Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

Safety Effectiveness of the HAWK

Pedestrian Crossing Treatment

Publication No. FHWA-HRT-10-042 July 2010
FOREWORD

The Federal Highway Administration (FHWA) Pedestrian and Bicycle Safety Research 

Program’s overall goal is to increase pedestrian and bicycle safety and mobility. From better and 

safer crosswalks, sidewalks, and pedestrian technologies to growing educational and safety 

programs, the program strives to make it safer and easier for pedestrians, bicyclists, and drivers 

to share roadways in the future.

This study was part of a larger FHWA study to quantify the effectiveness of engineering 

countermeasures in improving safety and operations for pedestrians and bicyclists. The project 

focused on existing and new engineering countermeasures for pedestrians and bicyclists that 

have not yet been comprehensively evaluated in terms of effectiveness. This effort involved data 

collection and analysis to determine whether these countermeasures reduced fatalities and 

injuries or increased appropriate driving behaviors. In this study, the safety effectiveness of 

the High intensity Activated crossWalK (HAWK) pedestrian beacon was evaluated using a

before-after empirical Bayes (EB) approach.

This report will interest engineers, planners, and other practitioners who have an interest in 

implementing pedestrian and bicycle treatments, as well as city, State, and local authorities who 

have a shared responsibility for public safety. 

Monique R. Evans

Director, Office of Safety

Research and Development

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation 

in the interest of information exchange. The U.S. Government assumes no liability for the use 

of the information contained in this document. This report does not constitute a standard, 

specification, or regulation.

The U.S. Government does not endorse products or manufacturers. Trademarks or 

manufacturers’ names appear in this report only because they are considered essential to the 

objective of the document.

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-quality information to serve

Government, industry, and the public in a manner that promotes public understanding. Standards 

and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its 

information. FHWA periodically reviews quality issues and adjusts its programs and processes to 

ensure continuous quality improvement.
TECHNICAL REPORT DOCUMENTATION PAGE 

 1. Report No. 

FHWA-HRT-10-042 

 2. Government Accession No. 3. Recipient’s Catalog No. 

 4. Title and Subtitle 

Safety Effectiveness of the HAWK Pedestrian Crossing Treatment 

 5. Report Date 

July 2010 

 6. Performing Organization Code 

 7. Author(s) 

Kay Fitzpatrick and Eun Sug Park 

 8. Performing Organization Report No. 

 9. Performing Organization Name and Address 

Texas Transportation Institute 

The Texas A&M University System 

College Station, TX 77843-3135 

10. Work Unit No. (TRAIS) 

11. Contract or Grant No. 

DTH61-01-C-00049 

Task Order #25 

12. Sponsoring Agency Name and Address 

Office of Safety Research and Development 

Federal Highway Administration 

6300 Georgetown Pike 

McLean, VA 22101-2296 

13. Type of Report and Period Covered 

Technical Report: 

October 2007–March 2010 

14. Sponsoring Agency Code 

15. Supplementary Notes 

The Contracting Officer’s Technical Representative (COTR) was Ann Do, HRDS-07. 

16. Abstract 

The High intensity Activated crossWalK (HAWK) is a pedestrian-activated beacon located on the roadside and on mast arms 

over major approaches to an intersection. It was created in Tucson, AZ, and at the time of this study, it was used at more than

60 locations throughout the city. The HAWK head consists of two red lenses over a single yellow lens. It displays a red 

indication to drivers when activated, which creates a gap for pedestrians to use to cross a major roadway. A before-after study

of the safety performance of the HAWK was conducted. The evaluations used an empirical Bayes (EB) method to compare the 

crash prediction for the after period if the treatment had not been applied to the observed crash frequency for the after period 

with the treatment installed. 

To develop the datasets used in this evaluation, crashes were counted if they occurred within the study period, typically 3 years 

before the HAWK installation and 3 years after the HAWK installation or up to the limit of the available crash data for the after 

period. Two crash datasets were created. The first dataset included intersecting street name (ISN) crashes, which were all 

crashes with the same intersecting street names that matched the intersections used in the study. The second dataset included 

intersection-related (IR) crashes, which were only those ISN crashes that had “yes” for the intersection-related code. The crash 

types that were examined included total, severe, and pedestrian crashes. From the evaluation that considered data for 21 HAWK 

sites (treatment sites) and 102 unsignalized intersections (reference group), the following changes in crashes were found after

the HAWK was installed: a 29 percent reduction in total crashes (statistically significant), a 15 percent reduction in severe 

crashes (not statistically significant), and a 69 percent reduction in pedestrian crashes (statistically significant). 

17. Key Words 

HAWK, Pedestrian treatment, Pedestrian crashes, Unsignalized 

intersection, Pedestrian hybrid beacon 

18. Distribution Statement 

No restrictions. This document is available to the public 

through NTIS: 

National Technical Information Service 

5301 Shawnee Road 

Alexandria, VA 22312 

http://www.ntis.gov/about/contact.aspx 

19. Security Classif.(of this report) 

Unclassified 

20. Security Classif.(of this page) 

Unclassified 

21. No. of Pages 

76 

22. Price 

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized 
ii

SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS

Symbol When You Know Multiply By To Find Symbol 

LENGTH

in inches 25.4 millimeters mm 

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA 

in2 square inches 645.2 square millimeters mm2

ft2 square feet 0.093 square meters m2

yd2 square yard 0.836 square meters m2

ac acres 0.405 hectares ha

mi2 square miles 2.59 square kilometers km2

VOLUME 

fl oz fluid ounces 29.57 milliliters mL 

gal gallons 3.785 liters L 

ft3 cubic feet 0.028 cubic meters m3 

yd3 cubic yards 0.765 cubic meters m3 

NOTE: volumes greater than 1000 L shall be shown in m3

MASS oz ounces 28.35 grams g

lb pounds 0.454 kilograms kg

T short tons (2000 lb) 0.907 megagrams (or "metric ton") Mg (or "t") 

TEMPERATURE (exact degrees) o

F Fahrenheit 5 (F-32)/9 Celsius oC 

or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux lx

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N 

lbf/in2 poundforce per square inch 6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH mm millimeters 0.039 inches in 

m meters 3.28 feet ft 

m meters 1.09 yards yd 

km kilometers 0.621 miles mi 

AREA mm2 square millimeters 0.0016 square inches in2 

m2 square meters 10.764 square feet ft2 

m2 square meters 1.195 square yards yd2 

ha hectares 2.47 acres ac

km2 square kilometers 0.386 square miles mi2 

VOLUME 

mL milliliters 0.034 fluid ounces fl oz 

L liters 0.264 gallons gal 

m3 cubic meters 35.314 cubic feet ft3 

m3 cubic meters 1.307 cubic yards yd3 

MASS 

g grams 0.035 ounces oz

kg kilograms 2.202 pounds lb

Mg (or "t") megagrams (or "metric ton") 1.103 short tons (2000 lb) T 

TEMPERATURE (exact degrees) o

C Celsius 1.8C+32 Fahrenheit oF 

ILLUMINATION 

lx lux 0.0929 foot-candles fc 

cd/m2 candela/m2 0.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS 

N newtons 0.225 poundforce lbf 

kPa kilopascals 0.145 poundforce per square inch lbf/in2

*SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380. 

(Revised March 2003)
iii

TABLE OF CONTENTS

CHAPTER 1. INTRODUCTION.................................................................................................1

BACKGROUND ......................................................................................................................1

STUDY APPROACH ..............................................................................................................4

2009 MUTCD ...........................................................................................................................4

CHAPTER 2. LITERATURE REVIEW.....................................................................................7

CHAPTER 3. DATA COLLECTION .........................................................................................9

SITE SELECTION AND GEOMETRIC DATA..................................................................9

Potential Reference Groups .................................................................................................9

Reference Group 1 ...............................................................................................................9

Reference Group 2 .............................................................................................................10

TRAFFIC COUNTS ..............................................................................................................11

STUDY PERIODS .................................................................................................................12

CRASH DATA .......................................................................................................................13

CHAPTER 4. OBSERVATIONS ...............................................................................................15

BEFORE-AFTER CRASH DATA.......................................................................................15

OTHER CRASH CHARACTERISTICS ............................................................................17

CHAPTER 5. BEFORE-AFTER EVALUATION....................................................................21

BEFORE-AFTER CRASH DATA.......................................................................................21

EB PROCEDURE..................................................................................................................22

SPF DEVELOPMENT..........................................................................................................24

Reference Group 1 Aggregate Data...................................................................................25

Reference Group 2 Aggregate Data...................................................................................29

Reference Group 2 Disaggregate Data ..............................................................................32

Comparison of SPFs ..........................................................................................................35

FINDINGS..............................................................................................................................36

CHAPTER 6. SUMMARY, CONCLUSION, AND DISCUSSION ........................................41

SUMMARY ............................................................................................................................41

CONCLUSION ......................................................................................................................41

DISCUSSION.........................................................................................................................42

APPENDIX: TABLES OF RESULTS.......................................................................................45

ACKNOWLEDGMENTS...........................................................................................................65

REFERENCES.............................................................................................................................67
iv

LIST OF FIGURES

Figure 1. Photo. Example of a HAWK head .................................................................................. 1

Figure 2. Photo. Example of a HAWK treatment in Tucson, AZ................................................... 2

Figure 3. Chart. Example of phase sequence for a HAWK............................................................ 3

Figure 4. Photo. R10-23 sign from the 2009 MUTCD................................................................... 5

Figure 5. Photo. Typical signs used at HAWK crossings in Tucson, AZ....................................... 5

Figure 6. Graph. Driver yielding..................................................................................................... 7

Figure 7. Graph. Distribution of manner of collision by control for ISN crashes........................ 20

Figure 8. Graph. Distribution of manner of collision by control for IR crashes........................... 20

Figure 9. Equation. Estimate of expected number of crashes during the before period............... 22

Figure 10. Equation. Weight......................................................................................................... 22

Figure 11. Equation. Estimated variance of expected number of crashes during the

before period ................................................................................................................................. 22

Figure 12. Equation. Adjustment factors...................................................................................... 22

Figure 13. Equation. Predicted crashes during the after period.................................................... 23

Figure 14. Equation. Estimated variance of predicted crashes during the after period ................ 23

Figure 15. Equation. Sum of predicted crashes ............................................................................ 23

Figure 16. Equation. Estimated variance of sum of predicted number of crashes........................ 23

Figure 17. Equation. Sum of observed crashes............................................................................. 23

Figure 18. Equation. Estimated index of effectiveness................................................................. 23

Figure 19. Equation. Percent change in number of crashes.......................................................... 23

Figure 20. Equation. Estimated variance of estimated index of effectiveness ............................. 24

Figure 21. Equation. Standard error of estimated index of effectiveness..................................... 24

Figure 22. Equation. General form for expected number of crashes............................................ 25
v

LIST OF TABLES

Table 1. Distribution of intersection characteristics for HAWKs and reference group 1............. 10

Table 2. Distribution of intersection characteristics for HAWKs and reference group 2............. 11

Table 3. After study period length ................................................................................................ 13

Table 4. Crash data for before-after study by groups ................................................................... 16

Table 5. Number and percent of crashes by manner of collision.................................................. 19

Table 6. Number of crashes in before and after periods............................................................... 21

Table 7. Estimate of regression coefficients of SPFs for ISN crashes using reference group 1... 27

Table 8. Estimate of regression coefficients of SPFs for IR crashes using reference group 1 ..... 28

Table 9. Estimate of regression coefficients of SPFs for ISN crashes using reference group 2... 30

Table 10. Estimate of regression coefficients of SPFs for IR crashes using reference group 2 ... 31

Table 11. Estimate of regression coefficients of SPFs with the period indicator obtained 

by GEE for ISN crashes using reference group 2 ......................................................................... 33

Table 12. Estimate of regression coefficients of SPFs with the period indicator obtained 

by GEE for IR crashes using reference group 2 ........................................................................... 34

Table 13. Summary of results....................................................................................................... 35

Table 14. ISN crashes results........................................................................................................ 37

Table 15. IR crashes results.......................................................................................................... 38

Table 16. Estimate of regression coefficients of SPFs for ISN total crashes 

using reference group 1................................................................................................................. 46

Table 17. Estimate of regression coefficients of SPFs for IR total crashes 

using reference group 1................................................................................................................. 47

Table 18. Estimate of regression coefficients of SPFs for ISN severe crashes 

using reference group 1................................................................................................................. 48

Table 19. Estimate of regression coefficients of SPFs for IR severe crashes 

using reference group 1................................................................................................................. 49

Table 20. Estimate of regression coefficients of SPFs for ISN and IR pedestrian crashes

using reference group 1................................................................................................................. 50

Table 21. Estimate of regression coefficients of SPFs for ISN total crashes 

using reference group 2................................................................................................................. 51

Table 22. Estimate of regression coefficients of SPFs for IR total crashes 

using reference group 2................................................................................................................. 52

Table 23. Estimate of regression coefficients of SPFs for ISN severe crashes 

using reference group 2................................................................................................................. 53

Table 24. Estimates of regression coefficients of SPFs for IR severe crashes 

using reference group 2................................................................................................................. 54

Table 25. Estimate of regression coefficients of SPFs for ISN pedestrian crashes 

using reference group 2................................................................................................................. 55

