Institute of Transportation Studies
UC Berkeley Traffic Safety Center
( University of California, Berkeley)
Year 2005 Paper UCB - TSC - RR - 2005 - TRB3
The Continuing Debate about Safety in
Numbers— Data From Oakland, CA
Judy Geyer Noah Raford
Traffic Safety Center Traffic Safety Center
David Ragland Trinh Pham
Traffic Safety Center Department of Statistics
This paper is posted at the eScholarship Repository, University of California.
http:// repositories. cdlib. org/ its/ tsc/ UCB- TSC- RR- 2005- TRB3
Copyright  c 2005 by the authors.
The Continuing Debate about Safety in
Numbers— Data From Oakland, CA
Abstract
The primary objective of this paper is to review the appropriate use of ratio
variables in the study of pedestrian injury exposure. We provide a discussion
that rejects the assumption that the relationship between a random variable
( e. g., a population X) and a ratio ( e. g., injury or disease per population Y/ X)
is necessarily negative. In the study of pedestrian risk, the null hypothesis is
that pedestrian injury risk is constant with respect to pedestrian volume. This
study employs a unique data set containing the number of pedestrian collisions,
average annual pedestrian volume, average annual vehicle volume, and physical
intersection characteristics for 247 intersections in Oakland, California. We use
a GLM to estimate the expected injury risk given average annual pedestrian
volume and other explanatory variables. Consistent with studies by Leden,
Ekman and Jacobsen, the null hypothesis is rejected. Indeed, the risk of collision
for pedestrians decreases with increasing pedestrian flows, and it increases with
increasing vehicle flows. We also find that pedestrians are more likely to be
struck by motorists in commercial and mixed areas than in residential areas.
Geyer, Ragland 1
TRB Paper # 06- 2616
Title: The Continuing Debate about Safety in Numbers— Data From Oakland, CA
Submission Date: November 15, 2005
Word Count: 3,672
Number of Figures and Tables: 8
Authors:
Judy Geyer
Traffic Safety Center
University of California, Berkeley
140 Warren Hall # 7360
Berkeley, CA 94709
510- 643- 5659
jgeyer@ berkeley. edu
Noah Raford
Traffic Safety Center
University of California, Berkeley
140 Warren Hall # 7360
Berkeley, CA 94709
510- 643- 5659
noahraford@ gmail. com
David Ragland ( corresponding author)
Traffic Safety Center
University of California, Berkeley
140 Warren Hall # 7360
Berkeley, CA 94709
510- 642- 0655
davidr@ berkeley. edu
Trinh Pham
Department of Statistics
University of California, Berkeley
tpham@ stat. berkeley. edu
TRB 2006 Annual Meeting CD- ROM Paper revised from original submittal.
Geyer, Ragland 2
Abstract:
The primary objective of this paper is to review the appropriate use of ratio variables in the study
of pedestrian injury exposure. We provide a discussion that rejects the assumption that the
relationship between a random variable ( e. g., a population X) and a ratio ( e. g., injury or disease
per population Y/ X) is necessarily negative. In the study of pedestrian risk, the null hypothesis is
that pedestrian injury risk is constant with respect to pedestrian volume. This study employs a
unique data set containing the number of pedestrian collisions, average annual pedestrian
volume, average annual vehicle volume, and physical intersection characteristics for 247
intersections in Oakland, California. We use a GLM to estimate the expected injury risk given
average annual pedestrian volume and other explanatory variables. Consistent with studies by
Leden, Ekman and Jacobsen, the null hypothesis is rejected. Indeed, the risk of collision for
pedestrians decreases with increasing pedestrian flows, and it increases with increasing vehicle
flows. We also find that pedestrians are more likely to be struck by motorists in commercial and
mixed areas than in residential areas.
TRB 2006 Annual Meeting CD- ROM Paper revised from original submittal.
