RESEARCH REPORT

To Risk or Not to Risk: Anxiety and the Calibration Between RiskPerception and Danger Mitigation

Lies Notebaert, Stijn Masschelein, Bridget Wright, and Colin MacLeodUniversity of Western Australia

Anxiety prepares an organism for dealing with threats by recruiting cognitive resources to processinformation about the threat, and by engaging physiological systems to prepare a response. Heightenedtrait anxiety is associated with biases in both these processes: high trait-anxious individuals tend to reportheightened risk perceptions, and inappropriate engagement in danger mitigation behavior. However, noresearch has addressed whether the calibration between risk perception and danger mitigation behavioris affected by anxiety, though it is well recognized that this calibration is crucial for adaptive functioning.The current study aimed to examine whether anxiety is characterized by better or worse calibration ofdanger mitigation behavior to variations in risk magnitude. Low and high trait-anxious participants werepresented with information about the likelihood and severity of a danger (loud noise burst) on each trial.Participants could decide to mitigate this danger by investing a virtual coin, at the cost of losing dangermitigation ability on subsequent trials. Importantly, level of risk likelihood and severity were variedindependently, and the multiplicative relationship between the 2 defined total danger. Multilevelmodeling showed that the magnitude of total danger predicted the probability of coin investments, overand above the effects of risk likelihood and severity, suggesting that participants calibrated their dangermitigation behavior to integrated risk information. Crucially, this calibration was affected by trait anxiety,indicating better calibration in high trait-anxious individuals. These results are discussed in light ofexisting knowledge and models of the effect of anxiety on risk perception and decision-making.

Keywords: risk perception, danger mitigation, anxiety, decision-making, individual differences

Supplemental materials: http://dx.doi.org/10.1037/xlm0000210.supp

Anxiety is generally thought to have evolved to help organismsdeal with dangerous environments, by acting on a number ofphysiological and cognitive systems to enhance an individual’sability and motivation to deal with potential threats (Barlow, 2002;Beck, Emery, & Greenberg, 1985; Marks & Nesse, 1994). Height-ened dispositional anxiety is associated with biases in both cog-

nitive and behavioral responding to risks. At the cognitive level,research has shown that individuals with high levels of trait anx-iety have heightened perceptions of the severity of potential neg-ative events and heightened perceptions of the likelihood of neg-ative events happening (e.g., Butler & Mathews, 1987; Maner &Schmidt, 2006; Stöber, 1997). At the behavioral level, studiesinvestigating risk taking using the Iowa gambling task (Miu,Heilman, & Houser, 2008) and the balloon analogue risk task(BART; Lejuez et al., 2002; Lorian & Grisham, 2010) have shownthat high anxious participants have a reduced tendency to takerisks. These findings have been linked to a pervasive behavioralsafety bias in high trait-anxious and clinically anxious individuals,which refers to a persistent tendency to avoid all perceived risks(Lorian & Grisham, 2010). The safety bias can manifest itself as anactive engagement in perceived risk reduction behavior, but it canalso be expressed as a more passive avoidance of possible risksand a reduction in risk-taking behavior (Cicolini & Rees, 2003;Lorian & Grisham, 2010).

These cognitive and behavioral patterns suggest trait anxietymay affect the calibration between perceptions of risk and dangermitigation behavior. While it is well recognized that such calibra-tion between risk perception and danger mitigation is important(Blanchard, Griebel, Pobbe, & Blanchard, 2011; Dolan, 2002;O’Donovan, Slavich, Epel, & Neylan, 2013), there is a paucity of

This article was published Online First December 21, 2015.Lies Notebaert, School of Psychology, University of Western Australia;

Stijn Masschelein, Accounting and Finance, Business School, Universityof Western Australia; Bridget Wright and Colin MacLeod, School ofPsychology, University of Western Australia.

While conducting this study, Lies Notebaert was supported by an Aus-tralian Bushfire Cooperative Research Centre grant on managing threatthrough the modification of thought. Colin MacLeod is supported in part bythe Australian Research Council under Grant DP140104448, and by a grantfrom the Romanian National Authority for Scientific Research, CNCS–UEFISCDI, project number PNII-ID-PCCE-2011-2–0045. The fundershad no role in study design, data collection and analysis, decision topublish, or preparation of the manuscript.

Correspondence concerning this article should be addressed to LiesNotebaert, School of Psychology, University of Western Australia, 35Stirling Highway, Crawley 6009, Australia. E-mail: lies.notebaert@uwa.edu.au

Journal of Experimental Psychology:Learning, Memory, and Cognition

© 2015 American Psychological Association

2016, Vol. 42, No. 6, 985–9950278-7393/16/$12.00 http://dx.doi.org/10.1037/xlm0000210

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research investigating the factors that improve or impair thiscalibration. In order to better understand the precise influence oftrait anxiety on perceiving and responding to risks, it is crucial toinvestigate how anxiety affects the calibration between these twoprocesses. This paper therefore presents the results of an experi-mental study to investigate whether high trait-anxious individualsshow better or worse calibration of danger mitigation behavior tovariation in risk magnitude than low anxious individuals.