Table 26. Estimate of regression coefficients of SPFs for IR pedestrian crashes 

using reference group 2 (page 1 of 2)........................................................................................... 56

Table 27. Estimate of regression coefficients of SPFs for IR pedestrian crashes 

using reference group 2 (page 2 of 2)........................................................................................... 57

Table 28. Estimate of regression coefficients of SPFs for ISN total crashes 

using reference group 2 and the period indicator variable............................................................ 58
vi 

Table 29. Estimate of regression coefficients of SPFs for IR total crashes 

using reference group 2 and the period indicator variable ............................................................ 59

Table 30. Estimate of regression coefficients of SPFs for ISN severe crashes 

using reference group 2 and the period indicator variable ............................................................ 60

Table 31. Estimate of regression coefficients of SPFs for IR severe crashes 

using reference group 2 and the period indicator variable ............................................................ 61

Table 32. Estimate of regression coefficients of SPFs for ISN pedestrian crashes 

using reference group 2 and the period indicator variable ............................................................ 62

Table 33. Estimate of regression coefficients of SPFs for IR pedestrian crashes 

using reference group 2 and the period indicator variable ............................................................ 63
vii 

LIST OF ABBREVIATIONS AND SYMBOLS 

Abbreviations 

AADT Annual average daily traffic 

ADT Average daily traffic 

EB Empirical Bayes 

FHWA Federal Highway Administration 

GEE Generalized estimating equation 

HAWK High intensity Activated crossWalK 

IR Intersection-related 

ISN Intersecting street name 

MEP Million entering pedestrians 

MEV&P Million entering vehicles and pedestrians 

MOTORV Noncontact recreational vehicle 

MUTCD Manual on Uniform Traffic Control Devices 

NCM Noncontact motorcycle 

NCNM Noncontact nonmotorcycle 

SPF Safety performance function 

SWOPP Sideswipe opposite direction 

SWSAME Sideswipe same direction 

Symbols 

ˆ Estimated index of effectiveness 

ˆ Predicted number of crashes in after period had HAWK not been installed 

0,, 1, 2,..., k Regression coefficients 

Ci Adjustment factors 

An estimate of the general trend including the change in extraneous factors 

 between the before and after periods 

Ei Expected number of crashes 

i Expected number of crashes at intersection i per unit time interval 

I Total number of intersections or sites 

i ith intersection or site 

  ˆ exp  period
viii

k Estimated dispersion parameter of the negative binomial regression model 

Ki Total crash counts during the before period at site i

L Number of crashes observed during the after period

Li Total crash count during the after period at site i

ln log

Mi Estimate of the expected number of crashes 

d i r , Adjustment factor for the duration of the study period 

T i, r Adjustment factor for differences in traffic volumes and general time trend (if 

any exists)

wi Weight

X1i, ..., Xki Predictors corresponding to the characteristics of intersection i
1

CHAPTER 1. INTRODUCTION

BACKGROUND

The city of Tucson, AZ, developed the High intensity Activated crossWalK (HAWK) pedestrian 

crossing beacon in the late 1990s to assist in pedestrian crossings, especially for major arterials at 

minor street intersections.

(1) The purpose of a HAWK is to stop vehicles to allow pedestrians to 

cross the roadway and then permit drivers to proceed as soon as the pedestrians have passed.

This application provides a pedestrian crossing without signal control for the side street because 

signal control on the side street can encourage unwanted additional traffic through the 

neighborhood. Figure 1 shows an example of the current head configuration for the HAWK.

Figure 1. Photo. Example of a HAWK head.

The HAWK head consists of two red lenses over a single yellow lens. The heads are located both 

on a mast arm over the roadway and on the roadside. Figure 2 shows a HAWK at an intersection.
2

Figure 2. Photo. Example of a HAWK treatment in Tucson, AZ.

A typical HAWK includes the following:

An overhead red-yellow-red beacon (similar to an emergency vehicle beacon) facing

both directions of the major street. Supplementing the beacons are signs labeled 

“CROSSWALK STOP ON RED” and “PEDESTRIAN CROSSING,” which indicate that 

the location is associated with a pedestrian crosswalk.

STOP sign(s) on the minor street.

A marked crosswalk on only one major street approach.

A pedestrian pushbutton with a supplemental educational plaque.

Pedestrian signal indications with a pedestrian interval countdown display.

Figure 3 provides the phase sequence for a HAWK. The unit is dark until it is activated by a 

pedestrian. When pedestrians want to cross the street, they press a button that activates the warning 

flashing yellow on the major street. After a set amount of time, the indication changes to a solid 

yellow light to inform drivers to prepare to stop. The device then displays a dual solid red light for 

drivers on the major street and a walking person symbol (symbolizing WALK) for the pedestrians. 

The beacon then displays an alternating flashing red light, and pedestrians are shown a flashing 

upraised hand (symbolizing DONT WALK) with a countdown display advising them of the time 
3

left to cross. During the alternating flashing red operation, drivers can proceed after coming to a 

full stop and checking that pedestrians have already crossed their lane of travel.

1. Dark until 

activated

2. Flashing yellow 

light for 3–6 s

3. Steady yellow 

light for 3–6 s

4. Steady red light 

during pedestrian 

interval

5. Alternating flashing red lights during 

pedestrian clearance interval

Figure 3. Chart. Example of phase sequence for a HAWK.(2)

Swartz discusses how the timing for the HAWK phases is selected in Tucson, AZ.

(3) The flashing 

yellow light typically lasts for 3 s. The duration of the solid yellow light is equal to the yellow 

change interval for a standard traffic signal. The solid red light that is displayed to drivers is the 

same as the walk indication, which is 7–10 s long. A longer walk indication is implemented at 

locations with older, disabled, and/or young users. The width of the crossing affects the duration 

of the flashing red operation. The city has been using an interval of 4 ft/s for timing the HAWK 

crossing based on the Manual on Uniform Traffic Control Devices (MUTCD).

(4) City officials are 

moving to 3.5 ft/s in anticipation of changes to the MUTCD. All new HAWKs are being 

implemented with countdown pedestrian heads.

The alternating flashing red operation allows vehicles to stop for the actual time period that 

is necessary for pedestrians to cross. Drivers can proceed with a stop-and-go operation during 

the flashing red phase if a pedestrian walks faster than the assumed walking speed and clears the 

lanes or roadway. If pedestrians need more time, then the drivers remain stopped. The ability to 

balance the needs of the pedestrians and the delay of the drivers is a valuable component of the 

HAWK treatment. Extensive red-light time when pedestrians no longer need it to cross safely can 

encourage violations.

Public outreach was extensive during the early years of the HAWK operation. Concerns have 

been expressed regarding confusion that may result from the dark beacon display, as some

drivers may interpret it as a power outage. However, anecdotal experiences in Tucson, AZ, have 

indicated that the dark display does not create such a problem.

Another concern is in regards to drivers not stopping at the crosswalk during the flashing red 

operation. In some cases, once the queue began to disperse, drivers behind the lead vehicle 

continued through the intersection rather than coming to a complete stop at the head of the 
4 

queue. This concern is an education and enforcement issue. Officials in Tucson, AZ, have 

indicated that they have received complaints that drivers were traveling through the flashing red 

lights without stopping (a second time) at the stop bar. The Tucson Police Department has 

conducted targeted enforcement at HAWKs in response to this complaint. 

STUDY APPROACH 

The objective of the research effort was to evaluate the safety effectiveness of HAWKs. The 

safety benefits of the HAWK treatment were determined by reviewing crash data before and 

after HAWKs were installed. The before-after evaluation used an empirical Bayes (EB) method 

that considered nearby intersections without the HAWK treatment as reference sites to develop 

safety performance functions (SPFs). EB uses a crash prediction for the after period assuming 

the treatment has not been applied and compares this predicted value to the observed crash 

frequency for the after period with the treatment installed.(5)

2009 MUTCD 

Following its completion but prior to the publication of this Federal Highway Administration 

(FHWA) study, the 2009 edition of the MUTCD was released.(6) The 2009 MUTCD includes 

information on the pedestrian hybrid beacon, which is similar to the HAWK. Chapter 4F of the 

2009 MUTCD has information on the following: 

 The application of pedestrian hybrid beacons. 

 The design of pedestrian hybrid beacons. 

 The operation of pedestrian hybrid beacons. 

Section 2B.52 (and figure 2B-27) of the 2009 MUTCD has details on the sign to be used with the 

pedestrian hybrid beacon.(6)

The pedestrian hybrid beacons described in the 2009 MUTCD differ from the HAWKs included 

in this safety study in the following ways:(6)

 Section 4F.02 of the 2009 MUTCD, has the following guidance statement: 

“When an engineering study finds that installation of a pedestrian hybrid beacon is 

justified, then: 

A. The pedestrian hybrid beacon should be installed at least 100 feet from side 

streets or driveways that are controlled by STOP or YIELD signs.” 

All 21 HAWKs included in this safety study were located either at a minor intersection 

(where the minor street was controlled by a STOP sign) or at a major driveway (where 

the driveway was controlled by a STOP sign). 

 The 2009 MUTCD includes an R10-23 sign with the symbolic red circle and a white 

background for the CROSSWALK section of the sign (see figure 4). The signs typically 

used at the HAWK locations in Tucson, AZ, do not have the symbolic red circle, and the 

CROSSWALK background is yellow (see figure 5). 
5

Figure 4. Photo. R10-23 sign from the 2009 MUTCD.

(6)

Figure 5. Photo. Typical signs used at HAWK crossings in Tucson, AZ.

7

CHAPTER 2. LITERATURE REVIEW

A 2006 Transit Cooperative Research Program/National Cooperative Highway Research 

Program project used driver compliance (yielding or stopping where required) as the primary 

measure of effectiveness for evaluating engineering treatments at unsignalized roadway 

crossings.(2) Driver compliance data were collected at 42 study sites that included 9 different 

types of pedestrian crossing treatments. In addition to collecting driver yielding behavior for 

general population pedestrians, the data collection personnel also staged street crossings to 

ensure consistency among all sites as well as adequate sample sizes. The study found that the

type of crossing treatment did have an impact on driver compliance. Treatments showing a red 

indication to the driver had a significantly higher compliance rate (both statistically and 

practically) than devices that did not show a red indication. These red signal or beacon devices, 

which included midblock signals, half signals, and HAWKs, had compliance rates greater than 

95 percent, as shown in figure 6. Nearly all of the red signal or beacon treatments that were 

evaluated were used on busy, high-speed arterial streets. Pedestrian crossing flags and in-street 

crossing signs were also effective in prompting driver yielding, achieving 65 and 87 percent 

compliance, respectively. However, most of these crossing treatments were installed on 

lower-volume, two-lane roadways.

Based on the findings from the driver compliance study, the research team recommended the 

addition of red signal or beacon devices to the engineer’s toolbox for pedestrian crossings.

(2)

The study results indicated that only the devices that showed a red indication were effective at 

prompting high levels of driver compliance on high-volume, high-speed streets. However, at the 

time of the study, only a traffic signal was recognized in the MUTCD, and the pedestrian signal 

warrant was difficult to meet.(4) Thus, engineers were unable to easily employ those traffic control 

devices that appear to be most effective for pedestrians on wide, high-speed streets. The Signal 

Technical Committee of the National Committee of Uniform Traffic Control Devices, along with 

representatives of the research team, developed language for the inclusion of the HAWK 

pedestrian beacon in the proposed revision to the MUTCD.

(7)

0

20

40

60

80

100

Midblock 

Signal

HAWK 

Beacon

Half 

Signal

In-Street 

Sign

Flags Overhead 

Push

Refuge 

Island

High 

Visibility

Overhead 

Passive

Motorist Yielding (%)

Maximum site value

Average of all sites

Minimum site value

Figure 6. Graph. Driver yielding.(2)
8

In June 2006, Nassi and Barton reported that Tucson, AZ, had over 60 HAWKs, had not 

experienced a high occurrence of crashes at these locations, and had no pedestrian fatalities at any 

of the locations.(1) The report indicated that there had been only nine pedestrian accidents over a 

5-year period at the HAWK locations. The breakdown of pedestrian accidents is as follows:

2002: One accident.

2003: Four accidents.

2004: Zero accidents.

2005: Two accidents.

2006: Two accidents (through December).

(1)

While research has demonstrated that driver compliance is high for the HAWK and that there has 

been a positive safety experience in Tucson, AZ, a comprehensive study of the safety 

performance of the HAWK has not been conducted. As a result, this current study was created.
9 

CHAPTER 3. DATA COLLECTION 

SITE SELECTION AND GEOMETRIC DATA 

The city of Tucson, AZ, provided the research team with a list of all HAWKs that were installed 

or planned. Sites that were planned or installed less than 18 months prior to this study were not 

evaluated. The head configuration for the HAWKs was initially similar to a vertical traffic 

signal. Because of criticisms that such a configuration appears to be a malfunctioning traffic 

signal when dark, officials in Tucson revised the head configuration to the current “Mickey 

Mouse ears” arrangement (see figure 1) in an effort to develop a unique configuration that would 

be associated with special types of crossings. Only sites where the current head configuration 

was newly installed (21 locations) were included in the before-after study. 

Crash evaluations benefit when a set of similar sites without the treatment of interest (referred to 

as the reference group) are identified. When selecting these sites, the goal is that they are as 

similar as possible to the sites with the HAWK treatment without actually having the treatment. 

