-
96
Transportation Research Record: Journal of the Transportation
Research Board, No. 2223, Transportation Research Board of the
National Academies, Washington, D.C., 2011, pp. 96103.DOI:
10.3141/2223-12
years to more accurately determine the effectiveness of roadway
safety measures.One newly released tool to aid in transportation
safety analysis is
the Highway Safety Manual (HSM) published by AASHTO (1). The HSM
was developed to incorporate the explicit role of highway safety in
decisions on roadway planning, design, maintenance, construction,
and operations. Currently, there are no such widely accepted tools
available for agencies responsible for managing the safety of
road-ways. As a result, safety considerations often carry little
weight in decision making.The purpose of this paper is to summarize
a statistical methodology
that can be used to analyze the effectiveness of roadway safety
treatments. The paper analyzes the effectiveness of raised median
installations in Utah by using a hierarchical Bayesian model to
compare crash distributions before and after installation of a
raised median. The paper first presents an overview of the
background necessitating the research and then discusses the safety
model devel-oped for use in the research. The raised median
analysis site selection and data collection components are then
addressed, followed by the analysis results for individual sites
and a combined site analysis. Finally, conclusions and
recommendations are presented.
Background
raised Medians
In this study, the safety data collection and analysis
techniques devel-oped are applied to study sites at which raised
medians have been installed throughout the state of Utah. A raised
median is a physical barrier, such as a concrete or landscaped
island, in the center portion of the roadway that separates
opposing lanes of traffic and is designed so that it is not easily
traversed. Raised medians are appropriate in some, although not
all, locations and have been found to be most useful on
high-volume, high-speed roadways (2).Raised medians have frequently
been used as an access man-
agement technique to improve roadway safety in two primary ways:
(a) raised medians reduce the number of conflict points by allowing
turning movements to be made only at designated openings or at
signalized intersections, and (b) raised medians provide a physical
barrier separating opposing traffic in an effort to eliminate
head-on collisions (3).Raised medians are not always used to
mitigate one specific
type of crash or factor (2). Raised medians have been installed
for beautification purposes, as an access management technique, as
a traffic calming device, for pedestrian refuge, and for various
other purposes (3). Regardless of the purpose, raised medians have
had a
Analyzing Raised Median Safety Impacts Using Bayesian
Methods
Grant G. Schultz, Daniel J. Thurgood, Andrew N. Olsen, and C.
Shane Reese
Because traffic safety studies are not performed in a controlled
envi-ronment such as a laboratory, but rather in an uncontrolled
real-world setting, traditional analysis methods often lack the
capability to evaluate the effectiveness of roadway safety measures
adequately. In recent years, however, advanced statistical methods
have been used in traffic safety studies to determine the
effectiveness of such measures more accurately. These methods,
especially Bayesian statistical techniques, can account for the
shortcomings of traditional methods. Hierarchical Bayesian modeling
is a powerful tool for expressing rich statistical models that more
fully reflect a given problem than traditional safety evaluation
methods could. This paper uses a hierarchical Bayesian model to
ana-lyze the effectiveness of raised medians on overall and severe
crash fre-quency in Utah by determining the effect each newly
installed median has on crash frequency and frequency of severe
crashes at study sites before and after installation of the
medians. Several sites at which raised medians have been installed
in the past 10 years were evaluated with available crash data. The
results show that the installation of a raised median is an
effective technique to reduce the overall crash frequency and
frequency of severe crashes on Utah roadways, with results showing
a reduction in overall crash frequency of 39% and frequency of
severe crashes of 44% along corridors where raised medians were
installed. The results also show that hierarchical Bayesian
modeling is a useful method for evaluating effectiveness of roadway
safety measures.
Because traffic safety studies are not performed in a controlled
environment, such as a laboratory, but rather in an uncontrolled
real-world setting, traditional analysis methods often lack the
capa-bility to adequately evaluate the effectiveness of roadway
safety measures. However, safety studies have historically had to
rely on these traditional methods because of the complexity of more
effec-tive models. Fortunately, the development of advanced
statistical software and methodologies in recent years has helped
overcome the complexity of the models and made advanced statistical
meth-ods more attainable. These advanced statistical methods,
especially Bayesian statistical methods, have the capabilities to
account for the shortcomings of traditional methods and have thus
been used in recent
G. G. Schultz, Department of Civil and Environmental
Engineering, 368 Clyde Building, and A. N. Olsen, 223 TMCB, and C.
