DISPATCH INFORMATION AND POLICE USE OF FORCE:
COMPUTATIONALLY MODELING SIMULATED DECISIONS TO SHOOT
By
David J. Johnson

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Psychology—Doctor of Philosophy
2017

ABSTRACT
DISPATCH INFORMATION AND POLICE USE OF FORCE:
COMPUTATIONALLY MODELING SIMULATED DECISIONS TO SHOOT
By
David J. Johnson
The decision to use lethal force against a civilian is one of the most difficult decisions
police officers face. There has been increasing concern that racial bias amongst police officers
has led to increased shootings of Black Americans. Researchers have used simplified shooting
tasks to test this question in the laboratory. Such studies typically reveal a bias shoot unarmed
Black men more than unarmed White men. However, such studies have major shortcomings in
that they do not include several important features of the real world decision environment. The
following four studies tested whether dispatch information, information about a suspect given to
police by dispatch, influenced shooting decisions and racial bias. Untrained civilians and trained
officers made better decisions when dispatch information was correct. Dispatch information was
also sufficient to eliminate racial bias in shooting decisions. This demonstrates a limitation in
generalizing findings of racial bias in the laboratory to real world shooting decisions. In addition,
I also used a computational model, the drift diffusion model, to test how dispatch information,
race, and expertise influence shooting decisions. This modeling showed these factors influence
how individuals collect information for the decision to shoot in an online fashion, rather than
creating an a priori bias to favor the decision to shoot. I discuss what part of dispatch information
may reduce racial bias, as well as implications for police recruitment and training.

This work is dedicated to my parents, Anne and Jeff Johnson. Your love and support provided
the foundation I needed to succeed. This work is also dedicated to Fish and Lisa Seylar, who
were always there for me when I needed encouragement.

iii

ACKNOWLEDGEMENTS

This work would not have been possible without help from dozens of police officers from
the Midwest who took the time to participate in this research. In addition to dutifully completing
the experimental tasks, they also gave insightful comments on ways to improve the study design.
They also provided revealing comments about their on the job experiences and the hardships that
officers face in a time where officer-civilian relations are particularly strained. Without their
support and trust this work would not be possible. I hope that this work provides a foundation for
developing programs to help officers perform their duties and restore trust between officers and
the communities they police.
I am also thankful for the guidance given by my graduate advisor, Joseph Cesario, and
the rest of my committee. Without Joe’s assistance I would never have pursued this avenue of
research, let alone had the resources necessary to successfully partner with law enforcement
agencies. The computational modeling class that Timothy Pleskac taught introduced me to the
world of modeling that would prove to be an integral part of my dissertation and work more
generally. Despite being half a world away, Tim was willing to answer my numerous emails and
requests to meet. I am indebted to him for inadvertently becoming my second advisor.
I would also like to thank my fellow graduate students, especially Peter Kvam, who
helped me sort through some of the more complex analytical issues in my dissertation. These
students—my friends—gave me the motivation to come into work each day and the support to
keep working when I encountered difficulties. Finally, I’m grateful to Kesha Sebert, who
provided the soundtrack to this manuscript.

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TABLE OF CONTENTS

LIST OF TABLES ........................................................................................................................ vii
LIST OF FIGURES ....................................................................................................................... ix
INTRODUCTION ...........................................................................................................................1
Understanding the Decision to Shoot ..................................................................................2
Drift Diffusion Model ..........................................................................................................7
Existing DDM Research on the FPST .....................................................................9
Advantages of the DDM Approach .......................................................................11
Conceptual Advances.........................................................................................................13
Bayesian Estimation of the DDM ......................................................................................14
METHOD AND RESULTS ..........................................................................................................17
Overview of the Studies .....................................................................................................17
Study 1: The Role of Dispatch Information and Expertise ................................................18
Method ...................................................................................................................18
Participants.................................................................................................18
Procedure ...................................................................................................19
Results ....................................................................................................................20
Behavioral Analyses ..................................................................................20
Summary ........................................................................................23
Hierarchical DDM .....................................................................................24
Model Specification and Selection ................................................24
Hierarchical DDM Analysis ..........................................................24
Summary ........................................................................................28
Discussion ..............................................................................................................29
Role of Dispatch Information ....................................................................29
Unpacking Response Time Differences.....................................................30
The Lack of a Race Effect .........................................................................31
Study 2: Separating the Role of Race and Weapon Information .......................................32
Method ...................................................................................................................33
Participants and Study Design ...................................................................33
Results ....................................................................................................................33
Behavioral Analyses ..................................................................................33
Summary ........................................................................................36
Hierarchical DDM .....................................................................................37
Model Specification and Selection ................................................37
Hierarchical DDM Analyses ..........................................................37
Summary ........................................................................................40
Discussion ..............................................................................................................40
Study 3: Model Recovery of Start Point ............................................................................42
Method and Results................................................................................................42
Discussion ..............................................................................................................44
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Study 4: Model Validation with Payoff Manipulation ......................................................45
Method ...................................................................................................................45
Results ....................................................................................................................46
Behavioral Analysis ...................................................................................46
Summary ........................................................................................48
Hierarchical DDM .....................................................................................48
Model Specification and Selection ................................................48
Hierarchical DDM Analyses ..........................................................48
Summary ........................................................................................50
Discussion ..............................................................................................................51
GENERAL DISCUSSION ............................................................................................................54
What Part of Dispatch Information Reduces Racial Bias? ....................................................56
Modeling the Role of Dispatch Information and Expertise ...................................................58
Individual Differences in Racial Bias ....................................................................................61
Benefits of a Diffusion Model Approach to Decisions ..........................................................63
Conclusion .............................................................................................................................65
APPENDICES ...............................................................................................................................66
APPENDIX A: ANOVA Tables........................................................................................67
APPENDIX B: DDM Effects Tables.................................................................................73
APPENDIX C: Hierarchical Drift Diffusion Model ..........................................................76
APPENDIX D: JAGS Code ...............................................................................................77
APPENDIX E: Posterior Predictions .................................................................................79
REFERENCES ..............................................................................................................................92

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LIST OF TABLES

Table 1: Summary of Parameter Recovery Study..........................................................................44
Table 2: Payoff Values for the FPST by Block .............................................................................46
Table 3: ANOVA Summary Table for Study 1 Error Rates ..........................................................67
Table 4: ANOVA Summary Table for Study 1 Response Times ..................................................68
Table 5: ANOVA Summary Table for Study 2 Error Rates (Weapon vs. Control) ......................69
Table 6: ANOVA Summary Table for Study 2 Error Rates (Race vs. Control) ...........................69
Table 7: ANOVA Summary Table for Study 2 Error Rates (Weapon Condition) ........................70
Table 8: ANOVA Summary Table for Study 2 Error Rates (Race Condition) .............................70
Table 9: ANOVA Summary Table for Study 2 Response Times (Weapon vs. Control) ..............71
Table 10: ANOVA Summary Table for Study 2 Response Times (Race vs. Control) .................71
Table 11: ANOVA Summary Table for Study 4 Error Rates ........................................................72
Table 12: ANOVA Summary Table for Study 4 Response Times ................................................72
Table 13: Summary of Effects on Condition Level Threshold for Study 1 Students ....................73
Table 14: Summary of Effects on Condition Level Start Point for Study 1 Students ...................73
Table 15: Summary of Effects on Condition Level Non-Decision Time for Study 1 Students ....73
Table 16: Summary of Effects on Condition Level Drift Rate for Study 1 Students ....................73
Table 17: Summary of Effects on Condition Level Threshold for Study 1 Officers .....................74
Table 18: Summary of Effects on Condition Level Start Point for Study 1 Officers ....................74
Table 19: Summary of Effects on Condition Level Non-Decision Time for Study 1 Officers .....74
Table 20: Summary of Effects on Condition Level Drift Rate for Study 1 Officers .....................74
Table 21: Summary of Effects on Condition Level Threshold for Study 4 ...................................75

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Table 22: Summary of Effects on Condition Level Start Point for Study 4 ..................................75
Table 23: Summary of Effects on Condition Level Non-Decision Time for Study 4 ...................75
Table 24: Summary of Effects on Condition Level Drift Rate for Study 4 ...................................75

viii

LIST OF FIGURES

Figure 1: The FPST. Participants must respond with “shoot” or “don’t shoot” and are given
feedback after each trial. ..................................................................................................................4
Figure 2: The drift diffusion model. ................................................................................................8
Figure 3: The modified FPST used in Study 1. Participants always received accurate information
about the race and sex of the target before each trial. On half of the trials they were informed
(with 75% accuracy) that the target was armed. ............................................................................19
Figure 4: Proportion errors for students (left panel) and police (right panel) for all conditions. NI
= No weapon information. WI = Weapon information. 95% confidence intervals were calculated
using the methods outlined by Morey (2008). ...............................................................................21
Figure 5: Correct response times for students (left panel) and police (right panel) for all
conditions. NI = No weapon information. WI = Weapon information. 95% confidence intervals
were calculated using the methods outlined by Morey (2008). .....................................................22
Figure 6: Diffusion model parameters as a function of target race, dispatch information, and
object for Study 1. Dots represent modal posterior predictions at the condition level; bars are
95% HDI. W = White, B = Black. NG = Nongun. GU = Gun. .....................................................25
Figure 7: Proportion errors (top panel) and correct response times (bottom panel) for all
conditions. Response times were omitted for 22 participants because they failed to respond
correctly in at least one condition. NG = Nongun. GU = Gun. 95% confidence intervals were
calculated using the methods outlined by Morey (2008). ..............................................................35
Figure 8: Diffusion model parameters as a function of target race, dispatch information, and
object for Study 2. Dots represent modal posterior predictions at the condition level; bars are
95% HDI. W = White, B = Black, NI = No Information...............................................................38
Figure 9: Proportion errors (left panel) and correct response times (right panel) for all conditions.
DS = Payoff favors not shooting. SH = Payoff favors shooting. 95% confidence intervals were
calculated using the methods outlined by Morey (2008). ..............................................................47
Figure 10: Diffusion model parameters as a function of target race, payoff structure, and object
for Study 2. Dots represent modal posterior predictions at the condition level; bars are 95% HDI.
DS = payoff favors not shooting, SH = payoff favors shooting. ...................................................49
Figure 11: Generic diagram of the hierarchical drift diffusion model. The kth response for subject
j within condition i are generated by a drift diffusion process. Vertical lines on the normal
distributions indicate that the priors were truncated normals. Prec = precision. ...........................76
Figure 12: Posterior predictions of hit and false alarm rates for Study 1. Squares represent
ix

observed condition level choice proportions. Diamonds represent predicted condition level
choice proportions. Blue dots represent individual participant response times and have been
jittered to better show the distribution of scores. W = White, B = Black ......................................81
Figure 13: Posterior predictions of response times for Study 1. Squares represent observed
condition level choice proportions. Diamonds represent predicted condition level choice
proportions. Blue dots represent individual participant response times and have been jittered to
better show the distribution of scores. W = White, B = Black ......................................................82
Figure 14: Observed (black) and predicted (gray) response time distributions for each response
type at the condition level for students in Study 1. .......................................................................83
Figure 15: Observed (black) and predicted (gray) response time distributions for each response
type at the condition level for officers in Study 1. ........................................................................84
Figure 16: Posterior predictions of hit and false alarm rates for Study 2. Squares represent
observed condition level choice proportions. Diamonds represent predicted condition level
choice proportions. Blue dots represent individual participant response times and have been
jittered to better show the distribution of scores. W = White, B = Black ......................................85
Figure 17: Posterior predictions of response times for Study 2. Squares represent observed
condition level choice proportions. Diamonds represent predicted condition level choice
proportions. Blue dots represent individual participant response times and have been jittered to
better show the distribution of scores. W = White, B = Black ......................................................86
Figure 18: Observed (black) and predicted (gray) response time distributions for the shoot
response at the condition level for students in Study 2. ................................................................87
Figure 19: Observed (black) and predicted (gray) response time distributions for the don’t shoot
response at the condition level for students in Study 2. ................................................................88
Figure 20: Posterior predictions of hit and false alarm rates for Study 4. Squares represent
observed condition level choice proportions. Diamonds represent predicted condition level
choice proportions. Blue dots represent individual participant response times and have been
jittered to better show the distribution of scores. DS = payoff favors not shooting, SH = payoff
favors shooting. .............................................................................................................................89
Figure 21: Posterior predictions of response times for Study 4. Squares represent observed
condition level choice proportions. Diamonds represent predicted condition level choice
proportions. Blue dots represent individual participant response times and have been jittered to
better show the distribution of scores. DS = payoff favors not shooting, SH = payoff favors
shooting. ........................................................................................................................................90
Figure 22: Observed (black) and predicted (gray) response time distributions for each response
type at the condition level for Study 4. .........................................................................................91

x

INTRODUCTION
In November 2014, two police officers responded to information from dispatch about a
“Black male sitting on the swings…pointing [a gun] at people” (Lee, 2015a). When officers
arrived on the scene they shot the individual within seconds, killing him. Unfortunately, the
Black male was twelve-year-old Tamir Rice, who was playing with an airsoft pistol replica.
For many people, Rice’s shooting represents bias in use of lethal force against Black
Americans (Lee, 2015b). There is a widespread belief that Black men are shot at higher rates
than White men due to racial biases held by police officers, and this belief compromises the
legitimacy of the police institution. This results in civilians who are less likely to obey the law
(Tyler, 2006), which undermines the ability of police to perform their duties (Jackson et al.,
2012; Kane, 2005; Sunshine & Tyler, 2003; Tyler & Fagan, 2008). However the shooting of
Tamir Rice also raises the possibility that dispatch information—information given to officers by
police dispatch before seeing a suspect—might impact officers’ decisions to shoot civilians. The
caller who reported Rice also told dispatch the pistol was “probably fake” and that he was
“probably a juvenile” (Smith, 2015). Had the officers been given this information, they may not
have decided to use lethal force.
To avoid the negative consequences associated with (the perception of) police bias, there
is a critical need to understand how officers make the decision to shoot, and whether dispatch
information impacts this decision-making process. The current research addresses these
questions by using a process model to demonstrate how this information impacts the decision to
shoot, with a specific focus on how dispatch influences the effects of suspect race on shooting
errors. In addition, this research also tests how expertise influences the role of suspect race and
dispatch information in the decision to shoot. Because most experimental research on the

1

decision to shoot is based on untrained civilians (Correll, Park, Judd, & Wittenbrink, 2002; 2007;
Correll, Park, Judd, Wittenbrink, Sadler, & Keesee, 2007; Correll, Wittenbrink, Park, Judd, &
Goyle, 2011; Kenworthy, Barden, Diamond, & del Carmen, 2011; Ma, Correll, Wittenbrink,
Bar-Anan, Sriram, & Nosek, 2011; Plant, Goplen, & Kunstman, 2011; Plant & Peruche, 2005),
firm conclusions about the pervasiveness of race bias or lack thereof within the police are
unclear. Furthermore, there is no research on how police officers might respond differently to
dispatch information than untrained civilians.
To address these questions I analyze data from a well-known laboratory shooting
paradigm, the First-Person Shooter Task (Correll et al., 2002) using a sequential sampling model,
the drift diffusion model (Ratcliff, 1978; Ratcliff & McKoon, 2008). This model of fast decisionmaking specifies how basic cognitive processes give rise to the decision to shoot. In addition I
present data from both untrained (college students) and trained individuals (police officers).
Thus, this research takes an initial step towards providing the information necessary to develop
effective use of force training programs and good dispatch policies.
Understanding the Decision to Shoot
In 2015, at least 96 unarmed men were fatally shot by police in the United States (Tate,
Jenkins, Kindy, Lowery, Alexander, & Rich, 2015; Swaine, Laughland, Lartey, & McCarthy,
2015). Although Blacks comprise only 12.0% of the male population, 39.6% of those killed were
Black. In contrast, although Whites comprise 62.1% of the male population, only 34.4% of those
killed were White.1 These reports are consistent with other recent studies of police shootings
(Ross, 2015) and FBI data (US Department of Justice, 2001).
Although incident reports are crucial for understanding the factors that influence the use
of lethal force, they suffer from three problems. First, any conclusions depend on the accuracy
1

20.8% were Hispanics (17.9% of the male population), and 5.2% were another race (8.0% of the male population).

2

and completeness of those reports (James, Klinger, & Vila, 2014; James, Vila, & Klinger, 2013).
If details are not recorded there is no way to understand how they impact decisions. Second,
deadly force encounters involve many factors other than dispatch information and race (e.g., the
suspect’s demeanor, attire, and location). This makes it difficult to isolate the impact that any one
factor might have in these decisions. Finally, relying on these after-the-fact reports precludes
examining how specific factors impact the psychological decision process. To overcome these
problems, researchers have designed experimental tasks to study the decision to shoot.
The most extensively used experimental paradigm to study the decision to shoot is the
First-Person Shooter Task (FPST; Correll et al., 2002). On any given trial in the FPST,
participants see a fixation point, followed by a series of neighborhood scenes (see Figure 1).
Eventually, a person appears in a scene with an object. Participants are told to press a “shoot”
button if the object is a gun or a “don’t shoot” button if the object is harmless. They are given
feedback after each trial in the form of points. Correct decisions earn points: shooting an armed
target earns 10 points and not shooting an unarmed target earns 5 points. Incorrect decisions
incur penalties: shooting an unarmed target yields a penalty of 20 points and not shooting an
armed target yields a penalty of 40 points. Thus, missing an armed target results in the worst
outcome, somewhat mirroring payoffs faced by officers in the field (i.e., failing to shoot an
armed target may result in the loss of the officer’s life). Finally, participants are penalized 50
points for responding slowly (after the response window has ended), as the decision to use force
often requires a fast judgment. Because researchers have been most interested in how race
impacts the decision to shoot, targets are typically Black men and White men.

3

FixaCon	Point	
250	–	1000ms	

1	–	4	Backgrounds	
500	–	1000ms	each	

Response	Window	
630ms	

Feedback	
2000ms	

good	shot	+10	
Total	points	=	100	

+	

Time	

Figure 1: The FPST. Participants must respond with “shoot” or “don’t shoot” and are given
feedback after each trial.
A major limitation of this design is that participants know nothing about a target until he
appears on screen. Clearly, this is a gross oversimplification of what police officers face in the
field. Officers often have dispatch information about a suspect before they are required to make
any decision involving force. Yet, all existing variants of the shooter task provide no dispatch
information about targets. Although the information dispatchers ask for varies widely based on
the situation, dispatchers generally ask four interrogative questions: where is the emergency,
what is the emergency, when did it happen, and who is involved (Norcomm, 2017; Kobb, 2016).
The answers to these questions are passed onto officers who respond to the call. Importantly,
answering the “who” question involves getting an accurate description of the suspect, including
information about their sex, race, age, height, weight, hair color, and clothing. Thus, in many
cases officers have accurate information about the race and sex of the suspect they are looking
for far before they encounter that individual.
In the case of a crime, dispatchers will routinely ask if weapons are present (Norcom,
2017). The presence of a weapon, particularly a gun, raises the priority of a call. Higher priority
calls are responded to more quickly because of their sensitive nature. Information about whether
a weapon is present (as well as who is in possession of that weapon) is also given to officers.