As engagement in danger mitigation behavior is costly, requiringthe investment of time, energy, and/or resources, it is important fororganisms to closely calibrate their investment in danger mitigation tothe magnitude of the risk encountered (O’Donovan et al., 2013). Themagnitude of a risk is not a one-dimensional construct, but consists ofdifferent components. The two components that have been studiedmost extensively are the likelihood and the severity of the risk. Risklikelihood refers to how likely it is a negative event will occur if nomitigating behavior is performed. Risk severity conceptualizes how“bad” the outcome of a negative event will be, if no preventative ormitigating behavior is undertaken (Weinstein, 2000). Both increasesin the perception of risk likelihood and risk severity have been foundto contribute to people’s engagement in danger mitigation behavior(Floyd, Prentice-Dunn, & Rogers, 2000). However, research on riskperception has typically investigated how individual risk componentscontribute to risk perception, without taking into account how theintegration of different components affects the perception of risk andthe consequent engagement in danger mitigation behavior. Neverthe-less, this integration is crucially important (Blanchard et al., 2011;Weinstein, 2000). If an event is very likely to happen but has lowseverity (e.g., getting the sniffles in winter), the overall magnitude ofthe risk is rather low. Likewise, if an event has very high severity butis very unlikely to happen (e.g., a nuclear bomb being dropped onone’s country), the overall magnitude of this risk is again rather low.It would therefore be maladaptive to align danger mitigation behaviorwith only one component of risk while ignoring others. Thus, optimalfunctioning should involve calibrating one’s investment in dangermitigation to the magnitude of risk, computed by integrating the twodimensions of risk information.

A few studies have touched upon the relation between anxiety,risk perception, and danger mitigation. However, upon closerinvestigation, these studies are not well suited to provide insightinto the calibration of danger mitigation to the magnitude of risk.Maner and Schmidt (2006) presented undergraduate students witha list of positive and negative scenarios (such as “I won somemoney while gambling” and “I tripped and broke a bone”), andasked them to rate the likelihood and severity of each of these.Danger mitigation behavior was assessed on a questionnaire inwhich participants reported their willingness to engage in riskydecision-making across a range of domains. The results showedthat trait anxiety was associated with risk-avoidant decision mak-ing, which was moderated by subjective ratings of the severity ofnegative events. Mitte (2007) presented participants with scenariosdescribing an event (e.g., an infectious disease is spreading in thecountry of your holiday destination) and asked them to choosebetween a risky alternative (e.g., traveling to the destination) anda safe alternative (e.g., cancelling the vacation). Participants werealso asked to rate the severity of both outcomes (in terms of howbad it would be), and the probability of the threatening event (e.g.,the probability of getting sick). Consistent with the results fromManer and Schmidt (2006), findings showed that high trait-

anxious participants more often chose the safe alternative, and thiswas mediated by the rating of the severity of the negative outcome.

These studies suggest that high trait-anxious individuals mightcalibrate their danger mitigation behavior more closely to the per-ceived severity of risky events. However, several aspects of thesestudies warrant further investigation. The first is that these studies donot allow drawing conclusions on whether appropriate engagement indanger mitigation was observed, as choosing a safe over a dangerousalternative in risky situations is not necessarily a sign of excessive riskavoidance. It is important to assess danger mitigation behavior inresponse to risks that objectively vary in magnitude such that it is clearto participants that the likelihood and/or severity of some dangers isgreater than the likelihood and/or severity of other dangers. In thisway, engagement in danger mitigation in response to low risks ver-sus high risks can be properly compared. Second, these previousstudies did not manipulate risk magnitude, but relied on subjectiveperceptions of a variety of risks. Given the lack of manipulation, itremains unknown whether the inflated perceptions of risk constituteda cause or a symptom of risk-avoidant decision making. To remedythis, the relationship between perception and behavior should bemeasured using a paradigm where the magnitude of the risk (bothlikelihood and severity) is explicitly manipulated. In the current study,we included conditions where the magnitude of the risk is manipu-lated and participants are presented with information about the mag-nitude of the risk, as well as conditions in which the magnitude of therisk is unknown. This allows simultaneous assessment of the calibra-tion of danger mitigation behavior to objective variation in riskmagnitude, and the subjective perception of information about riskswith an unknown magnitude. Third, many studies examining therelationship between risk perception and danger mitigation rely onself-report measurements of either or both of these constructs. As theresponses on these self-report measures can be biased in the absenceof biases in the cognitive or behavior constructs assessed (Eysenck,2014), objective measures constitute a better way to examine therelationship between risk perception and danger mitigation. The lastimportant issue is that previous studies did not model the multiplica-tive relationship between risk likelihood and risk severity. Therefore,they do not allow investigating the possibility that investment indanger mitigation might be calibrated to integrated information aboutdifferent components of risk.

The aim of the current study was to examine the relationshipbetween variation in different risk components and danger mitigationbehavior, and investigate whether anxiety is characterized by anenhanced or compromised calibration of danger mitigation behaviorto variation in risk magnitude. To this end, a task was developed inwhich the magnitude of two components (likelihood and severity) ofrisk was varied, and the probability to engage in danger mitigationbehavior as a function of this variation in risk magnitude was as-sessed. High and low trait-anxious participants were exposed to a riskof receiving a loud noise burst (the danger), which could differ inlikelihood or severity on every trial. The likelihood of the risk referredto the chance the noise burst would be delivered, while the severity ofthe risk referred to the volume with which the noise burst would bedelivered. On every trial, information about the likelihood of this riskand information about its severity was communicated through twodifferently colored squares. Five shades of each color represented fivelevels in each risk component. Thus, as the color intensity of therectangle increased, the level of risk likelihood or severity increased.In this manner, participants were presented with objective information

986 NOTEBAERT, MASSCHELEIN, WRIGHT, AND MACLEOD

about the magnitude of the risk. The level of risk likelihood and riskseverity were manipulated independently, and the multiplicative re-lationship between the likelihood and severity of the risk defined therisk magnitude (Robinson-Riegler, 1994; Weinstein, 2000). To assessthe calibration of danger mitigation behavior to the variation in riskmagnitude, participants were given the opportunity to mitigate thedanger on some trials. To this end, participants were given a virtualcoin which, when invested, would mitigate the danger, that is, annulthe delivery of the noise burst. However when the coin was invested,two trials with no coin and hence no opportunity for danger mitigationwould follow before a new coin was made available. Therefore,participants had to be selective in choosing when best to invest thecoin. Changes in the probability of investing a coin for differentcombinations of risk likelihood and risk severity served as a measureof the calibration of danger mitigation behavior to variation in riskmagnitude.