Geyer, Ragland 3
INTRODUCTION
In the urban planning and traffic safety research communities, there is an ongoing debate about
whether a higher number of pedestrians correlates with lower risk of motor vehicle injury for
pedestrians. Several researchers have found that areas with higher numbers of pedestrian exhibit
lower pedestrian injury rates per pedestrian than areas with fewer pedestrians ( 1, 2). However,
others are concerned that correlating collision rate ( C/ P) with pedestrian volume ( P), ( where C
equals collisions and P equals pedestrian volume) will almost always yield a decreasing
relationship due to the intrinsic relationship of the variable P and the fraction 1/ P. This paper
considers both sides of this debate and offers a model of pedestrian injury at roadway
intersections in Oakland, California, in relation to both pedestrian volume and physical
intersection characteristics.
Until recently, relatively little research has been conducted that looks at pedestrian-vehicle
collisions in relation to pedestrian exposure ( i. e, collisions per unit of pedestrian
volume). This is because pedestrian volume data are necessary to calculate pedestrian risk, and
since such data are not commonly collected by municipalities, pedestrian volume is difficult to
measure ( 3). Having data on pedestrian volumes allows investigation into the impact of
pedestrian volumes on risk; that is, if a higher pedestrian volume effects risk per pedestrian.
Several recent studies have attempted to integrate pedestrian volumes into the risk- analysis
process. Jacobsen analyzed ecological data from five studies in European cities and found that
pedestrian risk, defined as the number of injuries per pedestrian km- traveled, decreased as a
function of pedestrian km- traveled ( 2). Leden reported similar results in a detailed study of
Hamilton, Ontario ( 1), but focused his research to the question of the effects of turning vehicles.
Modeling risk per pedestrian as a function of pedestrian volume is problematic in that
pedestrian volume appears on both sides of the equation. In a critique of this type of modeling,
Brindle published a paper showing that if variables C, P, and A are randomly generated, C/ P and
P/ A produce a " spurious" association ( 4). In the case of pedestrians and intersections, let:
C = number of injuries
P = number of pedestrians or pedestrian km- traveled
A = a single intersection = 1 ( i. e., because each intersection is a single unit)
Then, the correlation ratio between C/ P and P/ A will almost always be negative ( 5).
When expanding this analysis to multiple intersections, there is cause for concern when
randomly generating values for C and P, and then studying the relationship between P and C/ P.
The number of pedestrians varies by intersection ( A). This means that pedestrians in different
intersections have, in effect, been assigned a different probability of being injured. In
intersections with more pedestrians, randomly distributing injuries by intersections means that
these pedestrians are assigned a lower probability of being injured. Conversely, in intersections
with fewer pedestrians, randomly distributing injuries by intersection means that, in effect, these
pedestrians actually are assigned a higher probability of being injured. In other words, the
randomization exercise suggested by Brindle is producing a real association assumed implicitly
in the context of the " stratified" randomization.
Several statisticians have debated this use of ratio variables ( 5, 6). Ratio variables are
used in almost all types of scientific inquiry, from disease rates to crime rates. In many of these
areas, the concern that C/ P and P/ A will almost always be negative ignores the fact that often C
and P are related. Suppose, for example, that one measures an outcome for pedestrians ( P)
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Geyer, Ragland 4
traversing a crosswalk. Let C be the number of pedestrians who were involved in a motor
vehicle collision while traversing a specific crosswalk , and let N be the number of pedestrians
who traversed the crosswalk without incident ( 6). Clearly,
P = C + N
In this example, C/ P and N/ P are both ratios of random variables, but it is false to say that both
are inversely related to P. One consequence of the equation P = C + N is that as one of the
correlations between P and C/ P or N/ P decreases, the other must increase. Indeed, we repeated
the Brindle randomization study but weighted the random number generator for injuries by the
proportion of pedestrians in each intersection. The plot of C/ P by P is then a straight line.
