Safety Evaluation of Edge-Line

Rumble Stripes on Rural Two-Lane

Horizontal Curves

PUBLICATION NO. FHWA-HRT-17-069 DECEMBER 2017

Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296
FOREWORD

The research documented in this report was conducted as part of the Federal Highway 

Administration’s (FHWA) Evaluation of Low-Cost Safety Improvements Pooled Fund Study 

(ELCSI-PFS). FHWA established this PFS in 2005 to conduct research on the effectiveness of 

the safety improvements identified by the National Cooperative Highway Research Program 

Report 500 guides as part of the implementation of the American Association of State Highway 

and Transportation Officials Strategic Highway Safety Plan. The ELCSI-PFS studies provide a 

crash modification factor and benefit–cost (B/C) economic analysis for each of the targeted 

safety strategies identified as priorities by the pooled fund member States.

This study evaluated application of edge-line rumble stripes (ELRSs) on rural two-lane 

horizontal curves. ELRSs are a variation of common shoulder rumble strips used to alert drowsy 

or distracted drivers when they are leaving the travel lane to the right. ELRSs are installed with 

the edge-line pavement marking placed directly over the rumble strip. Data were obtained at 

treated rural two-lane horizontal curves in Kentucky and Ohio. The results for Kentucky indicate 

statistically significant reductions for total, injury, run-off-road (ROR), and nighttime crashes. 

The results for Ohio indicate statistically significant reductions for all crash types (i.e., total, 

injury, ROR, nighttime, and nighttime ROR). The B/C analysis results suggest that this treatment 

can be highly cost-effective. This report is intended for State departments of transportation, 

transportation agencies, academics, researchers, and other practitioners.

Jonathan Porter, Ph.D.

Acting Director, Office of Safety

Research and Development

Notice

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

(USDOT) in the interest of information exchange. The U.S. Government assumes no liability for 

the use of the information contained in this document.

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-17-069

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

4. Title and Subtitle

Safety Evaluation of Edge-Line Rumble Stripes on Rural Two-Lane 

Horizontal Curves

5. Report Date

December 2017

6. Performing Organization Code

7. Author(s)

Scott Himes, Frank Gross, Bhagwant Persaud, and Kimberly Eccles

8. Performing Organization Report No.

9. Performing Organization Name and Address

VHB

8300 Boone Boulevard, Suite 700

Vienna, VA 22182-2626

10. Work Unit No. (TRAIS)

11. Contract or Grant No.

DTFH61-13-D-00001

12. Sponsoring Agency Name and Address

U.S. Department of Transportation

Federal Highway Administration

1200 New Jersey Avenue, SE

Washington, DC 20590-3660

13. Type of Report and Period Covered

Safety Evaluation; 2014–2016

14. Sponsoring Agency Code

15. Supplementary Notes

The Federal Highway Administration (FHWA) Office of Safety Research and Development managed this study 

under the Development of Crash Modification Factors program. The FHWA Office of Safety Research and 

Development Contracting Officer’s Program and Task Manager was Roya Amjadi (HRDS-20).

16. Abstract

The Development of Crash Modification Factors (DCMF) program conducted safety evaluations of edge-line rumble 

stripes (ELRSs) on rural two-lane horizontal curves for the Evaluation of Low-Cost Safety Improvements Pooled 

Fund Study. This study evaluated the application of ELRSs on rural two-lane horizontal curves. ELRSs are a 

variation of common shoulder rumble strips used to alert drowsy or distracted drivers when they are leaving the 

travel lane to the right. ELRSs are installed with the edge-line pavement marking placed directly over the rumble 

strip. Geometric, traffic, and crash data were obtained at treated rural two-lane horizontal curves in Kentucky and 

Ohio. To account for potential selection bias and regression-to-the-mean, an empirical Bayes before–after analysis 

was conducted using reference groups of untreated rural horizontal curves with similar characteristics to the treated 

sites. The analysis also controlled for changes in traffic volumes over time and time trends in crash counts unrelated 

to the treatment. Owing to a small sample for the reference group in Kentucky and a simultaneous statewide curve 

warning sign upgrade program in Ohio, alternative reference sites were used to account for annual trends. The results 

for Kentucky indicated statistically significant reductions for total, injury, run-off-road (ROR), and nighttime 

crashes, with crash modification factors (CMFs) of 0.75, 0.64, 0.74, and 0.63, respectively. The results for Ohio 

indicated statistically significant reductions for all crash types, with total, injury, ROR, nighttime, and nighttime 