Method

Participants

Seventy-six undergraduate psychology students from the Uni-versity of Western Australia participated in this study for partialcourse credit. In order to recruit both high and low anxiousparticipants, students (n � 1,134) completed the SpielbergerState–Trait Anxiety Inventory (STAI; Spielberger, Gorsuch, Lush-ene, Vagg, & Jacobs, 1983) and were invited to participate if theyobtained scores in the top or bottom third of this sample. The finalsample consisted of those students who responded to the invitationfirst. This sample consisted of 37 low trait-anxious participants (24male, mean age 20.7, SD � 6.1) and 39 high trait-anxiousparticipants (16 male, mean age 19.6, SD � 5.7). High trait-anxious participants had significantly higher trait anxiety scores(M � 53.56, SD � 6.26) and state anxiety scores (M � 44.51,SD � 7.60) than low trait-anxious participants (trait: M � 30.62,SD � 5.04; state: M � 27.24, SD � 7.56), ttrait(74) � 17.55, p �.001 and tstate(74) � 9.93, p � .001. The average trait anxietyscore in the high anxious group corresponds to the 93rd percentilerank in college students, while the average trait anxiety score in thelow anxious group corresponds to the 25th percentile rank incollege students, averaged across male and female students (Spiel-berger et al., 1983). The STAI does not suggest clinical cutoffs;however, studies have reported average trait anxiety scores rangingfrom 51.8 to 56.4 in clinically diagnosed anxious samples (Bork-ovec & Costello, 1993; Mathews & MacLeod, 1985). There wereno significant differences between groups in age, p � .1. Therewere more women in the high trait-anxious group than in the lowtrait-anxious group, Mann–Whitney U � 549.50, p � .039, whichis consistent with the higher prevalence rates of heightened anxietyin women than in men (McLean, Asnaani, Litz, & Hofmann,2011). No participants reported hearing problems. All participantsprovided their informed consent and were informed that they couldterminate the experiment at any time. The study was approved bythe ethical committee of the University of Western Australia.

Tasks and Materials

Anxiety questionnaires. The STAI (Spielberger et al., 1983)was used to screen candidate participants for trait anxiety and to

confirm state and trait anxiety levels at the time of testing. The traitscale of the STAI consists of 20 items assessing the frequency withwhich anxiety symptoms occur. The state scale consists of 20items assessing the intensity of current anxiety symptoms. Thisquestionnaire instrument yields a reliable and valid measure ofdispositional anxiety (Barnes, Harp, & Jung, 2002; Spielberger etal., 1983). Participants completed a paper version of the traitanxiety subscale prior to the test session. These scores were usedto guide study invitations. During the test session, participantscompleted an electronic version of both the state and trait sub-scales. The latter scores were used in the analysis.

Calibration task. The calibration task served to assess indi-vidual differences in the calibration between danger mitigationbehavior and risk magnitude. Participants were presented with arisk of receiving a loud noise burst (� danger). Information aboutthe likelihood of the risk (probability of the noise burst beingpresented) and its severity (loudness of the noise burst) wasconveyed on screen via two colored rectangles. On each trial,participants could choose to mitigate the danger (i.e., avoid thenoise burst) by investing a coin that was made available to them.However, investing the coin came at the cost of losing the dangermitigation opportunity on the next two trials. This way, partici-pants were encouraged to be selective in choosing when to miti-gate the danger.

Two 3.8 cm � 2.2 cm colored rectangles (blue and orange)represented information about the likelihood and severity of thedanger (colors counterbalanced across participants), with a darkerhue indicative of a higher likelihood or severity (see Figure 1).There were five levels of the likelihood a noise burst would bedelivered: 20%, 40%, 60%, 80%, and 100%, and five levels ofseverity: 60 db, 70 db, 80 db, 90 db, or 100 db. The hue intensityfor each level was matched for both colors. By presenting infor-mation about the magnitude of the likelihood and severity of risksthrough different hues and not using specific numbers, we aimedto present objective information about the variation in risk mag-nitude, without encouraging participants to respond in an artificialmanner by simply multiplying numbers. Additionally, for each ofthe two colors, a scrambled rectangle consisting of all five hueswas created (see Figure 1), indicating that the level of severity andlikelihood was to be determined at random. This allowed us tocompare danger mitigation behavior on trials with unknown riskinformation to danger mitigation on trials with objective informa-tion.

To allow variability in the information participants could attendto, a neutral gray square, shaded darker to either the left of right,was also presented, indicating whether the noise burst would bedelivered through the left or right earpiece of the headphones. Animage of a coin, 2 cm in diameter, signaled the opportunity fordanger mitigation. The noise burst was a 500-ms burst of whitenoise, presented to participants through headphones. Participantsreceived their first coin in one of the first three trials. The coinremained available until it was invested, after which two trialsfollowed in which no coin was available. On the third trial fol-lowing a coin investment, participants received a new coin.