They should be located near the treated sites and have similar volumes, numbers of lanes, 

numbers and types of turn bays, medians, etc. These sites allow the evaluations to account for 

possible (or potential) regression-to-the-mean bias as well as traffic, weather, road-user behavior, 

citywide public relations campaigns, vehicle fleet, and other factors that change over time. 

The city of Tucson, AZ, maintains a map center that provides online access to geographic 

information system maps and databases.(8) The Web site includes aerial photographs along with 

selected roadway characteristics and a tool for measuring distance. The roadway characteristics 

that were used to select reference sites included traffic signal locations, STOP sign locations, 

speed limit, bus routes, and bike treatment. 

Potential Reference Groups 

Care must be taken in selecting an appropriate reference group because the safety effectiveness 

estimate might change significantly depending on what reference group is used, as observed 

by Persaud and Lyon.(9) In the current study, researchers considered two potential reference 

groups—reference group 1 and reference group 2—and derived the safety effectiveness 

estimate for HAWK sites using each reference group. 

Reference Group 1 

After each HAWK site was located, unsignalized and signalized intersections were identified 

near the HAWK crossing, typically within 0.25 mi of the HAWK. These sites had at least one 

roadway in common with the HAWK location. Preferably, the sites had a similar number of 

approaches (e.g., three-leg intersection or four-leg intersection), and that goal was generally met 

for unsignalized intersections. A similar number of approaches could not be met for signalized 

intersections because most of the signalized intersections near the HAWKs had four-leg 

configurations. For the unsignalized intersections, the reference sites had a similar number of 

lanes on each approach (e.g., if the minor approach to the HAWK was a two-lane, undivided 

roadway, then the reference location also should have been a two-lane, undivided roadway). The 

preference was to find two unsignalized intersections and two signalized intersections for each 
10 

HAWK. Because in some cases suitable reference sites were not available, the dataset included 

approximately 3.4 reference sites for each HAWK site. The distribution of key variables for each 

intersection group is provided in table 1. 

Table 1. Distribution of intersection characteristics for HAWKs and reference group 1. 

Variable Value 

Number of Intersections (Percent of Total) 

HAWK Signalized Unsignalized 

Major cross 

section 

Four-lane undivided 

or with two-way 

left-turn lane 12 (57) 22 (61) 22 (63)

Four-lane divided 1 (5) 2 (6) 1 (3)

Six-lane divided 8 (38) 12 (33) 12 (34)

Major speed 

limit (mi/h) 

30 1 (5) 5 (14) 2 (6)

35 9 (43) 12 (33) 16 (46)

40 11 (52) 19 (53) 17 (49)

Refuge island on 

major 

No 12 (57) 21 (58) 22 (63)

Yes 9 (43) 15 (42) 13 (37)

Intersection type Four-leg 12 (57) 35 (97) 17 (49)

Three-leg 9 (43) 1 (3) 18 (52)

Total 21 36 35

Variable Average After Volume (Standard Deviation)

Major road (vehicles/day) 

39,771 

(9,673)

38,803 

(8,592) 

39,626 

(9,966)

Minor road (vehicles/day) 711 (434)

25,480 

(16,044) 594 (871)

Pedestrians (pedestrians/day) 405 (447) 657 (622) 180 (239)

Reference Group 2 

Due to concerns with using signalized intersections as part of the reference group, a second 

reference group was developed. Reference group 2 consisted of 102 unsignalized intersections 

typically located within 2 mi of the HAWKs. The distribution of key variables for each 

intersection group is listed in table 2. 
11

Table 2. Distribution of intersection characteristics for HAWKs and reference group 2.

Variable Value

Number of Intersections 

(Percent of Total)

HAWK Unsignalized

Number of 

lanes on major 

cross section

Two 0 (0) 2 (2)

Four 13 (63) 57 (56)

Six 8 (38) 43 (42)

Major speed 

limit (mi/h)

30 1 (5) 11 (11)

35 9 (43) 41 (40)

40 11 (52) 50 (49)

Refuge island 

on major

No 12 (57) 52 (51)

Yes 9 (43) 50 (49)

Intersection 

type

Four-leg 12 (57) 48 (47)

Three-leg 9 (43) 54 (53)

Total 21 102

Variable

Average After Volume 

(Standard Deviation)

Major road (vehicles/day)

39,771 

(9,673)

37,961 

(12,396)

Minor road (vehicles/day) 711 (434) 741 (793)

Pedestrians (pedestrians/day) 405 (447) 185 (212)

TRAFFIC COUNTS

Several sources were used to obtain traffic counts. Traffic counts (or historical maps) were made 

available on the Web for selected intersections or segments by the city of Tucson, AZ, and the 

Pima Association of Governments.

(10, 11) The Pima Association of Governments also provided 

historical counts upon request. Traffic maps and counts between 1996 and 2007 were reviewed.

Relevant count information (count value and year of count) was transferred from the list of 

counts or traffic maps into the geometric database for each major street and minor road approach 

for all intersections when available. Vehicle counts from existing sources were identified for 

most of the major streets of the intersections.

None of the existing sources had available pedestrian counts. Therefore, 2-h pedestrian counts 

were collected during spring 2008 and spring 2009. The city of Tucson, AZ, provided 24-h video 

surveillance of five HAWK sites; however, one of the sites was eliminated due to a gap in the 

video tape. From the tapes, the number of pedestrians crossing for each hour was counted for

the remaining sites, and the distribution was used to adjust the 2-h pedestrian counts into 

24-h pedestrian counts. The 24-h volumes were also adjusted for seasonal variability. Traffic 

Volumes Map provided information on monthly variations, noting that winter visitors and college 

students contribute to higher volumes during the spring.

(11) Converting the counts made in March

2008 and March 2009 to average annual daily traffic (AADT) counts (pedestrians and/or minor

road vehicles) required multiplying the 24-h March volumes by 87 percent. The March counts 

were higher than the average annual values.
12 

The 2-h pedestrian counts were gathered at all HAWK intersections except for those sites with 

24-h counts. The 2-h pedestrian counts were also gathered at all reference intersections. When 

the minor road volume for an intersection was not available from existing counts, the minor road 

approach volume was also counted. 

The available volumes were averaged for the relevant study period to generate the AADT (vehicle 

or pedestrian) for each study period for a site. If the available volumes were for a different time 

period than the period being used for the crashes, a 2 percent growth rate was assumed. For 

example, if counts were available for 2004 and 2005 but the crash data covered 2003, 2004, and 

2005, the volume for 2003 was estimated as being 98 percent of the 2004 volume. 

STUDY PERIODS 

For the before-after study, the goal was to have 36 months of before data and 36 months of after 

data. The before period was set at 36 months and reflected month 38 to month 2 prior to the 

installation date of the HAWK. The 2-month period prior to the installation date was assumed for 

construction. The after period was set as beginning 2 months following the installation of the 

HAWK until 36 months later or December 31, 2007, which was the limit of crash data available. 

The 2-month period following the installation of the HAWK was assumed to be a learning period 

for the treatment. Therefore, a site with an installation date of December 31, 2002, would have 

the before-after analysis periods as follows: 

 Before period: November 1, 1999–October 31, 2002. 

 Installation period: November 1, 2002–December 31, 2002. 

 Learning period: January 1, 2003–February 28, 2003. 

 After period: March 1, 2003–February 28, 2006. 

The number of months in the after period for the 21 HAWK sites varied depending when the 

HAWK was installed. Table 3 lists the number of months in the after period for the 21 sites. 

The shortest after period was 19.5 months. The majority of the sites had a 32-month or greater after 

period, with more than 80 percent of the sites having at least a 28-month after period. Note that 

each reference site had the same number of days in its after period as its matched HAWK site. 
13

Table 3. After study period length.

Number 

of Days in 

After 

Period

Number of 

Months in 

After 

Period

Number 

of 

HAWKs

Percentage of 

HAWKs with 

After Study 

Period Less 

than or Equal 

to Column 1 

Value

Percentage of 

HAWKs with 

After Study 

Period Greater 

than or Equal 

to Column 1 

Value

595 19.5 1 5 100

630 20.7 1 10 95

637 20.9 1 14 90

790 25.9 1 19 86

866 28.4 1 24 81

888 29.1 1 29 76

904 29.6 1 33 71

988 32.4 4 52 67

1,030 33.8 1 57 48

1,095 35.9 9 100 43

Total 21

CRASH DATA

Crash data were supplied by the city of Tucson, AZ. Street names were used to match the crashes 

with the geometric database. Because different spellings could be present for a street name

(e.g., St. Mary’s, St Marys, Saint Mary’s, etc.), the research team manually searched the datasets 

to verify that consistent spelling was used in both the crash dataset and the geometric dataset. A 

check was also performed with the street names reversed to ensure that all crashes associated 

with an intersection were identified. For example, crashes for Oak and Pine along with crashes 

for Pine and Oak (reverse order) were identified.

A review of the crash dataset revealed that some of the crashes were coded to a block address, 

with most associated with an intersection. Identifying all crashes associated with an intersection 

should capture the crashes that could be influenced by the intersection’s traffic control; however, 

it may also capture crashes that occurred near the intersection that would not have been 

influenced by the intersection’s traffic control. The Arizona traffic accident report form includes 

a space to record the distance from an intersection (measured or approximate). The distance 

could provide an appreciation of whether the crash should be associated with the intersection.

The information, however, was not available to the research team. Another variable that can 

provide insight into whether the crash may be related to the intersection’s traffic control is the 

variable “intersection-related” (IR). The permitted responses for the IR field were “yes,” “no,” or 

blank, and about 1⁄3 of the crashes had this field blank. A comparison of the number of IR crashes 

for the intersections reviewed in a previous study indicated that the IR variable may be too 

restrictive.

(1) Therefore, both the crash dataset that included all crashes identified when the 

intersecting street names (ISNs) matched and the smaller crash dataset that reduced the data to 
14

only those with “yes” for the IR code were used in the evaluations. Descriptions of the crash 

datasets used in this study are as follows:

ISN crashes: identified by matching the street names for the intersection.

IR crashes: identified as those crashes in the ISN crash dataset with “yes” for the IR code.

Different types of crashes from each of the crash datasets were used in the evaluations. The types 

of crashes are as follows:

Total crashes: included all identified crashes. 

Severe crashes: included all crashes with an injury severity code of possible injury, 

nonincapacitating injury, incapacitating injury, or fatal injury.

Pedestrian crashes: included all crashes with the manner of collision coded as pedestrian.
 15 

CHAPTER 4. OBSERVATIONS 

BEFORE-AFTER CRASH DATA 

Table 4 summarizes the number of crashes by control type for the before-after study periods for 

both the dataset where the crashes were matched by ISNs and the smaller dataset that only 

included IR crashes. For all crashes and specific crash types of interest, the rates were calculated 

with the number of entering vehicles and pedestrians. 

The HAWK was installed to assist pedestrians in crossing the roadway; therefore, installing the 

device should have a notable impact on pedestrian crashes. The rates shown for pedestrian 

crashes in table 4 were calculated using both the number of vehicles and number of pedestrians 

entering the intersection and only the number of pedestrians entering the intersection. The 

pedestrian crashes per million entering pedestrians (pedestrian crashes/MEP) rate is not 

commonly used in crash evaluations; however, it was calculated to provide an appreciation of the 

relationship between pedestrian crashes and pedestrian usage by control type. Because vehicle 

counts were so much larger than pedestrian counts at an intersection, the crash rate that included 

vehicle exposure may mask the effects on pedestrian crashes. The crash rate that included both 

vehicles and pedestrians is expressed as crashes per million entering vehicles and pedestrians 

(crashes/MEV&P). 

Using ISN crashes, the HAWK sites experienced a decrease of about 17 percent in the total crash 

rate after the installation of the beacon. The 102 unsignalized intersections experienced a 3 percent 

increase in total crash rate. When IR crashes were used, the HAWK sites experienced a larger 

decrease in their crash rate. IR crash rates also showed a reduction at unsignalized intersections. 
16

Table 4. Crash data for before-after study by groups.

Treatment

Group Measure

ISN Crashes IR Crashes

Before After

Percent

Change Before After

Percent 

Change

HAWK 

sites (21)

Frequency 11.0 9.2 -17 5.0 3.3 -34

Total crashes/MEV&P 0.748 0.618 -17 0.341 0.223 -35

Severe crashes/MEV&P 0.265 0.210 -21 0.138 0.094 -32

Pedestrian

crashes/MEV&P 0.029 0.005 -83 0.017 0.002 -86

Pedestrian crashes/MEP 3.081 0.511 -83 1.826 0.255 -86

Reference 

group 1: 

signalized 

intersections

(36)

Frequency 44.9 41.9 -7 19.6 16.8 -14

Total crashes/MEV&P 1.953 1.788 -8 0.854 0.716 -16

Severe crashes/MEV&P 0.549 0.503 -8 0.294 0.241 -18

Pedestrian 

crashes/MEV&P 0.020 0.016 -23 0.010 0.008 -16

Pedestrian crashes/MEP 2.051 1.546 -25 1.025 0.839 -18

Reference 

group 1: 

unsignalized 

intersections

(35)

Frequency 4.2 4.3 3 1.6 1.3 -17

Total crashes/MEV&P 0.285 0.292 2 0.108 0.090 -17

Severe crashes/MEV&P 0.098 0.088 -10 0.043 0.038 -10

Pedestrian 

crashes/MEV&P 0.006 0.009 52 0.003 0.004 42

Pedestrian crashes/MEP 1.383 2.078 50 0.615 0.866 41

Reference 

group 2: 

unsignalized 

intersections

(102)

Frequency 5.9 6.1 3 2.4 2.1 -9

Total crashes/MEV&P 0.418 0.430 3 0.166 0.150 -9

Severe crashes/MEV&P 0.140 0.141 0 0.060 0.056 -6

Pedestrian 

crashes/MEV&P 0.006 0.011 93 0.001 0.003 143

Pedestrian crashes/MEP 1.233 2.297 86 0.257 0.602 134

Crashes/MEV&P = Type of given crash (total, severe, or pedestrian crashes) per million entering vehicles and pedestrians.