ROR CMFs of 0.79, 0.79, 0.78, 0.75, and 0.71, respectively. The two States’ results could not be combined because

of the statewide curve signing program in Ohio. It is important to note that all crash types considered in this research 

excluded intersection-related and animal crashes. Benefit–cost (B/C) ratios were estimated to be 331:1 for Kentucky 

and 477:1 for Ohio. If ELRSs were used as a curve-specific treatment, the B/C ratio would likely be much smaller 

because of the higher installation cost; however, these results suggest that the treatment can be highly cost effective.

17. Key Words

ELRS, two-lane rural roads, horizontal curves, distracted 

driver, rumble strips, rumble stripes, low-cost, safety 

improvements, empirical Bayesian.

18. Distribution Statement.

No restrictions. This document is available through the 

National Technical Information Service, 

Springfield, VA 22161.

http://www.ntis.gov

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

61

22. Price

Form DOT F 1700.7 (8-72) Reproduction of completed pages authorized.
ii
iii

TABLE OF CONTENTS

EXECUTIVE SUMMARY ...........................................................................................................1

CHAPTER 1. INTRODUCTION.................................................................................................3

BACKGROUND ON STRATEGY ..........................................................................................3

BACKGROUND ON STUDY...................................................................................................4

LITERATURE REVIEW .........................................................................................................4

CHAPTER 2. OBJECTIVE........................................................................................................15

CHAPTER 3. STUDY DESIGN.................................................................................................17

CHAPTER 4. METHODOLOGY..............................................................................................23

CHAPTER 5. DATA COLLECTION........................................................................................25

KENTUCKY ............................................................................................................................25

Installation Data.................................................................................................................. 25

Reference Sites..................................................................................................................... 25

Roadway Data ..................................................................................................................... 26

Traffic Data ......................................................................................................................... 26

Crash Data........................................................................................................................... 26

Treatment Cost Data .......................................................................................................... 26

OHIO.........................................................................................................................................27

Installation Data.................................................................................................................. 27

Reference Sites..................................................................................................................... 27

Roadway Data ..................................................................................................................... 27

Traffic Data ......................................................................................................................... 27

Crash Data........................................................................................................................... 27

Treatment Cost Data .......................................................................................................... 28

DATA CHARACTERISTICS AND SUMMARY ................................................................28

CHAPTER 6. DEVELOPMENT OF SAFETY PERFORMANCE FUNCTIONS ...............31

CRASH SPILLOVER AND MIGRATION ..........................................................................31

SAFETY PERFORMANCE FUNCTIONS...........................................................................34

CHAPTER 7. BEFORE–AFTER EVALUATION RESULTS................................................37

AGGREGATE ANALYSIS ....................................................................................................37

DISAGGREGATE ANALYSIS OF OHIO DATA...............................................................38

CHAPTER 8. ECONOMIC ANALYSIS...................................................................................41

CHAPTER 9. SUMMARY AND CONCLUSIONS..................................................................43

APPENDIX: ADDITIONAL INSTALLATION DETAILS ....................................................45

RESPONSES FROM KENTUCKY.......................................................................................46

RESPONSES FROM OHIO...................................................................................................46

ACKNOWLEDGEMENTS ........................................................................................................49

REFERENCES.............................................................................................................................51
iv

LIST OF FIGURES

Figure 1. Illustration. Examples of longitudinal rumble strip markings......................................... 5

Figure 2. Illustration. Overview of rumble strip dimensions.......................................................... 6

Figure 3. Equation. Estimated change in safety............................................................................ 23

Figure 4. Equation. EB estimate of expected crashes................................................................... 23

Figure 5. Equation. EB weight...................................................................................................... 24

Figure 6. Equation. Index of effectiveness ................................................................................... 24

Figure 7. Equation. Standard deviation of index of effectiveness................................................ 24

Figure 8. Equation. SPF model form for crash migration or spillover effects.............................. 31

Figure 9. Graph. Yearly multiplier by year for reference groups in Kentucky ............................ 32

Figure 10. Graph. Yearly multiplier by year for reference groups in Ohio .................................. 34

Figure 11. Equation. SPF model form for Kentucky and Ohio .................................................... 34