4

This information is sometimes inaccurate because objects are misidentified as weapons and
dispatchers receive false reports about weapons. The former error is exemplified by shootings
like Tamir Rice and John Crawford (Balko, 2014), where officers received incorrect information
that the suspect was holding a firearm (both had airsoft replicas). However, a more common
reason officers receive bad information that a suspect is armed is because civilians falsely report
weapons to get faster police responses (Lance Langdon, personal communication, June 1, 2016).
These faster responses come at a cost; officers are trained to approach these situations differently
and this training and information may influence an officer’s perception of how threatening a
suspect is acting. As highlighted in the shooting of Tamir Rice, officers’ decisions to use lethal
force may have had more to do with the inaccurate description of him as armed than racial bias
on the part of the officers.
In addition to the omission of relevant factors like dispatch information in the FPST,
there are also shortcomings in how these data are typically analyzed. In the FPST, two types of
data are collected each trial: the decision (“shoot” or “don’t shoot”) and the speed of the decision
(response time, in milliseconds). Standard practice in social psychology is to analyze these data
separately. The typical finding is that participants are more likely (and faster) to shoot unarmed
Black men than unarmed White men (Correll et al., 2002; 2007; 2011). Although race impacts
the decision to shoot in this task, it is less clear how it does so. At least two competing accounts
of how race impacts this decision have been proposed: that the “the police have one trigger
finger for whites and another for blacks” (Takagi, 1974, p. 30), or that “a gun looks more like a
gun when it appears in the hands of a Black man” (Correll, Wittenbrink, Crawford, & Sadler,
2015, p. 221).
Although both of these proposed accounts are consistent with data that participants are

5

more likely to shoot unarmed Black men than unarmed White men, they are quite different with
respect to which part of the decision process they predict to be influenced by race. In the “trigger
finger” case, race bias is a predisposition to favor the shoot decision for Black men. In the other
account, race bias is in the interpretation: objects look more like guns when held by Black men.
Although process models such as signal detection and process dissociation have been used to
understand race bias in the decision to shoot, these models have limitations (described later) that
prevent them from being able to definitively address this question.
To better address this issue, I use a computational model—the drift diffusion model
(Ratcliff, 1978; Ratcliff & McKoon, 2008)—to identify how the race of a target affects the
decision process, thus distinguishing between the two accounts above. This process-level
analysis can also be used to understand how dispatch information impacts the decision process.
Although dispatch information and race should influence the use of lethal force, the ways in
which they impact the decision process may be very different. The benefits of a process-level
analysis are more than theoretical; knowing how factors like dispatch information and race
impact the decision process is crucial for designing effective training protocols. For example, a
very different training program would be required to reduce perceptual bias in weapon
identification for Black men than would be for a program designed to reduce a category bias to
shoot Black men.
In sum, two critical issues must be resolved in order to extrapolate current research from
the FPST to real-world contexts. First, the effect of dispatch information on shooting decisions
must be considered, given its potential to have a powerful impact on officers’ decisions. Second,
decisions must be examined from a process-level analysis in order to understand how factors
such as race and dispatch information influence the decision process.

6

Drift Diffusion Model
A major limitation of prior analytic approaches to understanding the decision to shoot is
that they typically focus on the behavioral level, examining either decisions made or the speed of
those decisions (response times). These analyses are not well equipped to investigate processes
that underlie those decisions, because no task is a “pure” indicator of an underlying process
(Jacoby, 1991; Payne, 2005).2 To better understand these processes, I modeled the decision to
shoot as a drift diffusion process. This sequential sampling model and others like it (e.g., the
linear ballistic accumulator model) are commonly used in cognitive psychology to study how
people make quick decisions (Bogacz, Brown, Moehlis, Holmes, & Cohen, 2006; Ratcliff &
Smith, 2004), but are relatively underused in social psychology (but see Correll et al., 2015;
Klauer, Voss, Schmitz, & Teige-Mocigemba, 2007). The drift diffusion model incorporates
decision and response time data to provide a process-level account of the decision to shoot.
Figure 2 displays a model of the diffusion process and lists its parameters.
In the FPST, participants accumulate evidence towards a decision based on the features
of a scene. As strength of evidence can vary over time, the drift rate (δ; delta) indicates the
average strength of evidence (see Figure 2). It is most affected by the features relevant to the
decision: the presence of a weapon. However, evidence accumulation is a noisy process and can
be biased by other features, such as dispatch information or target race. Thus, participants may
drift towards the wrong threshold (e.g., shoot when a gun is not present), resulting in an error.
The amount of evidence that participants require to make a decision is indicated by the
threshold (α; alpha). Crossing the upper or lower threshold boundary triggers a “shoot” or “don’t
shoot” decision, respectively. Threshold captures the speed-accuracy trade-off and cannot be
2

Decisions are often analyzed using signal detection models, which reveal that participants set a more liberal shoot
criterion (decision rule) for Black men. However, these models do not provide information about the psychological
processes that give rise to criterion differences.

7

lower than zero. When threshold is high, decisions are more accurate but slower. When threshold
is low, decisions are faster but less accurate.

Shoot

β∙α

τ

δ

Îą
Don’t Shoot
Time

Figure 2: The drift diffusion model.
A preexisting bias to shoot or not shoot at the start of the evidence accumulation process
is indicated by the start point (β; beta). When the start point is closer to the shoot threshold,
participants are more likely to decide to shoot. Given the steep penalties for failing to shoot an
armed target in the FPST, participants often show a start point favoring the shoot decision
(Pleskac, Cesario, & Johnson 2017).
All components of a response unrelated to deliberation, including encoding and motor
response time are indicated by non-decision time (τ; tau). Non-decision time is an error term,
reflecting these extraneous processes and other unknown contaminants. These contaminants are
generally not separable and so a single estimate of non-decision time is produced. This estimate

8

is directly interpretable as the length of time that these unknown processes take.
Existing DDM Research on the FPST
Although the DDM has not been applied to explore the effects of dispatch information on
the decision to shoot, it has been previously used to model data from the FPST. Across different
parameterizations and populations, the key finding from this research is that the race of a target
influences the evidence accumulation process, such that objects look more like guns when held
by Black men than White men (Correll et al., 2015, Pleskac, Cesario, & Johnson, 2017). This is
in contrast to the idea that early interpretation of a target’s race might bias the start point of the
diffusion process. Said differently, participants do not appear more “trigger happy” for Black
men than White men. This suggests that higher shooting rates (and faster decisions) for unarmed
Black men versus unarmed White men in the FPST does not result from individuals ignoring
relevant information. Rather, the race of a target influences the interpretation of the object,
perhaps through stereotypic associations between Black men and violence (Correll et al., 2015).
The race of a target may influence more than just the interpretation of the gun or nongun
object. Across three studies, Pleskac et al. (2017) found that participants required more evidence
(i.e., they set higher thresholds) when making decisions for Black targets than White targets.
This may reflect the use of motivated strategies to reduce racial bias in the decision to shoot.
Insofar as this process requires motivation and ability, it is possible that this threshold difference
might be enhanced when participants are motivated to act accordance with egalitarian beliefs and
have the ability to do so (i.e., under longer response windows). This demonstrates a benefit of the
DDM; it can show how the race of a suspect may have opposing effects on the decision process.
Although race pushes individuals to favor the shoot decision for Black men, increasing decision
speed and false alarm rates, this tendency is attenuated by a countervailing increase in the

9

amount of evidence needed to make a decision. This makes decisions slower but more accurate.
Initial work validating the appropriateness of the DDM as a process model of the FPST
has also begun. For example, the structure of the DDM necessitates that start point should be
influenced by task payoffs. Given that the payoff matrix in the FPST ensures better outcomes
(more points on average) when the shoot decision is favored, the DDM would predict a start
difference a priori. Consistent with this hypothesis, Pleskac et al. (2017) found that start points
for all targets (both Black and White men) favored the shoot response. This difference is also
reflected in the observed data; participants typically make fewer errors on trials where guns are
present compared to trials where harmless objects are present.3 However, strong tests of this
assumption require manipulations of the payoff matrix in order to see if the start point moves
accordingly.
In addition, the DDM also predicts that response window differences should influence
the threshold parameter, which measures the speed-accuracy trade-off. The model predicts that
threshold changes should lead to higher error rates for stereotype incongruent targets when the
response window is short, and few error differences but slower correct responses for stereotype
incongruent trials when response window is longer. Across three experiments with varying
response windows (630, 750, and 850ms), Pleskac et al. (2017) found that the threshold
parameter did in fact increase as response window was lengthened.
In sum, existing work on the FPST shows that race influences the decision process by
changing the accumulation of evidence, rather than by biasing individuals to favor one decision
over another. The race of a target may also influence how much information individuals collect
before making a decision. When a target is Black participants may withhold making a decision
3

Correll et al. (2015) actually found that start points were shifted towards the don’t shoot threshold, despite fewer
errors on gun trials than nongun trials. These divergent results may be due to inadequacies in the estimation
approach used (see Pleskac et al., 2017).

10

longer to ensure its accuracy. Finally, initial work has validated the psychological interpretation
of the DDM parameters. The model adequately captures a general bias to shoot and responds
appropriately to changes in response window.
Advantages of the DDM Approach
Why rely on the DDM approach over other models commonly used to understand
decisions in the FPST, such as signal detection theory? A major strength of the drift diffusion
model is that it can distinguish between the various accounts of how race bias affects shooting
decisions. Specifically, race appears to change how evidence is accumulated (a drift rate change)
rather than create an a priori bias towards a decision (a start point change). Dispatch information
might also impact decision parameters in different ways. For example, information that a target
is armed might bias participants to shoot before they even see the target, and might be reflected
in movement of the start point towards the shoot decision.
In contrast, within the FPST signal detection merely provides estimates of the ability to
distinguish between guns and harmless objects (d’; sensitivity) and the decision rule set for how
strong evidence must be before responding with shoot (c, criterion). While the criterion provides
useful information about whether individuals are more likely to favor the shoot decision for
Black or White targets, it does not describe the process that led to that decision rule. Again, only
the DDM reveals this bias occurs because race influences the accumulation of evidence to shoot.
A second advantage of the DDM is that its parameters map well onto how researchers
have theoretically divided the decision-making process in the FPST. For example, consider the
theoretical model of shooter bias proposed by Correll et al. (2002). Like most social cognition
researchers, they invoke dual process theories (e.g., Chaiken & Trope, 1999, Sherman,
Gawronski, & Trope, 2014) to explain shooting decisions. When a Black target is seen in the

11

FPST they assume (e.g., Bargh, 1989) “automatic” (efficient, uncontrollable, unintentional)
stereotypic associations are activated first. These associations dominate decisions unless slower
“controlled” processes have time to influence the decision. Although they describe three
controlled processes that might be influenced by stereotypical associations (perception,
interpretation, and decision certainty), they ultimately conclude that these automatic associations
“may theoretically affect any or all of these processes, and it is difficult to disentangle them
theoretically, let alone empirically” (p. 1326).
The main problem is that dual process have difficulty unraveling the effects stereotypic
associations might have on the decision-making process because “controlled” processes like
perception, interpretation, and decision certainty are lumped together. The DDM eschews the
controlled versus automatic dichotomy and instead focuses on those components. Thus, the
effect of stereotypic associations can be estimated for each component. Specifically, start point
reflects the perception stage, the degree to which participants use perceptual information (i.e.,
whether they are biased towards shoot or don’t shoot). Drift rate reflects the interpretation stage,
whether a stimulus seems to look like a weapon or not. Finally, threshold captures the decision
certainty stage, as it measures the level of information required to make a shoot or don’t shoot
decision. In sum, the formulation of the DDM clearly separates the underlying components of the
decision process and in doing so allows tests of theoretically motivated questions of process that
have eluded examination.
Finally, the DDM offers advantages over other common formal approaches to modeling
the FPST, such as multinomial models like the process dissociation procedure (Payne, 2001) and
the quadruple model (Conrey, Sherman, Gawronski, Hugenberg, & Groom, 2005). While these
models explain decision data well, they do not model response times. Given that race bias in the

12

FPST is typically found in both decisions and response times, these models are ignoring useful
information. Perhaps more important, they are also silent on whether the same processes that
generate bias in decisions also produce bias in response times. The DDM shows how the same
process can generate both correct and incorrect decisions as well as their speed. It utilizes all of
the available data, making it a more complete account of the shooting decision process.
Conceptual Advances
Aside from the methodological advances of modeling the shoot decision via the DDM,
what conceptual advances does the current research provide? The clearest answer is that this
research provides an initial examination of how dispatch information impacts the decision to
shoot in the FPST. In fact, almost no FPST research has examined how any prior information
about weapons or the race of a target might impact the decision to shoot. One exception is work
demonstrating that information about the dangerousness of the neighborhood impacts race bias in
the decision to shoot. Correll et al. (2011) manipulated whether targets appeared in dangerous or
neutral backgrounds, so that participants had prior information about the dangerousness of the
situation. This information overwhelmed race bias, resulting in all targets being shot to the same
high degree when they were presented in dangerous backgrounds. However, it is unclear where
this change occurred in the decision process: were participants more “trigger happy,” were they
rushing to make decisions, or did objects look more like guns to them?
One reason there is little work on how dispatch information might impact the decision to
shoot is because past research has almost exclusively focused on how suspect race, as perceived
by the officer, impacts the decision to shoot. Some research suggests race can bias the shooting
decision process (Correll et al., 2015; Pleskac et al., 2017), but how dispatch information might
either exacerbate or attenuate race bias has yet to be tested. In the Rice case, many people

13

believe that the race information from dispatch made the officers more likely to use lethal force
(Lee, 2015a). At the same time, officers may be highly motivated to avoid prejudiced actions and
errors (e.g., officer Jesse Kidder refused to shoot a murder suspect that repeatedly charged him;
Mazza, 2015). In other words, providing race information could decrease shooting errors for
Black men because officers will wait longer to ensure their decision is correct. This would
suggest that the decision to use force against Rice might be explained more by the dispatch
information that he was armed.
Although there are certainly cases where officers only receive dispatch information about
the race of a target or whether a weapon is present (e.g., reports of “shots fired”), in many cases
officers receive information about the race of a suspect and whether they have a weapon (Lance
Langdon, personal communication, June 1, 2016). Thus, it is important to examine how dispatch
reports with both types of information might influence officers’ decisions.
Finally, research on the FPST has typically examined the decision to shoot using
untrained individuals, although some work has examined trained police officers (Correll et al.,
2007, James et al., 2013; Ma et al., 2013; Plant & Peruche, 2005; Sadler et al., 2012; Sim et al;
2013). Recruiting police officers is crucial because they likely respond differently than untrained
civilians when faced with the decision to use lethal force. Indeed, past research shows that police
officers typically outperform untrained civilians and show less race bias. However, no work has
investigated how the decision process varies from officers to civilians, nor how officers might
use dispatch information differently than civilians. Understanding how officers respond to these
factors is crucial for establishing good dispatch practices and effective training programs.
Bayesian Estimation of the DDM
Like many paradigms in social psychology, data from the FPST is based on a relatively

14

small number of trials per condition (typically 20; see Correll et al., 2002; 2007; 2011), whereas
relatively larger numbers of participants are collected. Thus, analyses focus on population level
estimates. This can be contrasted with cognitive psychology research, where large amounts of
data (thousands of trials; e.g., Ratcliff & Rouder, 1998) are collected from relatively few
participants. Estimates then focus on the participant level. In order to reliably estimate the DDM
parameters from the FPST, I embed my analyses in a hierarchical framework. Participants’
estimates inform other participants’ estimates as well as group level estimates. This is a more
reliable method for estimating parameters because of the relatively few trials completed by any
given participant.
A consequence of this hierarchical framework is that it produces estimates at both the
individual and group levels. Because I assume that individuals are randomly drawn from an
unspecified population, the individual level estimates for all parameters are also random. This
creates a complex random structure that is computational prohibitive to solve using maximum
likelihood methods, which rely on optimization algorithms to find parameter values that
maximize the likelihood of the data (Vandekerckhove et al., 2011). However, Bayesian methods
only require the specification of a prior distribution and a tractable likelihood function to update
that distribution, making such complex structures less problematic (see p. 115, Kruschke, 2014).
Bayesian estimation provides an estimate of the posterior distribution of parameters after
observing the data and in light of prior beliefs. The posterior distribution represents the degree of
certainty regarding the parameters after observing the data. I allow the data to dominate the
posterior estimate by setting uninformative priors, and I estimate the distributions via Markov
Chain Monte Carlo methods, which approximate the posterior distribution given a large enough
sample. More details on the estimation procedure, including the statistical model and priors used

15

can be found in the Appendix.
Because the (marginal) posterior distribution represents certainty about a parameter, it
can be used in hypothesis testing. I describe the posterior parameter distributions using their
modal posterior value and 95% Highest Density Interval (HDI). The modal posterior value has
the highest probability density, making it the most credible parameter estimate. Similarly, values
within the 95% HDI have a higher probability density than values outside and so are more
credible (Kruschke, 2014). Testing condition effects is accomplished by determining whether the
95% HDI for a contrast contains zero. When it does not, the effect of condition is credible. For
example, to test whether target race impacts drift rate, I analyze whether the condition level
posterior distribution for White targets is credibly different than that for Black targets.
To verify that the DDM was an appropriate model of the FPST data, I conducted
posterior predictive checks for each study and condition for the choice probabilities, mean
response times, and response time distributions. Those checks are included in the Appendix.
They indicated that the model gave a good account of the data relative to other work (e.g.,
Ratcliff, Thapar, and McKoon, 2006), although there is room for improvement.

16

METHOD AND RESULTS
Overview of the Studies
The following four studies tested how dispatch information and expertise impacts the
decision to shoot and changes the effects of race on shooting decisions. Study 1 and 2 tested the
whether dispatch information impacted the decision to shoot and whether those effects depended
on expertise. Untrained students (Study 1 and 2) and trained police officers (Study 1) completed
a modified version of the FPST where they received demographic information about targets
before they saw them. They also occasionally received accurate information that those targets
were armed. Data were examined using behavior-level analyses as well as process-level DDM
analyses.
Results from the first two studies demonstrated a clear effect of dispatch information on
behavior and at the process level. However, the DDM also revealed a counterintuitive effect of
dispatch information in Study 1, where information that a target was armed shifted participants
start point away from the decision to shoot. Study 2 revealed the opposite pattern. To probe
whether this effect was due to problems with the DDM, Study 3 tested whether the model could
recover a simulated change in start point in the expected direction under conditions similar to
Study 1. Results showed that the DDM could precisely recover the simulated difference between
conditions. Study 4 was a validation study that demonstrated that the start point could be
manipulated experimentally in predictable ways using an experimental manipulation of decision
payoffs. In sum, these experiments provide evidence that the DDM is a reasonable and
informative model of the FPST that provides novel insight into how dispatch information
influences the decision to shoot.