Based on this discussion, the null hypothesis for testing the association between
pedestrian injury risk and pedestrian volume is that each pedestrian has an equal chance of being
in a collision at an intersection, regardless of the pedestrian volume at the time of specific
crossing. If each pedestrian has the same chance of an injury, then the observed relationship
between C/ P and P would be a straight line. We test this hypothesis on data gathered from 247
intersections in Oakland, California, controlling for various intersection variables such as traffic
control devices, lane width, number of lanes, and other intersection fixtures.
ANALYSIS
Data
All research was conducted in Oakland, California, which is located directly across the San
Francisco bay from the city of San Francisco. Oakland has an economically and racially diverse
population of about 400,000 people. Pedestrian volume data were generated for Oakland using
the pedestrian modeling process known as space syntax ( 7). This method combined Census
2000 population and employment densities with a network analysis of pedestrian routes in order
to develop annual pedestrian volume estimates for each of the city’s 670 individual intersections.
First, annual pedestrian trips were estimated using density data and observed movement samples.
These were then distributed for every street in the city using space syntax route choice
algorithms. Estimated average annual pedestrian volume for the intersections ranged from
76,896 to over 3,058,752 pedestrians per year. The output of the model demonstrated a strong
correlation between predicted and observed volume counts at a sample of 42 intersections
throughout the city ( r- squared = 0.7717, p < 0.001). The model was compared with 92 different
observed counts at 42 different locations, which makes r- squared of 0.7717 a relatively robust
finding. Figure 1 displays the distribution of average annual pedestrian volumes in Oakland by
intersection.
People choose routes based on aesthetics, noise, traffic volume and public transit. Space
syntax route choice algorithms can include these criteria via multiple regression analysis.
However, these specific variables were not included in the original Oakland study. That study
found that route directness, residential and employment density were found to account for the
0.77 correlation. Additional factors such as those mentioned would likely increase this
correlation. The original article on space syntax ( 7) noted that the model under- predicted
volumes at several locations, most notably those which were by parks or other quiet,
aesthetically pleasing areas. It also over- predicted some routes which were one high volume,
noisy vehicular streets. This confirms that those variables mentioned are important aspects of
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Geyer, Ragland 5
route choice, and these limitations were suggested as areas of future research. Numerous
projects including these variables have been completed since the first publication of space syntax
route choice algorithms.
Vehicle volumes were then procured for 455 street segments and intersections from the
City of Oakland. The data were originally gathered by the City for on- going traffic studies and
comprised observations over a period of three years, between January 1, 2000 and December
31st, 2002. This data set is based upon a sample of major arterials, secondary, and local streets.
Counts were conducted using a combination of automatic vehicle counters and radar speed guns.
Roadway geometrics, adjacent land use, street type, number of lanes, street width, signal
presence and type, and average daily traffic were all recorded and converted to Geographic
Information Systems ( GIS) for analysis with the Crossroads Accident Analysis Software Suite.
Average vehicular traffic ranged from 11,392 vehicles per year to over 19,282,384 per year.
Figure 2 displays the distribution of average annual vehicle volumes by intersection.
Annual pedestrian- vehicle collision data were gathered from the Statewide Integrated
Traffic Reporting System ( SWITRS), a database of reported motor vehicle collisions that is
created and maintained by the California Highway Patrol ( CHP). Three years of pedestrian-vehicle
collision data on 247 intersections identified 185 incidents. Mid- block collisions were
linked to the nearest intersection. Only 6 out of 247 intersections were cases of mid- block linked
to the nearest intersection. Average annual collisions by intersection ranged from 0 to 5.
The actual average annual collisions might be slightly underestimated, since SWITRS database
does not include crashes involving pedestrians that are never reported.