LIST OF TABLES

Table 1. Summary of studies on changes in target collision frequency from application of 

SRSs.......................................................................................................................................... 8

Table 2. Rumble strip dimensions from Lyon et al. ..................................................................... 12

Table 3. Before-period crash rate assumptions............................................................................. 18

Table 4. Minimum required before-period mile-years for treated sites—total crashes................ 19

Table 5. Minimum required before-period mile-years for treated sites—injury crashes ............. 19

Table 6. Minimum required before-period mile-years for treated sites—ROR crashes............... 20

Table 7. Minimum required before-period mile-years for treated sites—nighttime crashes........ 20

Table 8. Minimum required before-period mile-years for treated sites—nighttime ROR 

crashes..................................................................................................................................... 21

Table 9. Analysis for crash effects in Kentucky........................................................................... 22

Table 10. Analysis for crash effects in Ohio................................................................................. 22

Table 11. Kentucky treatment cost and service life data .............................................................. 26

Table 12. Ohio treatment cost data ............................................................................................... 28

Table 13. Definitions of crash types............................................................................................. 28

Table 14. Data summary for treatment sites................................................................................. 29

Table 15. Data summary for Kentucky reference sites................................................................. 30

Table 16. Data summary for Ohio reference sites ........................................................................ 30

Table 17. Reference group SPF for total crashes—parameter estimates...................................... 31

Table 18. Observed and predicted crashes for reference groups in Kentucky.............................. 32

Table 19. Observed and predicted crashes for reference groups in Ohio ..................................... 34

Table 20. SPFs by crash type........................................................................................................ 35

Table 21. Time trend factors for predicted crashes....................................................................... 36

Table 22. Aggregate analysis results for Kentucky ...................................................................... 37

Table 23. Aggregate analysis results for Ohio.............................................................................. 37

Table 24. Ohio results by AADT.................................................................................................. 39

Table 25. Ohio results by before-period expected crash frequency.............................................. 39

Table 26. Recommended CMFs for ELRSs based on Kentucky data .......................................... 43

Table 27. Recommended CMFs for ELRSs and curve signage based on Ohio data.................... 43
v

LIST OF ABBREVIATIONS

AADT average annual daily traffic 

AASHTO American Association of State Highway and Transportation Officials

B/C benefit–cost

C-G comparison group

CLRS center-line rumble strip

CMF crash modification factor

DCMF Development of Crash Modification Factors (program)

EB empirical Bayes 

ELCSI-PFS Evaluation of Low-Cost Safety Improvements Pooled Fund Study

ELRS edge-line rumble stripe

FHWA Federal Highway Administration 

FTM flat thermoplastic edge marking

GIS geographic information system

HPMS Highway Performance Monitoring System

HSIS Highway Safety Information System

KABCO Scale used to represent injury severity in crash reporting (K is fatal injury, A is 

incapacitating injury, B is non-incapacitating injury, C is possible injury, O is 

property damage only)

KYTC Kentucky Transportation Cabinet

MUTCD Manual on Uniform Traffic Control Devices

NCHRP National Cooperative Highway Research Program

ODOT Ohio Department of Transportation

PFS pooled fund study

ROR run-off-road

SE standard error

SPF safety performance function 

SRS shoulder rumble strip

SVROR single-vehicle run-off-road

1

EXECUTIVE SUMMARY

The Federal Highway Administration (FHWA) established the Development of Crash 

Modification Factors (DCMF) program in 2012 to address highway safety research needs for 

evaluating new and innovative safety strategies (improvements) by developing reliable 

quantitative estimates of their effectiveness in reducing crashes. The ultimate goal of the DCMF 

program is to save lives by identifying new safety strategies that effectively reduce crashes and 

promote those strategies for nationwide implementation by providing measures of their safety 

effectiveness and benefit–cost (B/C) ratios through research. State transportation departments 

and other transportation agencies need to have objective measures for safety effectiveness and 

B/C ratios before investing in new strategies for statewide safety improvements. Forty State 

transportation departments have provided technical feedback on safety improvements to the 

DCMF program and have implemented new safety improvements to facilitate evaluations. These 

States are members of the Evaluation of Low-Cost Safety Improvements-Pooled Fund Study, 

which functions under the DCMF program.