17

Study 1: The Role of Dispatch Information and Expertise
The purpose of Study 1 was to test how dispatch information indicating a person is armed
influences the decision to shoot. In addition, by recruiting trained officers and untrained students,
this experiment tested how trained police officers responded differently to dispatch information.
Officer and student data were examined at the process level with the DDM. As no work has
examined officer decisions to shoot through the lens of the DDM, this study provided the first
test of how officers’ shooting decision process varied from untrained students.
Method
Participants. One hundred and six undergraduates completed a version of the FPST with
dispatch information. One participant was removed for not following instructions (they always
chose to not shoot), and three participants were removed for responding carelessly (responding
faster than 300ms on 20% or more trials). The remaining 102 participants (Mage = 19.0, SD = 1.2)
were 72.5% White, 13.7% Asian, 3.9% Black, with 9.8% from other groups. Men (88.2%) were
oversampled to better match the demographics of officers nationally, who are overwhelmingly
male (87.8%; Reaves, 2015).
I also collected officer data from four different police departments in the Midwestern
United States. Fifty-one officers from departments of various sizes (from 30 – 1,800 sworn
officers) were recruited. The study was advertised to the officers during police training or shift
briefings. Officers completed the study in the department before or after their shift, or during
their training. They either were paid $30 for their participation or did the study voluntarily during
their training. Officers were 68.6% men, with an average of 11.7 years of experience (SD = 9.5,
range [0, 45]; not all officers reported their experience).

18

Procedure. Participants completed 160 trials (officers) or 320 trials (students) of a
modified FPST with a 650ms response window. The task was the same as the traditional FPST
expect participants were given dispatch information about the target before each trial. They were
always given accurate demographic (race and sex) information. This experimental design reflects
that misidentification of race and sex is unlikely for these targets, which were easily accurately
categorizable by race and sex. In addition, on half of the trials participants received information
that the target was armed. This information was accurate 75% of the time. Figure 3 shows an
example of one trial from this task.

InformaCon	
2000ms	

1	–	4	Backgrounds	
500	–	1000ms	each	

Response	Window	
650ms	

Dispatch:	The	
suspect	is	an	armed	
Black	male.	

Feedback	
2000ms	

good	shot	

Time	

Figure 3: The modified FPST used in Study 1. Participants always received accurate information
about the race and sex of the target before each trial. On half of the trials they were informed
(with 75% accuracy) that the target was armed.
The study was a 2 (object: gun, nongun) × 2 (race: Black, White) × 2 (dispatch: no
weapons information, weapons information) within-subjects design with expertise (officers,
students) as a between-subjects factor. Targets were more likely to be armed when this dispatch
information was presented (75% armed) than when it was not (25% armed). This made the
information (and its absence) informative as to whether the participant would encounter
someone with a weapon. This also made the task more realistic. Officers encounter individuals
with guns less frequently outside of calls where weapons are reported.

19

As another departure from the typical FPST design, I also did not give point-based
feedback to students and officers on their performance. However, they did receive feedback
about their decision accuracy. This decision was driven by the choice to recruit officers. The
purpose of point-based feedback is to mimic the payoffs that officers receive on the job based on
their decisions to use lethal force. Officers likely do not need this reminder and might find that
allocating points trivializes these important decisions. I removed the point-based system for both
groups to prevent this issue. This decision may influence the general bias of participants to shoot
more often than not because the point-based system encourages shooting behavior. However,
given that officers and students likely understand the nature of the task and are aware of the real
world payoffs, they may continue to show a bias to shoot.
Results
Behavioral Analyses. To test whether dispatch information impacted the decision to
shoot, I conducted an ANOVA on error rates, with target race, object, and information as withinsubjects factors.4 Expertise was entered as a between-subjects factor. Figure 4 shows the decision
data for all conditions. Only two effects emerged. First, officers made fewer errors (M = .179, SD
= .140) than students (M = .240, SD = .149), F(1, 151) = 13.23, p < .001. Second, the predicted
two-way interaction between object and dispatch information was significant, F(1, 151) = 58.13,
p < .001. As expected, when dispatch correctly indicated that the target was armed, participants
made fewer errors (M = .191, SD = .106) than when dispatch was incorrect (M = .243, SD =
.178), t(152) = -3.90, p < .001. In addition, when no dispatch information was given (thus
unarmed individuals were more likely) participants made fewer mistakes for unarmed targets (M
= .185, SD = .123) than armed targets (M = .260, SD = .162), t(152) = 6.33, p < .001.

4

Full ANOVA tables for all behavioral analyses are listed in the appendix.

20

0.35

0.35

white
black

0.25

0.20

white

0.30

Proportion Errors

Proportion Errors

0.30

black
0.25

0.20

0.15

0.15

0.10

0.10
Unarmed NI Armed NI Unarmed WI Armed WI

Unarmed NI Armed NI Unarmed WI Armed WI

Students

Police

Figure 4: Proportion errors for students (left panel) and police (right panel) for all conditions. NI
= No weapon information. WI = Weapon information. 95% confidence intervals were calculated
using the methods outlined by Morey (2008).
The typical race by object interaction in error rates that is indicative of racial bias was not
significant, F(1, 151) = 1.70, p = .19, nor was the three-way interaction with condition, F(1, 151)
= 0.60, p = .44. In sum, there was no evidence that students or officers were impacted by the race
of a target when dispatch information was incorporated into the task. This occurred regardless of
whether dispatch information that the target was armed was given or not.
An ANOVA with identical predictors was run on the correct response times. Figure 5
shows the response time data for all conditions. Response times 2.5 standard deviations above a
participant’s mean were truncated to this value to reduce skew from inattentive responses.
Officers (M = 612ms, SD = 83ms) were slower to respond than students (M = 560ms, SD =
79ms), F(1, 151) = 29.39, p < .001. Participants were also faster to respond to guns (M = 550ms,
SD = 83ms) than nonguns (M = 604ms, SD = 76ms), F(1, 151) = 196.70, p < .001.

21

750

725

725

700

white

675

black

650
625
600
575
550

Correct Response Time (ms)

Correct Response Time (ms)

750

700

white

675

black

650
625
600
575
550

525

525

500

500
Unarmed NI Armed NI Unarmed WI Armed WI

Unarmed NI Armed NI Unarmed WI Armed WI

Students

Police

Figure 5: Correct response times for students (left panel) and police (right panel) for all
conditions. NI = No weapon information. WI = Weapon information. 95% confidence intervals
were calculated using the methods outlined by Morey (2008).
Mirroring the decision data, there was also an interaction between object and dispatch
information, F(1, 151) = 10.93, p < .001. When dispatch indicated a target was armed,
participants correctly shot (M = 540ms, SD = 72ms) armed targets faster than they correctly
chose to not shot unarmed targets (M = 609ms, SD = 77ms), t(152) = 13.65, p < .001. When no
dispatch information was provided (and thus unarmed individuals were more likely), participants
were still faster to correctly shoot (M = 560, SD = 92ms) than to not shoot (M = 599, SD =
75ms), t(152) = 6.39, p < .001, but this difference was smaller (d = .84 vs. .46).
There was also a two-way interaction between object and expertise, F(1, 151) = 16.38, p
< .001. Officers correctly shot armed targets faster (M = 574ms, SD = 79ms) than they correctly
chose to not shot unarmed targets (M = 650ms, SD = 68ms), t(50) = 11.97, p < .001. Students
also correctly shot armed targets faster (M = 538ms, SD = 83ms) than they correctly chose to not
shot unarmed targets (M = 581ms, SD = 69ms), t(101) = 8.35, p < .001, but this difference was

22

smaller (d = .93 vs. .54).
Summary. Both students and officers made more mistakes and were slower to respond
when dispatch information was wrong. This pattern could be due to increased bias to choose the
decision associated with the dispatch information. Alternatively, dispatch information may
change how participants accumulate information in an online fashion. The DDM can disentangle
these hypotheses, as the former would show up as an effect of dispatch information on start
point, and the latter an effect of dispatch information on drift rate.
When dispatch information was incorporated into the task there was no evidence that race
influenced students’ and officers’ errors. Participants were no more likely to shoot unarmed
Black men than unarmed White men, nor did they not shoot armed White men more than armed
Black men. The absence of bias occurred regardless of whether targets were described as armed
or not. This raises the question of whether the demographic information (e.g., target race) or the
weapon information might reduce race bias in shooting decisions.
Although officers made fewer mistakes, they were also much slower to respond. This
pattern is consistent with at least two process level explanations. The first is that officers require
more information to make a decision, perhaps because these decisions are more important to
them than they are to students. An effect of expertise on the threshold parameter would support
this hypothesis. However, given that officers receive extensive training and have professional
experience identifying objects, I actually expect them to be better at distinguishing between guns
and harmless objects. This could result in them having higher drift rates than students, and—all
else equal—would mean that officers would be faster and more accurate than students.
If officers are better at distinguishing guns from harmless objects, they would have to be
slower for other reasons. One possibility is that their slower response times might be explained

23

by aging. Reaction times slow with age, and this slowing is predominantly due to an increase in
the length of non-decision processes (Ratcliff, Thapar, & McKoon, 2001; Ratcliff, Thapar,
Gomez, & McKoon, 2004; Thapar, Ratcliff, & McKoon, 2005). If non-decision times are slower
for officers than students (who are generally older than students), this might explain why officers
are slower than students even if they are better at distinguishing guns from harmless objects.
Hierarchical DDM.
Model Specification and Selection. The hierarchical DDM was specified according to
the guidelines set by Pleskac et al. (2017). All parameters were allowed to vary as a function of
race and information, but only drift rate and non-decision time were allowed to vary by object. A
diagram of the model is provided in the Appendix. This model estimates individual variation in
the parameters of the DDM, but assumes that the parameters are fixed across trials (i.e., there is
no trial-by-trial variability). I also tested more complicated versions of the model with trial-bytrial variability in drift rate and start point. However, the group-level conclusions drawn from
these models did not vary from the simpler versions without variability. For the sake of
parsimony, I report the model without trial-by-trial variability.
Hierarchical DDM Analysis. Figure 6 shows condition-level estimates of the threshold,
start point, drift rate, and non-decision time.5 I first examined whether officers collected more
information than students. There was a small effect of expertise on threshold, Âľdiff = 0.028, 95%
HDI [0.002, 0.57]), d = 0.20 [0.02, 0.42]. Officers had higher thresholds (Âľ = 1.069, 95% HDI
[1.047, 1.092] than students (Âľ = 1.039, 95% HDI [1.024, 1.057]). This main effect was primarily
driven by an effect of expertise when no weapon dispatch information was given, Âľdiff = 0.051,
95% HDI [.012, .090], d = .389 [.099, .687]. Officers had higher thresholds (Âľ = 1.123, 95% HDI
[1.089, 1.153]) than students (Âľ = 1.07, 95% HDI [1.047, 1.093]). Although this effect partially
5

All parameter effects and interactions are reported in the Appendix for Studies 1 and 4.

24

explains why officers are slower than students when no dispatch information is given, it is not
sufficient to explain the large difference in response time.

1.2
●

●

1.1

●

police

●

students

0.65
●

●

Îą

●

●

0.60

β

1.0

●
●

0.55

●
●

●

●

●

●

0.50

●
●

0.9
W None

B None

W Armed

0.45

B Armed

0.45

W None

B None

0.45
●

●

0.42

0.42
●

●

τNG 0.39

●

τGU 0.39

0.36

●

●

●

●
●

0.36

●

●

●

0.33

0.33

●

0.30

●

●

0.30
W None

B None W Armed B Armed

W None

3.0

B None W Armed B Armed

3.0

2.7
2.4

W Armed B Armed

2.7
2.4

●
●

2.1

2.1
●

|δNG| 1.8
1.5

●

●

δGU 1.8

●

●

●

1.2

1.2

●

0.9

0.9

0.6

0.6
W None

B None W Armed B Armed

●

●

●

1.5
●
●

●

W None

●

B None

W Armed B Armed

Figure 6: Diffusion model parameters as a function of target race, dispatch information, and
object for Study 1. Dots represent modal posterior predictions at the condition level; bars are
95% HDI. W = White, B = Black. NG = Nongun. GU = Gun.
Moving onto the non-decision time parameters, there was strong evidence that officers
non-decision processes (Âľ = 403ms, 95% HDI [398ms, 409ms]) took longer than students (Âľ =

25

338ms, 95% HDI [.332, .344]), Âľdiff = 66ms, 95% HDI [57ms, 73ms], d = 1.09, 95% HDI [0.93,
1.22]. This finding provides strong evidence against the hypothesis that officers are slower
because they are waiting longer to make decisions. Rather, their non-decision processes take
much longer (67ms), which may be partially due to a slowdown of motor responses.
Replicating past research (Correll et al., 2015; Pleskac et al., 2017) non-decision times
were shorter for guns (Âľ = 360ms, [354ms, 365ms]) than harmless objects (Âľ = 382ms, 95% HDI
[376ms, 387ms]), Âľdiff = 21ms, 95% HDI [14ms, 30ms], d = 0.34, 95% HDI [0.23, 0.48]. One
possibility is that this reflects faster encoding for a well-defined category of objects (guns) than
an ill-defined category (harmless objects). This difference was larger for police officers, Âľint =
20ms, 95% HDI [5ms, 36ms]. For officers, non-decision times were shorter for guns (Âľ = 388ms,
95% HDI [380ms, 395ms]) than for harmless objects (Âľ = 420ms, 95% HDI [412ms, 427ms]), Âľ
= 32ms, 95% HDI [22ms, 42ms], d = 0.53, 95% HDI [0.35, 0.69].
There was a significant interaction between dispatch information and object in nondecision time, Âľint = 41ms, 95% HDI [25ms, 57ms]. When dispatch information was not given,
non-decision processes were shorter for unarmed targets (Âľ = 369ms, 95% [361ms, 377ms]) than
armed targets (Âľ = 394ms, 95% [386ms, 402ms]), Âľdiff = 25ms [13ms, 36ms], d = .0.41, 95% HDI
[.23, .60]. When dispatch information that the target was armed was given, non-decision
processes were shorter for armed targets (Âľ = 352ms, 95% [344ms, 360ms]) than unarmed targets
(Âľ = 367ms, 95% [360ms, 376ms]), Âľdiff = 16ms [5ms, 27ms], d = 0.26, 95% HDI [0.08, 0.44].
Shorter non-decision times when the dispatch information was correct were not influenced by
expertise.
To test whether officers were better at distinguishing guns from non-guns than students, I
tested whether drift rates varied as a function of expertise. Supporting this hypothesis, there was

26

a small effect of expertise on drift rate, Âľdiff = 0.35, 95% HDI [.26, .48], d = 0.47, 95% HDI [0.34,
0.64]. Officer drift rates (1.75, 95% HDI [1.66, 1.84]) were higher than student drift rates (Âľ =
1.39, 95% HDI [1.33, 1.45]). This was particularly true when the target was unarmed; officer
drift rates (Âľ = 2.06, 95% HDI [1.91, 2.19]) were moderately higher than student drift rates (Âľ =
1.55, 95% HDI 1.45, 1.64), Âľdiff = .50, 95% HDI [.35, .68], d = 0.66, 95% HDI [0.46, 0.90].
In addition to this effect of expertise, there was a clear interaction between dispatch
information and object, Âľint = 1.19, 95% CI [0.94, 1.42]. When dispatch correctly indicated that a
target was armed, both students and officers accumulated evidence much more quickly to shoot
(Âľ = 1.65, 95% HDI [1.55, 1.76]) than when no information was provided (Âľ = 1.04, 95% HDI
[0.92, 1.17]), Âľdiff = 0.62, 95% HDI [0.43, 0.77], d = 0.81, [0.58, 1.04]. In contrast, when targets
were unarmed and dispatch incorrectly identified the target as armed, participants accumulated
evidence to not shoot more slowly (Âľ = 1.51, 95% HDI [1.39, 1.64]) than when this information
was not given (Âľ = 2.07, 95% HDI [1.97, 2.19]), Âľdiff = -0.57, 95% HDI [-.73, .39], d = -0.75,
95% HDI [.52, .98]. Thus, dispatch information strongly shaped how participants collected
information. When information was correct, both students and officers accumulated information
for the correct decision more quickly.
Similar to the behavioral analysis, there was no evidence of a race by object interaction in
the accumulation of information for both students (Âľint = 0.17, 95% HDI [-0.09, 0.46]) and
officers (Âľint = 0.12, 95% HDI [-0.29, 0.51]). Thus, there was no evidence that participants were
influenced by the race of the target when they accumulated information for their decision.
Finally, I examined the effect of the manipulations on participants’ start point. There
were only two main effects. First, officers had a higher starting point (Âľ = .577, 95% HDI [.565,
.589]) than students (Âľ = .533, 95% HDI [.526, .539]), Âľdiff = .043, 95% HDI [.030, .058], d =

27

0.86, 95% HDI [0.58, 1.16]. Second, both students and officers had lower start points when they
received dispatch information that targets were armed (Âľ = .519, 95% HDI [.510, .530]) than
when no dispatch information was given (Âľ = .590, 95% HDI [.580, .599]), Âľdiff = .070, 95% HDI
[.056, .083], d = 1.35, 95% HDI [1.06, 1.69]. This is counterintuitive because dispatch was a
reliable indicator (with 75% accuracy) of the presence of a weapon and should have biased
participants to favor the shoot decision. This suggests that participants are interpreting the
information given to them in an unusual way, or that there are limitations in the DDM as a
description of this decision process.
As an exploratory analysis, I examined whether officer experience in years predicted the
rate at which participants collected evidence.6 There was no correlation between the individuallevel officer drift rates (collapsed across condition) and years of experience, r(44) = -.14, p = .34.
Experience was not significantly correlated with start point r(44) = .09, p = .54, threshold, r(44)
= .10, p = .50, or non-decision time, r(44) = .09, p = .56. Although officers showed higher rates
of evidence accumulation than students, these differences may be primarily due to training
officers receive as recruits, rather than on the job experience. Similarly, although officers had
longer non-decision times than students, this is likely due to their increased age (which was not
recorded) and not their experience. Although experience is correlated with age, it may be a poor
proxy. This is especially true for officers who had another job before they became police.
Summary. While the behavioral data showed that information and expertise influenced
the speed and accuracy of participants’ decisions, the DDM revealed how these manipulations
influenced the decision-making process. Officers’ slower and more accurate responses compared
to students were due to longer non-decision times and stronger drift rates, respectively. Dispatch
information also influenced decisions by increasing the accumulation of information when it was
6

Only 46 officers reported their years of experience.