In 2005 the following aspects of the 247 study intersections were recorded:
Number of lanes on the primary street [ natural number]
Number of lanes on the secondary street [ natural number]
Traffic signal present [ Boolean]
Two- way stop sign [ Boolean]
Four- way stop sign [ Boolean]
Other traffic control [ Boolean]
Marked crosswalks [ natural number]
Unmarked crosswalks [ natural number]
Median present on either primary or secondary street [ Boolean]
Median present on both primary and secondary streets [ Boolean]
Bike Lane present on either street [ Boolean]
Residential area [ Boolean]
Commercial area [ Boolean]
Mixed- use area [ Boolean]
Methodology
The first step was to accurately model the number of pedestrian collisions as a function of
pedestrian volume and control variables, including vehicle volume and intersection attributes.
Next, we used the results from our regression model to test the hypothesis, that the pedestrian-collision
rate remains constant as pedestrian volume increases.
To model the data, we assumed that the number of collisions has a Poisson distribution.
In the data, the variance was larger than the mean, which lead us to use the quasipoisson model
in R, a statistical software package, to account for over- dispersion in Poisson Generalized Linear
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Geyer, Ragland 6
Models. The quasipoisson model accounts for over- dispersion and also estimates the dispersion
parameter. A GLM was used because it extends linear models to accommodate both non- normal
response distributions and transformations to linearity. Moreover, GLMs allow a unified
treatment of statistical methodology for several important classes of models, which also include
the Poisson model ( 8).
For a Poisson distribution, we have:
T !
g( E( Ci )) = Xi
where i C ~ Pois( i " ), is the number of collisions at a given intersection i , T
Xi is the transpose of
the design matrix that contains the independent variables, and ! is the vector of unknown
parameters. The function below is the natural link function:
g( x) = log x
So we now have:
T !
log( E( Ci )) = Xi
and hence, the Poisson regression model is as follow:
T !
xi
E( Ci ) = e
Note: log( e) is an example of a GLM link function.
Since we observed that var( Ci ) > E( Ci ) for all intersections i , we must use the quasipoisson
model in R to account for over- dispersion in Poisson GLMs.
We performed backward elimination on the initial model with ten predictors at 247
intersections: annual vehicle volume, annual pedestrian volume, number of lanes on the primary
street, number of lanes on the secondary street, a categorical variable to capture the geometry of
the intersection ( signalized or zero- way stop to 4 way- stop), number of marked cross- walk,
number of unmarked cross- walk, a dummy variable to indicate whether the intersection has a
median or not, a dummy variable for bike- lane, and a categorical variable for neighborhood type
( residential, commercial, or mixed). Predictors with p- values higher than the test level of .05
were eliminated from the model.
One might consider whether backward elimination is an appropriate procedure for the
selection of our final model. Both forward and backward selections have their own drawbacks.
In forward selection, each addition of a new variable may render one or more of the already
included variables non- significant. In backward selection, sometimes variables are dropped that
would be significant when added to the final reduced models. Stepwise selection is a
compromise between forward and backward selection methods. It allows for moves in either
direction, dropping or adding variables at the various steps. Stepwise selection was not an option
with the regression here using quasipoisson GLM, because in quasi models, there is no
likelihood, and hence no Akaike Information Criterion ( AIC) statistics ( 8). The first check we
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Geyer, Ragland 7
made to confirm the appropriateness of using backward selection to select our final model was
by running both backward and forward selections. Both directions resulted in the same model
for our case. This means that stepwise selection will also result in the same model. There is no
guarantee that both backward and forward selections will always yield the same results,
however. The second check was by using stepwise selection in the Poisson GLM, since a
Poisson distribution was reasonable because the dispersion parameter was not greatly different
from 1, where 1 indicates that there is no over- dispersion in the data. The final model using
stepwise selection in the Poisson GLM resulted in the same predictors. The two checks that we
performed support the appropriateness of using backward elimination.
We hypothesized that the predictors mentioned above are significant variables that
belong in our model. For example, the number of lanes on the primary street would be highly
correlated with the number of collisions at an intersection since wider streets increase a
pedestrian’s exposure to vehicular traffic. Also, additional lanes are indications of heavier
traffic, which might make a pedestrian less visible and a driver feel less accountable for yielding
to a pedestrian. The categorical variable to capture the geometry of the intersection is another
relevant variable. Besides capturing the geometry of the intersection, it also measures the safety
of the intersections. For example, intersections with a signal or an increase in the number of
stops are thought to be safer; hence we would expect there would be fewer collisions in those
intersections.