Pedestrian crashes/MEP = Pedestrian crashes per million entering pedestrians.

Note: Frequency is expressed as the average annual number of total crashes for a site with the given intersection 

control and study period.

The HAWK sites experienced an 83 percent reduction in the pedestrian crash rate after 

installation. The 102 unsignalized intersections experienced a 93 percent increase in pedestrian 

ISN crashes/MEV&P. When IR crashes were used, the trends were the same.

As seen in table 4, HAWK sites had crash rates that were higher than unsignalized intersections.

The HAWK locations were associated with a slightly greater number of crashes/MEV&P as 

compared to the nearby unsignalized intersections in both the before and after periods. This 

observation does not imply that if the HAWK were removed, the crash rate for a given 

intersection would be similar to the crash rate identified for the neighboring unsignalized 

intersections. The crash rate at the HAWK sites prior to installation also exceeded the crash rate 

for nearby unsignalized intersections (the IR crash rate when the intersections were unsignalized 

and before the HAWK was installed was 0.341 crashes/MEV&P, while that of the nearby 

unsignalized intersections was 0.166 crashes/MEV&P). Therefore, conditions at the HAWK sites
17

before the treatments were installed were generating crashes in greater numbers than the 

unsignalized intersections. This indicates that those intersections were associated with conditions 

that resulted in a higher number of crashes. Addressing those conditions by installing a HAWK 

appeared to result in a decrease in total crashes and pedestrian crashes. Chapter 5 of this report 

provides the statistical evaluations of these observations.

OTHER CRASH CHARACTERISTICS 

The installation of the HAWK could also cause changes in the types of crashes occurring.

Within the Tucson, AZ, crash database, the following manner-of-collision choices are available 

(officers can check only one): 

Angle. 

Backing.

Bicycle. 

Fixed object.

Head-on.

Left turn. 

Noncontact recreational vehicle (MOTORV).

Noncontact motorcycle (NCM). 

Noncontact nonmotorcycle (NCNM). 

Other.

Pedestrian. 

Rear-end. 

Right turn. 

Sideswipe opposite direction (SWOPP). 

Sideswipe same direction (SWSAME). 

Single vehicle. 

U-turn. 

The number of crashes by manner of collision is listed in table 5. Figure 7 and figure 8 show 

plots of the distributions. To make figure 7 and figure 8 more understandable, the following 
18

manners of collision were summed to create the grouped category: backing, fixed object, 

head-on, MOTORV, NCM, NCNM, other, SWOPP, and U-turn.

The manner-of-collision variable was not checked in approximately 20 percent of the 

ISN crashes, and those crashes were not included in the generated distributions shown in

table 5, figure 7, and figure 8. For each of the IR crashes, a manner of collision was selected

by an officer.

Rear-end is the most common crash type for all types of intersection control, representing 

between 40 and 60 percent of the crashes for a given type of traffic control at the intersection.

After rear-end, the most common crash types were left-turn and angle.

The dataset shows rear-end as the most common manner of collision for the HAWK intersections

in both the before and after periods (illustrated in figure 7 and figure 8). The distribution of 

IR crashes at the HAWK sites before the HAWK was installed included rear-end (55 percent), 

angle (13 percent), left-turn (15 percent), and pedestrian (5 percent) crashes. After the 

installation, the greatest changes in the distribution of crash type were an increase in angle 

crashes to 19 percent and a decrease in pedestrian crashes to 1 percent.
19

Table 5. Number and percent of crashes by manner of collision.

Manner of 

Collision

Before HAWK

(21 Sites)

After HAWK

(21 Sites)

Signalized

(36 Sites)

Unsignalized

(102 Sites)

Frequency Percent Frequency Percent Frequency Percent Frequency Percent

ISN Crashes

Angle 58 9 53 13 1,069 15 395 13

Backing 10 2 6 1 69 1 52 2

Bicycle 13 2 7 2 76 1 34 1

Fixed 8 1 1 0 42 1 40 1

Head-on 3 0 0 0 50 1 32 1

Left turn 57 9 35 8 1,188 17 438 14

MOTORV 2 0 0 0 2 0 2 0

NCM 1 0 0 0 16 0 6 0

NCNM 1 0 0 0 9 0 5 0

Other 15 2 6 1 86 1 58 2

Pedestrian 27 4 4 1 85 1 66 2

Rear-end 382 60 245 59 3,345 47 1,481 47

Right turn 14 2 7 2 206 3 114 4

Single 19 3 20 5 195 3 142 5

SWOPP 1 0 1 0 41 1 16 1

SWSAME 29 5 27 6 543 8 235 7

U-turn 2 0 6 1 52 1 37 1

Blank 53 NI 90 NI 1,789 NI 357 NI

Total 695 100 508 100 8,863 100 3,510 100

IR Crashes

Angle 40 13 35 19 694 19 248 19

Backing 0 0 1 1 33 1 9 1

Bicycle 8 3 2 1 42 1 23 2

Fixed 2 1 0 0 13 0 14 1

Head-on 1 0 0 0 35 1 10 1

Left turn 46 15 25 14 889 24 318 24

NCM 1 0 0 0 7 0 1 0

NCNM 1 0 0 0 1 0 3 0

Other 5 2 2 1 29 1 18 1

Pedestrian 16 5 2 1 44 1 16 1

Rear-end 175 55 98 54 1,515 41 458 35

Right turn 6 2 4 2 96 3 74 6

Single 7 2 4 2 78 2 33 3

SWOPP 0 0 1 1 27 1 8 1

SWSAME 7 2 6 3 187 5 57 4

U-turn 2 1 3 2 36 1 23 2

Total 317 100 183 100 3,726 100 1,313 100

Note: Blank indicates that the manner of collision was not provided for crash; NI indicates condition was not included in 

calculation of percent distribution.
20

0%

10%

20%

30%

40%

50%

60%

Percent of Crashes

HAWK, Before

HAWK, After

Signalized

Unsignalized

Figure 7. Graph. Distribution of manner of collision by control for ISN crashes.

0%

10%

20%

30%

40%

50%

60%

Percent of Crashes

HAWK, Before

HAWK, After

Signalized

Unsignalized

Figure 8. Graph. Distribution of manner of collision by control for IR crashes.
21

CHAPTER 5. BEFORE-AFTER EVALUATION 

This chapter presents the results from safety evaluations of the HAWK. To evaluate the 

effectiveness of the HAWK, a before-after evaluation using the EB approach was used.

BEFORE-AFTER CRASH DATA 

The treated sites included 21 intersections with the HAWK installed during the study period.

Reference group 1 included 71 intersections (36 signalized and 35 unsignalized), and reference 

group 2 included 102 unsignalized intersections. The following crash types were examined in 

this study:

Total crashes.

Severe crashes.

Pedestrian crashes.

Table 6 summarizes the total number of each type of crash by site type for the before and after 

study periods. Additional crash statistics are provided in table 4.

As can be observed from table 6, crashes decreased from before to after at both treatment and 

reference sites, which implies that the decrease at the treatment sites was not caused solely by 

installation of HAWKs. Other variables and extraneous factors that might have contributed to the 

observed decreases in crashes include AADT, changes in weather, vehicle mix, driver behavior, 

crash reporting practices, etc. To account for the effects of those variables in crash reduction as 

well as potential regression-to-the-mean bias, the EB approach was employed to identify the 

safety effectiveness of the HAWK.

Table 6. Number of crashes in before and after periods.

Type of Site Type of Crash

Number of Crashes 

ISN Crashes IR Crashes

Before After Before After

HAWKs

Total 695 508 317 183

Severe 246 173 128 77

Pedestrian 27 4 16 2

Reference group 1: 

signalized intersections 

(36)

Total 4,849 4,014 2,119 1,607

Severe 1,362 1,129 729 540

Pedestrian 50 35 25 19

Reference group 1:

unsignalized 

intersections (35)

Total 438 394 167 121

Severe 151 119 66 52

Pedestrian 9 12 4 5

Reference group 2:

unsignalized 

intersections (102)

Total 1,817 1,693 720 593

Severe 610 555 260 221

Pedestrian 24 42 5 11
22 

EB PROCEDURE 

The statistical method used to evaluate the effectiveness of the HAWK was a before-after 

evaluation using the EB method. The EB method can account for the effect of regression to the 

mean on evaluation results along with changes in traffic volume levels and general time trend 

(if any exists) in the accident frequencies. Details on the EB method are available elsewhere.(5, 12, 13)

For the purpose of completeness, the steps of the EB procedure are as follows: 

1. Develop an SPF, usually by adopting negative binomial regression models, and estimate 

the regression coefficients and a negative binomial dispersion parameter (k) using data 

from the reference group. 

2. Estimate the expected number of crashes Ei in the before period at each treatment site i 

as the (per-day) SPF prediction multiplied by the number of days in the before period. 

3. Obtain an estimate of the expected number of crashes (Mi) before implementation of the 

HAWK at each treatment site by using the equation in figure 9, where Ki is the total crash 

count during the before period at site i and the weight wi is given by the equation in 

figure 10. Within the weight equation, k is the estimated dispersion parameter of the 

negative binomial regression model developed in step 1. An estimated variance (var) of 

Mi is given by the equation in figure 11. 

  1  Mi i i ii   wE w K 

Figure 9. Equation. Estimate of expected number of crashes during the before period. 

 

1

1 i

i

w

kE   

Figure 10. Equation. Weight. 

ˆ   1  Var M w M i ii  

Figure 11. Equation. Estimated variance of expected number of crashes during the 

before period. 

4. Compute the adjustment factors to account for differences in traffic volumes (and general 

trend if any exists) and duration between the before and after periods. The adjustment 

factor for differences in traffic volumes (and general trends), T i, r is computed as the ratio 

of the per-day SPF prediction for the after period and that for the before period at each 

site. The adjustment factor for the duration of the study period ( d i r , ) is computed as the 

ratio of the number of days for the after period and that for the before period at each site. 

Let Ci represent the adjustment factors. The equation for Ci is provided in figure 12. 

C rr i Tidi  , ,

Figure 12. Equation. Adjustment factors. 
 23 

5. Obtain the predicted crashes ( ˆi) during the after period that would have occurred 

without implementing HAWK by the equation in figure 13. The estimated variance of ˆi

is given by the equation in figure 14. 

ˆ i ii  M C

Figure 13. Equation. Predicted crashes during the after period. 

Varˆ ˆi 2  Ci Varˆ     2 1 M C wM i i ii  

Figure 14. Equation. Estimated variance of predicted crashes during the after period. 

6. Compute the sum of the predicted crashes over all sites in the treatment group by the 

equation in figure 15. Compute its estimated variance by the equation in figure 16 where 

I is the total number of sites in the treatment group, which is 21 in this study. 

ˆ i

1

I

i

  ˆ i

Figure 15. Equation. Sum of predicted crashes. 

Varˆ ˆ i



1

I

i

Varˆ ˆi

Figure 16. Equation. Estimated variance of sum of predicted number of crashes. 

7. Compute the sum of the observed crashes over all sites in the treatment group using the 

equation in figure 17, where Li is the total crash count during the after period at site i. 

1

I

i

i

L L





Figure 17. Equation. Sum of observed crashes. 

8. Estimate the index of effectiveness (  L  ) for the HAWK by the equation in figure 18 

and the percent change in the number of crashes by the equation in figure 19. If ˆ

 is less 

than 1, then the HAWK has a positive effect on safety. 

    2

ˆ

ˆ ˆˆ 1 var

L 

    

Figure 18. Equation. Estimated index of effectiveness. 

  Percent change in number of crashes = 100 1 ˆ 

Figure 19. Equation. Percent change in number of crashes. 
24 

9. Compute the estimated variance and standard error of the estimated index of 

effectiveness. The estimated variance and standard error of the estimated index of 

effectiveness are given by figure 20 and figure 21, respectively. 

     

   

2

2

2 2

1 ˆˆˆ ˆ ˆ ˆ

1 ˆˆˆ

L Var

Var

Var

 

 

 

 



Figure 20. Equation. Estimated variance of estimated index of effectiveness. 

    ˆ ˆ s e Var . .   ˆ 

Figure 21. Equation. Standard error of estimated index of effectiveness. 

10. Construct the confidence interval by adding and subtracting 2  ˆ z se. .    from ˆ

 where 

2 z is the z critical value corresponding to a predetermined confidence level (1 - α) × 100 

percent. Different confidence levels and the corresponding z critical values are as follows: 

 95 percent confidence level ( = 0.05) 2 0.025 z z   = 1.96. 