28

correct, and decreasing it when it was incorrect. Finally, dispatch information had an unexpected
effect on participants start points where participants were biased towards the option inconsistent
with the information.
Discussion
To test the role of dispatch information on the decision to shoot, I modified the FPST so
that participants received prior information about the person they would encounter. Participants
always received accurate demographic information about the person, and occasionally received
information that the target was armed (with 75% accuracy). To better understand the role of
expertise, I recruited trained police officers as well as untrained students. This design made the
shooter task more realistic and allowed me to test how dispatch information influenced decisions.
Behavioral analyses showed that accurate dispatch information improved decision
accuracy and speed for both students and officers, whereas inaccurate information increased
errors and slowed responding. Officers were slower and more accurate than students, and the
DDM provided a process-level explanation for why. Interestingly, race did not influence the
decision to shoot when dispatch information was provided. I discuss each of these points below.
Role of Dispatch Information. Dispatch information that a target was armed had a
powerful influence on participants’ decisions. When this information was accurate, errors and
response times decreased. Despite these clear behavioral effects, the results are consistent with
different process level explanations for how dispatch information might impact the decision to
shoot. Two possibilities were explored in this study. First, dispatch information might create a
bias to favor the information consistent decision. Second, information might influence how
people accumulate information when they are making the decision. The diffusion model
provided a way to test these hypotheses. Results showed clear support for the latter. Participants

29

accumulated information more quickly when dispatch information was correct. This might be
due to dispatch information changing how people search for information. In the absence of any
prior information, individuals may search in an exploratory way, asking, “what object is that
person holding?” But when participants receive information that the person is armed, they may
search for confirmatory information, asking, “is the person holding a gun?”
Although the current experiment cannot directly test whether dispatch information
influences search strategies, self-reports from participants suggest it is a possibility. Multiple
officers and students reported they ignored the dispatch information because it distracted them.
The behavioral data clearly show these attempts were unsuccessful. However, insofar as ignoring
information was a common strategy, it might explain why dispatch information influenced the
decision process in unusual ways. Participants may have attempted to ignore the dispatch
information that a person was armed by changing their bias to favor not shooting. This would
explain the counterintuitive effect of such information on participants’ start point. Despite their
attempts to correct the influence of this information, these expectations may have leaked into
their information search. A central finding of research on confirmation bias is that individuals are
unaware they are searching for expectation consistent information (Mynatt, Doherty, & Tweney,
1976; Wason & Johnson-Laird, 1972, for a review see Nickerson, 1998). This would explain
why participants thought they had successfully ignored the information even though they
accumulated evidence more quickly (had stronger drift rates) when the information was correct.
Unpacking Response Time Differences. One of the clearest benefits of the DDM was to
test hypotheses about differences in the underlying decision process for untrained students and
trained officers. Recall that officers were both more accurate and slower than students when
making shooting decisions. Without a formal model of decisions, it would be reasonable to

30

conclude that this was due to greater caution among officers. There are plausible reasons to
support this logic; the task may be more meaningful to officers or they may be more concerned
about appearing biased. The DDM provided a way to test this caution hypothesis directly and
compare it to alternative explanations.
As the DDM showed, although officers did in fact have higher thresholds than students
for unarmed targets, the main reason why officers were slower than students was because their
non-decision processes took longer. The protracted length of these processes obscures the fact
that—all else equal—officers are better than students at distinguishing guns from harmless
objects. In fact, if non-decision time were controlled for, officers would on average respond
faster than untrained students because they accumulate information relevant to the decision to
shoot more quickly.
The Lack of a Race Effect. The race of a target did not influence participants’ decisions
to shoot in the current study. This stands in contrast to past work that has found racial bias in
shooting decisions (e.g., Correll et al., 2002; 2011; Pleskac et al., 2017). However, the current
study modified the traditional FPST by providing dispatch information about targets race and
armed status before each trial. These are relevant pieces of information that impact shooting
decisions. If providing dispatch information eliminates bias in the decision to shoot, this would
suggest that findings of racial bias in the FPST might not translate into real world decisions,
because officers often have dispatch information about whom they will encounter. Race may bias
decisions in the absence of contextual information, but be quickly undercut by more reliable
information. This leads to a troubling possibility: current FPST work may provide a skewed
picture of the degree to which officers show bias in the field.
The dispatch information provided before each trial included race information as well as

31

information about whether the target was armed. This makes it difficult to disentangle exactly
which part of the information was responsible for the reduction in racial bias in decisions. There
are plausible reasons that both types of information might reduce racial bias. Starting with the
information that a target is armed, this information may reduce impact racial bias in shooting
decisions because it strongly shapes how participants collect information at the process level.
This may be sufficient to suppress the effects of irrelevant information like race. In contrast,
accurate race information might also reduce bias in participants’ decisions because it may enable
them to better control automatic stereotypic associations between Black men and violence that
would lead to higher rates of shooting Black targets.
Study 2 directly tested these competing accounts by having participants receive each
piece of dispatch information independently in a blocked design. Participants also completed a
version of the FPST where no information was given before each trial, which served as a control
condition. This condition replicated past FPST designs and tested whether there was evidence for
racial bias in shooting decisions when no dispatch information was given.
Study 2: Separating the Role of Race and Weapon Information
The goal of Study 2 was to investigate what part of the dispatch information (race or
weapon information) was relevant to the decision to shoot, as well as whether the accuracy of
that information mattered. This study used the same modified FPST design as Study 1, except
that the race and weapon information were blocked and counterbalanced. Information was
presented in blocks of 80 trials, so that participants always received race information or weapon
information. As a control, participants also completed a block of 80 trials of the traditional FPST
where no dispatch information was presented.

32

Method
Participants and Study Design. Undergraduate students (N = 122) completed 240 trials
of the FPST across three blocks. Six participants were removed for responding carelessly
(responding faster than 300ms on 20% or more trials). The remaining 116 participants (Mage =
19.1, SD = 2.0) were 77.6% White, 12.9% Black, 5.1% Asian, with 4.3% from other groups. The
majority of participants (64.6%) were women; men were not oversampled in this study.
Block order was counterbalanced. Each block contained 80 trials where target race
(Black, White) and object (gun, nongun) were crossed. In the control block, no dispatch
information was provided. In the other blocks, participants were given dispatch information
about whether the target was Black/White or armed/unarmed, prior to the start of the trial. This
information was accurate 75% of the time, reflecting that dispatch information is generally but
not always accurate. The experiment was a 2 (target race: Black, White) by 2 (object: gun,
nongun) by 3 (information: none, weapon, race) by 2 (information accuracy: correct, incorrect)
within-subjects design.7
Results
Behavioral Analyses. To test whether race and weapon dispatch information impacted
the decision to shoot, I conducted ANOVAs on participants’ error rates, with target race, object,
and information as within-subjects factors. Each ANOVA tested the effect of information (race
or weapon) against the no information control. Follow up analyses tested how the accuracy of
information impacted decisions. The same analyses were also conducted on response times for
correct decisions. Error rates and response times for each condition are displayed in Figure 7.
A follow up ANOVA with race, object, and information (unarmed, armed) as factors was
conducted on the error rates from the weapon information condition. The expected interaction
7

In the case of the control condition, information accuracy was not applicable.

33

between object and information was significant, F(1, 115) = 99.89, p < .001. When dispatch
correctly identified a target as armed, participants made far fewer errors (M = .232, SD = .157)
than when dispatch incorrectly identified a person as unarmed (M = .403, SD = .275), t(115) =
8.25, p < .001. When dispatch correctly identified a target as unarmed, participants made far
fewer errors (M = .199, SD = .128) than when dispatch incorrectly identified a person as armed
(M = .393, SD = .258), t(115) = 8.77, p < .001. Thus, there was strong evidence that participants
were using the dispatch information presented to them. The race by object interaction was also
significant, F(1, 115) = 5.78, p = .018. Importantly, this interaction was not influenced by the
accuracy of the dispatch information, F(1, 115) = 0.20, p = .65.
Focusing on the response time data, an ANOVA with target race, object, and condition
(weapon information, no information) as factors was run on the correct response time results.
Only an effect of object emerged; participants were faster to respond to guns (M = 509ms, SD =
70ms) than harmless objects (M = 567ms, SD = 165ms), F(1, 115) = 70.99, p < .001. Follow up
analyses looking at how the accuracy of dispatch information influenced decisions were not run
because many participants had missing data (i.e., they made no correct responses when given
incorrect information). Descriptively, participants were faster to respond when dispatch
information was correct and slower when it was not.
To test the role of race information, I conducted an ANOVA on error rates, with target
race, object, and condition (race information, no information) as factors. The expected two-way
interaction between object and target race was significant, F(1, 115) = 37.29, p < .001.
Participants shot more unarmed Black men (M = .331, SD = .164) relative to unarmed White
men (M = .272 SD = .164), t(115) = 6.26, p < .001. They also failed to shoot more armed White
men (M = .275, SD = .128) relative to armed Black men (M = .256 SD = .137), t(115) = 2.18, p =

34

.031. Unlike the weapon dispatch information, this interaction was not influenced by condition,
F(1, 115) = 2.07, p = .15.

White

0.45

Proportion Errors

Black
0.40
0.35
0.30
0.25
0.20

U
k
Bl
ac

Bl
ac

700

Correct Response Time (ms)

G

G
k

N

U
te
hi
W

W

hi

te

N

G

G

U
m
Ar

ed

m
Ar

ed

N

G

G

U
rm
ed
U

na
U

na

rm
ed

N

G

G

U
e
on
N

N

on

e

N

G

G

0.15

White

680

Black

660
640
620
600
580
560
540
520
500
480

U
G
k
Bl
ac

G
Bl
ac

k

N

U
hi
te
W

W

hi
te

N

G

G

U
ed
m
Ar

Ar

m

ed

N

G

G

U
ed
na
U

rm
na
U

rm

ed

N

G

G

U
e
on
N

N

on

e

N

G

G

460

Figure 7: Proportion errors (top panel) and correct response times (bottom panel) for all
conditions. Response times were omitted for 22 participants because they failed to respond
correctly in at least one condition. NG = Nongun. GU = Gun. 95% confidence intervals were
calculated using the methods outlined by Morey (2008).

35

A follow up ANOVA with race, object, and race information (White, Black) as factors
was conducted on error rates from the race information condition. The race by object interaction
was significant, F(1, 115) = 5.78, p = .018. This interaction was primarily driven by unarmed
targets; participants shot more unarmed Black men (M = .327, SD = .206) relative to unarmed
White men (M = .274 SD = .210), t(115) = 3.67, p < .001. However this interaction was qualified
by a significant interaction with information, F(1, 115) = 4.00, p = .048. Participants only shot
more unarmed Black men (M = .330, SD = .158) than unarmed White men (M = .259, SD = .239)
when given information that targets were Black, t(115) = 3.55, p < .001. No such difference was
observed when dispatch stated the target was White, t(115) = 1.67, p = .097.
Turning to the response time data, an ANOVA with target race, object, and condition
(race information, no information) as factors was run on the correct response time results. Only a
significant effect of object emerged; participants were faster to respond to guns (M = 522ms, SD
= 164ms) than harmless objects (M = 568ms, SD = 75ms), F(1, 115) = 29.60, p < .001.
Summary. The behavioral data demonstrate a clear effect of dispatch information about
whether a person is armed. Participants made half as many errors when information was correct
versus incorrect. The inclusion of weapon information also reduced racial bias in the shooting of
unarmed targets. In contrast, the inclusion of weapons information did not influence racial bias in
shooting decisions relative to a no information control condition. This suggests that the reduction
in racial bias seen in Study 1 where both weapon and race information were given might be at
least partially due to the presence of information that targets were armed. To further probe this
question and to better understand the shooting decision-making process, I conducted a DDM
analysis of the data.

36

Hierarchical DDM.
Model Specification and Selection. The hierarchical DDM was again specified according
to the guidelines set by Pleskac et al. (2017). All parameters were allowed to vary as a function
of race and information, but only drift rate and non-decision time were allowed to vary by object.
Hierarchical DDM Analysis. Figure 8 shows condition-level parameter estimates.
Focusing on the threshold, I replicated the finding that participants thresholds were lower when
dispatch listed them as armed (Âľ = 0.875, 95% HDI [0.855, 0.897]), than unarmed (Âľ = 0.923,
95% HDI [0.900, 0.943]), Âľdiff = -0.046, 95% HDI [-0.076, -0.017], d = -0.41, 95% HDI [-0.67, 0.14]. Thresholds were also higher for Black men (Âľ = 0.913, 95% HDI [0.893, 0.936]) than
White men (Âľ = 0.884, 95% HDI [0.863, 0.904]), Âľdiff = 0.032, 95% HDI [0.000, 0.059], d = 0.28,
95% HDI [0.01, 0.53] when weapon information was given. Finally, thresholds were lower when
incorrect race information was given (Âľ = 0.804, 95% HDI [0.778, 0.827]) than when the
information was correct (Âľ = 0.889, 95% HDI [0.871, 0.908]), Âľdiff = -0.089, 95% HDI [-0.117, 0.057], d = -0.77, 95% HDI [-1.04, -0.49].
Moving onto the relative start point, there was not a credible effect of race on start point
regardless of what type of dispatch information was (not) given. Although not credible, weapon
information had the expected effect on start point, Âľdiff = .020, 95% HDI [.000, .039], d = 0.50,
95% HDI [-0.02, 0.96]. Participants’ favored the shoot decision more when targets were
described as armed (Âľ = .542, 95% HDI [.529, .558]) than unarmed (Âľ = .523, 95% HDI [.510,
.538]). This diverges from Study 1, where information that a target was armed decreased
participants’ start point to more favor the don’t shoot decision.

37

0.96

0.58
●

0.92

0.56

●
●

●

Îą 0.88

●

●

●

●

●

β 0.54

●

●

●

0.84

0.52

●

0.80

●

●

●

●

●
●

●

0.50
IW
N hite
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m
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W dB
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N

N

IW
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U I B te
na la
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Ar ed
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W W
hi
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ac
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B

0.76

0.40

0.40
●

●

0.38

τNG

0.38
●
●

0.36

τGU

●
●

●
●

0.34

●

●

●

●

●

●
●

0.34

●

●

IW
N hit
U IB e
na la
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W eW
hi
Bl te B
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k
Bl W
ac
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B

N

IW
N hit
U IB e
na la
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m B
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Ar d W
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t
W eW
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Bl te B
ac
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Bl W
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B

0.32

N

●
●

●

●

●

●

●

δGU

●
●

1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2

●

●

●

●
●

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N

N

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N hite
U IB
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W W
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ac
k
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B

●

IW
N hit
U IB e
na la
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U me ck
na d
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Ar ed
m B
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Ar d W
m
W ed
hi B
t
W eW
hi
Bl te B
ac
k
Bl W
ac
k
B

|δNG|

0.36

●

0.32

1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2

●
●

Figure 8: Diffusion model parameters as a function of target race, dispatch information, and
object for Study 2. Dots represent modal posterior predictions at the condition level; bars are
95% HDI. W = White, B = Black, NI = No Information.
Participant non-decision time for both guns and nonguns was shorter when the weapon

38

information was correct (Âľ = 343ms, 95% HDI [337ms, 349ms]) than incorrect (Âľ = 359ms, 95%
HDI [352ms, 365ms]), Âľdiff = -16ms, 95% HDI [-25ms, -7ms], d = -0.24, 95% HDI [-0.37, -0.10].
Similarly, non-decision time for both guns and nonguns was shorter when the race information
was correct (Âľ = 355ms, 95% HDI [349ms, 361ms]) than incorrect (Âľ = 386ms, 95% HDI
[379ms, 393ms]), Âľdiff = -31ms, 95% HDI [-40ms, -22ms], d = -0.47, 95% HDI [-0.60, -0.33].
Replicating Study 1, non-decision time was smaller for guns (Âľ = 354ms, 95% HDI [350ms,
358ms]) than for nonguns (Âľ = 365ms, 95% HDI [361ms, 369ms]) objects, Âľdiff = -11ms, 95%
HDI [-17ms, -5ms], d = -0.17, 95% HDI [-0.25, -0.08].
Turning to the drift rate, I replicated the interaction between dispatch information and
object for weapon dispatch information, Âľint = 1.88, 95% CI [1.50, 2.24]. When dispatch
correctly indicated that a target was armed, participants accumulated evidence much more
quickly to shoot (Âľ = 1.59, 95% HDI [1.42, 1.73]) than when no information was provided (Âľ =
0.52, 95% HDI [0.32, 0.71]), Âľdiff = 1.08, 95% HDI [0.83, 1.32], d = 1.38, [1.06, 1.72]. When
targets were unarmed and dispatch incorrectly identified the target as armed, participants
accumulated evidence to not shoot more slowly (Âľ = 0.72, 95% HDI [0.54, 0.92]) than when this
information was not given (Âľ = 1.53, 95% HDI [1.38, 1.67]), Âľdiff = -0.78, 95% HDI [-1.05, 0.57], d = -1.06, 95% HDI [1.37, 0.75].
When participants did not receive dispatch information race had a different effect on drift
rate for armed and unarmed targets, Âľint = 0.64, 95% HDI [0.25, 1.02]. This is consistent with
past work showing that race is accumulated as evidence to shoot alongside the object being held.
Specifically, participants accumulated evidence more quickly to not shoot unarmed White targets
(Âľ = 1.41, 95% HDI [1.21, 1.58]) than unarmed Black targets (Âľ = 1.00, 95% HDI [0.81, 1.17]),
Âľdiff = 0.41, 95% HDI [0.16, 0.67], d = 0.51, 95% HDI [0.20, 0.87]. They also accumulated

39

evidence more quickly to shoot armed Black targets (Âľ = 1.44, 95% HDI [1.27, 1.64]) than armed
White targets (Âľ = 1.19, 95% HDI [1.01, 1.38]), although this difference was not credible, Âľdiff =
0.24, 95% HDI [-0.02, 0.50], d = 0.34, 95% HDI [-0.02, 0.67].
Unlike Study 1, the same pattern of race bias was observed when participants were given
weapon dispatch information, Âľint = 0.44, 95% HDI [0.07, 0.82]. Participants showed race bias
for armed targets, Âľdiff = 0.28, 95% HDI [0.01, 0.51], d = 0.36, 95% HDI [0.00, 0.65] and
unarmed targets, Âľdiff = 0.22, 95% HDI [-0.02, 0.46], d = 0.27, 95% HDI [-0.03, 0.59]. When
participants were given race dispatch information they did not show a general pattern of bias, Âľint
= 0.27, 95% HDI [-0.11, 0.69]. This was because participants only showed bias for unarmed
targets, Âľdiff = 0.29, 95% HDI [0.05, 0.54], d = 0.38, 95% HDI [0.07, 0.71], and not for armed
targets, Âľdiff = 0.01, 95% HDI [-0.27, 0.27], d = 0.02, 95% HDI [-0.35, 0.35].
Summary. The DDM results were largely consistent with and clarified the findings from
Study 1. Dispatch information strongly influenced how participants collected information.
Thresholds were lower when dispatch information stated that the target was armed. Non-decision
times were also longer when information was incorrect. However, there were some differences
between the studies. In the current study, both types of dispatch information reduced bias in the
accumulation of information as measured by the drift rate, but neither eliminated it. Second,
weapon information shifted participants’ starting bias to factor the decision that matched the
information (although this was not credible).
Discussion
Both race and weapon dispatch information had unique influences on decisions to shoot
and the underlying decision process. Weapon dispatch information had the primary effect of
reducing errors when correct, due to changes in how participants accumulated evidence. This

40

process level finding could reflect changes in visual search strategies. Both types of information
reduced the influence of race on evidence accumulation, but only race dispatch information
eliminated racial bias in the accumulation of evidence for armed targets. In sum, there is some
evidence that both race and weapon information have independent effects on the decision to
shoot that reduce racial bias.
Unlike Study 1, race generally impacted how participants accumulated evidence to shoot
regardless of whether they did or did not receive dispatch information. This difference could be
due to the fact that both pieces of information were presented separately, rather than together. If
dispatch information reduces racial bias in the decision to shoot because it provides relevant
information, giving demographic information about who to look for (race information) and
information about whether they are armed (weapon information) may override the influence of
stereotypic associations between Black men and violence.
A related issue with the DDM is the mixed findings that dispatch information that the
target was armed pushed participants start point to favor not shooting in Study 1 and to favor
shooting in Study 2. Interpreting the start point parameter as a measure of prior bias is dependent
on the measure being sensitive to factors that should change biases in a consistent way. If one
holds an a priori assumption that probabilistic information about what response is correct should
only create a prior bias to favor that response, the results of Study 1 rule out the DDM as a viable
model. Even if this assumption is relaxed for a specific manipulation (e.g., dispatch information),
interpreting the start point still requires validating it in other ways. Studies 3 and 4 did this two
different ways. Study 3 tested whether the DDM could detect a simulated change in start point in
the predicted direction under conditions similar to Study 1. Study 4 used an experimental
manipulation to show that the start point responds predictably to a manipulation of payoffs when

41

using actual participants.
Study 3: Model Recovery of Start Point
The purpose of Study 3 was to demonstrate that the current hierarchical implementation
of the DDM can detect predicted changes in start point. In Study 1 dispatch information had a
counterintuitive effect on start point and also influenced how people accumulated information (a
drift rate effect). In contrast, Study 2 showed a (noncredible) effect in the predicted direction. To
rule out the possibility that this unusual pattern was due to tradeoffs between the model
parameters that render the results of the model uninformative, I simulated 100 datasets based on
the data from Study 1 but with the expected effect of information on start point. If the model can
accurately recover differences in start point from simulated data, it would suggest that this
unusual finding is not merely an artifact of the analytic method used.
Method and Results
I conducted a parameter recovery analysis to test whether the DDM can detect start point
changes in a study design similar to the experimental studies described subsequently. Decision
and reaction time data were simulated from the Study 1 condition level parameter estimates
using the RWiener package (Wabersich & Vandekerckhove, 2014). In the absence of a strong a
priori estimate for the effect size of a potential start point difference, I based the simulations on a
medium-sized effect (Cohen’s d = .65). Taking into account the precision around the start point,
this corresponds to start point difference of .033 between information conditions.8 I used this
estimate to generate an information effect across the two information conditions.
To make the design of the simulations as close to those studies as possible, I used the no
dispatch and armed dispatch information conditions, collapsed across race and expertise. The
8

Given the condition level standard deviation of .052 from Study 1and a d of .65, the predicted difference required
!

is

!!"##
.!"#

!