RESULTS
Contrary to our beliefs, some of the variables that we believed to be relevant dropped out of the
final model. The variables that dropped out of the regression during the process of backward
elimination are number of lanes on the primary street, number of lanes on the secondary street, a
categorical variable to capture the geometry of the intersection, number of marked cross- walks,
number of unmarked cross- walks, presence of a median, and presence of a bike- lane. It was a
surprising result that the number of lanes on both the primary and secondary streets dropped out
of the final model. A possible explanation for this result is that the variable number of lanes is
highly correlated to the neighborhood type.
Three statistically significant variables remained in the model. These three variables are
annual pedestrian volume, annual vehicle volume, and neighborhood type ( residential,
commercial, or mixed- used areas). The dispersion parameter of collisions, as a quasipoisson
random variable, is 1.169. This is not greatly different from 1, where 1 indicates that there exists
no over- dispersion. Hence, a Poisson distribution is sufficiently reasonable to describe the
distribution of collisions. Moreover, when the results from the quasipoisson regression are
compared with the results from the Poisson regression, the parameter estimates are precisely the
same; the standard errors corresponding to the estimates are slightly different, but the difference
is not significant. Tables 1 and 2 provide the parameter estimates, standard errors, t- values or z-values,
and p- values for the quasipoisson model and Poisson model, respectively.
We also looked at Cook’s distance plot, which showed three potential influential
observations that might require further investigation. In R, there is a function called robust linear
model ( rlm), which fits a linear model by robust regression. The original model was run using
this function to determine whether the potential influential points actually had a great impact on
our results. If the estimates and their corresponding statistics were not significantly different,
then we could conclude that those observations were not influential enough to change our
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Geyer, Ragland 8
estimates. Since this was the case, the three significant variables in the original model were
retained in the model.
In the categorical variable for neighborhood type, the category ‘ residential area’ was
omitted. The estimates for the categories ‘ commercial area’ and ‘ mixed area’ were positive,
which indicated that there were more collisions in these areas. The interpretation of the
estimates in GLMs for quasipoisson models is slightly different than in ordinary linear models.
The value of 0.4977 for commercial areas means that the number of collisions will be higher by
e^ 0.4977 in commercial area where all other variables are held constant. The interpretation for
all of the other predictors is similar to the one just described.
The estimates for annual pedestrian volume and annual vehicle volume were very close
to zero, indicating that for each additional pedestrian or car on the street, the number of
pedestrian- vehicle collisions increases only slightly. If the number of pedestrians is increased by
100,000 pedestrians at a particular intersection in a given year, the number of collisions will
increase by only 1.06 where all other variables are held constant. Figure 3 plots the number of
pedestrians against the number of collisions. It shows that the rate of the number of collisions
increases, but very slowly and the increase is not consistent over each interval of pedestrian
volume. In other words, this curve lies deeply below the line of x = y on this graph. In fact, the
collision rate per pedestrian decreases as the number of pedestrians increases. Figure 4 plots the
number of pedestrians against the rate of collisions over pedestrians using the fitted values from
our regression model as estimates for the true number of collisions. However, the rate of
collisions per pedestrian increases as the number of vehicles increases. Figure 5 plots the
number of vehicles against the rate of collisions per pedestrian.
The earlier argument in the introduction that collisions ( C) and pedestrian volume ( P) are
related implies that the negative relationship between C/ P and P is not spurious. As stated
earlier, if P = C + N where N is the number of pedestrians who traversed the crosswalk without
incident, then the ratios C/ P and N/ P cannot both decrease as P increases.