A more detailed overview of the trial sequence is presented inFigure 1. At the start of each trial, the statement “New Trial” waspresented for 1,000 ms. Next, participants were shown whether ornot they had a coin available on the current trial (A). On trials inwhich a new coin was gained, the caption “You have gained” and

987CALIBRATING RISK PERCEPTION AND DANGER MITIGATION

an image of the coin was displayed. On the remainder of the trials,the caption “You currently have:” was presented with a coin imageif a coin was available, or no coin image if no coin was available.Next, participants were encouraged to focus on the center of thescreen in order not to bias initial allocation of attention. This wasdone by presenting a central fixation cross (B; Notebaert, Crom-bez, Van Damme, Durnez, & Theeuwes, 2013). Next, the threerectangles were presented (C). The gray rectangle was presented atfixation, and the other two rectangles were presented to its left andright (with the centers of the distal and central rectangles 6 cmapart). To ensure participants remained attentive to the informationpresented, this was followed by a task requiring the discriminationof a visual target presented on screen (D; MacLeod, Mathews, &Tata, 1986). Participants were instructed to click the left mousebutton if the target consisted of two horizontally aligned dots andthe right mouse button if the target consisted of two verticallyaligned dots. Following this response, feedback on the targetdiscrimination response (“Correct” or “Incorrect”) was presentedon screen for 1,000 ms. On trials in which a coin was available,participants were next asked if they wanted to invest the coin (E).The image of the coin was displayed with the caption “Invest coin?Y/N” until a response had been made. Following this response anda 500-ms delay, a noise burst (500 ms) could be delivered. Thedelivery and dB value of the noise burst was dependent on thelikelihood and severity in that trial, and whether or not a partici-pant had used the coin to mitigate the danger. There was a 500-msinterval before the next trial commenced.

The severity and likelihood of the danger were manipulatedindependently, such that each level of severity was crossed witheach level of likelihood. This was crossed with the location of thedot probe, which could be presented at each of the three locations,for a total of 108 trials. To be able to assess how likely aparticipant was to mitigate the danger (i.e., invest the coin) on eachof these 108 trials, trials in which no coin was available wererepeated until each of these 108 trials had been presented with theopportunity for danger mitigation (i.e., the participant had theopportunity to invest a coin on that trial).

Procedure

After obtaining informed consent, participants were seated ap-proximately 60 cm from the screen. The experiment was pro-

grammed using the E-Prime software package (Psychology Soft-ware Tools, Sharpsburg, PA). The study consisted of assessingdemographic information (age and gender), followed by the anx-iety questionnaires and the calibration task. The entire study lasted25 to 50 min, depending on the speed of responding and thenumber of trials that had to be repeated.

Data Analysis

For each participant, responses on the 108 trials in which a coinwas available were analyzed using a multilevel model. The mul-tilevel approach allows modeling the observable differences in thecalibration of danger mitigation behavior to variation in risk mag-nitude due to trait anxiety, while accounting for other unmeasuredindividual differences (Langford et al., 1999), such as participants’aversion to noise bursts.

Calibration of Danger Mitigation Behavior to KnownRisk Magnitude

The probability, pij, that participant j invested the coin on trial ifollows a multilevel logit model (Gelman & Hill, 2007; Kruschke,2010), as presented in equation:

log� pij

1 � pij�� �ij

0 � �ijLLij � �ij

SSij � �ijLSLijSij (1)

The log odds of the probability of investing versus not invest-ing were defined as a function of the likelihood, Lij, the severity,Sij, and their interaction. The five levels of risk likelihood and riskseverity were coded from �2 to 2. �ij

0 represents the average logodds for participant j while the other coefficients represent to whatextent participants calibrated their coin investments to the likeli-hood and severity of the noise.

The logit link function was used, as it is one of the standardmethods to transform a linear model to a probability scale between0 and 1, and ensures that the model cannot predict negativeprobabilities or probabilities larger than 1 (Gelman & Hill, 2006).Furthermore, mathematical models often use the logit function tomodel an individual’s probability of taking one of two possibleactions based on an underlying latent variable (see van Ravenz-waaij, Dutilh, & Wagenmakers, 2011 for an example with theBART task). The probability that a participant will invest the coin

1000ms 1000ms 1000ms Until response Until response

(A)

You have gained:

(B)

x

(C) (D)

:

(E)

Invest coin? y/n

Color shades

Figure 1. Calibration task stimuli and trial overview. See the online article for the color version of this figure.

988 NOTEBAERT, MASSCHELEIN, WRIGHT, AND MACLEOD

was thus modeled according to equation (2), which reexpresses thelogit link function with the probability on the right-hand side.

pij � 11 � exp����ij

0 � �ijLLij � �ij

SSij � �ijLSLijSij��

(2)

One interpretation of this formulation is that the linear func-tion of the likelihood, severity, and the interaction, �ij

0 ��ij

LLij � �ijs Sij � �ij

LSLijSij, is a model of participant j’s unobservedwillingness to mitigate the danger. The willingness to mitigateincludes not only the total danger (i.e., the interaction) but also theindividual components, likelihood and severity. This allows con-trolling for individual variation in the weighting of informationabout likelihood and severity, such as the tendency of high anxiousindividuals to overweigh the severity of the danger (Maner &Schmidt, 2006; Mitte, 2007).