This study evaluated the application of edge-line rumble stripes (ELRSs) on rural two-lane 

horizontal curves. ELRSs are a variation of common shoulder rumble strips (SRSs) used to alert 

drowsy or distracted drivers when they leave the travel lane to the right. ELRSs are installed 

where edge-line pavement markings would normally be placed, and the pavement marking is 

installed directly over the rumble strip. In this way, the ELRSs are installed closer to the travel 

lane than common SRSs. In addition, the vertical faces that are created within the milled rumble 

strip to which pavement markings are applied have the effect of enhancing the visibility of the 

edge line during nighttime and wet-weather conditions. 

The project team obtained geometric, traffic, and crash data at treated rural horizontal curve 

locations in Kentucky and Ohio. To account for potential selection bias and regression-to-themean, the project team conducted an empirical Bayes (EB) before–after analysis using reference

groups of untreated rural horizontal curves with similar characteristics to the treated sites. The 

analysis also controlled for changes in traffic volumes over time and time trends in crash counts 

unrelated to the treatment. While the analysis focused on the safety effectiveness on horizontal 

curves, the treatment applications were not limited only to horizontal curves. The treatment was 

a corridor treatment applied to segments consisting of both tangents and curves; however, the 

analysis removed horizontal tangents and only considered the effectiveness on curves.

The results for Kentucky indicated statistically significant reductions for total, injury, run-offroad (ROR), and nighttime crashes at the 95-percent confidence level. Nighttime crashes had the 

smallest crash modification factor (CMF), or the greatest reduction, with a value of 0.63. Total, 

injury, and ROR crashes had CMFs of 0.75, 0.64, and 0.74, respectively. The CMF for nighttime 

ROR crashes was 0.75 and was consistent with the same CMF from Ohio; however, it was 

significant only at the 80-percent level, suggesting that sample size was the reason for the lack of 

statistical significance at the 95-percent level. The results for Ohio indicated statistically 

significant reductions for all crash types. Nighttime ROR crashes had the smallest CMF of 0.71. 

Total, injury, ROR, and nighttime crashes had CMFs of 0.79, 0.79, 0.78, and 0.75, respectively. 

The resulting Ohio installation CMFs reflected the installation of ELRSs on horizontal curves as 
2

well as the impact of the statewide signing program. It is also important to note that all crash 

types considered in this research excluded intersection-related and animal crashes. 

A disaggregate analysis of the results indicated larger safety benefits for horizontal curves with 

average annual daily traffic (AADT) greater than 4,000 for all crash types; however, the 

differences by AADT were not statistically significant at the 95-percent confidence level. The 

disaggregate analysis further indicated larger safety benefits for horizontal curves with a higher 

before-period expected crash frequency. The results suggested no benefit for curves with low 

before-period expected crash frequencies for all crash types. The difference in CMFs between 

low before-period expected crash frequency and high before-period expected crash frequency

was statistically significant for total and ROR crashes. Due to correlation between variables, 

caution should be used in interpreting and applying these disaggregate results; however, the 

disaggregate analysis CMFs may be used to inform the process of prioritizing treatment sites for 

ELRSs.

Estimated B/C ratios range from 189:1 to 467:1 for Kentucky and from 272:1 to 672:1 for Ohio.

On first inspection, the B/C ratios were larger than expected for an installation of this type. 

However, the installations took place on corridors, while the analysis only looked at the safety 

effects on horizontal curves. Horizontal curves have higher crash rates than overall corridors, and 

the cost per mile of installation would not be representative for installations only on horizontal 

curves. As a curve-specific treatment, the B/C ratio would likely be reduced owing to the higher 

deployment cost for spot-specific installations. Regardless, these results suggest that the 

treatment, even in its most expensive variation, can be highly cost effective. 
3

CHAPTER 1. INTRODUCTION

This chapter presents background information on the strategy of using edge-line rumble stripes 

(ELRSs), the goals of the study reported here, and a review of the existing literature on the use of 

rumble strips.

BACKGROUND ON STRATEGY

ELRSs are a variation of the common shoulder rumble strips (SRSs) used to alert drowsy or 

distracted drivers when they leave the travel lane to the right. SRSs and ELRSs both target runoff-road (ROR) crashes. Key distinctions between SRSs and ELRSs are provided in the 

following points:

• SRSs are provided on the shoulder between the pavement marking and the outside edge 

of the pavement and can be defined by their offset from the edge-line pavement marking. 