 90 percent ( = 0.1) 2 0.05 z z   = 1.645. 

 85 percent ( = 0.15) 2 0.075 z z   = 1.44. 

If the confidence interval does not contain the value 1, then a significant effect at the 

(1 - α) × 100 percent level has been observed. 

SPF DEVELOPMENT 

As presented previously, the first step in the before-after EB method is to develop and calibrate 

an SPF using data from a reference group. Reference group 1 included both signalized (36) 

and unsignalized (35) intersections, and reference group 2 consisted of 102 unsignalized 

intersections. Within the SPF, the log of the number of days was included as an offset variable 

(the SPFs were developed for the expected number of crashes per day). 

SPF development first involved determining which predictor variables should be used in the 

model, how variables should be grouped, and what model form should be used. The major street 

and minor road average daily traffic (ADT) values are often the key variables in developing 

SPFs for intersections. In addition, pedestrian volumes are likely to play an important role in 

pedestrian crashes. Typically, using the log of the sum of entering vehicles and pedestrians (or 

the log of the entering vehicles and the log of pedestrian volumes) as predictors seemed to be 

most appropriate for the data. Other combinations of ADT values, such as separating the vehicle 

volumes by major and minor approaches or using the ratio of major to minor approach volume, 

were considered during model development. 
 25 

To account for additional intersection-to-intersection variability other than that caused by the 

differences in traffic volumes and pedestrian volumes, intersection type, median refuge presence, 

number of lanes, and major street speed limit were also considered in the SPF predictions. Other 

variables, such as parking on the minor road, were considered but were eliminated because most 

sites had the same characteristic. Variables were eliminated if the corresponding coefficient was 

not significant at  = 0.2 and had a counterintuitive sign at the same time. 

For the SPF predictions in EB analysis, it is typical to adopt negative binomial regression 

models. The general form of the expected number of crashes in a negative binomial regression 

model is shown in figure 22. After exploring various negative binomial regression model forms 

with different predictors, the best model for the different types of crashes was identified. 

  0 11 2 2 exp     i i i k ki     X X X 

Figure 22. Equation. General form for expected number of crashes. 

Where: 

i = The expected number of crashes at intersection i per unit time interval (1 day). 

X1i, ..., Xki = The predictors corresponding to the characteristics of i. 

0,, 1, 2,..., k = The regression coefficients. 

In developing the SPFs, the crash counts at reference sites could be treated as aggregated data 

over the entire study period (including both the before and after periods) or as disaggregated data 

with two crash counts from each intersection, one for the before period and one for the after 

period. Aggregating the data can account for the correlations that might be present in the crash 

counts when the intersections are included twice (once for the before period and once for the 

after period) in estimating the SPFs. Disaggregating the data provides the opportunity to account 

for general time trend (if any exists) within the two periods. 

Several SPFs were generated as part of the evaluations. The coefficients for models with 

potential are included in the appendix of this report. The tables presented in this section include 

the best model for the conditions based on the assessment of the research team. 

Reference Group 1 Aggregate Data 

Initial efforts used aggregated data from reference group 1. Results for models identified by the 

research team are included in the appendix. Table 7 and table 8 present the best SPFs for total, 

severe, and pedestrian ISN and IR crashes when using aggregated data. The tables also provide 

the corresponding EB safety effectiveness estimates. Higher percent reductions were found for 

IR total crashes (29 percent) as compared to ISN total crashes (15 percent). For pedestrian 

crashes, a 57 percent reduction (statistically significant) in ISN crashes and a 56 percent 

reduction (not statistically significant) in IR crashes were found. For severe crashes, an 

11 percent reduction in ISN crashes and an 18 percent reduction in IR crashes were found, 

although those results were not statistically significant at the 95 percent confidence levels. 

Although the 95 percent confidence level was used throughout this report, a selection of 

prespecified confidence levels may vary with researchers or with the problem. The statistical 
26

significance may also vary depending on what confidence level is chosen. It needs to be noted 

that the statistically insignificant results at the 95 percent confidence level for severe crashes may 

still be important. The statistically insignificant 11 percent reduction in crashes could have been 

due to the lack of power resulting from a small sample size or due to chance. The size of the 

sample for severe crashes as well as for IR pedestrian crashes was a concern. For ISN pedestrian 

crashes, a statistically significant reduction in crashes was achieved despite a small sample size 

due to a huge effect size (57 percent). For IR crashes, the sample size was even smaller than that 

for the ISN crashes, which led to a statistically insignificant result, although the effect size 

(56 percent) was about the same as that for the ISN crashes. For severe crashes, the effect size 

was much smaller (11 and 18 percent, although still practically significant) than those for 

pedestrian crashes, and a much larger sample will be required to achieve statistical significance.

It is possible that with a larger sample, the effect of the HAWK on severe crashes may become 

significant at the 95 percent confidence level.

While there has been a case where a HAWK replaced a signal, in most cases, the HAWK was

installed at a previously unsignalized intersection. Therefore, an alternative reference group that

only contains unsignalized intersections was developed.
27

Table 7. Estimate of regression coefficients of SPFs for ISN crashes

using reference group 1.

Variable

Total 

Crashes

Coefficient

Estimate

(p-Value)

Severe 

Crashes

Coefficient 

Estimate

(p-Value)

Pedestrian

Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-34.3200

(< 0.0001)

-32.2219

(< 0.0001)

-26.5372

(< 0.0001)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.9932

(< 0.0001)

-0.9557

(< 0.0001)

-0.8826

(0.0137)

Major street speed limit (mi/h)

0.0951

(0.0016)

0.1110

(0.0003)

0.1048

(0.0031)

Median refuge present

-0.7478

(0.0003)

-0.6998

(0.0012)

-0.4731

(0.0545)

LnVeh&Ped

2.6005

(< 0.0001) —

1.4433

(0.0002)

LnVeh —

2.1704

(< 0.0001) —

LnPed —

0.1390

(0.0834) —

Dispersion 0.4452 0.4235 0.0588

Pearson chi-square/degree of freedom 0.9702 1.0360 1.1428

EB Results

L, Number of crashes observed during 

the after period 508 173 4

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 594.744 192.979 9.35410

ˆ, Estimated index of effectiveness 0.853 0.893 0.426

( )ˆ se , Standard error of ˆ 0.050 0.086 0.214

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 15 11 57

Results are statistically significant at 

95 percent confidence level Yes No Yes

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
28

Table 8. Estimate of regression coefficients of SPFs for IR crashes 

using reference group 1.

Variable

Total 

Crashes

Coefficient 

Estimate

(p-Value)

Severe 

Crashes

Coefficient 

Estimate

(p-Value)

Pedestrian

Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-34.2206

(< 0.0001)

-32.9071

(< 0.0001)

-31.9455

(< 0.0001)

Intersection type 

(three-leg = 1, four-leg = 0)

-1.2010

(< 0.0001)

-1.1455

(< 0.0001)

-0.8626

(0.1096)

Major street speed limit (mi/h)

0.0889

(0.0080)

0.1057

(0.0031)

0.1313

(0.0173)

Median refuge present

-0.5582

(0.0172)

-0.5465

(0.0277)

-0.1824

(0.6126)

LnVeh&Ped

2.5262

(< 0.0001)

2.2558

(< 0.0001)

1.7660

(0.0028)

LnVeh — — —

LnPed — — —

Dispersion 0.5276 0.5425 0.1978

Pearson chi-square/degree of freedom 0.9983 1.0243 1.2738

EB Results

L, Number of crashes observed during 

the after period 183 77 2

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 256.501 93.5850 4.49476

ˆ, Estimated index of effectiveness 0.711 0.817 0.439

( )ˆ se , Standard error of ˆ 0.065 0.114 0.311

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 29 18 56

Results are statistically significant at 

95 percent confidence level Yes No No

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
29

Reference Group 2 Aggregate Data

The results for reference group 2 with an aggregated data approach are shown in table 9 and 

table 10. These tables present the best SPFs for total, severe, and pedestrian ISN and IR crashes, 

along with the corresponding EB safety effectiveness estimates. Results for other models 

identified by the research team for reference group 2 are included in the appendix.

It can be observed from a comparison of table 7 through table 10 that the safety effectiveness 

estimates ( ˆ) from both reference groups are close, while the coefficients of SPFs calibrated 

based on reference group 1 are somewhat different from those calibrated using reference 

group 2. For total crashes, similar results were obtained between the two reference groups—

about a 14 percent reduction in ISN crashes and a 29 percent reduction in IR crashes, both being 

statistically significant at the 95 percent confidence level. The results for pedestrian crashes were 

fairly similar—about a 59 percent reduction (statistically significant) in ISN crashes and about a 

51 percent reduction (not statistically significant) in IR crashes. The results for severe crashes 

were also similar; an 11 and 18 percent reduction were found for ISN crashes and IR crashes, 

respectively, although the results were not statistically significant at the 95 percent level. Note 

again that statistically insignificant results may still be important, and with a larger sample, those 

results may become significant at the 95 percent confidence level.
30

Table 9. Estimate of regression coefficients of SPFs for ISN crashes 

using reference group 2.

Variable

Total 

Crashes

Coefficient 

Estimate

(p-Value)

Severe 

Crashes

Coefficient 

Estimate

(p-Value)

Pedestrian

Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept

-16.8197

(< 0.0001)

-17.7484

(< 0.0001)

-16.8225

(0.0004)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.3732

(0.0116)

-0.3586

(0.0370)

-0.0292

(0.9207)

Major street speed limit (mi/h)

0.0673

(0.0062)

0.0860

(0.0031)

0.0248

(0.6263)

LnVeh&Ped

0.9827

(< 0.0001)

0.8990

(0.0003) —

LnVeh — —

0.6518

(0.1787)

LnPed — —

0.1999

(0.1186)

Dispersion 0.4592 0.5560 0.2712

Pearson chi-square/degree of freedom 1.1011 1.0367 1.0967

EB Results

L, Number of crashes observed during 

the after period 508 173 4

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 588.646 198.106 9.71056

ˆ, Estimated index of effectiveness 0.862 0.870 0.408

( )ˆ se , Standard error of ˆ 0.050 0.084 0.206

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 14 13 59

Results are statistically significant at 

95 percent confidence level Yes No Yes

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
31

Table 10. Estimate of regression coefficients of SPFs for IR crashes

using reference group 2.

Variable

Total 

Crashes

Coefficient 

Estimate

(p-Value)

Severe

Crashes

Coefficient 

Estimate

(p-Value)

Pedestrian

Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept

-18.5272

(< 0.0001)

-18.3149

(< 0.0001)

-25.4693

(0.0222)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.6012

(0.0012)

-0.5635

(0.0050)

-0.3600

(0.5457)

Major street speed limit (mi/h)

0.0917

(0.0025)

0.1128

(0.0012)

0.0497

(0.6429)

LnVeh&Ped

0.9740

(0.0003) — —

LnVeh —

0.7829

(0.0087) —

LnPed — —

0.3056

(0.2692)

LnMajor — —

1.1741 

(0.2829)

LnMinor — —

0.0692

(0.8003)

Dispersion 0.6461 0.6297 1.2769

Pearson chi-square/degree of freedom 1.1445 1.0049 0.9878

EB Results

L, Number of crashes observed during 

the after period 183 77 2

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 256.423 90.0872 3.94071

ˆ, Estimated index of effectiveness 0.712 0.849 0.490

( )ˆ se , Standard error of ˆ 0.065 0.118 0.347

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 29 15 51

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed Yes No No

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

LnMajor = Ln(entering vehicles from major approaches).

LnMinor = Ln(entering vehicles from minor approaches).

— Indicates that the variable was not included in model.
32 

Reference Group 2 Disaggregate Data 

SPFs may also be developed based on disaggregated crash count data between before and after 

periods at reference sites. In that case, each intersection is represented twice in the dataset, and 

the general time trend between the before and after periods may be estimated by specifying 

“Period” as a dummy variable. Because the crash counts from the same intersection are likely to 

be correlated, it is desirable to use the generalized estimating equation (GEE) approach in 

estimating the SPF coefficients to incorporate this potential correlation. 

Table 11 and table 12 present the summary of the SPFs estimated by GEE for total, severe, and 

pedestrian ISN and IR crashes based on the before and after crash counts from reference 

group 2. Note that the period indicator is “0” for the before period and “1” for the after period. 

The after period SPF multiplier, obtained by taking the exponential of the estimated coefficient 

of period ( ˆ

 period ), exp ( ˆ period ), can be considered as an estimate of the general trend including 

the change in extraneous factors between the before and after periods. Hauer notes that a 

disaggregate crash count approach (a multivariate model approach based on disaggregated data 

in time) can serve a dual purpose of being an SPF and a comparison group (to estimate the 

general trend).(5) For this approach, the ratio of the per-day SPF prediction for the after period 

and that for the before period ( tf i r , ) described in step 4 of the EB procedure in this chapter play a 

role of adjusting for differences in both traffic volumes and general trends between the before 

and after periods. 

The EB safety effectiveness estimates are also given below the corresponding SPFs with the 

period indicator included in table 11 and table 12. Results were similar for ISN and IR crashes. 