The interaction coefficient, �jLS, is of critical interest because it

indicates how well the willingness to mitigate the danger wascalibrated to the combined information about the likelihood andseverity. Because Lij and Sij can take on positive as well asnegative values and all conditions have an equal number of ob-servations, a positive interaction effect, �ij

LS, cannot be explainedby a main effect, such as participants’ higher willingness to miti-gate danger with either higher likelihood or higher severity. Forinstance, with a positive interaction coefficient �ij

LS and likelihoodLij � �1 (40% likelihood), the contribution of the total danger tothe log odds, �ij

LSLijSij, decreases as the level of severity increases.However, with the same �ij

LS and a Lij � 1 (80% likelihood), �ijLS

Lij Sij, increases as the level of severity increases.Because of the nonlinearity in the logit function, this interaction

effect on the willingness to mitigate danger cannot necessarily betranslated to the probability of danger mitigation.1 In order tointerpret the interaction effect on the probability of the coin in-vestment directly, Gelman and Pardoe’s (2007) average predictivecomparison (APC) methodology was adapted. Based on the resultsof the estimation procedure and equation, the probability, pnjls, ofdanger mitigation was simulated for every participant and everycombination of severity and likelihood. For every simulation, n,and participant, j, the interaction effect, �njls, was calculated ac-cording to equation (3).

�njls � (pnjls � pnjl(s�1)) � (pnj(l�1)s � pnj(l�1)(s�1))

for l, s in {1, 0, 1, 2} (3)

Similar to a linear interaction effect, the �’s represent theincrease in predicted probability of the coin investment from acombined increase in likelihood and severity that is not accountedfor by the main effects of increasing likelihood or severity. Thereported APC was calculated as the average difference in � be-tween 2 participants from the same gender and age who differ twostandard deviations in trait anxiety (see the online supplementalmaterial for more details). As such, APC provides a direct estimateof the effect of trait anxiety on calibration of the coin investmentto the magnitude of the total danger.

Individual differences and time trends. The model furtherdecomposed each of the �’s into several components. Specifically,for a given participant, calibration of behavior to information aboutrisk likelihood (�j

L), was decomposed into the average samplecalibration, L, a participant specific deviation, j

L, a time trend TL

trial, and the effect of measured individual differences in traitanxiety (TA

L TAj), gender (GL Gj), and age (A

L Aj). Similarly,

calibration to severity and calibration to the total danger weredecomposed into a sample average, an unobserved individualcomponent, and the effect of trait anxiety, time, gender, and ageaccording to equation (4).

�ij. � �. � �.

j � �.Ttrial � �.

TA TAj � �.AAj � �.

GGj (4)

An overview of all parameters in this model is provided in Table1. The estimates for the d.

TA’s are of critical interest because theymeasure the difference in calibration explained by trait anxiety,that is, they represent the interaction between trait anxiety andlikelihood, severity, and the total danger magnitude. The unob-served individual components take into account, for example, ifsome participants perceived noise bursts as more aversive (j

0), orif some participants calibrated their investment more to the like-lihood and severity than others (j

L, jS, j

LS).

Calibration of Danger Mitigation Behavior toUnknown Risk Magnitude

The model also allowed estimating participants’ interpretation ofunknown likelihood and severity information on trials where scram-bled squares were presented. For these trials, the unobserved valueparticipants attach to the scrambled likelihood (severity) square ismodeled as Lj (Sj), which is assumed to lie between �2 and 2.2 Theestimated Lj and Sj is plugged into equations (1) and (2) for the trialswith scrambled squares. As before, those parameters depend on thesample average, a participant-specific deviation, a time effect, andobservable individual differences and a logit link function is used toconstrain Lj and Sj to the interval between �2 an 2 in equation (5; seealso Table 1). The result of this formulation is that a participant whomitigates danger more often with scrambled likelihood (severity)squares than with the average likelihood (severity) of 60% (80 dB)will have a positive Lj (Sj).

Lj � �2 � 41 � exp���0

L � jL � T

LTrial � TAL TAj

� ALAgej � G

LGenderj��Sj � �2 � 4

1 � exp���0S � j

S � TSTrial � TA

S TAj

� ASAgej � G

S Genderj��

(5)

Results

Calibration of Danger Mitigation Behavior to KnownRisk Magnitude

The average and the 95% credibility interval for each param-eter are presented in Figure 2. Bayesian credibility intervals canbe directly interpreted as the interval that includes the value ofthe underlying parameter with 95% probability. Because of theBayesian estimation procedure for the model, it is not possibleto report traditional p values. As an alternative, the probability

1 We thank the editor for this suggestion.2 In other words, participants interpret a scrambled likelihood (severity)

square as a likelihood (severity) between 20% and 100% (60 dB and 100dB).

989CALIBRATING RISK PERCEPTION AND DANGER MITIGATION

that a given parameter is larger than 0 is reported. The advan-tage of the technique is that 1 minus this probability can beinterpreted as the probability that the parameter is negative.

The results showed that a 20% increase in the likelihood of anoise burst increased the willingness to mitigate danger withL � 0.63. A 10-dB increase in severity increased the willing-ness to mitigate danger with L � 1.06. Thus, these estimatesshow that participants calibrated their danger mitigation behav-ior to the individual components of risk magnitude, as theywere more likely to invest the coin as the likelihood andseverity increased. The nonoverlapping credibility intervals forL (95% CI � [0.51, 0.76]) and S (95% CI � [0.92, 1.22])show that participants calibrated their behavior more to infor-mation about severity than to information about likelihood.Furthermore, a joint increase of one level in the level oflikelihood and severity increased the log odds ratio with anadditional factor of LS � 1.18 over and above the main effects.This interaction effect indicates that participants were calibrat-ing their danger mitigation behavior to integrated informationabout the likelihood and severity of the risk.