• ELRSs are installed where the edge-line pavement marking would normally be placed,

and the pavement marking is installed directly over the rumble strip. In this way, the 

rumble stripes are installed closer to the travel lane than common SRSs. In addition, 

vertical faces are created within the milled rumble strip to which pavement markings are 

applied, thereby enhancing the visibility of the edge line during nighttime and wetweather conditions.

Application of ELRSs varies among States depending on climate and roadway surface type. In 

colder areas, rumble strips are milled into the surface of the roadway, allowing them to be

snowplowable. In areas that do not receive snowfall, profiled thermoplastic pavement markings 

can be used. In addition, profiled thermoplastic pavement markings have been used as an 

alternative to milled ELRSs for roadways with a chip seal surface. The research in this study

focused on the safety effectiveness of milled ELRSs.

Several research studies have examined the use of SRSs; however, research into the performance 

of ELRSs has been rare and has not been rigorously evaluated. In addition, milled rumble strips 

have been installed on roadway segments consisting of both horizontal tangents and horizontal 

curves. Installations on only horizontal curves have been uncommon, and therefore, safety 

effectiveness evaluations have not focused on their effectiveness on horizontal curves specifically. 

This study focused on the safety effectiveness of ELRSs on rural two-lane horizontal curves taken 

from rumble strip installations that were not specific to horizontal curves.

Additional details concerning current practice with rumble strips can be found on the Federal 

Highway Administration (FHWA) Rumble Strip Community of Practice Web page.

(1) This site 

provides a description of the three major types of rumble strips (milled, rolled (or formed), and 

raised), detailed construction drawings, effectiveness estimates, interviews with users and other 

experts, and other important material.
4

BACKGROUND ON STUDY

In 1997, the American Association of State Highway and Transportation Officials (AASHTO) 

Standing Committee on Highway Traffic Safety, with the assistance of FHWA, the National 

Highway Traffic Safety Administration, and the Transportation Research Board Committee on 

Transportation Safety Management, met with safety experts in the field of driver, vehicle, and 

highway issues from various organizations to develop a strategic plan for highway safety. These 

participants developed 22 key emphasis areas that affect highway safety. The 22 emphasis areas 

were published in the AASHTO Strategic Highway Safety Plan.

(2)

The National Cooperative Highway Research Program (NCHRP) then published a series of 

guides to advance the implementation of countermeasures targeted to reduce crashes and 

injuries. Each guide addresses one of the key emphasis areas and includes an introduction to the 

problem, a list of objectives for improving safety, and strategies for each objective. Each strategy 

is designated as proven, tried, or experimental. Many of the strategies discussed in these guides 

have not been rigorously evaluated; about 80 percent of the strategies are considered tried or 

experimental.

In 2005, to support the implementation of the guides, FHWA organized a pooled fund study

(PFS) to evaluate low-cost safety strategies as part of this strategic highway safety effort. Over 

time, the pooled fund has grown in size and, at the time of this study, included 40 States. The 

PFS evaluates the safety effectiveness of several tried and experimental, low-cost safety 

strategies through scientifically rigorous crash-based studies. FHWA selected the use of ELRSs

as a strategy to be evaluated as part of this effort. 

LITERATURE REVIEW

The Manual on Uniform Traffic Control Devices (MUTCD) defines rumble strips as either 

slightly raised or depressed road surfaces with a rough texture designed to provide a haptic alert

for inattentive drivers leaving the travel lane.(3) As shown in figure 1, rumble strips may be 

installed either on the shoulders or center line on rural two-lane highways, and the edge line may 

be adjacent to the rumble strip or overlapping with it, creating a rumble stripe. 
5

A. Edge line not on rumble 

strip.

B. Edge line on rumble strip. C. Center line on rumble 

strip.

Source: FHWA.

Note: (A) Edge lines may be located alongside the rumble strip, (B) on the rumble strip, or (C) the center line 

markings may also be located on a center line rumble strip. Arrows indicate direction of travel. Empty squares 

indicate rumble strip.

Figure 1. Illustration. Examples of longitudinal rumble strip markings.

(3)

Figure 2 provides an illustration of rumble strip dimensions, which are explained as follows:(4)

• A—Offset: Distance from the pavement marking (delineating the edge of the traveled 

way) to the inside edge of the rumble strip.

• B—Length: Dimension of the strip that is perpendicular to the travel directions of the 

roadway. This is often referred to as the transverse width of the rumble strip.

