally laden stimulus
(photo of a child with Down’s syndrome) could result in emotional habituation, thus the difference between evaluating affect-poor and affect-rich stimuli
disappeared. The present experiments do not allow
us to decide which of the above explanations is correct. Further research is needed to answer this question. Similarly of interest to future research would
be the claim that when the individual is required
to make a cognitive assessment, the rational system
should be better than the experiential system at extracting frequency information from the probability
presentations.
4. GENERAL DISCUSSION
Our results show some advantages of using the
experience-based format for communicating probabilistic information. Firstly, the experience-based
probability format seems to weaken the tendency to
overrate the probability of rare events. Secondly, under all but the experience-based probability format,
people are less sensitive to probabilistic information
when it is affectively laden. These are two important
advantages, as people’s overrating of small probabilities and their insensitivity to probability variations in
the case of emotionally laden stimuli seem to be the
two most serious problems concerning communicating probabilities to ordinary people.
Where do these advantages of using the
experience-based format for probability information
come from? According to Cosmides and Tooby,(11)
in the evolutionary process, humans had to develop
mechanisms allowing them to utilize frequency information (e.g., when going hunting for game in a given
direction, you were successful in 5 out of 20 hunts).
In any case, there is much evidence that people easily learn frequencies from their environment and use
this when performing various tasks. For example,
research on reading shows that the frequency with
which words are used strongly influences the speed of
reading.(27) Hasher and Zacks(28) showed that even
very young (preschool) children encode frequency
Sensitivity to Probabilistic Information
information accurately. They also found no developmental differences in the accuracy of judgments
about frequency. Based on these findings, the authors
claim that frequency is automatically encoded and
stored in human memory.
Gigerenzer and his collaborators(9,10) claim that
the “natural” format for probability information is
the frequency (“as actually experienced in a series
of events, rather than probabilities or percentages,”
p. 5). We certainly agree with this claim. However,
we are surprised that in their experiments, these authors did not present “actual series of events” to
their subjects, but numbers—although in the format of frequencies rather than probabilities or percentages. Our results show that what really matters is whether one uses numbers (frequencies or
probabilities or percentages) or an “actual series of
events.” We think that only in the latter case can
people fully comprehend the meaning of frequencies. Thus, information on probability should be presented not in the form of numbers, but as a sequential display of events. As our research shows,
only this format facilitates the accuracy of evaluating the risk level, as well as sensitivity to probability
variations.
Naturally, there are also disadvantages to using an experience-based format. First, using this format to communicate probabilities requires a certain
amount of time. Actually, not very much time is
needed, as shown in our experiment. The more serious disadvantage for practitioners is the need to prepare material fitting events, the probability of which
we want to communicate. More specifically, one has
to construct a series of events corresponding to the
problem in question. For example, a physician could
prepare a series similar to the one used in our experiment (a sequence of pictures of a child with the disease versus a child without the disease), and present
this to patients (or parents) interested in knowing the
risk of birthing a child with a given disease. Still, such
a procedure seems to be superior over the one proposed by Kunreuther, Novemsky, and Kahneman,(6)
which requires looking for familiar context information to create appropriate comparison stories (scenarios). Perhaps, the most serious problem with using an experience-based format is that it is not suitable for cases dealing with extremely small probabilities, such as considered by Kunreuther et al.(6) One
cannot feasibly produce a series when the event of
interest occurs once in a million, etc. So perhaps for
such cases, the procedure proposed by Kunreuther et
al.(6) is necessary.
13
ACKNOWLEDGMENTS
The authors thank two anonymous reviewers for
their helpful comments on the earlier version of this
article. This article is based on work supported by
EC Contact LSHB-CT-2004-505243, “Special NonInvasive Advances in Foetal and Neonatal Evaluation Network” (SAFE).
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