Trait anxiety. The effect of trait anxiety on calibration wasestimated by the TA’s in Figure 3. The results show that highanxious participants were significantly more likely to invest thecoin when risk severity increased, TA

S � 0.18, Pr (TAS � 0) �

0.999. Thus, anxiety was associated with an increased calibra-tion of danger mitigation behavior to risk severity. In contrast,higher anxiety was not associated with an increased calibrationto risk likelihood (TA

L � 0.00). Importantly, the results showthat the coin investments of higher anxious participants weremore sensitive to the combination of likelihood and severitythan lower anxious participants, TA

LS � 0.06, Pr (TAS � � 0) �

0.977. This indicates that anxiety was associated with enhancedcalibration of danger mitigation behavior to integrated infor-mation about risk likelihood and severity. To illustrate themagnitude of the contribution of trait anxiety to calibration, theinteraction effect for a low anxious and high anxious individualwas calculated. A participant with a trait anxiety score of onestandard deviation below the sample average showed an esti-mated calibration to the combined risk magnitude of LS –TA

LS � 0.09 (95% CI � [0.01, 0.19]), while a participant with atrait anxiety score of one standard deviation above the averageshowed an estimated calibration of LS � TA

LS � 0.21 (95%CI � [0.12, 0.33]).

The effect of trait anxiety, likelihood, and severity on theprobability of danger mitigation is illustrated in Figure 3. The

figure graphs the actual and the estimated probability (inthe curves) of the coin investment across the different levels ofseverity and likelihood for low anxious (triangles) and highanxious participants (circles). The sample-wide calibration tothe total danger can be seen in the steeper curves in the lastpanel compared with the first panel, which means that the effectof an increase in severity on danger mitigation increased withthe likelihood. Furthermore, the increase in steepness from thefirst to the last panel is stronger for the curves of the highanxious participants (circles) than the low anxious participants(triangles). A vivid illustration of this effect is the lack of acrossover point between the curves in the first panel, and acrossover point at ever lower severity levels in the panels withhigher likelihood.

To test the effect of total risk magnitude on the probability ofinvestment directly, the simulated �’s were analyzed. The sim-ulations quantify the additional probability of engaging in dan-ger mitigation over and above the main effects for a 10-dBincrease in severity and 20% increase in likelihood, that is, theinteraction effect of likelihood and severity on the probabilityof danger mitigation. The average � was higher for high anxiousparticipants than for low anxious participants (�H � 3.5%, 95%,CIH � [3.1%, 4.0%], �L � 2.5%, 95% CIL � [2.0%, 3.0%]). Tocontrol for the possible confounding effects of age and gender,the APC was calculated. The APC quantifies the increase in �between participants of equal age and gender, which differ twostandard deviations in trait anxiety.3 The APC indicated that anincrease of two standard deviations in trait anxiety was associ-ated with an increase in calibration of danger mitigation to theinteraction of likelihood and severity, APC � 0.89%, 95% CI �[�0.12%, 1.89%], Pr (APC � 0) � 0.958.

Demographic variables and time trends. The demographiccharacteristics, age and gender, only explain some of the variationin calibration to the likelihood and severity interaction. The will-ingness to mitigate the danger tended to be less calibrated to theinteraction for younger participants (A

LS � �0.05, 95% CI �[�0.12, 0.01]) and female participants (G

LS � �0.07, 95% CI �[�0.19, 0.05]). The results in Figure 2 also show that the calibra-tion to likelihood (T

L � 0.12, 95% CI � [0.05, 0.18]), severity(T

S � 0.14, 95% CI � [0.08, 0.19]), and the interaction (TL � 0.05,

95% CI � [0.00, 0.09]) increased over time.

3 The average high anxious participant differed about two standarddeviations from the average low anxious participant.

Table 1An Overview of the Parameters Estimated in the Known Risk Magnitude Model

For participant jSampleaverage

Participantspecific

Timetrend

Traitanxiety Age Gender

Log odds for average likelihood and severity (�0j) 0 j0 T

0 TA0 A

0 G0

Calibration to risk likelihood (�Lj) L jL T

L TAL A

L GL

Calibration to risk severity (�sj) S jS T

S TAS A

S GS

Calibration to likelihood � Severity interaction (�LSj) LS jLS T

LS TALS A

LS GLS

Latent likelihood (Lj) �L �jL �T

L �TAL �A

L �GL

Latent severity (Sj) �S �jS �T

S �TAS �A

S �GS

990 NOTEBAERT, MASSCHELEIN, WRIGHT, AND MACLEOD

Calibration of Danger Mitigation Behavior toUnknown Risk Magnitude

The estimates for the effects of the danger mitigation behaviorto unknown risk magnitude are depicted in Figure 4. The resultsshow that participants acted as if the unknown severity was lowerthan the average severity of 80 dB (�0

S � �1.91, 95% CI �[�3.70, �0.82]) and to lesser extent as if the unknown likelihoodwas lower than the average likelihood of 60% (�0

L � �0.73, 95%CI � [�1.86, 0.04]). The individual characteristics of trait anxiety,age, and gender or the time trend did not explain more of thevariation in participants’ danger mitigation behavior in response torisks of unknown magnitude.