= .65, where 𝜇!"## = .033.

42

condition level means and standard deviations for these conditions are reported in Table 1. From
these condition level distributions, I created 100 unique parameter estimates, each representing a
study with 100 participants. Forty trials were simulated for each participant in each condition:
unarmed with no dispatch information, armed with no dispatch information, unarmed with armed
dispatch information, and armed with armed dispatch information. The number of trials and
participants were based on the experimental design that would be used in Study 4.
I then fit the hierarchical DDM to each simulated experiment, but used the simpler fourcondition variant described above to minimize computation time. Table 1 reports the most
credible parameter estimates across the 100 simulations, as well as the 95% HDI for each
parameter. The model accurately captures all parameter values, including the start point for the
no dispatch and armed dispatch information conditions. In addition, I examined whether the
DDM recovered a credible information effect on start point by examining the difference between
the condition level start points for each simulation. The proportion of times an effect was
recovered an effect provides an estimate of power (Kruschke, 2014). This analysis revealed 85%
power (95% HDI [.77, .91]) to detect a medium-sized condition level start point difference.
In sum, the model recovery study shows that the hierarchical DDM can accurately and
reliably recover the parameters used to generate data in simulated datasets. In particular, the
model has an acceptable level of power to detect a medium-sized difference in start point across
conditions. In other words, there is little evidence that within the current analytical framework—
using the sample sizes and numbers of trials in used in this set of studies—that the model cannot
accurately capture a start point difference.

43

Table 1: Summary of Parameter Recovery Study.
Parameter
True Value
Mode
95% HDI
!
𝜇!
1.096
1.101
1.074
1.014
1.104
0.985
𝜇!!
!
0.134
0.135
0.119
1 𝜏
!
.538
.538
0.522
𝜇!
!
.572
.569
0.556
𝜇!
.052
.054
.044
1 𝜏!
!
𝜇!,!
0.369
0.368
0.354
!
𝜇!,!
0.367
0.368
0.355
!
𝜇!,!
0.394
0.393
0.382
!
𝜇!,!
0.352
0.350
0.339
!
0.061
0.061
0.058
1 𝜏
!
𝜇!,!
-2.07
-2.07
-2.20
!
𝜇!,!
1.04
1.07
0.88
!
𝜇!,!
-1.52
-1.49
-1.66
!
𝜇!,!
1.65
1.64
1.51
0.75
0.76
0.70
1 𝜏!
!
!
.033
.034
.009
𝜇! − 𝜇!
Note. Values for the mean and 95% HDI are averaged across the simulations.

1.122
1.043
0.152
.551
.582
.060
0.377
0.379
0.405
0.364
0.066
-1.89
1.20
-1.37
1.86
0.81
.054

Discussion
The purpose of the model recovery study was to determine whether the DDM could
detect simulated start point changes. This is important given the Study 1 result that dispatch
information had a counterintuitive effect on the start point and also influenced the accumulation
of evidence. This unusual finding raises the possibility that parameters in the DDM might trade
off and create implausible parameter estimates. This concern was not supported by the
simulation analysis. The DDM captured the difference in start point accurately, precisely, and
with no evidence of trade-offs with any of the other parameters. The other model parameter
estimates also showed no evidence of bias. Thus, there seems to be little reason to suggest that
pilot study results are a mere artifact of the modeling process. However, there is still a question
of whether the start point parameter actually measures bias to favor the shoot decision. In the

44

next study I validated the psychological interpretation of this parameter by testing whether a
targeted experimental manipulation influences start point.
Study 4: Model Validation with Payoff Manipulation
The purpose of Study 4 was to validate the start point parameter as an index of bias to
favor the shoot or don’t shoot decision. Unlike Study 5, which showed that the DDM can detect
simulated differences in start point, this study tested whether the start point is sensitive to
experimental manipulations that should influence this parameter. To test this, I manipulated the
payoff matrix used in the FPST to award and deduct points based on performance. If this
manipulation influences the start point, it would provide construct validity for the interpretation
of the start point parameter, and would also show that it can be influenced experimentally. As the
start point is not influenced by dispatch information, this would further support the interpretation
that dispatch information exerts its effects on the evidence accumulation process, perhaps by
changing how people search for information.
Method
One hundred five undergraduate women9 completed two blocks of the FPST with
decision payoffs manipulated across blocks. Three participants were removed for responding
carelessly, defined as responding faster than 300ms on 20% or more trials. The remaining 102
participants (Mage = 19.0, SD = 1.4) were 78.4% White, 7.8% Black, 9.8% Asian, with 3.9%
from other groups. Each block contained 160 trials and the order of blocks was counterbalanced
across participants.
In order to change the likelihood of shoot or don’t shoot decisions, I manipulated the
payoff matrix for decisions across the two blocks (see Table 2). To encourage a bias to shoot in
9

Studies 1 and 3 came from the same pool of undergraduates. Men comprise less of this subject pool than women
and were oversampled in Study 1, which was completed before Study 3. There were either no men left to participate
in Study 3 or they did not sign up before women filled the sign ups.

45

one block, shooting an armed target earned participants 25 points, whereas shooting an unarmed
target only cost participants 5 points. In contrast, not shooting an armed target cost participants
25 points, whereas not shooting an unarmed target only earned participants 5 points. This creates
a situation where choosing to shoot consistently leads to an average payoff of 10 points per trial
(versus -10 for not shooting) when collapsing across object type. In contrast, in the block where
shooting is discouraged the payoffs are mirrored so that choosing to not shoot consistently leads
to an average payoff of 10 points per trial. In sum, the different payoff rates in the blocks should
create a bias to shoot or not shoot.

Table 2: Payoff Values for the FPST by Block.
Shooting Encouraged Block
Armed Target
Unarmed Target
Shoot
25
-5
Don’t Shoot
-25
5
Note. FPST = First Person Shooter Task.

Shooting Discouraged Block
Armed Target
Unarmed Target
5
-25
-5
25

Results
Behavioral Analysis. To test whether the payoff manipulation impacted the decision to
shoot, I conducted a within-subjects ANOVA on error rates, with target race, object, and payoff
as factors. Figure 9 (left panel) shows the decision data for all conditions. The predicted two-way
interaction between object and payoff was significant, F(1, 100) = 126.58, p < .001. As expected,
when the payoff structure favored shooting, participants shot more unarmed targets (M = .399,
SD = .203) than when it favored not shooting (M = .228, SD = .098), t(100) = 8.49, p < .001. In
addition, participants failed to shoot armed targets less (M = .205, SD = .092) when the payoff
structure favored shooting than when it favored not shooting (M = .410, SD = .166), t(100) =
12.60, p < .001.

46

0.45

550

Proportion Errors

white
0.35

black

0.30
0.25
0.20

Correct Response Time (ms)

540

0.40

white
530

black

520
510
500
490

0.15

480

0.10

470
Unarmed DS Armed DS Unarmed SH Armed SH

Unarmed DS Armed DS Unarmed SH Armed SH

Figure 9: Proportion errors (left panel) and correct response times (right panel) for all conditions.
DS = Payoff favors not shooting. SH = Payoff favors shooting. 95% confidence intervals were
calculated using the methods outlined by Morey (2008).
The typical interaction between race and object was also evident in error rates, F(1, 100)
= 48.82, p < .001. Participants were more likely to shoot unarmed Black men (M = .340, SD =
.179) than unarmed White men (M = .288 SD = .179), t(100) = 8.28, p < .001. They were also
more likely to fail to shoot armed White men (M = .298, SD = .176) than armed Black men (M =
.319, SD = .169), t(100) = 2.83, p = .006. Like Study 2, I replicated the typical finding of racial
bias in the decision to shoot when dispatch information was not provided. There was no evidence
for a three-way interaction, F(1, 100) = 0.46, p = .50.
Focusing on the response time data, an ANOVA with identical predictors was run on the
correct responses. Figure 9 (right panel) shows the response time data for all conditions.
Consistent with past work, participants were faster to respond to guns (M = 501ms, SD = 54ms)
than nonguns (M = 5132ms, SD = 66ms), F(1, 100) = 258.66, p < .001. This effect was qualified

47

by an interaction with payoff, F(1, 100) = 20.49, p < .001. Participants were faster to shoot
armed targets (M = 495ms, SD = 63ms) when the payoff structure favored shooting than when it
favored not shooting (M = 506ms, SD = 43ms), t(100) = 11.18, p < .001. Participants were not
faster to not shoot unarmed targets when the payoff structure favored not shooting (M = 531ms,
SD = 52ms) than when it favored shooting (M = 533ms, SD = 78ms), t(100) = 2.17, p = .72.
Summary. The behavioral data show a clear effect of payoff structure. Participants more
quickly and accurately shot armed targets when shooting was rewarded more than punished, and
they more quickly and accurately chose to not shoot unarmed targets when the opposite was true.
From a process perspective, these results are encouraging because they show a pattern consistent
with a change in start bias to favor the shoot (or don’t shoot) decision. However, these results
could also be explained by changes in participants’ accumulation of information, as indicated by
the drift rate. If drift rate changes solely account for these findings, this would provide evidence
against the start point as an index of bias. I disentangled these possibilities using the DDM.
Hierarchical DDM.
Model Specification and Selection. The DDM was embedded within a hierarchical
framework. All parameters were allowed to vary as a function of race and payoff, but only drift
rate and non-decision time were allowed to vary as a function of object (Pleskac et al., 2017).
Hierarchical DDM Analysis. Figure 10 shows condition-level estimates of the threshold,
start point, drift rate, and non-decision time. The central question motivating this experiment was
whether the start point parameter would capture the effect of the payoff manipulation. There was
a credible medium-sized effect of payoff on start point, Âľdiff = .037, 95% HDI [.024, .050], d =
.771, 95% HDI [0.48, 1.05]. Participants showed an initial bias to favor the shoot response more
when the payoff structure rewarded shooting (Âľ = .535, 95% HDI [.524, .543]) than when it

48

favored not shooting (Âľ = .496, 95% HDI [.488, .506]). This provides convergent validity for the
start point parameter as an index of bias.

1.00

0.56

0.98

Îą

0.54

0.96

●

●

●
●

●

0.94

β 0.52

●

0.50

0.92

●
●

0.48

0.90
White DS Black DS

White S

Black S

White DS Black DS

0.36

White S

Black S

0.36
●

0.34

0.34

τNG

●

0.32

●

τGU

●

●
●

●

●

0.32

0.30

0.30
White DS Black DS White S

Black S

White DS Black DS White S

1.8

1.8

1.6

●

1.6

●

●

1.4

|δNG|

1.2

1.4
●

δGU

1.0
0.8

Black S

●

1.2
1.0
0.8

0.6

0.6
●

0.4

0.4
White DS Black DS White S

Black S

●
●

White DS Black DS

White S

Black S

Figure 10: Diffusion model parameters as a function of target race, payoff structure, and object
for Study 2. Dots represent modal posterior predictions at the condition level; bars are 95% HDI.
DS = payoff favors not shooting, SH = payoff favors shooting.

I also tested whether the payoff matrix influenced other DDM parameters. The payoff

49

manipulation did not influence participants thresholds (Âľ = 0.012, 95% HDI [ -0.017, 0.038),
non-decision time (Âľ = 8ms, 95% HDI [3ms, 19ms]), or drift rates (Âľ = 0.18, 95% HDI [0.05,
0.30]), providing provides divergent validity for the start point parameter as a measure of bias.
However, I did find a credible interaction between drift rate and object, Âľ = 1.75, 95% HDI [1.47,
2.00]. For armed targets, participants showed stronger drift rates towards shoot when shooting
was encouraged (Âľ = 1.58, 95% CI [1.44, 1.70]) than when it was discouraged (Âľ = 0.52, 95%
HDI [0.40, 0.65]), d = 1.32, 95% HDI [1.07, 1.54]. For unarmed targets, participants showed
stronger drift rates towards not shooting when shooting was discouraged (Âľ = -1.34, 95% HDI [1.47, -1.22]) than when it was encouraged (Âľ = -.65, 95% HDI [-0.53, -0.52]), d = 0.84, 95% HDI
[.63, 1.09]. Both of these effects were large and demonstrate that the payoff manipulation
influences multiple parts of the decision process.
I also replicated the typical race effect in drift rates found Study 2 and other research
(Correll et al., 2015; Pleskac et al., 2017). The interaction between race and object was credible,
Âľ = 0.46, 95% HDI [0.21, 0.72]. Participants showed weaker rates to not shoot unarmed Black
men (Âľ = -0.85, [-0.98, -.73]) than unarmed White men (Âľ = -1.16, 95% HDI [-1.28, 1.03]), d =
0.39, 95% HDI [0.16, 0.60]). In contrast, participants showed stronger drift rates to shoot armed
Black men (Âľ = 1.11, 95% HDI [1.00, 1.25]) than armed White men (Âľ = .98, HDI [0.85, 1.10]),
although this difference was not credible, d = -0.18, 95% HDI [-0.40, 0.03]. There was no
evidence of a three-way interaction with payoff structure, Âľ = -0.10, 95% HDI [-0.62, 0.44], and
race did not impact any other parameters in the model.
Summary. As predicted, manipulating the payoff structure of the FPST influenced
individuals’ start point. Individuals set start points closer to the shoot decision when the payoff
structured rewarded shooting. This provides convergent evidence that the start point indexes an

50

initial bias to favor the shoot decision. The payoff manipulation did not influence the length of
non-decision processes or participants’ threshold level, providing some divergent evidence that
the effect of bias is isolated to the start point. However, there was also strong evidence that the
payoff manipulation did influence participants’ drift rate. Insofar as the payoff manipulation is
assumed to selectively influence the start point, interpreting the start point parameter as solely
indicating a bias on the process level may be premature. Finally, I observed racial bias in drift
rate; evidence for the shoot decision was stronger when targets were Black rather than White.
Discussion
Moving from the level of model parameters to the level of psychological processes
requires validating the presumed interpretations of those parameters experimentally. To validate
the interpretation of the start point parameter as a measure of initial bias to shoot, I adjusted the
payoff structure of the FPST to reward or penalize shooting behavior. These payoffs had a clear
effect on behavior that was reflected in changes in the DDM parameters. As predicted, when
shooting was rewarded, the start point parameter shifted towards the shoot decision. When the
opposite was true, participants start point shifted towards the don’t shoot decision. Combined
with fact that the payoff manipulation did not influence participants’ threshold or non-decision
time, this provides some validation that the start point parameter does index initial bias, and that
changes in the start point parameter can be observed using experimental manipulations.
One unexpected effect of the payoff manipulation was that it also influenced the rate at
which participants accumulated evidence. Drift rates were stronger (weaker) for guns when the
payoff information favored (not) shooting. This violates the principle of selective influence,
where manipulations designed to target a single parameter should only influence that parameter.
When selective influence is achieved, it provides powerful evidence that the parameter indexes

51

the relevant psychological construct. However, a lack of selective influence does not necessarily
indicate that the psychological interpretation of a parameter is invalid. Another possibility is that
the targeted experimental manipulation may have unintended consequences for other aspects of
the decision process.
For example, the manipulation of payoff structure was designed to influence participants
bias for the shoot or don’t shoot decision. If this effect was not found, it would provide strong
evidence against the start point as a valid index of bias, and the DDM as a model of the decision
to shoot. However, the finding that the payoff manipulation influenced both the start point and
drift rate is more ambiguous. It is possible that although the payoff manipulation was intended to
solely influence an initial bias to favor one option or the other, it may have also influenced how
they accumulated information during the decision process. Insofar as people were motivated to
earn the most points that they could, this manipulation may have changed participants’ search
strategies so that they were looking for confirmatory evidence for the decision that on average
earned them more points.
In addition to the effects of payoff structure on start point, I also replicated the typical
pattern of race bias in shooting decisions. Participants shot unarmed Black men than unarmed
White men, and failed to shoot armed White men more than armed Black men. In the DDM, this
difference was isolated to changes in the drift rate as function of race. Participants accumulated
evidence to not shoot unarmed Black men more slowly than unarmed White men, and they
accumulated evidence to shoot armed Black men more quickly than armed White men, although
this difference was not credible. This result differed starkly from Study 1, where participants
showed no racial bias when they were given race and weapon dispatch information beforehand.
Although not a direct test, this suggests that giving reliable dispatch information does mute the

52

influence of irrelevant information like race on the decision to shoot.