Both total and pedestrian crash reductions (19 and 23 percent for total and 69 and 65 percent 

for pedestrian) were significant at the 95 percent confidence level. Although severe crashes 

showed reductions (14 and 8 percent), the changes were not statistically significant at the 

95 percent confidence level. 
33

Table 11. Estimate of regression coefficients of SPFs with the period indicator

obtained by GEE for ISN crashes using reference group 2.

Variable

Total 

Crashes

Coefficient 

Estimate

(p-Value)

Severe 

Crashes

Coefficient 

Estimate

(p-Value)

Pedestrian

Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-16.5961

(< 0.0001)

-17.5186

(< 0.0001)

-17.5699

(< 0.0001)

Period 

(after = 1, before = 0)

0.0613

(0.1639)

0.0080

(0.8923)

0.6444

(0.0103)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.3665

(0.0313)

-0.3434

(0.0729) —

Major street speed limit (mi/h)

0.0653

(0.0409)

0.0832

(0.0125) —

LnVeh&Ped

0.9655

(0.0003)

0.8858

(0.0042) —

LnVeh — —

0.7673

(0.0347)

LnPed — —

0.2203

(0.0402)

Dispersion 0.4720 0.5709 0.2205

Pearson chi-square/degree of freedom 1.0757 0.9802 1.0513

EB Results

L, Number of crashes observed during 

the after period 508 173 4

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 624.517 199.818 12.8256

ˆ, Estimated index of effectiveness 0.812 0.863 0.309

( )ˆ se , Standard error of ˆ 0.047 0.084 0.156

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 19 14 69

Results are statistically significant at 

95 percent confidence level Yes No Yes

— Indicates that the variable was not included in model.

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).
34

Table 12. Estimate of regression coefficients of SPFs with the period indicator 

obtained by GEE for IR crashes using reference group 2.

Variable

Total 

Crashes

Coefficient 

Estimate

(p-Value)

Severe 

Crashes

Coefficient 

Estimate

(p-Value)

Pedestrian

Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-17.9300

(< 0.0001)

-17.9507

(< 0.0001)

-27.2540

(0.0048)

Period 

(after = 1, before = 0)

-0.0870

(0.2651)

-0.1117

(0.2582)

0.8232

(0.0222)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.5831

(0.0017)

-0.5374

(0.0064) —

Major street speed limit (mi/h)

0.0905

(0.0227)

0.1125

(0.0016) —

LnVeh&Ped

0.9247

(0.0006)

0.7522

(0.0180) —

LnVeh — —

1.4937

(0.0506)

LnPed — —

0.3066

(0.1202)

Dispersion 0.6628 0.6829 1.2431

Pearson chi-square/degree of freedom 1.1767 0.9708 1.0946

EB Results

L, Number of crashes observed during 

the after period 183 77 2

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 237.043 83.0204 5.51422

ˆ, Estimated index of effectiveness 0.770 0.921 0.351

( )ˆ se , Standard error of ˆ 0.071 0.128 0.248

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 23 8 65

Results are statistically significant at 

95 percent confidence level Yes No Yes

— Indicates that the variable was not included in model.

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

In comparing the results obtained from aggregated and disaggregated data, the conclusions did 

not change significantly, although the magnitude of crash reduction was slightly changed by 

inclusion of consideration of general time trends.
35

Comparison of SPFs

The appendix includes other SPFs identified in this study. The SPFs selected within each 

evaluation approach are provided in table 7 through table 12. Although the magnitude of the 

safety effectiveness estimate varies to some extent as different predictors are included in the 

SPFs, the results did not seem to change materially. Table 13 summarizes the percent reduction 

from the different approaches used in evaluating the HAWK.

The results for total crashes were similar regardless of the approach used to evaluate the data.

The reduction was about 16 percent for ISN crashes (14–19 percent) and 27 percent for 

IR crashes (23–29 percent), all significant at a 95 percent confidence level.

Table 13. Summary of results.

Reference Group 

(Aggregation)

Percent Reduction 

(Significant at the 95 Percent Confidence Level)

Total

Crashes

Severe 

Crashes

Pedestrian 

Crashes

ISN Crashes

1 (aggregated) 15 (Yes) 11 (No) 57 (Yes)

2 (aggregated) 14 (Yes) 13 (No) 59 (Yes)

2 (disaggregated) 19 (Yes) 14 (No) 69 (Yes)

IR Crashes

1 (aggregated) 29 (Yes) 18 (No) 56 (No)

2 (aggregated) 29 (Yes) 15 (No) 51 (No)

2 (disaggregated) 23 (Yes) 8 (No) 65 (Yes)

For pedestrian crashes, the results were fairly similar, with the disaggregate approach resulting in 

higher reductions (69 percent) than the aggregate approaches (51–59 percent). While the number 

of total crashes was either decreasing or had only a small increase over the time period studied, 

the number of pedestrian crashes had large increases, as can be seen for unsignalized intersections 

in table 4. The effects of the time trend are better considered in the SPFs developed based on 

disaggregate data, which contributed to the higher percent reduction found for pedestrian crashes.

Severe crash results were not statistically significant at the 95 percent confidence level. The 

smaller sample size along with the smaller influence the HAWK has on reducing severe crashes 

(as compared to pedestrian crashes) probably affected the results.

Although the safety effectiveness estimate does not change significantly depending on which 

reference group is used (which is desirable), reference group 2 was chosen as the more 

appropriate reference group since in most cases, the HAWK was installed at a previously 

unsignalized intersection. There has not been a clear guideline in the literature on when to 

include the period indicator in the SPFs. Harwood et al. and Persaud et al. did not consider it, 

while Persaud and Lyon suggest including it.

(12, 13, 9) The decision of whether to include the 

period indicator in the SPFs could be made based on some objective criterion such as the 

corresponding p-value (the significance of the term) as in the case of other predictors. If a 

stringent criterion such that the corresponding p-value is less than or equal to 0.05 is used as a 
36

basis for the inclusion in the SPF, only the period indicator for pedestrian ISN crashes 

(p = 0.0106) and pedestrian IR crashes (p = 0.0222) can be retained in the model. In variable 

selection, however, it is typical to use a less stringent criterion such as including the variable if the 

corresponding p-value is less than or equal to 0.2, as mentioned earlier. Under such a criterion, the 

period indicator for total ISN crashes (p = 0.1639) can also be retained in the model.

FINDINGS

The preferred SPFs for total, severe, and pedestrian ISN and IR crashes (considering the 

goodness of fit, interpretability of models, and significance of the coefficients, especially the 

period indicator) are listed in table 14 and table 15.

The results from the EB analyses based on the final SPFs applied on ISN crashes are given in 

table 14. The key findings are as follows:

A 19 percent reduction in total crashes was achieved, which was statistically significant 

at the 95 percent confidence level.

A 69 percent reduction in pedestrian crashes was achieved, which was statistically 

significant at the 95 percent confidence level.

A 13 percent reduction in severe crashes was achieved, which was not statistically 

significant at the 95 percent confidence level.

Table 15 summarizes the results from the EB analyses applied on IR crashes. The key findings 

after the installation of a HAWK are as follows:

A 29 percent reduction in total crashes was achieved, which was statistically significant 

at the 95 percent confidence level.

A 65 percent reduction in pedestrian crashes was achieved, which was statistically 

significant at the 95 percent confidence level.

A 15 percent reduction in severe crashes was achieved, which was not statistically 

significant at the 95 percent confidence level.
37

Table 14. ISN crashes results.

Variable

Total

Crashes

Coefficient 

Estimate

(p-Value)

Severe

Crashes

Coefficient 

Estimate

(p-Value)

Pedestrian

Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-16.5961

(< 0.0001)

-17.7484

(< 0.0001)

-17.5699

(< 0.0001)

Period 

(after = 1, before = 0)

0.0613

(0.1639) —

0.6444

(0.0103)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.3665

(0.0313)

-0.3586

(0.0370) —

Major street speed limit (mi/h)

0.0653

(0.0409)

0.0860

(0.0031) —

LnVeh&Ped

0.9655

(0.0003)

0.8990

(0.0003) —

LnVeh — —

0.7673

(0.0347)

LnPed — —

0.2203

(0.0402)

Dispersion 0.4720 0.5560 0.2205

Pearson chi-square/degree of freedom 1.0757 1.0367 1.0513

EB Results

L, Number of crashes observed during 

the after period 508 173 4

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 624.517 198.106 12.8256

ˆ, Estimated index of effectiveness 0.812 0.870 0.309

( )ˆ se , Standard error of ˆ 0.047 0.084 0.156

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 19 13 69

Results are statistically significant at 

95 percent confidence level Yes No Yes

— Indicates that the variable was not included in model.

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).
38

Table 15. IR crashes results.

Variable

Total 

Crashes

Coefficient 

Estimate

(p-Value)

Severe 

Crashes

Coefficient 

Estimate

(p-Value)

Pedestrian

Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-18.5272

(< 0.0001)

-18.3149

(< 0.0001)

-27.2540

(0.0048)

Period 

(after = 1, before = 0) — —

0.8232

(0.0222)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.6012

(0.0012)

-0.5635

(0.0050) —

Major street speed limit (mi/h)

0.0917

(0.0025)

0.1128

(0.0012) —

LnVeh&Ped

0.9740

(0.0003) — —

LnVeh —

0.7829

(0.0087)

1.4937

(0.0506)

LnPed — —

0.3066

(0.1202)

Dispersion 0.6461 0.6297 1.2431

Pearson chi-square/degree of freedom 1.1445 1.0049 1.0946

EB Results

L, Number of crashes observed during 

the after period 183 77 2

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 256.423 90.0872 5.51422

ˆ, Estimated index of effectiveness 0.712 0.849 0.351

( )ˆ se , Standard error of ˆ 0.065 0.118 0.248

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 29 15 65

Results are statistically significant at 

95 percent confidence level Yes No Yes

— Indicates that the variable was not included in model.

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

A safety treatment at an intersection should influence the crash pattern occurring at the 

intersection. Crashes that occur a distance away from the intersection that are influenced by a 

specific intersection treatment would be a function of the type of treatment. For example, a 

left-turn prohibition could cause drivers to find a travel path through developments to achieve 
39

their goal. They might use an upstream or downstream driveway located a distance away from 

the intersection. Those driveway turns made in response to the left-turn prohibition could result 

in a crash that may not be counted because it did not occur at the intersection.

A HAWK may also influence crashes occurring away from the intersection. Before the HAWK 

is installed, pedestrians might be crossing away from the intersection because no benefit is 

provided to the pedestrians to walk the extra distance to the pedestrian crossing (i.e., because 

there is no active traffic control device informing drivers of the crossing pedestrians). When the 

HAWK is installed, pedestrians benefit from the activated traffic control device and may be 

more willing to walk the extra distance. Simply, the HAWK may consolidate pedestrian 

crossings within an area that extends beyond the typical limits of an intersection. Therefore, the

ISN crash evaluation in this study may be more representative of the change in pedestrian 

crashes as compared to IR crashes. While using the ISN evaluation results for pedestrians seems 

more reasonable for that type of crash, the IR crash evaluation results are probably more 

representative for total or severe crashes.

41

CHAPTER 6. SUMMARY, CONCLUSION, AND DISCUSSION

SUMMARY 

The HAWK is a pedestrian-activated beacon located at the roadside and on mast arms over the 

major approaches to an intersection. It was created in Tucson, AZ, and at the time of this study, it

was used at more than 60 locations throughout the city. The HAWK head consists of two red 

lenses over a single yellow lens. It appears red to drivers when activated and creates gaps during 

which pedestrians can cross the major street. It also transitions to a flashing red phase to allow 

vehicles to proceed as soon as the pedestrians have passed. Previous research found driver

yielding percentages above 95 percent for the HAWK treatment even on major streets with 

multiple lanes or higher speeds. Because of the limited number of treatments with high yielding 

rates for major arterials, the FWHA sponsored this study to determine the safety benefits of the 

HAWK. It considered 21 intersections where a HAWK had been installed. Evaluation 

approaches considered included the following:

Three types of crashes (total, severe, and pedestrian).

Two methods for identifying crashes (ISN and IR).

Two reference groups (reference group 1 with 36 signalized and 35 unsignalized 

intersections and reference group 2 with 102 unsignalized intersections).

Two ways to combine the reference group before and after data (aggregated where each 

intersection is only included once and disaggregated where each intersection is included 

twice and a period indicator variable represents the before and after periods).

This report documents a study of the safety performance of HAWKs using a before-after 

EB method. The EB method permits the evaluations to account for possible regression-to-the-mean 

bias as well as traffic, weather, citywide public relations campaigns, and other factors that change 

over time. SPFs were developed using reference site data consisting of nearby intersections without 

the HAWK treatment. The crash prediction during the before period is calculated from SPFs and 

combined with the observed crash count for the before period by using a weighted average to 

control for regression-to-the-mean bias. This weighted average is adjusted for differences in 

duration and traffic volumes (and general time trend if any exists) between the before and after 

periods to lead to a crash prediction for the after period had the treatment not been applied. EB then 

compares this predicted value to the observed crash frequency for the after period with the 

treatment installed. 

CONCLUSION

In conclusion, the before-after evaluation found the following:

A 29 percent reduction in total crashes, which is statistically significant at the 95 percent 

confidence level.
42

A 69 percent reduction in pedestrian crashes, which is statistically significant at the 

95 percent confidence level.

A 15 percent reduction in severe crashes, which is not statistically significant at the 

95 percent confidence level.