Discussion

The aim of the current study was to investigate whether anxietyis characterized by better or worse calibration of danger mitigationbehavior to variations in risk magnitude. Importantly, the magni-tude of the total danger was defined as the multiplicative relation-ship between the level of risk likelihood and risk severity. Theresults suggest that anxiety is characterized by better calibration, ashigh trait-anxious participants were less likely than low trait-anxious participants to engage in danger mitigation behavior whenthe total magnitude of the danger was small, and more likely to

engage in danger mitigation when the danger magnitude waslargest. Consistent with previous research, our results indicatedthat high anxious risk-taking behavior was more sensitive to theseverity of the risk (Maner & Schmidt, 2006; Mitte, 2007). How-ever, the current findings show that the interaction of risk likeli-hood and severity served to additionally predict danger mitigationbehavior, and more so in high anxious participants. To our knowl-edge, this is the first study to show that individuals calibrate theirdanger mitigation behavior to integrated information about differ-ent components of risk, and that this calibration is more pro-nounced in individuals with higher levels of trait anxiety.

The calibration between risk perception and danger mitigation isparamount for adaptive functioning (Blanchard et al., 2011). Neuro-imaging research has shown that the same brain regions are involvedin the perception of threats and in behavioral and biological respond-ing to such threats (Bishop, 2007; Shin, Rauch, & Pitman, 2006).Therefore, this calibration between perception and behavior is sup-ported by shared activation in an integrated network consisting of theamygdala, the hippocampus, and the medial prefrontal cortex(O’Donovan et al., 2013). The involvement of this network mightcontribute to our understanding of the current findings. In describinga neurobiological model for anxiety-linked sensitivity to threat,O’Donovan et al. (2013) review evidence that activity in this neuralnetwork is potentiated for individuals with anxiety disorders, as well

Figure 2. Parameter estimates for the log odds of coin investment and the calibration to the level of risklikelihood, to the level of risk severity, and to total danger. All effects are allowed to vary over time (T), andwith participants’ level of trait anxiety (TA), age (A), and gender (G).

991CALIBRATING RISK PERCEPTION AND DANGER MITIGATION

as for individuals exhibiting high levels of trait anxiety. Thus, whenconfronted with information about a risk or potential threat, highanxious individuals may show enhanced processing of this informa-tion, enhanced engagement in behavior aimed at minimizing harm,but crucially also increased calibration between these two.

This finding opens up several new avenues for research is this area.One important avenue is to investigate the nature of this calibration inclinical populations as compared with nonclinical populations.Whereas heightened trait anxiety might be associated with moreadaptive cognitive and behavioral responding to threat, the patterns ofcognitive and behavioral processes in clinical anxiety are thought tocontribute to the maintenance or exacerbation of dysfunctional anxi-ety (Lorian & Grisham, 2010; MacLeod & Mathews, 2012; Van

Bockstaele et al., 2014; Weinstein, 1980). Therefore, it is possible thatheightened anxiety is a driver for adaptive responding to threat,whereas clinical levels of anxiety only serve to impair performance.As such, the relative advantage shown in the current study by hightrait-anxious individuals could disappear or even be reversed in aclinically anxious group. In addition, individual differences in themanifestation of anxiety symptomatology may be characterized bydifferences in the calibration of behavior to varying risks. For exam-ple, some people suffering from social phobia might overestimate theseverity of risks encountered in certain social situations (e.g., publicspeaking), whereas other people might overestimate the probability ofnegative social evaluations across many social situations, causingpervasive avoidance behavior. Such differential weighting of risk

0.00

0.25

0.50

0.75

1.00

60dB 70dB 80dB 90dB 100dB

Panel 1: 20% likelihood

0.00

0.25

0.50

0.75

1.00

60dB 70dB 80dB 90dB 100dB

Panel 2: 40% likelihood

0.00

0.25

0.50

0.75

1.00

60dB 70dB 80dB 90dB 100dB

Panel 3: 60% likelihood

0.00

0.25

0.50

0.75

1.00

60dB 70dB 80dB 90dB 100dB

Panel 4: 80% likelihood

0.00

0.25

0.50

0.75

1.00

60dB 70dB 80dB 90dB 100dB

Panel 5: 100% likelihood

Trait AnxietyLow Anxiety

High Anxiety

Actual and Estimated Coin Investment Probability

Figure 3. The actual probability of danger mitigation for all participants for every combination of likelihood(over 5 panels) and severity (on the x axis) is depicted as a hollow triangle for low anxious and a hollow circlefor high anxious participants. The curves represent the average predicted probability and 95% credibilityintervals of the low anxious and high anxious groups.

992 NOTEBAERT, MASSCHELEIN, WRIGHT, AND MACLEOD

information and its influence on behavior might therefore contributeto the distinction between subtypes of a particular emotional disorder(e.g., the generalized vs. specific subtype of social anxiety disorder(Turner, Beidel, & Townsley, 1992), or even between different dis-orders.