S. Reese, 208 TMCB, Department of Statistics, Brigham Young
University, Provo, UT 84602. D. J. Thurgood, Depart-ment of Civil
and Environmental Engineering, Brigham Young University, 5865 West,
10100 North, Highland, UT 84003. Corresponding author: G. G.
Schultz, [email protected].
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Schultz, Thurgood, Olsen, and Reese 97
positive impact on safety that has generally been well
documented in the literature. For example, researchers have shown
that roadways with raised medians generally experience lower crash
rates than roadways of similar use and annual average daily traffic
(AADT) that are undivided or include a two-way left-turn lane (28).
These analyses were generally conducted using traditional
before-and-after approaches to analyze crash statistics. Over the
past several years, more statistically rigorous methodologies for
safety analysis have emerged.
Safety analysis
To determine the safety of a site during analysis, it is
essential to first define what safety is and how it is measured.
Roadway safety is usually defined and evaluated by recorded numbers
of crashes or crash rates. Severity of crashes also plays an
important role in the understanding of roadway safety. For example,
one site may experi-ence considerably more crashes than another
site. However, the second site may have a much larger proportion of
severe, even fatal, crashes. Therefore, both frequency of crashes
and severity of crashes are essential in determining the safety of
a facility.One of the key reasons it is difficult to understand why
crashes
occur is that crashes are usually not the result of one factor,
but instead the combination of several events, circumstances, and
factors. The combination of multiple events can significantly alter
the amount of risk a driver may face. Even if it were possible to
account for all possible factors that lead to a crash, the ability
to predict a crash is not absolute. The key principle is that
understanding the nature of crashes is a vastly complex and random
process when only the known factors are considered. It is also
important to remember that unknown factors also contribute to
crashes. The complexity of known and unknown contributing factors
can be overcome through the devel-opment and use of proper
statistical tools that can correctly model crash characteristics
and behavior. To properly analyze crash statis-tics, it is
essential to analyze the characteristics of crash statistics to
determine the proper statistical tools to use.
Characteristics of Crashes
One of the key concepts of a crash study is that although there
are trends and factors that increase the likelihood of crashes, the
occur-rence of a crash is not completely predictable. Crashes, by
nature, are random events. The frequencies of crashes will
naturally fluctuate from year to year. Fluctuations in crash
frequency make it difficult to determine whether a reduction in the
number of crashes is a result of a specific treatment, changes in
site conditions over time, or a result of natural fluctuations from
stochastic processes. These fluctuations present a phenomenon
referred to as regression-to-the-mean (RTM) bias. The RTM
phenomenon expects that a value that is determined to be extreme
will tend to regress to the long-term average over time. This means
that a period of high crash frequencies at a site is statistically
probable to be followed by a period of low crash frequencies
(9).Traditional methods have been used for many years to
analyze
crash statistics. Traditional methods use relatively
straightforward before-and-after approaches to compare the crash
frequency or rate of an entity immediately before an improvement
was made with the crash frequency or rate directly after the
improvement to determine the effectiveness of the treatment (9).
One of the problems with
many traditional analysis methods is that they do not account
for the RTM bias. If the RTM bias is not accounted for, the
effectiveness of a specific treatment is likely to be inaccurately
reported.
Predicting Crashes
The RTM bias provides evidence of limitations when short-term
data are used for analysis, which would lead to the assumption that
using data for longer periods provides a better representation of
crash behavior at a site. However, there are problems associated
with this method as well. The characteristics of a site, such as
traffic volume, weather, and pavement condition, change over time.
Some of these characteristics, such as weather, continually
fluctuate. Other factors, such as pavement condition and roadway
markings, dete-riorate gradually over years of use. These latter
factors create a legitimate limitation when using long-term crash
statistics for site analysis.Factors contributing to crashes can
never be completely controlled
or maintained, providing a level of difficulty in accurately
predicting crashes. Crash data are statistically classified as
count data and by nature are nonnegative integers; therefore
generalized linear models are insufficient because the assumption
that the dependent variable is continuous is not true for crash
studies (10). Previous studies have suggested the use of Poisson
models or negative-binomial models as more appropriate for count
statistics (1113).
Empirical Bayesian Method
Several methods have been developed that more accurately
determine the effectiveness of a safety measure than traditional
methods by combining observed crash statistics with predicted
values obtained by the use of safety performance functions (SPFs),
crash modification factors (CMFs), and local calibration factors
(1). In recent years, interest in the use of various Bayesian
approaches in traffic safety studies has increased significantly.