53

GENERAL DISCUSSION
When officers are forced to make a decision about whether or not to use lethal force, this
decision is not made in a vacuum. Officers responding to a call typically have, at minimum,
demographic information about the person they are to interact with. Any pertinent information
about the individual, such as whether or not he or she is armed, is also passed on to officers.
Despite these policies, past research on the decision to shoot has focused on how individuals
make such decisions in the absence of this information. While this is one reasonable starting
point to understand shooting behavior, the ability to extrapolate these findings to real world
shooting decisions is limited.
The current studies found that that untrained civilians reliably showed racial bias in the
decision to shoot when they were not given any additional contextual information. However,
when officers and students received accurate demographic information from dispatch as well as
information about whether a target was armed, they showed no racial bias in shooting decisions.
Thus, simply providing relevant information about the person an officer will encounter might
eliminate bias in shooting decisions. An important implication of this finding is that racial bias in
shooting decisions as observed in laboratory studies might be limited to rare cases of shootings
where an individual is holding an ambiguous object and the officer has no prior information
about the individual. That is, the race of an individual might only impact the decision to shoot in
the absence of more relevant disambiguating information.
Insofar as these findings can be extrapolated to real world shootings, they provide another
perspective for understanding why individuals like Tamir Rice are accidentally shot. The results
from these experimental studies suggest that when officers encounter an individual that has been
accurately identified by dispatch, information that the individual is armed influences how that

54

person’s actions are perceived. Rice’s movements may have seemed more dangerous to the
officers because of the dispatch information they had received, independent of any prior bias. In
sum, events like the shooting of Tamir Rice might result from inaccurate dispatch information in
addition to or instead of racial bias on the part of the officers.
The fact that race did not influence the decision to shoot when dispatch information was
provided raises the question of the pervasiveness of racial bias in officer shooting decisions.
Work using the traditional FPST with officers has found mixed results. Sometimes officers show
no racial bias in their decisions (Correll et al., 2007). However, officers who routinely interact
with minority individuals involved in gang-related crime show bias (Sim et al., 2013). Research
on racial disparities in the real world have also shown mixed evidence for the existence of bias in
shooting decisions, with some proposing that officers use lethal force more for Blacks than
Whites (Ross, 2015). Others have not found support for such a conclusion (Cesario, Johnson, &
Terrill, 2017; Fryer, 2016, Goff, Lloyd, Geller, Raphael, & Glaser, 2016).10 While a full
discussion of whether certain officers or departments use lethal force disproportionately for
Black civilians is beyond the scope of this research, this work highlights that bias is more likely
in situations where officers have little advance information about the person they encounter.
Even if under most circumstances the race of a civilian does not impact an officer’s use
of lethal force, preventing police shootings of unarmed individuals is of considerable importance.
Although there are other controversial policing practices that affect more people (e.g., stop and
frisk polices), shooting incidents are important because they receive a disproportionate share of
media coverage. Civilians trust and obey law enforcement when they believe their authority is
legitimate (Tyler, 2006; Tyler, Goff, & MacCoun, 2015), and shootings of unarmed individuals
10

Although officers may not use lethal force disproportionately against Black individuals, there is evidence for
greater law enforcement use of nonlethal force (e.g., Tazer use) more with Black individuals than White individuals
(Fryer, 2016, Goff et al., 2016).

55

undermine legitimacy. Given that Black individuals already have low confidence in the police
(31% of Blacks vs. 58% of Whites; Tyler et al., 2015), when police shoot individuals like Tamir
Rice this raises questions about whether race played a role in the mind of the officers. Thus, it is
particularly important to focus on improving officers’ abilities to rapidly and accurately identify
objects to avoid mistakes that could be perceived as being motivated by racial animus, even if
those mistakes were driven by other factors.
What Part of Dispatch Information Reduces Racial Bias?
Dispatch information refers to all information that officers receive from police dispatch
before they encounter a suspect. This information varies largely depending on what situation an
officer is called to, although certain information is always transmitted (where is the emergency,
what is the emergency, when did it happen, and who is involved; Norcomm, 2017; Kobb, 2016).
The current studies focused on two components commonly given by dispatch: demographic
(race) information, and information about whether the suspect was armed. When both pieces of
information were presented simultaneously (Study 1) it eliminated bias in the decision to shoot.
Yet it is unclear from this design whether this reduction was due to the presence of race or
weapon information.
Study 2 probed whether race or weapon dispatch information alone eliminated bias by
presenting information separately in a blocked design. In terms of the actual decision to shoot,
the addition of weapon information reduced bias to shoot unarmed Black men relative to White
men, but did not influence bias for armed targets. Race information did not significantly
influence shooting decisions for armed or unarmed targets. At the process level, both weapon
and race information weakened the effect of race on the evidence accumulation process. This
effect was strongest when race dispatch information was given for armed targets; participants

56

accumulated evidence to shoot equally for White and Black targets. Thus, providing individuals
with relevant information may independently decrease racial bias in the decision to shoot.
At this point it seems appropriate to speculate how weapon and race dispatch information
might separately reduce bias in the decision to shoot. Providing accurate weapon information is
perhaps most clear. The FPST is at heart a visual identification task; participants are instructed to
shoot when they see guns and not shoot when they see harmless objects. Whether a weapon is
present is directly relevant to the decision. This is reflected in the fact that participants
accumulate evidence to shoot much more quickly when they receive correct information that the
target is armed. When weapon information is generally accurate, as it is in the current task, it
reduces the ambiguity surrounding what decision individuals should make. Given that
stereotypes are most likely to influence judgments in the absence of disambiguating information
(Duncan, 1976; Sagar & Schofield, 1980), giving directly relevant information about weapons is
likely to undermine their effects.
For example, consider the role of race when evaluating job candidates. When candidates
of different races are equally qualified, White candidates are sometimes selected at higher rates
than Black candidates (Betrand & Mullainathan, 2004; McConahay, 1983). However, when there
are clear differences in qualifications between candidates, this bias disappears. A similar process
may occur for shooting decisions. When individuals have no prior information about whether a
suspect is armed, race may influence their decision to shoot. However, when they have accurate
information that the target is armed, the relevance of this information may overpower the
influence of stereotypes that lead to disproportionately more shootings of Black men than White
men.
Accurate dispatch information about the race of the target may also have impacted

57

participants’ decisions. Work using a similar paradigm, the weapon identification task (WIT;
Payne, 2001; 2006), has shown that individuals primed with pictures of Black men identify
weapons faster and more accurately than when primed with faces of White men. Although this
seems to suggest that the presence of race information might exacerbate bias in the decision to
shoot, an important difference is that in the current study dispatch information was presented for
a long period of time (2000ms) before the target appeared. In contrast, in the WIT, the prime
appears for only a short period of time (200ms) and is immediately replaced by the target. When
participants are given this information seconds in advance, they may be able to control automatic
stereotypic associations between Black men and violence that lead to higher shooting rates for
Black than White targets.
In sum, the current experiments showed evidence that both weapon and race information
might reduce race bias in shooting decisions. Future work should test the mechanisms by which
these factors influence decisions, as well as investigate other relevant dispatch information that
are missing from experimental shooting tasks.
Modeling the Role of Dispatch Information and Expertise
A secondary goal of these studies was to better understand how dispatch information and
expertise impact the shooting decision process. I investigated this by modeling the decision to
shoot using a common model of decision-making, the DDM. This model assumes that when
making decisions between two choices individuals repeatedly sample information from their
environment relevant to the decision. When they reach some threshold of evidence they make
their decision. Study 1 tested how dispatch information impacted the decision to shoot within
this model using a sample of untrained students and trained officers. Behaviorally, both officers
and students were faster and more likely to shoot armed targets when dispatch information was

58

correct, and were slower and less likely to not shoot unarmed targets when the information was
incorrect. The DDM isolated this pattern of results to changes in how participants accumulated
information and a counterintuitive bias to ignore the information.
A strength of the DDM is that it divides the decision process into different components
that map well onto psychological constructs. By testing what parts of the decision process
experimental factors influence, we can test different hypotheses about how those factors impact
the decision to shoot. In order to move from the model parameters in the DDM to psychological
constructs it is necessary to conduct studies validating that the parameters are good indicators of
the relevant underlying processes. For example, validating the start point parameter as an index
of bias to favor the shoot decision requires demonstrating the start point is sensitive to
experimental manipulations designed to change participants’ biases. This issue was particularly
important for the current work, given that providing participants with reliable information that
targets were armed had a counterintuitive effect on their start point. This raises the question of
whether the hierarchical DDM 1) can detect predicted differences in start point and 2) whether
the start point can be manipulated experimentally.
In Study 3, I tested the first question, whether the hierarchical DDM can detect simulated
differences in start point while also accurately recovering the values of other parameters. The
results from this study were unequivocal; given an experimental design very similar to Study 1,
the DDM was able to capture a medium-sized simulated difference between conditions in start
point with 85% power. In addition, the model showed no bias in recovering the other model
parameters. In Study 4, I tested whether the start point could be manipulated by changing the
payoff structure of the task. Participants in this study were more likely to shoot armed targets
when shooting was rewarded, and not shoot unarmed targets when not shooting was rewarded.

59

These behavioral changes were mirrored by a similar change in start point, such that participants
favored the decision consistent with higher payoffs. There was also evidence that these payoffs
also influenced how participants accumulate information.
Like dispatch information in Study 1, the payoff manipulation also influenced the
evidence accumulation process. These results contrast with work in the cognitive domain. For
example, Voss et al. (2004) validated the DDM parameters for a color discrimination task.
Participants were asked to identifying whether blue or orange was more prevalent on a grid.
When participants were rewarded for choosing one decision over the other, they showed a start
point bias to favor the rewarded response. Importantly, this manipulation did not effect evidence
accumulation. How do we reconcile these inconsistent results? One possibility is that the social
nature of the FPST changes how participants respond to information that encourages shooting.
Individuals may be easily biased to favor choosing orange over blue when those decisions have
little real world value. But in a task like the shooter task where decisions are perceived as more
impactful, individuals’ biases may be more rigid. Instead, this information may leak into how
individuals search for the object. If the influence of biasing information depends on the nature of
the task, other tasks where decisions are sensitive (e.g., an approach-avoidance task using
members from different groups as stimuli), should show a similar effect of biasing information
on the accumulation of evidence rather than the start point.
The results that dispatch information influences the decision to shoot by impacting the
process of information accumulation has important training implications. Both officers and
students accumulated information more slowly when dispatch information was incorrect, but
officers outperformed students because they were better at identifying objects than students.
Identifying what aspect of their weapons training or on the job experience improves officers’

60

performance is key to improving their ability to distinguish guns from harmless objects. This
weapon identification training could then be strategically employed to assist officers who are
particularly poor at rapidly identifying objects, as identified by tasks like the FPST.
Training officers to identify weapons accurately is most likely to help officer decisions in
high pressure situations where they need to rapidly identify an object in a suspect’s hand. Such
training would be just one component of a broader use of force training focused on addressing
other factors that officers must consider when using force (e.g., the intent of the person, the
presence of bystanders). In many cases these other components may be more important to officer
use of force. Nonetheless, given the gravity of accidentally shooting an unarmed individual, this
training has a place as a part of a multi-faceted approach to improve officer decisions to shoot.
Another way to tackle the issue that poor dispatch information increases mistakes in
officer decisions to shoot is to consider the role of policy in shaping the information that dispatch
passes onto officers. In the case of Tamir Rice, had dispatch passed on information that Rice was
a juvenile and that the weapon was probably fake, perhaps the officers would not have used
lethal force. Policy changes that ensure that this kind of information is passed on might well help
officers make better decisions. The limitation of this approach is that even if dispatch policies are
improved this will not prevent officers from getting incorrect information when it is misreported.
Dispatchers, especially in metropolitan areas, often receive false reports that weapons are present
on scene because civilians know this causes the police to respond more rapidly (Lance Langdon,
personal communication, June 1, 2016). Thus, even if dispatch policies are improved, individual
training to identify objects in these high-pressure situations is still needed.
Individual Differences in Racial Bias
The current studies were focused on racial bias in decisions at the group level. Especially

61

when dispatch information was given, participants did not show racial bias in shooting decisions.
However, these group-level differences can obscure individual variation in decisions. Although
on average participants did not show racial bias in shooting decisions, some participants were
more likely to shoot unarmed Black men than unarmed White men, and some participants were
more likely to shoot unarmed White men than unarmed Black men. Understanding what causes
variation in these decisions is crucial for knowing why individuals are more likely to shoot those
from certain racial groups. While the current experiments did not test this hypothesis, there are a
number of individual differences that might be relevant for understanding why some individuals
are more likely to shoot unarmed Black (or White men).
One individual difference that may predict racial bias in shooting decisions is attitudes
(measured directly or indirectly) towards White and Black individuals. Work in this area has
demonstrated that an explicit belief about the criminality of Black individuals predicts racial
officer bias in shooting decisions (Correll et al., 2007; Peruche & Plant, 2006). However, no
work has focused on the converse, that a belief about the criminality of White individuals
predicts anti-White shooter bias. In addition, this work has also relied on small sample sizes,
making it unclear how reliable these effects are.
Another individual difference that may to predict racial bias in shooting behavior is
motivation to control prejudice (Plant & Devine, 1998). If individuals do hold different attitudes
towards other groups that influence their shooting decisions, whether those biases translate into
behavior may depend on how motivated participants are to avoid acting on those biases. Past
research has not found evidence for the influence of internal or external motivation to respond
without prejudice in officer samples (Correll et al., 2007) but this work did not test whether the
influence of motivation to control prejudice depends on biased attitudes. Similarly, motivation to

62

control prejudice scales are explicitly designed to test motivation to avoid anti-Black prejudice,
not anti-White prejudice. Since some officers showed bias to shoot White targets more than
Black targets, it is important to devise measures that can tap into these attitudes and motivations.
Finding predictors of individual differences in officer biases is important for not only
isolating the psychological mechanisms responsible for shooting decisions, but for its practical
implications. Individuals who show unbiased attitudes and/or a motivation to avoid acting in
prejudiced ways could be favored during the officer recruitment and selection. In addition, the
FPST could be used to assess individual differences in officers’ risk for accidentally shooting
unarmed individuals. These individuals could receive weapon identification training to reduce
the likelihood of such an outcome. Individual differences could even be incorporated into the
DDM to understand not only whether they influence decisions, but how they influence them. For
example, motivation to control prejudice may reduce racial bias in shooting decisions by
increasing participant cautiousness, as indicated by increased thresholds for Black targets. Initial
support for this hypothesis has been observed in untrained civilians (Pleskac et al., 2017).
Benefits of a Diffusion Model Approach to Decisions
The current studies used the DDM to understand the decision to shoot because its
parameters map conceptually onto how researchers have theoretically divided the decision to
shoot. Consistent with past work (Correll et al., 2015; Pleskac et al., 2017), when no dispatch
information was provided, race influenced the decision to shoot by influencing the accumulation
of evidence during the decision (a drift rate change) rather than creating a prior bias to shoot
decision Black men relative to White men (a relative start point change). In addition to clarifying
the process by which race caused individuals to shoot unarmed Black men more than unarmed
White men, this process level examination also clarified that training to reduce bias in the

63

decision to shoot should focus on the accurate identification of weapons rather than trying to
prevent officers from being trigger happy for Black men relative to White men.
Similarly, the DDM also provided a framework for understanding the role of dispatch
information and expertise in the decision to shoot. Focusing on the role of expertise, the DDM
revealed that the reasons officers were more accurate and slower than students when making
decisions was due to two separate aspects of the decision process. First, officers were slower
than students because their non-decision processes took longer. Second, officers were more
accurate than students because they were better at distinguishing guns from harmless objects.
Without this process level analysis, it might be tempting to conclude that officers’ slower and
more accurate performance is simply due to increased cautiousness. This ability to precisely test
different process level accounts is a benefit of the DDM that extends beyond understanding the
decision to shoot.
As these examples show, the DDM provides a novel perspective to understand the effects
of categorical information on fast decisions compared to classic dual process accounts (Chaiken
& Trope, 1999; Sherman et al., 2014). From this account, bias in fast decisions like the decision
to shoot is explained by the influence of fast automatic associations between a category and
some concept. When these fast associations are at odds with slower controlled judgments, the
two processes compete to determine behavior. This competition explains how categorical
associations can automatically influence judgments, in this case, determining what object the
person is holding.
One consequence of this dual process account is that faster responses are often thought to
represent greater automatic activation of concepts. This is the basic logic behind tasks like the
lexical decision task and the implicit association task (Greenwald, McGhee, & Schwarz, 1998).

64

For example, faster responses to armed targets than unarmed targets in the FPST indicate that
guns are more activated than harmless objects. But the diffusion model shows us is that there are
different ways that fast or slow responses can come about. Within the FPST, shorter response
times for guns are primarily due to shorter non-decision times than nonguns, and not because of
differences in activation. Similarly, officers are slower than students despite being better able to
distinguish guns from harmless objects because their non-decision times are slower. In sum, the
DDM provides a new way to understand fast decision-making that does not assume slower
responses always represent changes in the activation of concepts.
Conclusion
Whenever a police officer accidentally shoots an unarmed individual the result is tragic.
When the victim is a twelve-year-old boy, the loss of life is even more grievous. Instances like
the shooting of Tamir Rice often become catalysts for broader concerns about racial disparities in
police use of force. However, it is difficult if not impossible to tease apart the various factors in
any one shooting that might have contributed to an officer’s decision to use lethal force. Using
the Rice case as an example, I designed an experimental shooting task to test whether dispatch
information, race, and expertise influence shooting decisions. This analysis revealed a powerful
impact of dispatch information on decisions. Good information helped individuals make better
decisions and poor information resulted in worse decisions. Furthermore, dispatch information,
whether accurate or not, overrode any influence the race had on the decision to shoot. Under
these circumstances, dispatch information may play a more important role in whether an officer
decides to use lethal force.

65

APPENDICES

66

APPENDIX A:

ANOVA Tables
Table 3: ANOVA Summary Table for Study 1 Error Rates
Sum of Squares
df
Mean Square
F
p
Race
0.008
1
0.008
1.062
0.304
Race × Exp
8.827e -4
1
8.827e -4
0.111
0.740
Residual
1.202
151
0.008
Object
0.023
1
0.023
0.852
0.358
Object × Exp
0.017
1
0.017
0.624
0.431
Residual
4.085
151
0.027
Info
0.003
1
0.003
0.379
0.539
Info × Exp
0.008
1
0.008
1.130
0.289
Residual
1.091
151
0.007
Race × Object
0.021
1
0.021
2.211
0.139
Race × Object × Exp
0.006
1
0.006
0.605
0.438
Residual
1.434
151
0.009
Race × Info
9.024e -5
1
9.024e -5
0.014
0.906
Race × Info × Exp
0.009
1
0.009
1.434
0.233
Residual
0.971
151
0.006
Object × Info
0.938
1
0.938
44.316
< .001
Object × Info × Exp
0.054
1
0.054
2.540
0.113
Residual
3.195
151
0.021
Race × Object × Info
8.589e -4
1
8.589e -4
0.117
0.733
Race × Object × Info × Exp
0.007
1
0.007
0.900
0.344
Residual
1.113
151
0.007
Exp
1.006
1
1.006
13.23
< .001
Residual
11.481
151
0.076
Note. Exp = Experience. Effects below the second solid black line are between subjects.

67

Table 4: ANOVA Summary Table for Study 1 Response Times
Sum of Squares
df
Mean Square
F
p
Race
3705.94
1
3705.94
1.620
0.205
Race × Exp
508.76
1
508.76
0.222
0.638
Residual
345384.29
151
2287.31
Object
974725.12
1
974725.12
196.699
< .001
Object × Exp
81167.16
1
81167.16
16.379
< .001
Residual
748269.49
151
4955.43
Info
11552.75
1
11552.75
6.222
0.014
Info × Exp
3449.69
1
3449.69
1.858
0.175
Residual
280354.48
151
1856.65
Race × Object
1085.33
1
1085.33
0.400
0.528
Race × Object × Exp
873.14
1
873.14
0.322
0.571
Residual
409316.61
151
2710.71
Race × Info
280.06
1
280.06
0.177
0.674
Race × Info × Exp
4048.16
1
4048.16
2.561
0.112
Residual
238668.82
151
1580.59
Object × Info
46106.77
1
46106.77
10.932
0.001
Object × Info × Exp
7483.01
1
7483.01
1.774
0.185
Residual
636857.02
151
4217.60
Race × Object × Info
840.01
1
840.01
0.379
0.539
Race × Object × Info × Exp
19.41
1
19.41
0.009
0.926
Residual
334746.87
151
2216.87
Exp
748510
1
748510
29.39
< .001
Residual
3.845e +6
151
25464
Note. Exp = Experience. Effects below the second solid black line are between subjects.