Figure 6 plots the number of pedestrians against the rate N/ P, where N is the difference
between the average annual pedestrians and the average annual collisions from our data set. The
reason why there are many points at N/ P = 1 is because we have many intersections where the
number of collisions is zero. Therefore, the lowess smooth line that summarizes the trend of the
rate N/ P as a function of P is pulled up in the first 1,000,000 pedestrians range. If we ignore the
intersections with no incidents, then the plot clearly shows that N/ P increases as the number of
pedestrians increases. This implies that the rate of C/ P and P has a negative relationship is a
valid result.
DISCUSSION
Our results suggest that the risk for pedestrian- vehicle collisions ( where risk is calculated as
collisions per pedestrian) is smaller in areas with greater pedestrian flows and greater in areas
with higher vehicle flows. These results from 247 Oakland intersections are consistent with
previous studies in Europe, Canada, and other California cities ( 1,2).
These findings may have important implications for pedestrian safety planning and
transportation policy. Policy makers and traffic engineers are often reluctant to make
modifications to the roadway network that will increase pedestrian traffic for fear that the change
might increase the total number of pedestrian injuries per year. This research suggests that the
risk of collision for individual pedestrians is significantly lower in areas with higher pedestrian
TRB 2006 Annual Meeting CD- ROM Paper revised from original submittal.
Geyer, Ragland 9
volume. The estimated rate of total collisions grows slowly as well. This finding, combined
with the finding that risk for pedestrian- vehicle collisions is higher in areas with more vehicles,
suggests that these fears may be unwarranted. Indeed this research suggests that the opposite
may be true, and that the more pedestrians on the street, the safer for everyone.
Posted speed limits are an important variable that we have not incorporated in our model
selection and analysis as these data were not available. Injury severity is not studied here, which
would be effected by speed limits. Slower vehicle speeds would be expected to contribute to
pedestrian safety since pedestrians would have more time to detect and avoid motor vehicles. If
this implication were valid, we would conclude that injuries per pedestrian volume can be
explained both by pedestrian volume and by vehicle speed.
In future work, this research team aspires to create a generalized model for the risk of
pedestrian- vehicle collisions. Such a model would include significant variables from the current
model as well as other relevant variables as our research continues. A question of interest is
whether it is more important to reduce the rate of collisions ( i. e., collisions per pedestrian) or to
reduce the number of collisions overall. Also, how might the increase in the number of
pedestrians affect traffic? If in response, vehicle traffic is slowed, then the average motorist trip
time might increase. We might want to develop a way to quantify the costs and benefits of such
changes to analyze this trade- off between reduced risk for pedestrians, and increase in vehicle
traffic and average motorist trip time.
ACKNOWLEDGEMENTS
The authors would like to thank Rasha Aweiss, who helped us in the process of collecting data.
We would also like to thank Jamie Hollander and Frances Tong, who are graduate students from
the department of statistics at University of California, Berkeley, for their contribution.
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Geyer, Ragland 10
REFERENCES
1. Leden, L. Pedestrian risk decrease with pedestrian flow. A case study based on data
from signalized intersections in Hamilton, Ontario. Accident Analysis and Prevention,
Volume 34, pp. 457- 464. 2002.
2. Jacobsen, PL. Safety in numbers: more walkers and bicyclists, safer walking and
bicycling. Injury Prevention, Volume 9, pp. 205- 209. 2003.
3. NHTSA/ FHWA Pedestrian and Bicycle Strategic Planning Research Workshops, Final
Report, April, 2000.
4. Brindle, R. Lies, damn lies, and “ automobile dependence”- some hyperbolic reflections.
Australasian Transport Research Forum, Vol. 19, pp 117- 131. 1994.
5. Schuessler, K. F. Analysis of ratio variables: Opportunities and pitfalls. American
Journal of Sociology, 1974. 80: 379- 396.
6. Long, Susan B. The Continuing Debate over the Use of Ratio Variables: Facts and
Fiction. Sociological Methodology, Vol. 11, 37- 67. 1980.