One of the common methods being used in safety studies is the use
of the empirical Bayesian (EB) method of analysis. The EB method
corrects for the RTM bias by determining the expected crash
frequency of an entity. The EB method combines an estimation of the
crash frequency of the study site with charac-teristics of similar
sites using SPFs to estimate the predicted number of crashes. The
EB approach is demonstrably better suited to estimate safety than
traditional methods (9).The EB method does suffer from deficiencies
of its own. Perhaps
most prominent is the need to spend time, resources, and effort
on the estimation of SPFs required for implementation of the EB
method. Another major disadvantage of the EB approach is that the
SPF is estimated using aggregate crash data for more than a year.
Therefore, to accurately apply this model, the units of crash
frequencies per three years needs to be maintained (i.e., annual
crash data cannot be used in place of three-year aggregated data)
(14). The EB method is also applicable only when both predicted and
observed crash frequencies are available for a roadway network.
Additionally, the EB approach has been criticized for its inability
to incorporate uncertainties in the model parameters. The EB
approach assumes the parameters are error free and can be replaced
simply by their estimates for the posterior analysis. These
limitations can be overcome with the use of the flexible modeling
associated with the hierarchical Bayesian method (15).
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98 Transportation Research Record 2223
Hierarchical Bayesian Method
In recent years, a full or hierarchical Bayesian approach has
been suggested as a useful alternative to the EB approach. Though
more complex, the hierarchical Bayesian approach has several
advantages over the EB approach in that the hierarchical approach
is believed to require less data for untreated reference sites, it
better accounts for uncertainty in data used, and it provides more
detailed causal inferences and more flexibility in selecting crash
count distributions (16).In a hierarchical Bayesian analysis, prior
(before) information
and all available data are integrated into posterior (after)
distributions from which inferences can be made; therefore, all
uncertainties are accounted for in the analyses. Hierarchical
Bayesian methods may well be less costly to implement and may
result in safety estimates with more realistic standard errors. A
study performed by Iowa State University argues that with the use
of a hierarchical Bayesian approach, it is possible to improve on
the prediction of the expected number of crashes at a site while at
the same time avoiding the need to obtain estimates of SPFs or CMFs
(17).One important difference between hierarchical Bayesian and
the EB approach is the manner in which the model parameters are
determined. In the EB approach, model parameters are dependent on
the data only. Model parameters are estimated using techniques
involving the use of crash data such as the maximum likelihood
technique. However, to produce results close to the true population
parameters, maximum likelihood estimators frequently require large
amounts of data. In the hierarchical Bayesian approach, the prior
distributions are fixed by modelers and are combined with the data
to create a joint posterior distribution. In situations in which
fewer data are available, the prior distribution simply receives
compara-tively more weight in the posterior distribution, and a
valid result is produced. Hence, hierarchical Bayesian methods are
still reliable with fewer data points when priors are chosen
carefully. Priors also account for RTM bias if the data
observations are extreme. There has been increased interest in this
approach over the past few years because of the modeling
flexibility associated with these methods (15).The hierarchical
Bayesian method was applied to evaluate the
safety effect of conversion from stop to signalized control at
rural intersections in California. The results were then compared
with those from the EB method, and it was found that the
hierarchical Bayesian method can provide results similar to, if not
better than, those of the EB approach (18).
Safety Model developMent
Because of the limitations and published concerns of traditional
analysis methods, and the benefit of using Bayesian techniques to
account for RTM bias and therefore more accurately evaluate safety
benefits, a hierarchical Bayesian model was constructed as the
analysis tool for this study. The analysis provides an opportunity
to estimate the safety impacts of the installation of raised
medians in Utah. The model uses crash frequency (overall crashes
and severe crashes) and AADT data for selected analysis sites as
inputs (although the model is developed such that other covariates
may also be included). The details of the model can be found in the
literature (19, 20); the basic model development is included in
this section to aid the reader in understanding the analysis
performed.For the model development, it was assumed that yi is
Poisson
distributed as outlined in Equation 1. The Poisson distribution
is
used because of the nature of crash data classified as count
data. The Poisson distribution also allows for an exposure
parameter, which in this case is the length of the roadway segment.