68

Table 5: ANOVA Summary Table for Study 2 Error Rates (Weapon vs. Control)
Sum of Squares
df
Mean Square
F
Cond
0.042
1
0.042
2.840
Residual
1.704
115
0.015
Race
0.017
1
0.017
1.762
Residual
1.097
115
0.010
Object
0.317
1
0.317
9.023
Residual
4.040
115
0.035
Cond × Race
0.038
1
0.038
4.751
Residual
0.923
115
0.008
Cond × Object
0.022
1
0.022
2.388
Residual
1.074
115
0.009
Race × Object
0.278
1
0.278
33.288
Residual
0.959
115
0.008
Cond × Race × Object
0.042
1
0.042
5.085
Residual
0.952
115
0.008
Note. Cond = Condition (no information, weapon information).
Table 6: ANOVA Summary Table for Study 2 Error Rates (Race vs. Control)
Sum of Squares
df
Mean Square
Cond
0.070
1
0.070
Residual
1.985
115
0.017
Race
0.090
1
0.090
Residual
1.081
115
0.009
Object
0.306
1
0.306
Residual
4.335
115
0.038
Cond × Race
6.061e -4
1
6.061e -4
Residual
1.100
115
0.010
Cond × Object
0.025
1
0.025
Residual
1.548
115
0.013
Race × Object
0.343
1
0.343
Residual
1.059
115
0.009
Cond × Race × Object
0.021
1
0.021
Residual
1.183
115
0.010
Note. Cond = Condition (no information, weapon information).

69

p
0.095
0.187
0.003
0.031
0.125
< .001
0.026

F
4.046

p
0.047

9.600

0.002

8.116

0.005

0.063

0.802

1.883

0.173

37.290

< .001

2.074

0.153

Table 7: ANOVA Summary Table for Study 2 Error Rates (Weapon Condition)
Sum of Squares
df
Mean Square
F
Info
0.030
1
0.030
1.008
Residual
3.377
115
0.029
Race
5.280e -4
1
5.280e -4
0.021
Residual
2.899
115
0.025
Object
0.109
1
0.109
1.937
Residual
6.451
115
0.056
Info × Race
0.009
1
0.009
0.381
Residual
2.808
115
0.024
Info × Object
7.742
1
7.742
99.885
Residual
8.913
115
0.078
Race × Object
0.142
1
0.142
5.778
Residual
2.817
115
0.024
Info × Race × Object
0.006
1
0.006
0.205
Residual
3.202
115
0.028
Note. Info = Information (unarmed, armed).
Table 8: ANOVA Summary Table for Study 2 Error Rates (Race Condition)
Sum of Squares
df
Mean Square
0.013
0.013
Info
1
2.771
0.024
Residual
115
0.111
0.111
Race
1
3.145
0.027
Residual
115
0.047
0.047
Object
1
7.015
0.061
Residual
115
0.005
0.005
Info × Race
1
2.805
0.024
Residual
115
0.005
0.005
Info × Object
1
3.071
0.027
Residual
115
0.228
0.228
Race × Object
1
3.233
0.028
Residual
115
0.122
0.122
Info × Race × Object
1
3.502
0.030
Residual
115
Note. Info = Information (White, Black).

70

p
0.318
0.885
0.167
0.538
< .001
0.018
0.652

F

p

0.539

0.465

4.043

0.047

0.777

0.380

0.220

0.640

0.204

0.652

8.116

0.005

3.998

0.048

Table 9: ANOVA Summary Table for Study 2 Response Times (Weapon vs. Control)
Sum of Squares
df
Mean Square
F
Cond
40585
1
40585
2.815
Residual
1.658e +6
115
14415
Race
1779
1
1779
0.112
Residual
1.831e +6
115
15918
Object
773908
1
773908
70.985
Residual
1.254e +6
115
10902
Cond × Race
4110
1
4110
0.336
Residual
1.408e +6
115
12245
Cond × Object
15881
1
15881
1.206
Residual
1.514e +6
115
13168
Race × Object
24017
1
24017
2.689
Residual
1.027e +6
115
8933
Cond × Race × Object
26393
1
26393
2.207
Residual
1.375e +6
115
11959
Note. Cond = Condition (no information, weapon information).
Table 10: ANOVA Summary Table for Study 2 Response Times (Race vs. Control)
Sum of Squares
df
Mean Square
F
Cond
200.2
1
200.2
0.016
Residual
1.450e +6
115
12609.4
Race
10780.8
1
10780.8
1.248
Residual
993798.1
115
8641.7
Object
501595.5
1
501595.5
29.596
Residual
1.949e +6
115
16948.2
Cond × Race
6708.0
1
6708.0
0.515
Residual
1.497e +6
115
13021.6
Cond × Object
2067.1
1
2067.1
0.181
Residual
1.313e +6
115
11417.6
Race × Object
8143.3
1
8143.3
0.665
Residual
1.408e +6
115
12243.6
Cond × Race × Object
9550.1
1
9550.1
0.540
Residual
2.033e +6
115
17677.9
Note. Cond = Condition (no information, weapon information).

71

p
0.096
0.739
< .001
0.563
0.274
0.104
0.140

p
0.900
0.266
< .001
0.474
0.671
0.416
0.464

Table 11: ANOVA Summary Table for Study 4 Error Rates
Sum of Squares
df
Mean Square
Race
0.046
1
0.046
Residual
0.401
100
0.004
Object
0.007
1
0.007
Residual
2.584
100
0.026
Bias
0.061
1
0.061
Residual
1.120
100
0.011
Race × Object
0.262
1
0.262
Residual
0.537
100
0.005
Race × Bias
0.001
1
0.001
Residual
0.527
100
0.005
Object × Bias
7.124
1
7.124
Residual
5.628
100
0.056
Race × Object × Bias
0.002
1
0.002
Residual
0.490
100
0.005
Table 12: ANOVA Summary Table for Study 4 Response Times
Sum of Squares
df
Mean Square
Race
37.04
1
37.04
Residual
34506.08
100
345.06
Object
196079.91
1
196079.91
Residual
75806.71
100
758.07
Bias
4104.01
1
4104.01
Residual
526138.11
100
5261.38
Race × Object
12.63
1
12.63
Residual
31964.00
100
319.64
Race × Bias
938.91
1
938.91
Residual
26680.21
100
266.80
Object × Bias
9002.24
1
9002.24
Residual
43926.39
100
439.26
Race × Object × Bias
133.96
1
133.96
Residual
33667.66
100
336.68

72

F
11.364

p
0.001

0.278

0.599

5.432

0.022

48.818

< .001

0.186

0.667

126.579

< .001

0.461

0.499

F
0.107

p
0.744

258.658

< .001

0.780

0.379

0.039

0.843

3.519

0.064

20.494

< .001

0.398

0.530

APPENDIX B:

DDM Effects Tables
Table 13: Summary of Effects on Condition Level Threshold for Study 1 Students
95% HDI
Factor
Mode
Lower
Upper
Race
0.008
-0.024
-0.041
Info
0.057
0.025
0.089
Race × Info
0.020
-0.026
0.082
Table 14: Summary of Effects on Condition Level Start Point for Study 1 Students
95% HDI
Factor
Mode
Lower
Upper
Race
.009
-.003
.022
Info
.070
.057
.083
Race × Info
-.003
-.030
.022
Table 15: Summary of Effects on Condition Level Non-decision Time for Study 1 Students
95% HDI
Factor
Mode
Lower
Upper
Race
0
-12
11
Info
-2
-14
9
Object
12
0
23
Race × Info
1
-22
25
Race × Object
4
-19
28
Info × Object
-42
-65
-18
Race × Info × Object
1
-46
48
Table 16: Summary of Effects on Condition Level Drift Rate for Study 1 Students
95% HDI
Factor
Mode
Lower
Race
0.04
-0.10
Info
-0.03
-0.18
Object
0.29
0.17
Race × Info
0.07
-0.17
Race × Object
0.17
-0.09
Info × Object
1.40
1.11
Race × Info × Object
-0.03
-0.59

73

Upper
0.16
0.09
0.43
0.35
0.46
1.66
0.50

Table 17: Summary of Effects on Condition Level Threshold for Study 1 Officers
95% HDI
Factor
Mode
Lower
Race
-0.007
-0.49
Info
0.102
0.059
Race × Info
0.016
-0.073

Upper
0.039
0.146
0.102

Table 18: Summary of Effects on Condition Level Start Point for Study 1 Officers
95% HDI
Factor
Mode
Lower
Upper
Race
-.001
-.024
.023
Info
.072
.045
.072
Race × Info
.007
-.041
.054
Table 19: Summary of Effects on Condition Level Non-Decision Time for Study 1 Officers
95% HDI
Factor
Mode
Lower
Upper
Race
5
-5
16
Info
-5
-17
4
Object
32
22
42
Race × Info
-6
-25
16
Race × Object
-8
-27
14
Info × Object
-39
-60
-19
Race × Info × Object
-7
-47
35
Table 20: Summary of Effects on Condition Level Drift Rate for Study 1 Officers
95% HDI
Factor
Mode
Lower
Race
0.03
-0.17
Info
0.00
-0.18
Object
.059
0.40
Race × Info
-0.01
-0.36
Race × Object
0.12
-0.29
Info × Object
0.96
0.54
Race × Info × Object
0.17
-0.53

74

Upper
0.19
0.18
0.80
0.37
0.51
1.35
1.07

Table 21: Summary of Effects on Condition Level Threshold for Study 4
95% HDI
Factor
Mode
Lower
Upper
Race
-0.003
-0.032
0.023
Payoff
0.012
-0.017
0.028
Race × Payoff
0.026
-0.031
-0.079
Table 22: Summary of Effects on Condition Level Start Point for Study 4
95% HDI
Factor
Mode
Lower
Upper
Race
.011
-.003
.023
Payoff
-.037
-.050
-.024
Race × Payoff
-.009
-.033
.018
Table 23: Summary of Effects on Condition Level Non-Decision Time for Study 4
95% HDI
Factor
Mode
Lower
Upper
Race
2
-9
13
Payoff
-8
-19
3
Object
4
-4
17
Race × Payoff
-12
-34
9
Race × Object
-5
-25
18
Payoff × Object
-6
-26
18
Race × Payoff × Object
-17
-59
27
Table 24: Summary of Effects on Condition Level Drift Rate for Study 4
95% HDI
Factor
Mode
Lower
Upper
Race
0.07
-0.05
0.20
Payoff
-0.18
-0.30
-0.05
Object
-0.04
-0.17
0.09
Race × Payoff
-0.07
-0.31
0.18
Race × Object
0.46
0.21
0.72
Payoff × Object
1.75
1.47
2.00
Race × Payoff × Object
-0.10
-0.62
0.44

75

APPENDIX C:

Hierarchical Drift Diffusion Model
Sβ , Rβ
Lβi , Uβi
uniform
~ ...

Sτ , Rτ

Sδ , Rδ

Lτi , Uτi
gamma δ
i,j
~ ...

uniform
~ ...

SÎą , RÎą

Lδi , Uδi
gamma
~ ...

LÎąi , UÎąi
gamma
~ ...

uniform
~ ...

uniform
~ ...

Οβi , precβ

μτi , precτ

Οδi , precδ

Οιi , precι

normal
~ ...

normal
~ ...

normal
~ ...

normal
~ ...

βi,j ⋅ αi,j

τi,j

δi,j

Îąi,j

gamma
~ ...

condition i
subject j
trial k

~ ...
yi,j,k

Figure 11: Generic diagram of the hierarchical drift diffusion model. The kth response for subject
j within condition i are generated by a drift diffusion process. Vertical lines on the normal
distributions indicate that the priors were truncated normals. Prec = precision.

76

APPENDIX D:

JAGS CODE
JAGS Code for Model Used in Study 1
model {
#likelihood function
for (t in 1:nTrials) {
y[t] ~ dwiener(alpha[Cond1[t], subject[t]],
tau[Cond2[t], subject[t]],
beta[Cond1[t], subject[t]],
delta[Cond2[t], subject[t]])
}
for (s in 1:nSubjects) {
for (c1 in 1:nCond1) {
alpha[c1, s] ~ dnorm(muAlpha[c1, [BCon[s]],
precAlpha[BCon[s]]) T(.1, 5)
beta[c1, s] ~ dnorm(muBeta[c1, [BCon[s]],
precBeta[BCon[s]]) T(.1, .9)
}
for (c2 in 1:nCond2) {
tau[c2, s] ~ dnorm(muTau[c2, [BCon[s]],
precTau[BCon[s]]) T(.0001, 1)
delta[c2, s] ~ dnorm(muDelta[c2, [BCon[s]],
precDelta[BCon[s]]) T(-5, 5)
}
}
#priors
for (b in 1:nBCon){
precAlpha[b] ~ dgamma(.001, .001)
precBeta[b] ~ dgamma(.001, .001)
precTau[b] ~ dgamma(.001, .001)
precDelta[b] ~ dgamma(.001, .001)
for (c1 in 1:nCond1){
muAlpha[c1] ~ dunif(.1, 5)
muBeta[c1] ~ dunif(.1, .9)
}
for (c2 in 1:nCond2){
muTau[c2] ~ dunif(.0001, 1)
muDelta[c2] ~ dunif(-5, 5)
}
}
}

77

JAGS Code for Model Used in Studies 2 – 4
model {
#likelihood function
for (t in 1:nTrials) {
y[t] ~ dwiener(alpha[Cond1[t], subject[t]],
tau[Cond2[t], subject[t]],
beta[Cond1[t], subject[t]],
delta[Cond2[t], subject[t]])
}
for (s in 1:nSubjects) {
for (c1 in 1:nCond1) {
alpha[c1, s] ~ dnorm(muAlpha[c1], precAlpha) T(.1, 5)
beta[c1, s] ~ dnorm(muBeta[c1], precBeta) T(.1, .9)
}
for (c2 in 1:nCond2) {
tau[c2, s] ~ dnorm(muTau[c2], precTau) T(.0001, 1)
delta[c2, s] ~ dnorm(muDelta[c2], precDelta) T(-5, 5)
}
}
#priors
for (c1 in 1:nCond1){
muAlpha[c1] ~ dunif(.1, 5)
muBeta[c1] ~ dunif(.1, .9)
}
for (c2 in 1:nCond2){
muTau[c2] ~ dunif(.0001, 1)
muDelta[c2] ~ dunif(-5, 5)
}
precAlpha ~ dgamma(.001, .001)
precBeta ~ dgamma(.001, .001)
precTau ~ dgamma(.001, .001)
precDelta ~ dgamma(.001, .001)
}

78

APPENDIX E:

Posterior Predictions
I tested how well the DDM predicted the data by examining the degree to which the
model predictions corresponded with observed choice probabilities, response times, and response
time distributions. This was done for each condition in Studies 1, 2, and 4. I used JAGS to
predict decision and response time data from the DDM using the posterior condition level
distributions. Decision and response time data were generated for each trial at each step in the
chain (6,000 steps). This leads to an incredibly large amount of data (e.g., Study 3: 320 trials
×102 participants × 6,000 sampled values). The data were summarized to the condition level
because 1) the study analyses were on condition level effects, and 2) there was not enough data
at the individual level to accurately estimate response time distributions.
I followed the procedures from Pleskac et al. (2017) to summarize the choice
probabilities, response times, and response time distributions. For the choice probabilities, I
plotted observed and model predicted means for each condition and response type. These plots
were overlaid with the mean performance for each individual to show the spread of the data. In
all studies there was less performance variability in conditions where the dispatch information
was correct or the point structure favored the response (e.g., shooting armed targets when
shooting was encouraged), and the DDM captured this change. In general the DDM recreated the
student data well but performed more poorly for police. This was particularly evident in
conditions with less data (the no information, armed target condition and armed information,
unarmed target conditions). One noteworthy prediction miss is the overestimate of false alarms
in the Study 2 no information conditions. However, this miss was not replicated in Study 1 or 4,

79

nor did it bias predicted response times, so I did not adjust the model to account for this.
I also examined the predicted response times for all conditions and all response times.
Generally, the model did a good job at predicting the spread of the data, although in Study 1 the
model systematically predicted slower correct rejections for students and faster correct rejections
for officers. One way to improve these fits would be to add in trial-by-trial variability in the
parameters. However, the deviance information criterion values for those models indicate that
although they have better fits, they come at a cost of parsimony. It is possible that these models
may actually overfit the data.
Finally, I examined the degree of correspondence between the observed and predicted
response time distributions for each condition for each study. These allowed for a more detailed
examination of whether the predicted response time distribution matches the shape of the
observed distribution, rather than focusing on the mean and variability in the data. In Study 1,
despite coming from two different populations, patterns of response times and misfits were
extremely similar across students and officers. The model did a reasonable job recreating the
data, although it consistently predicted more leptokurtic response time data for correct decisions
when correct dispatch information is provided. The model also underestimated the degree of
positive skew for misses when no dispatch information was provided. Study 2 showed high
correspondence between the observed and predicted response time distributions. Finally, in
Study 4, the model reasonably recreated the data, although it consistently predicted more
leptokurtic response time data when decisions are correct (i.e., not shooting unarmed targets,
shooting armed targets).

80

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Figure 12: Posterior predictions of hit and false alarm rates for Study 1. Squares represent
observed condition level choice proportions. Diamonds represent predicted condition level
choice proportions. Blue dots represent individual participant response times and have been
jittered to better show the distribution of scores. W = White, B = Black

81

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m
Ar
B

Ar

m

ed

ed

e
on
W

W

N

N

m
Ar
B

W

Ar

m

ed

ed

e
on
N
B

N
W

●

on
e

250
on
e

250

●

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B

Misses (ms)

●

False Alarms (ms)

●

Figure 13: Posterior predictions of response times for Study 1. Squares represent observed
condition level choice proportions. Diamonds represent predicted condition level choice
proportions. Blue dots represent individual participant response times and have been jittered to
better show the distribution of scores. W = White, B = Black

82

White, No Info,
No Gun, Don't Shoot

White, No Info,
Gun, Don't Shoot

White, No Info,
No Gun, Shoot

White, No Info,
Gun, Shoot

250

500

750

1000

0

250

500

750

1000

Density
750

1000

0

250

500

750

1000

Black, No Info,
No Gun, Shoot

Black, No Info,
Gun, Shoot

250

500

750

1000

0

250

500

750

1000

Density

Black, No Info,
Gun, Don't Shoot

Density

Black, No Info,
No Gun, Don't Shoot

Density

Response Time (ms)

0

250

500

750

1000

0

250

500

750

1000

Response Time (ms)

White, Armed Info,
No Gun, Don't Shoot

White, Armed Info,
Gun, Don't Shoot

White, Armed Info,
No Gun, Don't Shoot

White, Armed Info,
Gun, Shoot

250

500

750

1000

0

250

500

750

1000

Density

Response Time (ms)

Density

Response Time (ms)

Density

Response Time (ms)

0

250

500

750

1000

0

250

500

750

1000

Response Time (ms)

Response Time (ms)

Black, Armed Info,
No Gun, Don't Shoot

Black, Armed Info,
Gun, Shoot

Black, Armed Info,
No Gun, Shoot

Black, Armed Info,
Gun, Shoot

250

500

750

1000

Response Time (ms)

0

250

500

750

1000

Density

Response Time (ms)

Density

Response Time (ms)

Density
0

500

Response Time (ms)

Density

0

250

Response Time (ms)

Density

0

0

Response Time (ms)

Density

0

Density

Density

data

Density

model

0

Response Time (ms)

250

500

750

1000

Response Time (ms)

0

250

500

750

1000

Response Time (ms)

Figure 14: Observed (black) and predicted (gray) response time distributions for each response
type at the condition level for students in Study 1.