In addition to investigating how anxiety influences the calibrationbetween risk perception and danger mitigation, future research couldalso investigate anxiety-linked differences in the degree of investmentin danger mitigation behavior. In the current study, the task offeredlimited behavioral flexibility as the main goal was to examine whenparticipants chose to engage in danger mitigation. By allowing moreflexibility, it would be possible to investigate whether or not anxietycontributes to excessive investment of danger mitigation resources,relative to the type and magnitude of risk that is encountered; forexample, anxiety could be associated with excessive attempts tomitigate minor risks (such as in the case of obsessive compulsivebehavior), leading to a maladaptive balance between the effort in-vested in danger mitigation and the payoff in terms of risk reduction.The current paradigm could be adapted to investigate this relationshipbetween the degree of risk encountered, and the amount of effortinvested in danger mitigation. For example, participants could begiven a large number of coins at the start of the task and instructed toinvest as many coins as they want on each trial to mitigate the danger.The more coins would be invested, the greater reduction of risk.Critically, participants would not have enough coins to eliminate therisk on every trial. Therefore, selectivity is needed when deciding to

invest coins. This would allow investigating whether high anxiousparticipants “over-invest” coins as compared with low anxious par-ticipants when confronted with minor risks, which would be sugges-tive of maladaptive excessive danger mitigation behavior in anxiety.

Of course, the current study is not without its limitations. Onelimitation concerns the use of undergraduate psychology students.While there is sufficient variation in trait anxiety in this population toaddress the main aim of the study, it is possible that individuals in thispopulation may exhibit different risk management behavior as com-pared with other groups. In addition, the danger participants wereexposed to was an aversive auditory stimulus, which some popula-tions or some individuals within the current sample may have beenmore eager to avoid than others. Although some of this variation iscaptured in the regression model, future research could usefully ex-amine whether similar effects are obtained across a variety of popu-lations and in response to different types of risk (such as a monetaryloss). For example, while the “two-trial wait” after investment of thecoin in the current design can be interpreted as a cost (the loss ofdanger mitigation opportunity), this was not intended to represent thetypical costs that can be incurred by engaging in danger mitigationbehavior. Rather, the two-trial wait was introduced to encourageparticipants to be selective in when they chose to invest their coin,thereby revealing which aspects of risk this choice is calibratedagainst. The main aim of this two-trial wait was thus not to simulatecostly danger mitigation behavior, but to encourage selectivity, sim-ilar to how costly danger mitigation behavior encourages selectivity.

Figure 4. Parameter estimates for the participants’ unobserved interpretation of unknown severity andlikelihood. The effects are allowed to vary over time (T), and with participants’ level of trait anxiety (TA), age(A), and gender (G).

993CALIBRATING RISK PERCEPTION AND DANGER MITIGATION

Future research, however, could usefully implement and manipulateexternally valid danger mitigation costs, to examine how variation insuch costs may impact on investment choices. For example, partici-pants could be incentivized at the start of the study and required toinvest part of the money they have been allocated every time theychoose to mitigate the danger.

Second, it is possible that high and low anxious participantsexperienced the aversiveness of the noise burst differently, withhigh trait-anxious individuals assigning a higher threat value tothis noise burst than low trait-anxious individuals (Mogg &Bradley, 1998). However, such subjective differences in theperception of the noise burst do not necessarily present aproblem, and may even be a necessary condition for anxiety-linked biases in cognitive processes to manifest. When pre-sented with extremely high risks or extremely aversive stimuli,it is likely that there will be no room for individual differencesin trait anxiety to play a role. Evidence for such ceiling effectscomes from research examining anxiety-linked attentional vig-ilance for threat (Notebaert, Crombez, Van Damme, De Hou-wer, & Theeuwes, 2011; Wilson & MacLeod, 2003). Thesestudies show that when stimuli are highly threatening, both highand low anxious individuals show equivalent attentional vigi-lance for these stimuli. However, when stimuli are mildly ormoderately threatening (as is more common in everyday life),this vigilance is moderated by individual differences in traitanxiety. Specifically, in this case, high trait-anxious individualsshow more attentional vigilance to threat than low trait-anxiousindividuals (Bar-Haim, Lamy, Pergamin, Bakermans-Kranenburg, &van IJzendoorn, 2007). Thus, in the current study, we aimed topresent a threat of moderate intensity, allowing variation in re-sponding with individual differences in anxiety.

A third potential limitation concerns the lack of self-reportmeasures. Although the aim of this study was to measure riskperception and danger mitigation behavior in a manner that re-duces reliance on self-report, we do acknowledge that, in line withprevious research, self-report measures of risk level and strategyuse may have been informative, for example, to compare objectiveand subjective measures of the same construct.

Last, while the gender distribution in the current study is rep-resentative of the gender distribution in high and low anxiouspopulations, the lack of a balanced gender design prohibits anystrong conclusions about gender differences in risk perception,danger mitigation, and the calibration between the two in thecurrent study. Previous research has shown that women generallytake fewer risks than men (except in social domains), whichappears to be mediated by greater perceived likelihood of negativeoutcomes and less perceived enjoyment for some risks (gambling,recreation, health), or by increased perception of the severity ofpotential negative outcomes (for gambling and health; Byrnes,Miller, & Schafer, 1999; Harris, Jenkins, & Glaser, 2006). In thecurrent study, accounting for gender in the model did not revealany meaningful effects.

In conclusion, the current study developed a novel flexibleparadigm to investigate the calibration of danger mitigation be-havior to variation in different components of risk. The resultssuggested that high trait-anxious individuals calibrated their be-havior more to the integration of risk likelihood and severityinformation than low anxious individuals. These findings and thisparadigm open up a range of new avenues for future research to

investigate the nature of this calibration, and the person and eventmoderators that may impact on it. This line of research holds thepromise to shed new light on the influence of anxiety on cognitiveprocessing and behavior in risky environments.

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Received February 11, 2015Revision received August 31, 2015

Accepted September 9, 2015 �

995CALIBRATING RISK PERCEPTION AND DANGER MITIGATION