DISCUSSION

Two crash datasets were used in the before-after evaluation. The initial dataset, ISN crashes, 

included all crashes coded with the same street names that matched the HAWK or unsignalized 

intersections used in the study. The second dataset, IR crashes, included only those ISN crashes 

that had “yes” for the intersection-related code. In theory, the IR crash dataset should represent 

those crashes that would be affected by the traffic control at the intersection. A closer review 

revealed that the IR code was not used in over 1⁄3 of the crashes; therefore, the IR crash dataset 

may have eliminated too many of the crashes. The ISN crash dataset, however, may include 

crashes that are not related to the intersection. Therefore, both datasets were considered. The 

IR crashes may initially appear to be the more representative group for evaluating the benefits of 

the HAWK. The ISN crash evaluation, however, may be more representative of the change in 

pedestrian crashes as compared to IR crashes since the HAWK could induce pedestrians to walk 

an additional distance to receive the benefit of an activated traffic control device.

HAWK intersections are associated with a slightly greater number of total crashes

(0.223 crashes/MEV&P) as compared to nearby unsignalized intersections (0.150 crashes/MEV&P)

(see table 4). This observation should not indicate that the removal of a HAWK from a location 

will result in a crash rate similar to the unsignalized intersection rate. Rather, the conditions and 

characteristics at these locations are associated with more crashes. The before crash rate for 

the HAWK sites (i.e., before the HAWKs were installed) was greater (0.341 crashes/MEV&P) 

than the crash rate identified for the unsignalized intersections for the same time period

(0.166 crashes/MEV&P).

While the observed after crash rate is higher for total crashes at HAWKs as compared to nearby 

unsignalized intersections, the crash rate for total crashes at HAWK sites (0.223 crashes/MEV&P) 

is lower than the crash rate at signalized intersections (0.716 crashes/MEV&P). In addition, the 

pedestrian crash rates for HAWKs are lower than both the neighboring unsignalized intersections 

and the neighboring signalized intersections (see table 4). This difference is even more pronounced 

when only considering the number of entering pedestrians rather than both entering vehicles and 

pedestrians. The HAWK sites had 0.255 pedestrian crashes/MEP, while the unsignalized and 

signalized intersections had 0.602 and 0.839 pedestrian crashes/MEP, respectively.

The prime objective of a HAWK is to provide pedestrians with crossing opportunities. As such, 

a reduction in pedestrian crashes would be expected to be associated with the HAWK. The 

evaluation found a statistically significant reduction in pedestrian crashes for ISN (based on 

either aggregated or disaggregated data) and IR crashes (based on disaggregated data). The 

installation of the HAWK was also found to be associated with a statistically significant 

reduction in total crashes. The HAWK, however, just like any other warning traffic control 

device, may not work as well if overused. Also, such high crash reductions identified in this 
43

study may not be achieved at future locations if the site has different characteristics, such as less 

pedestrian activity.

While this study demonstrated safety benefits for the HAWK, there are still several questions 

that need to be investigated. The sample sizes for pedestrian crashes and for severe crashes were 

a concern during the evaluations. For pedestrian crashes, a statistically significant reduction in 

crashes (at the 95 percent confidence level) was achieved in spite of a small sample size due to a 

large effect size (69 percent). For severe crashes, the effect size was much smaller (15 percent,

although still practically significant) than that for pedestrian crashes, and a much larger sample 

will be required to achieve statistical significance. Further research with a larger sample should

examine the effectiveness of HAWKs in reducing severe crashes. It is possible that with a larger 

sample size, the effect of HAWKs on severe crashes may become statistically significant at the 

95 percent confidence level.

A preliminary review of crash type at the HAWK sites indicated a reduction in rear-end crashes, 

which is not typical when a higher level of control is implemented at an intersection. A potential 

reason for the reduction in rear-end crashes is that drivers behind the initial vehicle that has

stopped for a crossing pedestrian can view the traffic control device without needing to see the 

pedestrian, who may be obscured by the lead vehicle. Additional research to investigate the 

changes in crash patterns at the HAWK sites should be considered. Other questions include the 

minimum spacing between a HAWK and a signal and the criteria that should be used to warrant 

the device, especially near a school.

45 

APPENDIX: TABLES OF RESULTS 

Several SPF alternatives were developed. The following tables summarize the coefficients along 

with the EB results. The SPF alternative selected for each evaluation approach is shown in the 

first column of the tables. Although the magnitude of the safety effectiveness estimate varies to 

some extent as different predictors are included in the SPFs, the results did not seem to change 

materially. 
46

Table 16. Estimate of regression coefficients of SPFs for ISN total crashes

using reference group 1.

Variable

Alternative I:

Total Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Total Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept

-34.3200

(< 0.0001)

-32.1004

(< 0.0001)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.9932

(< 0.0001)

-0.9548

(< 0.0001)

Major street speed limit (mi/h)

0.0951

(0.0016)

0.0944

(0.0013)

Median refuge present

-0.7478

(0.0003)

-0.6844 

(0.0009)

LnVeh&Ped

2.6005

(< 0.0001) —

LnVeh —

2.3080

(< 0.0001)

LnPed —

0.1751

(0.0205)

Dispersion 0.4452 0.4192

Pearson chi-square/degree of freedom 0.9702 1.0125

EB Results

L, Number of crashes observed during 

the after period 508 508

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 594.744 601.915

ˆ, Estimated index of effectiveness 0.853 0.843

( )ˆ se , Standard error of ˆ 0.050 0.049

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 15 16

Results are statistically significant at 

95 percent confidence level Yes Yes

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
47

Table 17. Estimate of regression coefficients of SPFs for IR total crashes

using reference group 1.

Variable

Alternative I:

Total Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Total Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept

-34.2206

(< 0.0001)

-31.9988

(< 0.0001)

Intersection type 

(three-leg = 1, four-leg = 0)

-1.2010

(< 0.0001)

-1.1452

(< 0.0001)

Major street speed limit (mi/h)

0.0889

(0.0080)

0.0874

(0.0079)

Median refuge present

-0.5582

(0.0172)

-0.4851

(0.0370)

LnVeh&Ped

2.5262

(< 0.0001) —

LnVeh —

2.2308

(< 0.0001)

LnPed —

0.1841

(0.0287)

Dispersion 0.5276 0.4965

Pearson chi-square/degree of freedom 0.9983 1.0572

EB Results

L, Number of crashes observed during 

the after period 183 183

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 256.501 261.122

ˆ, Estimated index of effectiveness 0.711 0.699

( )ˆ se , Standard error of ˆ 0.065 0.064

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 29 30

Results are statistically significant at 

95 percent confidence level Yes Yes

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
48

Table 18. Estimate of regression coefficients of SPFs for ISN severe crashes

using reference group 1.

Variable

Alternative I:

Severe Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Severe Crashes

Coefficient 

Estimate

(p-Value)

Alternative III:

Severe Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept

-32.2219

(< 0.0001)

-34.1361

(< 0.0001)

-34.1789

(< 0.0001)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.9557

(< 0.0001)

-1.0020

(< 0.0001)

-1.0093

(< 0.0001)

Major street speed limit (mi/h)

0.1110

(0.0003)

0.1128

(0.0003)

0.1139

(0.0003)

Median refuge present

-0.6998

(0.0012)

-0.7657

(0.0004)

-0.7715

(0.0004)

LnVeh&Ped —

2.4128

(< 0.0001) —

LnVeh

2.1704

(< 0.0001) —

2.4153

(< .0001)

LnPed

0.1390

(0.0834) — —

Dispersion 0.4235 0.4426 0.4463

Pearson chi-square/degree of freedom 1.0360 0.9955 0.9912

EB Results

L, Number of crashes observed during 

the after period 173 173 173

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 192.979 188.366 188.025

ˆ, Estimated index of effectiveness 0.893 0.915 0.917

( )ˆ se , Standard error of ˆ 0.086 0.089 0.089

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 11 9 8

Results are statistically significant at 

95 percent confidence level No No No

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
49

Table 19. Estimate of regression coefficients of SPFs for IR severe crashes

using reference group 1.

Variable

Alternative I:

Severe Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Severe Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept

-32.9071

(< 0.0001)

-31.0082

(< 0.0001)

Intersection type 

(three-leg = 1, four-leg = 0)

-1.1455

(< 0.0001)

-1.0969

(< 0.0001)

Major street speed limit (mi/h)

0.1057

(0.0031)

0.1040

(0.0033)

Median refuge present

-0.5465

(0.0277)

-0.4726

(0.0606)

LnVeh&Ped

2.2558

(< 0.0001) —

LnVeh —

2.0141

(< 0.0001)

LnPed —

0.1385

(0.1344)

Dispersion 0.5425 0.5228

Pearson chi-square/degree of freedom 1.0243 1.0641

EB Results

L, Number of crashes observed during 

the after period 77 77

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 93.5850 96.4656

ˆ, Estimated index of effectiveness 0.817 0.793

( )ˆ se , Standard error of ˆ 0.114 0.110

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 18 21

Results are statistically significant at 

95 percent confidence level No No

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
50

Table 20. Estimate of regression coefficients of SPFs for ISN and IR pedestrian crashes 

using reference group 1.

Variable

Alternative I:

ISN Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

IR Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept

-26.5372

(< 0.0001)

-31.9455

(< 0.0001)

Intersection Type 

(three-leg = 1, four-leg = 0)

-0.8826

(0.0137)

-0.8626

(0.1096)

Major street speed limit (mi/h)

0.1048

(0.0031)

0.1313

(0.0173)

Median refuge present

-0.4731

(0.0545)

-0.1824

(0.6126)

LnVeh&Ped

1.4433

(0.0002)

1.7660

(0.0028)

LnVeh — —

LnPed — —

Dispersion 0.0588 0.1978

Pearson chi-square/degree of freedom 1.1428 1.2738

EB Results

L, Number of crashes observed during 

the after period 4 2

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 9.35410 4.49476

ˆ, Estimated index of effectiveness 0.426 0.439

( )ˆ se , Standard error of ˆ 0.214 0.311

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 57 56

Results are statistically significant at 

95 percent confidence level Yes No

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
51

Table 21. Estimate of regression coefficients of SPFs for ISN total crashes

using reference group 2.

Variable

Alternative I:

Total Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Total Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-16.8197

(< 0.0001)

-16.7870

(< 0.0001)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.3732

(0.0116)

-0.3731

(0.0116)

Major street speed limit (mi/h)

0.0673

(0.0062)

0.0672

(0.0062)

LnVeh&Ped

0.9827

(< 0.0001) —

LnVeh —

0.9804

(< 0.0001)

LnPed — —

Dispersion 0.4592 0.4589

Pearson chi-square/degree of freedom 1.1011 1.0995

EB Results

L, Number of crashes observed during 

the after period 508 508

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 588.646 588.054

ˆ, Estimated index of effectiveness 0.862 0.863

( )ˆ se , Standard error of ˆ 0.050 0.050

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 14 14

Results are statistically significant at 

95 percent confidence level Yes Yes

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
52

Table 22. Estimate of regression coefficients of SPFs for IR total crashes

using reference group 2.

Variable

Alternative I:

Total Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Total Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-18.5272

(< 0.0001)

-18.5557

(< 0.0001)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.6012

(0.0012)

-0.6018

(0.0012)

Major street speed limit (mi/h)

0.0917

(0.0025)

0.0915

(0.0025)

LnVeh&Ped

0.9740

(0.0003) —

LnVeh —

0.9778

(0.0002)

LnPed — —

Dispersion 0.6461 0.6450

Pearson chi-square/degree of freedom 1.1445 1.1455

EB Results

L, Number of crashes observed during 

the after period 183 183

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 256.423 256.071

ˆ, Estimated index of effectiveness 0.712 0.713

( )ˆ se , Standard error of ˆ 0.065 0.065

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 29 29

Results are statistically significant at 

95 percent confidence level Yes Yes

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
53

Table 23. Estimate of regression coefficients of SPFs for ISN severe crashes

using reference group 2.

Variable

Alternative I:

Severe Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Severe Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-17.7484

(< 0.0001)

-17.7487

(< 0.0001)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.3586

(0.0370)

-0.3585

(0.0368)

Major street speed limit (mi/h)

0.0860

(0.0031)

0.0858

(0.0031)

LnVeh&Ped

0.8990

(0.0003) —

LnVeh —

0.9001

(0.0003)

LnPed — —

Dispersion 0.5560 0.5552

Pearson chi-square/degree of freedom 1.0367 1.0353

EB Results

L, Number of crashes observed during 

the after period 173 173

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 198.106 197.805

ˆ, Estimated index of effectiveness 0.870 0.871

( )ˆ se , Standard error of ˆ 0.084 0.084

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 13 13

Results are statistically significant at 

95 percent confidence level No No

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
54

Table 24. Estimates of regression coefficients of SPFs for IR severe crashes

using reference group 2.

Variable

Alternative I:

Severe Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Severe Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-18.3149

(< 0.0001)

-18.2802

(< 0.0001)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.5635

(0.0050)

-0.5633

(0.0051)

Major street speed limit (mi/h)

0.01128

(0.0012)

0.1130

(0.0012)

LnVeh&Ped —

0.7785

(0.0094)

LnVeh

0.7829

(0.0087) —

LnPed — —

Dispersion 0.6297 0.6305

Pearson chi-square/degree of freedom 1.0049 1.0056

EB Results

L, Number of crashes observed during 

the after period 77 77

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 90.0872 90.2312

ˆ, Estimated index of effectiveness 0.849 0.848

( )ˆ se , Standard error of ˆ 0.118 0.118

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 15 15

Results are statistically significant at 

95 percent confidence level No No

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
55

Table 25. Estimate of regression coefficients of SPFs for ISN pedestrian crashes

using reference group 2.