83

White, No Info,
No Gun, Don't Shoot

White, No Info,
Gun, Don't Shoot

White, No Info,
No Gun, Shoot

White, No Info,
Gun, Shoot

250

500

750

1000

0

250

500

750

1000

Density
750

1000

0

250

500

750

1000

Black, No Info,
No Gun, Shoot

Black, No Info,
Gun, Shoot

250

500

750

1000

0

250

500

750

1000

Density

Black, No Info,
Gun, Don't Shoot

Density

Black, No Info,
No Gun, Don't Shoot

Density

Response Time (ms)

0

250

500

750

1000

0

250

500

750

1000

Response Time (ms)

White, Armed Info,
No Gun, Don't Shoot

White, Armed Info,
Gun, Don't Shoot

White, Armed Info,
No Gun, Don't Shoot

White, Armed Info,
Gun, Shoot

250

500

750

1000

0

250

500

750

1000

Density

Response Time (ms)

Density

Response Time (ms)

Density

Response Time (ms)

0

250

500

750

1000

0

250

500

750

1000

Response Time (ms)

Response Time (ms)

Black, Armed Info,
No Gun, Don't Shoot

Black, Armed Info,
Gun, Shoot

Black, Armed Info,
No Gun, Shoot

Black, Armed Info,
Gun, Shoot

250

500

750

1000

Response Time (ms)

0

250

500

750

1000

Density

Response Time (ms)

Density

Response Time (ms)

Density
0

500

Response Time (ms)

Density

0

250

Response Time (ms)

Density

0

0

Response Time (ms)

Density

0

Density

Density

data

Density

model

0

Response Time (ms)

250

500

750

1000

Response Time (ms)

0

250

500

750

1000

Response Time (ms)

Figure 15: Observed (black) and predicted (gray) response time distributions for each response
type at the condition level for officers in Study 1.

84

0.50

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●

N

N

on
e
U No W
na ne
r
U me B
na d
rm W
Ar ed
m B
e
Ar d W
m
e
W dB
hi
te
W W
hi
Bl te B
ac
k
Bl W
ac
k
B

0.00

●
●

●
●●
●
●

●
●
●
●●
●

●

●

●
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●

●●●

●
●●
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●

0.25

1.00

●
●
●
●
●

●
●●
●
●

●
●
●
●
●
●

●●

on
e
U No W
na ne
r
U me B
na d
rm W
Ar ed
m B
e
Ar d W
m
e
W dB
hi
te
W W
hi
Bl te B
ac
k
Bl W
ac
k
B

Hit Rate

0.75

●
●
●●

False Alarm Rate

1.00

Figure 16: Posterior predictions of hit and false alarm rates for Study 2. Squares represent
observed condition level choice proportions. Diamonds represent predicted condition level
choice proportions. Blue dots represent individual participant response times and have been
jittered to better show the distribution of scores. W = White, B = Black

85

●
●

900

●
●
●

800

●
●

●

Hits (ms)

●
●

●●

500
400

●

●

●

●

●

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●

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●
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600

●
●

●
●
●
●

700

●

●

●

●

Correct Rejections (ms)

900

●

●

●

●
●
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●

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700
600
500

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400

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300

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800

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300

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●

on
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U No W
na ne
r
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900

●

900

●
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●

Misses (ms)

●

500
400

●
●

●
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600

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700

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False Alarms (ms)

800

●

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●

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800

300

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600
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●

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●
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●

●
●

N
on
e
U No W
na ne
r
U me B
na d
rm W
Ar ed
m B
e
Ar d W
m
e
W dB
hi
te
W W
hi
Bl te B
ac
k
Bl W
ac
k
B

N
on
e
U No W
na ne
r
U me B
na d
rm W
Ar ed
m B
e
Ar d W
m
e
W dB
hi
te
W W
hi
Bl te B
ac
k
Bl W
ac
k
B

●
●

●

●

Figure 17: Posterior predictions of response times for Study 2. Squares represent observed
condition level choice proportions. Diamonds represent predicted condition level choice
proportions. Blue dots represent individual participant response times and have been jittered to
better show the distribution of scores. W = White, B = Black

86

White, No Info,
No Gun, Shoot

Black, Armed Info,
No Gun, Shoot

White, No Info,
Gun, Shoot

Black, Armed Info,
Gun, Shoot

250 500 750 1000
Response Time (ms)

0

250 500 750 1000
Response Time (ms)

250 500 750 1000
Response Time (ms)

250 500 750 1000
Response Time (ms)

250 500 750 1000
Response Time (ms)

Density
Density

Black, White Info,
Gun, Shoot

250 500 750 1000
Response Time (ms)

0

250 500 750 1000
Response Time (ms)
White, Black Info,
Gun, Shoot

250 500 750 1000
Response Time (ms)

0

Density

White, Armed Info,
Gun, Shoot

250 500 750 1000
Response Time (ms)

250 500 750 1000
Response Time (ms)

Density
0

Black, Black Info,
No Gun, Shoot

0

0

Black, Unarmed Info,
Gun, Shoot

Density

Density
250 500 750 1000
Response Time (ms)

250 500 750 1000
Response Time (ms)

Density
0

White, Armed Info,
No Gun, Shoot

0

0

White, Black Info,
No Gun, Shoot

Density

Density

Black, Unarmed Info,
No Gun, Shoot

0

0

Density
0

250 500 750 1000
Response Time (ms)
White, White Info,
Gun, Shoot

White, Unarmed Info,
Gun, Shoot

Density

Density

250 500 750 1000
Response Time (ms)
Black, White Info,
No Gun, Shoot

250 500 750 1000
Response Time (ms)

0

Black, No Info,
Gun, Shoot

Density
0

White, Unarmed Info,
No Gun, Shoot

0

250 500 750 1000
Response Time (ms)

Density

0

0

White, White Info,
No Gun, Shoot

Density

Density

Black, No Info,
No Gun, Shoot

250 500 750 1000
Response Time (ms)

250 500 750 1000
Response Time (ms)
Black, Black Info,
Gun, Shoot

Density

0

Density

data

Density

Density

model

0

250 500 750 1000
Response Time (ms)

0

250 500 750 1000
Response Time (ms)

Figure 18: Observed (black) and predicted (gray) response time distributions for the shoot
response at the condition level for students in Study 2.

87

White, No Info,
No Gun, Don't Shoot

Black, Armed Info,
No Gun, Don't Shoot

White, No Info,
Gun, Don't Shoot

Black, Armed Info,
Gun, Don't Shoot

250 500 750 1000
Response Time (ms)

0

250 500 750 1000
Response Time (ms)

250 500 750 1000
Response Time (ms)

250 500 750 1000
Response Time (ms)

250 500 750 1000
Response Time (ms)

Density
Density

Black, White Info,
Gun, Don't Shoot

250 500 750 1000
Response Time (ms)

0

250 500 750 1000
Response Time (ms)
White, Black Info,
Gun, Don't Shoot

250 500 750 1000
Response Time (ms)

0

Density

White, Armed Info,
Gun, Don't Shoot

250 500 750 1000
Response Time (ms)

250 500 750 1000
Response Time (ms)

Density
0

Black, Black Info,
No Gun, Don't Shoot

0

0

Black, Unarmed Info,
Gun, Don't Shoot

Density

Density
250 500 750 1000
Response Time (ms)

250 500 750 1000
Response Time (ms)

Density
0

White, Armed Info,
No Gun, Don't Shoot

0

0

White, Black Info,
No Gun, Don't Shoot

Density

Density

Black, Unarmed Info,
No Gun, Don't Shoot

0

0

Density
0

250 500 750 1000
Response Time (ms)
White, White Info,
Gun, Don't Shoot

White, Unarmed Info,
Gun, Don't Shoot

Density

Density

250 500 750 1000
Response Time (ms)
Black, White Info,
No Gun, Don't Shoot

250 500 750 1000
Response Time (ms)

0

Black, No Info,
Gun, Don't Shoot

Density
0

White, Unarmed Info,
No Gun, Don't Shoot

0

250 500 750 1000
Response Time (ms)

Density

0

0

White, White Info,
No Gun, Don't Shoot

Density

Density

Black, No Info,
No Gun, Don't Shoot

250 500 750 1000
Response Time (ms)

250 500 750 1000
Response Time (ms)
Black, Black Info,
Gun, Don't Shoot

Density

0

Density

data

Density

Density

model

0

250 500 750 1000
Response Time (ms)

0

250 500 750 1000
Response Time (ms)

Figure 19: Observed (black) and predicted (gray) response time distributions for the don’t shoot
response at the condition level for students in Study 2.

88

●
●
●

●●

●
● ● ●●

●
● ● ●
●

●

●●●
● ●

●

0.8

●
●

Hit Rate

●●

● ●
●

●●

●●

●

●●●
●●●

●● ●

● ● ● ● ●●
●
● ●●●

0.4

●

● ●●●

●

●

●●

●
●

● ●●●
●●

●

●
●

●
● ● ●

●

● ●
●●
● ●●
●

● ●
●
●
●

●● ● ●

●

●

●

●

●

●●

● ●●

●●
●

●

●

●
●
●
●●
●
●●●
●●
●
●● ●

● ●

● ●●
●

● ●

0.6

●●

●

●

●

●
●

0.4

●●

●●

●● ●
●● ●
●●
● ●●

● ●● ●
●

●●
●

● ● ●●●●
●
●
●
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● ●●●●●● ●●

●●●●
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●
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●
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●

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●

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● ●● ● ●

●
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●
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●

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●
●

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●

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●

●●
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●●

●
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● ●●

●● ● ● ●●
●●
●
●●●
●
●
●●

●● ●
● ● ●●●

●

●●
●
●●

● ●
●
●

●

● ● ● ● ●●
●
● ●●

●

●

●
● ●●

● ●● ●
●

●
●

●
●●

0.2

●

●

●

●●
● ●●

●●
●●
● ●

●●

●

●

●

●
●
●●●

●●

●
●●
●

●

●

●

●● ● ●

●

● ● ●●● ●

●

●●

●
●

●

● ●

●

●

●

●

● ●

● ● ●●
●● ●

●●● ●

● ●

●

●
●● ●●●
●
●●

●●
●● ●● ● ●
●

●

●
●
● ●

●

●●●
●●● ●●

●● ●
●

●
●

●

● ●

●●●● ●
●

●

● ●● ●

●
●

●

● ●●
●
●● ● ●
● ●

●
●

●

●

●
●
●

●

●

●●
●
● ●● ●
●

●●

●
● ●

●●●●● ●● ●
●●●

●

● ●● ● ●

●
●●
●

●

●
●
●●
●●●

●●●
●●
●
●●●
●

●●
● ● ● ●● ● ●

●●

●

●

● ●● ●●●●●

●

● ●
●●●●

● ●●

●

●
●

●
● ●●

●

● ●

●

●
●

●●

●●●

●●

●

●

●

●● ● ●

●

●
●
●●

●

●●●
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●
●●

●●

●

●

●●● ●
●●
●● ●
●●

●● ●

●
●
●
●

0.6

●
● ● ●●

●

●

●

●

●● ● ●
● ●
● ●

●
●●●

●

●

0.8

●

●

False Alarm Rate

1.0

●
● ●

●
● ●
●

●

●
●

0.2

●

●

0.0

●

White DS Black DS
●

White S

Black S

White DS Black DS

White S

Black S

Figure 20: Posterior predictions of hit and false alarm rates for Study 4. Squares represent
observed condition level choice proportions. Diamonds represent predicted condition level
choice proportions. Blue dots represent individual participant response times and have been
jittered to better show the distribution of scores. DS = payoff favors not shooting, SH = payoff
favors shooting.

89

900

900

Hits (ms)

●

700

●

●

●

●

●

●

●
●
●
●
● ●

●

600
500

●
●

●
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●

●

●
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●
●●
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● ●●
● ●
●
● ●
● ● ● ●●
●● ●● ● ●●
● ●
●
●● ● ● ●●
● ● ●● ●
● ● ●
●
●
● ●
●
●
● ●
●●
● ●●● ●● ●
● ● ●
●●
●
●
●
●● ● ●
● ●
●●
●
●

●
●
●
●
●●●
●

●
● ●
● ●
● ● ● ● ●
●
●
●
●●
●
●
●
● ●●●●
●
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● ●●
●
●
●● ● ● ●● ●
● ●● ● ●
● ●
●●
●
●● ●●●
● ●●
●
● ● ●●
●●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●

●

●
●

●
●

●

400

●

●
●
●
●
●
●
●●
●●●
●● ●●
●
●
● ● ●● ● ●
●●
●●
●●● ●
●
●
●
●
●
●
●●
●
●●
●●●
● ● ●●
●●● ● ●
●
●
●●● ●
●
●●
●
●
●● ●
●
●●● ●
● ●
●
●
●
●●
● ●●
●●
●
●
●● ●
●●●
●
●

●
●
●
● ●●
● ●● ●
●
●●
● ●●
● ●● ●
●
●●
● ●●
● ●●●● ●
●●
● ●●●
● ●●●
●
● ● ●●
● ●
●● ●
● ● ●●
●●
●●
●
●●
●●
●●●● ● ●●
●
●
●
●●
● ●
●
●
●
●
●
●
●

●

800

●
●
●
●
●

700

●

●

●
●

●

●

●●

●

●

●

●

●

●
●

600
500

●
●
●
● ● ●●
●
●
●
●
●
● ●
●●
●●
●
●
●
●●
●●
●
●
●●●
●
●
●● ● ● ●
●
●
●
●
●● ●● ●●●
●●
● ●
●● ●
● ● ●● ●
●●●●
●●
● ● ●●
●
●
● ●●
●
●
●● ● ●
●
●
●●
●
●
●

400

●

●

●

●

●

● ●
●

●

●
●
●

●
●

●
●
●
●
●
●
●
●● ●
●
●
●
●
●●
●●
●
●●●
● ●
●●
●●
●
●
● ● ●
● ● ●●
●
●
●
●●
●
●● ●
●
●
● ●●● ●●
●
●●●
●●
●●
●
●
● ●
● ●
●
●
●
●
●
● ● ●
●
● ●

●

●

●
●

●
●●

●

●●
● ●●
●
● ●
● ●●●
●●
●●
● ●
●
●
●●● ●
● ●
● ●●
●
●●
●●
●
●
● ● ●● ● ●
●
●
● ● ●●●●●●
●
● ●●
●
● ●
● ●
●●
● ● ●●
●
●●
● ●●
●
●
●● ●
●
●
●
●
●
●
●

● ●
●
●
●
●
●●●
●●
●
● ●
●
●
●● ● ●●●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●●●●
● ●
●
●●
●●
●
●
●
●●●
●
●
●●●
●● ●
●●
●
● ●●
●●
●
● ●●
●●
●
●
●●
●
●
●● ●
●
●
● ●
●
●
●

●

●
●●

●

●

●

●

●

●

●

●

Correct Rejections (ms)

●

800

●

●

300

300

●

White DS Black DS

White S

Black S

White DS Black DS
●

●●

900

White S

Black S

900
●

●

800

●

●

Misses (ms)

●

700
●

●

●

●

600
500
400

●

●

●
●

●●
●
●
●
●●
●
●● ●
●
● ●●
● ● ●
●
●
●
●
●
●● ●
●
● ● ● ● ●●●
●
●●
●
●
● ●●●● ●●
●
●●●●●
●●
● ● ●● ●
●●
●● ● ●●
●●●
● ●
●
●
● ●
●
●
●
● ●
●
●
●
●
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●
● ●●
●
●

●
●

●
●

●
●

●

●●

●

● ●
●●● ● ●
● ●●
●●
●
●
●●
●●
●●●
●
●●
● ● ●●●
●
●
●●
● ● ●●●
●
●● ●●
●●
●
● ● ●●●
●
●
●
●●
● ●
●
●
●
●●
● ● ●
●
●
●●
● ●
●●● ●
● ● ●
●
●

●

●

●

●
●
●●
●
●●
●
●
●
● ● ●
●
●
●●
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●●●●
●
● ● ●●●
●
●● ●
● ●
●
●
●
●●
● ●
●●
●
● ●● ● ●
●
●
●
●
●●●
● ●●●
●
●
●
●●
●●● ● ●● ●
●●
●● ● ●
●
●
●
●

●
●

●

●

●

●
● ●
●● ●

●

●

● ●
●

●
●
●
● ●
● ●
●● ●
●●
●

●
●

●
●●
●

●
●
●
●
● ●
●●● ●●
● ● ●● ●
●● ●
● ● ●● ●
●
●● ● ●
●●●
●●
●●●●●
●
●
●
● ●●
●
●
●
●
●●
●
●
●
●
●
● ● ●
●
●
●
●
●

●

False Alarms (ms)

800

300

●
●

●

●

●
●

●
●
●
●

●
●

600
500

●

●●
●

●●
●●●●

●
● ●
●●●● ●●●●
●●
●●
●
●●
● ●● ●●●
●● ●
●
● ● ●● ●● ●
●
● ● ●
●●
●●
● ● ●●
●
●●●
●●
●
●
●
● ● ● ● ●●
●
●●
●●
●●●● ●● ●
●
● ●
●● ●
●●
●

400

●

●

●

700

●
● ●
● ●

●
● ●●
●
● ●●
● ●●●
●
●
●●
●
●● ●●●
●●
● ●
● ● ●●●●
●
● ●
●●
●
●
●●● ●
● ●
●●● ●●●
●
●
●●
● ●
● ● ●●
●● ●●● ●
●●
●
●●
●
●●
●●
●
●
●
●
●

●
●

●
● ●

●
●

●

●
● ●
●
● ●
●
●● ●
●
●● ●
●●
●
●●
●● ●●
●●
●● ● ● ●
● ●●●
● ● ●●●●●
●● ● ●
●
●● ●●
● ●
● ●● ●
●
●
●●
●
●●●● ●
●
●
●
●●
●
●
●
● ● ● ●●
●
●

●
●
●

●
●

●●
●

●●

●●
●
●
●
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Figure 21: Posterior predictions of response times for Study 4. Squares represent observed
condition level choice proportions. Diamonds represent predicted condition level choice
proportions. Blue dots represent individual participant response times and have been jittered to
better show the distribution of scores. DS = payoff favors not shooting, SH = payoff favors
shooting.

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White, Shoot Payoff
No Gun, Don't Shoot

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Gun, Shoot

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Gun, Don't Shoot

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No Gun, Don't Shoot

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Figure 22: Observed (black) and predicted (gray) response time distributions for each response
type at the condition level for Study 4.

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