7. Raford, N. and Ragland, D. Space Syntax: An innovative pedestrian volume modeling
tool for pedestrian safety. Annual Meeting of the Transportation Review Board, 2003.
8. Venables, W. N. and Ripley, B. D. Statistics and Computing: Modern Applied Statistics
with S. Fourth Edition. 2002 Springer- Verlag New York, Inc.
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Geyer, Ragland 11
TABLES AND FIGURES
Table 1.
Model: Collision e # + ! 1 ( Vehicle)+ ! 2 ( Pedestrian)+ ! 3 ( Neighborhood ) = ,
where neighborhood is a categorical variable with 0 = residential, 1 = commercial, 2 = mixed
Family = quasipoisson
Variable Estimate Std. Error t- value p- value
Intercept - 1.712 2.694e- 01 - 6.354 1.03e- 09
Vehicle 6.027e- 08 2.424e- 08 2.487 0.0136
Pedestrian 5.942e- 07 1.267e- 07 4.692 4.54e- 06
Neighborhood1 4.977e- 01 2.349e- 01 2.119 0.0351
Neighborhood2 4.933e- 01 2.020e- 01 2.443 0.0153
Table 2.
Model: Collision e # + ! 1 ( Vehicle)+ ! 2 ( Pedestrian)+ ! 3 ( Neighborhood ) =
where neighborhood is a categorical variable with 0 = residential, 1 = commercial, 2 = mixed
Family = Poisson
Variable Estimate Std. Error z- value p- value
Intercept - 1.712 2.491e- 01 - 6.872 6.35e- 12
Vehicle 6.027e- 08 2.241e- 08 2.689 0.00717
Pedestrian 5.942e- 07 1.171e- 07 5.073 3.91e- 07
Neighborhood1 4.977e- 01 2.172e- 01 2.291 0.02196
Neighborhood2 4.933e- 01 1.868e- 01 2.641 0.00826
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Geyer, Ragland 12
Figure 1. Estimated Annual Pedestrian Volumes at Intersections Vary by Different Colors
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Geyer, Ragland 13
Figure 2. Vehicle Volume Counts at Intersections Vary by the Size of the Circles
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Figure 3. Average Annual Pedestrians by Number of Collisions at 247 intersections in
Oakland, California ( 01/ 01/ 2000 to 12/ 31/ 2002)
0 500000 1500000 2500000
2 4 6 8 10
Number of Pedestrians vs. Number of Collisions
Pedestrians
Collisions
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Geyer, Ragland 15
Figure 4. Rate of pedestrian- vehicle collisions per pedestrian by average annual number of
pedestrians at 247 intersections in Oakland, California ( 01/ 01/ 2000 to 12/ 31/ 2002)
0 500000 1500000 2500000
5.0 e- 06 1.0 e- 05 1.5 e- 05
Number of Pedestrians vs. Rate of Collisions/ Pedestrians
Pedestrians
Collisions/ Pedestrians
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Geyer, Ragland 16
Figure 5. Rate of pedestrian- vehicle collisions per pedestrian by average annual number of
vehicles at 247 intersections in Oakland, California ( 01/ 01/ 2000 to 12/ 31/ 2002)
0.0 e+ 00 5.0 e+ 06 1.0 e+ 07 1.5 e+ 07 2.0 e+ 07
5.0 e- 06 1.0 e- 05 1.5 e- 05
Number of Vehicles vs. Rate of Collisions/ Pedestrians
Vehicles
Collisions/ Pedestrians
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Figure 6. Rate of non- collisions ( N= P- C) per pedestrian by average annual number of
pedestrians at 247 intersections in Oakland, California ( 01/ 01/ 2000 to 12/ 31/ 2002)
0 500000 1500000 2500000
0.999990 0.999994 0.999998
Number of Pedestrians vs. Rate of Non- Collisions/ Pedestrians
Pedestrians
Non- Collisions/ Pedestrians
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