Variable

Alternative I:

Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

Alternative III:

Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

Alternative IV:

Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-16.8225

(0.0004)

-16.3873

(0.0003)

-16.5834

(0.0003)

-16.9442

(0.0004)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.0292

(0.9207)

-0.0719

(0.8093) — —

Major street speed limit (mi/h)

0.0248

(0.6263)

0.0317

(0.5388) — —

LnVeh&Ped —

0.6791

(0.1516)

0.8059

(0.0622) —

LnVeh

0.6518

(0.1787) — —

0.7527

(0.0893)

LnPed

0.1999

(0.1186) — —

0.1987

(0.1178)

Dispersion 0.2712 0.3516 0.3551 0.2716

Pearson chi-square/degree of freedom 1.0967 1.0113 0.9894 1.0816

EB Results

L, Number of crashes observed during 

the after period 4 4 4 4

ˆ , Predicted number of crashes 

during after period had the HAWK 

not been installed 9.71056 8.76300 8.65617 9.60233

ˆ, Estimated index of effectiveness 0.408 0.451 0.457 0.412

( )ˆ se , Standard error of ˆ 0.206 0.228 0.231 0.208

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash 

reduction) 59 55 54 59

Results are statistically significant at 

95 percent confidence level Yes Yes Yes Yes

— Indicates that the variable was not included in model.

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).
56

Table 26. Estimate of regression coefficients of SPFs for IR pedestrian crashes

using reference group 2 (page 1 of 2).

Variable

Alternative I:

Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

Alternative III:

Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-25.4693

(0.0222)

-26.1717

(0.0243)

-24.0449

(0.0258)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.3600

(0.5457)

-0.3681

(0.5335)

-0.4575

(0.4387)

Major street speed limit (mi/h)

0.0497

(0.6429)

0.0493

(0.6431)

0.0615

(0.5616)

LnVeh&Ped — —

1.1775

(0.2754)

LnVeh —

1.2820

(0.2650) —

LnPed

0.3056

(0.2692)

0.3026

(0.2800) —

LnMajor

1.1741 

(0.2829) — —

LnMinor

0.0692

(0.8003) — —

Dispersion 1.2769 1.2338 1.3763

Pearson chi-square/degree of freedom 0.9878 1.0279 0.9762

EB Results

L, Number of crashes observed during 

the after period 2 2 2

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 3.94071 3.86283 3.30109

ˆ, Estimated index of effectiveness 0.490 0.500 0.585

( )ˆ se , Standard error of ˆ 0.347 0.354 0.413

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 51 50 42

Results are statistically significant at 

95 percent confidence level No No No

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

LnMajor = Ln(entering vehicles from major approaches).

LnMinor = Ln(entering vehicles from minor approaches).

— Indicates that the variable was not included in model.
57

Table 27. Estimate of regression coefficients of SPFs for IR pedestrian crashes

using reference group 2 (page 2 of 2).

Variable

Alternative IV:

Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

Alternative V:

Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept

-27.1040

(0.0213)

-24.7119

(0.0228)

Intersection type 

(three-leg = 1, four-leg = 0) — —

Major street speed limit (mi/h) — —

LnVeh&Ped —

1.4370

(0.1589)

LnVeh

1.5182

(0.1582) —

LnPed

0.3230

(0.2402) —

Dispersion 1.2602 1.4822

Pearson chi-square/degree of freedom 0.9761 0.9160

EB Results

L, Number of crashes observed during 

the after period 2 2

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 3.81139 3.24767

ˆ, Estimated index of effectiveness 0.508 0.595

( )ˆ se , Standard error of ˆ 0.359 0.420

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 49 41

Results are statistically significant at 

95 percent confidence level No No

— Indicates that the variable was not included in model.

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).
58

Table 28. Estimate of regression coefficients of SPFs for ISN total crashes

using reference group 2 and the period indicator variable.

Variable

Alternative I:

Total Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Total Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-16.5961

(< 0.0001)

-16.5632

(< 0.0001)

Period 

(after = 1, before = 0)

0.0613

(0.1639)

0.0617

(0.1606)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.3665

(0.0313)

-0.3665

(0.0314)

Major street speed limit (mi/h)

0.0653

(0.0409)

0.0652

(0.0418)

LnVeh&Ped

0.9655

(0.0003) —

LnVeh —

0.9632

(0.0003)

LnPed — —

Dispersion 0.4720 0.4717

Pearson chi-square/degree of freedom 1.0757 1.0741

EB Results

L, Number of crashes observed during 

the after period 508 508

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 624.517 624.163

ˆ, Estimated index of effectiveness 0.812 0.813

( )ˆ se , Standard error of ˆ 0.047 0.047

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 19 19

Results are statistically significant at 

95 percent confidence level Yes Yes

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
59

Table 29. Estimate of regression coefficients of SPFs for IR total crashes 

using reference group 2 and the period indicator variable.

Variable

Alternative I:

Total Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Total Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-17.9300

(< 0.0001)

-17.9498

(< 0.0001)

Period 

(after = 1, before = 0)

-0.0870

(0.2651)

-0.0863

(0.2691)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.5831

(0.0017)

-0.5834

(0.0017)

Major street speed limit (mi/h)

0.0905

(0.0227)

0.0903

(0.0233)

LnVeh&Ped

0.9247

(0.0006) —

LnVeh —

0.9277

(0.0005)

LnPed — —

Dispersion 0.6628 0.6619

Pearson chi-square/degree of freedom 1.1767 1.1777

EB Results

L, Number of crashes observed during 

the after period 183 183

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 237.043 236.917

ˆ, Estimated index of effectiveness 0.770 0.770

( )ˆ se , Standard error of ˆ 0.071 0.071

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 23 23

Results are statistically significant at 

95 percent confidence level Yes Yes

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
60

Table 30. Estimate of regression coefficients of SPFs for ISN severe crashes

using reference group 2 and the period indicator variable.

Variable

Alternative I:

Severe Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Severe Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-17.5186

(< 0.0001)

-17.5169

(< 0.0001)

Period 

(after = 1, before = 0)

0.0080

(0.8923)

0.0085

(0.8851)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.3434

(0.0729)

-0.3434

(0.0730)

Major street speed limit (mi/h)

0.0832

(0.0125)

0.0830

(0.0130)

LnVeh&Ped

0.8858

(0.0042) —

LnVeh —

0.8867

(0.0041)

LnPed — —

Dispersion 0.5709 0.5702

Pearson chi-square/degrees of freedom 0.9802 0.9791

EB Results

L, Number of crashes observed during 

the after period 173 173

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 199.818 199.639

ˆ, Estimated index of effectiveness 0.863 0.863

( )ˆ se , Standard error of ˆ 0.084 0.084

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 14 14

Results are statistically significant at 

95 percent confidence level No No

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
61

Table 31. Estimate of regression coefficients of SPFs for IR severe crashes

using reference group 2 and the period indicator variable.

Variable

Alternative I:

Severe Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Severe Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-17.9507

(< 0.0001)

-17.9757

(< 0.0001)

Period 

(after = 1, before = 0)

-0.1117

(0.2582)

-0.1112

(0.2604)

Intersection type 

(three-leg = 1, four-leg = 0)

-0.5374

(0.0064)

-0.5375

(0.0064)

Major street speed limit (mi/h)

0.1125

(0.0016)

0.01123

(0.0017)

LnVeh&Ped

0.7522

(0.0180) —

LnVeh —

0.7556

(0.0174)

LnPed — —

Dispersion 0.6829 0.6822

Pearson chi-square/degree of freedom 0.9708 0.9700

EB Results

L, Number of crashes observed during 

the after period 77 77

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 83.0204 82.9242

ˆ, Estimated index of effectiveness 0.921 0.922

( )ˆ se , Standard error of ˆ 0.128 0.128

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash reduction) 8 8

Results are statistically significant at 

95 percent confidence level No No

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).

— Indicates that the variable was not included in model.
62

Table 32. Estimate of regression coefficients of SPFs for ISN pedestrian crashes 

using reference group 2 and the period indicator variable.

Variable

Alternative I:

Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

Alternative II:

Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

Alternative III:

Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

Alternative IV:

Pedestrian 

Crashes

Coefficient 

Estimate

(p-Value)

SPF Results

Intercept 

-17.5699

(< 0.0001)

-17.3841

(< 0.0001)

-16.2619

(< 0.0001)

-17.3941

(< 0.0001)

Period 

(after = 1, before = 0)

0.6444

(0.0103)

0.6408

(0.0106)

0.6582

(0.0091)

0.6406

(0.0106)

Intersection type 

(three-leg = 1, four-leg = 0) — — —

0.0088

(0.9738)

Major street speed limit (mi/h) —

0.0232

(0.6216) —

0.0227

(0.6348)

LnVeh&Ped — —

0.7408

(0.0258) —

LnVeh

0.7673

(0.0347)

0.6683

(0.1087) —

0.6709

(0.1144)

LnPed

0.2203

(0.0402)

0.2191

(0.0417) —

0.2196

(0.0367)

Dispersion 0.2205 0.2189 0.3158 0.2180

Pearson chi-square/degree of freedom 1.0513 1.0462 1.0160 1.0524

EB Results

L, Number of crashes observed 

during the after period 4 4 4 4

ˆ , Predicted number of crashes 

during after period had the HAWK 

not been installed 12.8256 12.8646 11.6274 12.8896

ˆ, Estimated index of effectiveness 0.309 0.308 0.340 0.308

( )ˆ se , Standard error of ˆ 0.156 0.155 0.172 0.155

( )ˆ 100 1 , Percent reduction in the 

number of crashes (i.e., crash 

reduction) 69 69 66 69

Results are statistically significant at 

95 percent confidence level Yes Yes Yes Yes

— Indicates that the variable was not included in model.

LnVeh&Ped = Ln(entering vehicles and pedestrians).

LnVeh = Ln(entering vehicles).

LnPed = Ln(entering pedestrians).
63 

Table 33. Estimate of regression coefficients of SPFs for IR pedestrian crashes 

using reference group 2 and the period indicator variable. 

Variable 

Alternative I: 

Pedestrian 

Crashes 

Coefficient 

Estimate 

(p-Value) 

Alternative II: 

Pedestrian 

Crashes 

Coefficient 

Estimate 

(p-Value) 

Alternative III:

Pedestrian 

Crashes 

Coefficient 

Estimate 

(p-Value) 

SPF Results

Intercept 

-27.2540

(0.0048)

-26.2689 

(0.0152) 

-24.7331

(0.0031)

Period 

(after = 1, before = 0) 

0.8232

(0.0222)

0.8392 

(0.1295) 

0.8641

(0.0252)

Intersection type 

(three-leg = 1, four-leg = 0) —

-0.4000 

(0.5594) —

Major street speed limit (mi/h) —

0.0496 

(0.6633) —

LnVeh&Ped — — 

1.3912

(0.0553)

LnVeh 

1.4937

(0.0506)

1.2530 

(0.2246) —

LnPed 

0.3066

(0.1202)

0.2842 

(0.1639) —

Dispersion 1.2431 1.3086 1.6436

Pearson chi-square/degree of freedom 1.0946 1.0133 1.0530

EB Results

L, Number of crashes observed during 

the after period 2 2 2

ˆ , Predicted number of crashes during 

after period had the HAWK not been 

installed 5.51422 6.03609 5.12614

ˆ , Estimated index of effectiveness 0.351 0.320 0.376

 ˆ se  , Standard error of ˆ 0.248 0.228 0.266

 ˆ 100 1   , Percent reduction in the 

number of crashes (i.e., crash reduction) 65 68 62

Results are statistically significant at 

95 percent confidence level Yes Yes Yes

— Indicates that the variable was not included in model. 

LnVeh&Ped = Ln(entering vehicles and pedestrians). 

LnVeh = Ln(entering vehicles). 

LnPed = Ln(entering pedestrians). 

65

ACKNOWLEDGMENTS

This research is sponsored by the FHWA as part of the Evaluation of Pedestrian and Bicycle 

Safety Engineering Countermeasures Project. The project is under the direction of Ann Do of 

FHWA. The research was performed at the Texas Transportation Institute. The contents of this 

report reflect the views of the authors, who are responsible for the facts and the accuracy of the 

data presented herein. The contents do not necessarily reflect the official views or polices of the 

FHWA. The authors appreciate the efforts of the volunteer reviewers of the papers prepared from 

this research in assisting with the creation of a superior product. The authors also recognize the 

reviews and feedback provided by those within the FHWA such as Scott Wainwright and others 

unnamed. Assisting the authors with volume data collection were Marcus Brewer and Katie 

Green. Also, Dominique Lord helped answer EB questions. The authors would like to 

acknowledge Richard Nassi and the city of Tucson, AZ, for their assistance in obtaining the 

needed crash dataset used in this study, along with the video tapes of selected intersections used 

to generate adjustment factors for the 2-h pedestrian counts.

67

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HRDS-07/07-10(Web)E