The number of crashes per mile (or severe crashes per mile), rather
than the number of crashes solely, is then modeled for each roadway
segment. Data from segments with varying segment length may thus be
included in the same model appropriately.
yi i~ ( )Poisson ( ) 1where yi is the number of crashes per mile
for each AADT segment and qi is the mean number of crashes per
mile.The estimation of the mean number of crashes per mile is
calculated
using Equation 2.
log ( ) i A i B i iA B( ) = + + 1 2AADTwhere
b = regression coefficient of the independent variable (A
represents the after period, B represents the before period, and 1
corresponds to AADT),
Ai = 1 if the ith observation is from the after period and 0
otherwise,
Bi = 1 if the ith observation is from the before period and 0
otherwise, and
AADTi = AADT for the ith observation.
The analysis result of this model is the consideration of two
intercepts, one for the before period and one for the after period,
with the coefficient for AADT constrained to be the same for both
periods. The log transformation was chosen as part of the standard
Poisson regression procedures (21). The prior distribution for each
bj where j {A, B, 1} is normally distributed as discussed in the
literature (12) and specifically defined in Equation 3.
j ~ , ( )norm 0 1 3( )The priors, p(bj), were selected with mean
zero because previous
analyses of this type have not been performed on the chosen
road-way segments to suggest higher or lower mean values for the
prior distributions. Zero mean values allow the posterior
distributions of the coefficients to be positive or negative
according to the data with-out the prior pulling the posterior
results in one way or the other. The posterior distribution, p(bA,
bB, b1y), for the b parameters, up to a constant, is expressed in
Equation 4.
pi pi pi pi
y P y
e
A B
eXi
i
n
( ) ( ) ( ) ( ) ( ) =( )
=
1
1 ( ) + +( ) =
( ) e ey Xin i i A B 12
1
2 212
(44)
where
Xi = matrix with Ai, Bi, and AADTi as its columns;b = matrix of
parameters bA, bB, and b1; and n = total number of
observations.
Because of the complexity of the normalizing constant of the
pos-terior distribution, rather than deriving the distribution
theoretically, Markov chain Monte Carlo methodology is used to
sample from the posterior distribution using the scaled
distribution shown in Equation 4 (12, 13, 22, 23). The results of
the algorithm are several
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Schultz, Thurgood, Olsen, and Reese 99
thousand random draws from the posterior distribution for each
of the bj parameters. Inference and conclusions may be made on the
basis of these random draws because they represent the appropriate
marginal posterior densities.In this study, frequencies of both
overall and severe crashes are
analyzed. The ability to consider more than one type of crash
without recalibrating SPFs or CMFs is one of the flexibility
features of the hierarchical Bayesian approach, which can be
immensely helpful if a safety project is targeted to reduce a
specific type of crash. Each of the raised median sites is analyzed
individually, which allows for insights as to why the project may
be effective at one study site but not at another. The sites are
also combined to perform an overall analysis of the effectiveness
of raised medians.
raiSed Median analySiS
Site Selection
Before a detailed crash analysis is conducted, study sites need
to be selected. The study sites that have been selected for
analysis where raised medians have been installed are discussed in
this section. For crash analysis purposes, the study sites will be
roadway segments where raised medians have been installed, as
outlined in previous research in Utah (24). The following study
sites were selected for analysis:
1. University Parkway (SR-265), Mile Point 1.21 to 1.96;2.
Alpine Highway (SR-74), Mile Point 2.40 to 4.29;3. 400/500 South
(SR-186), Mile Point 5.48 to 7.53;4. St. George Boulevard (SR-34),
Mile Point 0.00 to 1.74; and5. SR-36, Mile Point 59.29 to
60.82.
Listed mile points are current mile points at the time of this
study. More detail on the study sites is available in the
literature (25).
data collection
Raw crash statistics were provided by the Utah Department of
Trans-portation (DOT) Traffic and Safety Division from the Utah DOT
crash database. The database contains records and statistics
obtained from police reports for crashes that occurred on Utah
roadways. At the time of this study, consistent data were available
from 1998 to 2008.AADT data are used to measure total volume of
vehicle traffic of a
highway or road. Previous research has determined that a
relationship exists between crashes and AADT. Although the exact
relationship is still not entirely known, it is known that the
relationship is gener-ally nonlinear (9). However, AADT is still an
important parameter in predicting crash frequency and was used as a
covariant in the development of the model.Locations of crashes are
reported as the mile point at which the
crash occurred on the corresponding roadway. However, mile
points on Utah highways have undergone several changes over the
past 10 years. Shifts in mileposts are usually the result of either
a realign-ment of the roadway or an extension added on to either
end of the roadway. Although the segments of each roadway of
interest were held constant through each analysis year,
corresponding mile points have changed over the course of the study
period. To ensure that data for the correct segment was used for
each analysis year, correct mileposts were verified through the
Utah DOT.
An overall analysis on frequency of all crashes and a severe
crash analysis on frequency of severe crashes were performed for
the raised median study sites. Crash severity refers to the
severity correspond-ing to the most severe of injuries sustained as
a result of a crash. According to the National Safety Council,
There are five mutually exclusive categories of injury severity for
classification of road vehicle (crashes) (26). The five categories
are fatal, incapacitating injury, nonincapacitating evident injury,
possible injury, and non-injury. A common abbreviation for these
severity levels is the KABCO scale, with each letter representing
fatal through noninjury levels of severity, respectively. The five
severity classifications are mutually exclusive because a crash is
classified according to the most severe injury (e.g., a crash with
a fatality and a minor injury is classified as a fatal crash, not a
fatal crash and a minor injury crash). In this study, severe
crashes were determined to be crashes indicated on the report as
fatal (K) or incapacitating injury (A).
analySiS reSultS
individual Site analysis results
A hierarchical Bayesian analysis was performed at selected study
sites at which raised medians have been installed. An analysis was
performed on overall crash frequency and severe crash frequency for
each segment. The results of the hierarchical Bayesian model before
and after the raised median installation were used to calculate a
percent change in crash frequency. In addition to the percent
change, the probability that the crash frequency (overall or
severe) decreased was calculated. The probability of reduction
helps to identify the statistical significance of the change.The
analysis of the individual study sites at which raised medians
have been installed showed three of the five study sites
experienced a statistically significant (greater than 95%
probability) reduction (26% to 43%) in the overall crash frequency.
The probability of difference for the remaining two sites (SR-265
and SR-74) was too low to confidently determine whether a reduction
or increase occurred (although the results for SR-74 were
practically significant at a 93% probability of decrease). In these
situations the mean is increasing, but not at a statistically
significant rate. Table 1 provides a summary of the impact of
raised medians on all crashes.Similar to the overall crash
analysis, several of the study sites
also showed a reduction in the frequency of severe crashes.
Table 2 provides a summary of the impact of raised medians on
severe crashes. The results indicate that three of the five study
sites experienced a significant (greater than 95% probability)
reduction (60% to 67%) in the frequency of severe crashes along the
segment after raised medians were installed. The analysis indicated
an increase (55%) may have occurred at one of the remaining sites
(SR-74); however, the probability of a difference was too low to
confidently determine if a reduction or increase occurred. The
final site (SR-36) showed a 90% probability (practically
significant) that a decrease of 43% occurred. More detailed
analysis results for both overall and severe crash frequencies are
provided in the literature (25).
results of combined Site analysis
The safety impacts of all study sites chosen for analysis
combined are discussed in this section. Two types of plots are
produced for each analysis performed. The first plot is a plot of
the actual data.
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100 Transportation Research Record 2223
The data plot displays the actual data points and the mean of
the posterior predictive distribution, which is a representation of
the mean regression line through the points from a Bayesian
perspective. The reduction is calculated by taking the mean of the
posterior distribution of differences between the two intercepts.
The mathematical details are discussed in the literature (19, 20),
but are conceptually equivalent to taking the after curve and
dividing it by the before curve to obtain the percent reduction.The
second plot produced for the overall analysis results is the
plot of the distribution of the differences between the before
and after periods. The difference plots display the posterior
distributions of differences between the before and after
intercepts of the model. Negative values indicate that the after
time period saw a reduction in crashes. Because the exact form of
the posterior distributions is unknown, the model uses simulated
draws from the posterior with the Markov chain; because those draws
represent the actual poste-rior distribution, the proportion of the
draws less than zero repre-sents the probability that there was a
reduction in crashes from the before time period to the after time
period.Figure 1 displays the overall crash frequency for the before
and
after periods as a function of AADT. The overall analysis
results indicate a 39% reduction in overall crash frequency after
the raised medians were installed. Figure 2 shows the corresponding
probability distribution of the differences between the before and
after periods for overall crashes. The entire distribution of
differences in Figure 2 is less than zero, indicating a 100%
probability that a reduction in overall crash frequency occurred
after raised medians were installed.The analysis results of severe
crashes display an even greater
reduction. Figure 3 displays the results for all study sites at
which raised medians were installed. The severe crash analysis
results on all study sites show a 44% reduction in severe crash
frequency after raised median installation. Figure 4 shows the
corresponding prob-ability distribution of the differences between
the before and after periods for severe crashes. As with the
overall analysis, the entire distribution of differences shown in
Figure 4 is less than zero, indi-
cating a 100% probability that a reduction in severe crash
frequency occurred after raised medians were installed at the study
sites.
concluSionS
The analysis in this report was performed with a hierarchical
Bayesian model developed to analyze the effectiveness of various
treatments for improving roadway safety. The model is a valuable
tool with various applications to transportation safety. As part of
this research, the model was applied to study sites at which raised
medians had been installed throughout the state of Utah. This study
analyzed the effectiveness of raised medians on roadway safety by
determin-ing the effect each newly installed median has had on
frequency of overall crashes and of severe crashes at the study
sites. An analysis was performed on individual sites at which
raised medians have been installed as well as an overall analysis
on all study sites grouped together.The results of the raised
median analysis indicated a significant
improvement in both crash frequency and frequency of severe
crashes along corridors where raised medians were installed.
Results from all study sites combined show that the overall crash
frequency was reduced by 39% and the frequency of severe crashes
was reduced by 44% after the installation of raised medians along
the study sites. The reduction in frequency of severe crashes is
anticipated to be a result in the change in types of collisions.
This study provides fur-ther and more statistically significant
evidence that installing raised medians is an effective technique
to reduce crash frequency, especially severe crashes caused by
sideswipes or head-on collisions.The model developed for this
research can be expanded to
determine the impact of other safety measures on various crash
types. Additionally, AADT was the only covariate used in this
study. The model has been developed such that additional covariates
may be included in the analysis. Selection of the appropriate
covariates to be used depends on the scope of the study being
performed. Finally,
TABLE 1 Summary for All Crashes
State Year of Probability of Percent Study Site Route County
Installation Reduction (%) Change
University Parkway 265 Utah 2002 38 3Alpine Highway 74 Utah 2002
93 -19400/500 South 186 Salt Lake 2001 100 -29St. George Boulevard
34 Washington 2006 100 -26SR-36 36 Tooele 2005 100 -43
TABLE 2 Summary of Severe Crashes
State Year of Probability of Percent Study Site Route County
Installation Reduction (%) Change
University Parkway 265 Utah 2002 100 -60Alpine Highway 74 Utah
2002 41 55400/500 South 186 Salt Lake 2001 100 -67St. George
Boulevard 34 Washington 2006 99 -61SR-36 36 Tooele 2005 90 -49
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Schultz, Thurgood, Olsen, and Reese 101
30,000 AADT
10,000 20,000 40,000 50,000
100
Cras
hes
per M
ile p
er Y
ear
0 50
15
0 20
0
FIGURE 1 Crash frequency for all raised median study sites.
FIGURE 2 Distribution of differences for crashes on all raised
median study sites.
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102 Transportation Research Record 2223
30,000 AADT
10,000 20,000 40,000 50,000
10
Seve
re C
rash
es p
er M
ile p
er Y
ear
0 5
15
FIGURE 3 Severe crash frequency for all raised median study
sites.
FIGURE 4 Distribution of differences of severe crashes for all
raised median study sites.
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Schultz, Thurgood, Olsen, and Reese 103
one of the important elements of transportation safety planning
is identifying locations that experience an unusually high crash
fre-quency. The model outlined in this report can be used to
identify outlier sites for various types of crashes. The raised
median analysis revealed several outlier sites that experienced an
unusually high crash frequency in either overall or severe crashes.
Further exploration can be performed to identify any factors that
contribute to the unusually high crash frequency that can be
mitigated.
acknowledgMentS
This research was made possible with funding from the Utah DOT
and Brigham Young University. Special thanks to Robert Hull, W.
Scott Jones, Tim Taylor, David Stevens, Mitsuru Saito, Steven
Dudley, and others at the Utah DOT and the university who played
key roles as members of the technical advisory committee and
provided input to the research.
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The contents of this paper reflect the views of the authors, who
are responsible for the facts and accuracy of the information, and
are not necessarily representative of the sponsoring agency.
The Access Management Committee peer-reviewed this paper.