• C—Width: Dimension of the strip that is parallel to the travel direction of the roadway. 

• D—Depth: Maximum distance from the surface of the roadway to the bottom of the 

rumble strip.

• E—Spacing: Distance between adjacent rumble strips. It is most often measured from 

the center of the strip to the center of the adjacent strip.

• F—Gap: Distance from the edge of the rumble strip to edge of rumble strip when there is 

a break in the pattern. Gaps are commonly used to allow bicycles to cross the rumble 

strip pattern, to allow passing vehicles to cross center-line rumble strips (CLRSs), and to 

allow for turning movements at intersections and driveways. 
6

Source: FHWA.

Figure 2. Illustration. Overview of rumble strip dimensions.(4)

The University Transportation Center for Alabama conducted an evaluation of ELRS markings

in terms of service life, lifecycle cost, and wet and dry visibility in comparison with flat 

thermoplastic edge markings (FTMs).(5) The authors measured nighttime dry and wet 

retroreflectivity at 16 1-mi FTM segments and 5 2-mi ELRS segments. They found that initial 

dry retroreflectivity was similar between the two groups; however, ELRSs lost visibility at a 

lower rate due to cumulative traffic passes. ELRSs were found to provide a higher dry 

retroreflectivity and longer service life than FTMs under similar traffic conditions. For wet 

retroreflectivity, the ELRSs had a higher initial value than FTMs, but the degradation could not 

be compared between the two because of a lack of data for FTMs. The cost per mile for ELRSs

was $2,424 for a 5-year marking service life and an 8-year lifecycle. 

A study by Miles et al. used video data to examine the impacts of CLRSs and ELRSs on passing 

operations and lateral position on Texas highways.(6) After application of milled CLRSs on nopassing and passing zones, the authors found no change in passing opportunities or the 

percentage of vehicles that passed. However, center-line crossing time increased significantly,

and gap distance decreased significantly, irrespective of the speed of the data-recording vehicle. 

For lateral position, vehicle placement shifted farther from the center line after implementation 

of CLRSs. After implementation of ELRSs, researchers noted a decrease of about 50 percent in 

shoulder encroachments as well as a significant reduction in other encroachments, including

inadvertent contact with the edge line. 
7

Carlson et al. examined wet-night visibility of pavement markings using experimental drivers on 

a closed rain tunnel.(7,8) The study tested nine different treatments in random orders and 

measured perception distance for each sample location. The driver alerted the researcher when he 

or she observed a marking and when the type could be determined. This research included testing 

rumble stripes. The findings suggested there was little difference in detection distance between 

flat thermoplastic lines and rumble strip lines at low rainfall rates. However, the detection 

distance was 13 to 38 percent greater for rumble strip lines for medium and heavy rainfall rates. 

The Mississippi Department of Transportation installed ELRSs on a portion of Interstate 59 with 

generally encouraging results.(9) Preliminary data indicated that the strategy provided an 

excellent audible alert, increased visual awareness of the travel lane, increased reflectivity, and 

provided results similar to those for inverted profile striping, and Mississippi residents welcomed

the installation. However, some concerns associated with the rumble stripes arose, including

noise pollution and the potential for an increase in over-correcting and head-on crashes.

Torbic et al. summarized numerous studies on SRSs.

(10) Table 1 summarizes their results of 

many States’ studies (negative percentages indicate a decrease in crashes), and their NCHRP 

report outlines several key findings.(10) The report notes that SRSs installed along freeways made 

up the majority of the safety effectiveness evaluations and that only a small percentage of the 

studies evaluated the safety effectiveness of nonfreeway installations. While the evaluations 

generally focused on crash types most directly affected by rumble strip presence, such as singlevehicle ROR (SVROR) crashes, several studies looked at the safety effect on total crashes. 

Rumble strip application showed an average reduction of 36 percent in SVROR-type crashes, 

with a range of 10 to 80 percent. The reduction of total crashes ranged from 13 to 33 percent, 

with an average reduction of 21 percent.(10)
8

Table 1. Summary of studies on changes in target collision frequency from application of SRSs.

(10)

State Type of Facility

Type of Collision 

Targeted

Percent Change in 

Target Collision 

Frequency (Standard 

Deviation) Type of Analysis

Arizona(11)Interstate SVROR −80 Cross-sectional comparison

California(12)Interstate SVROR −49 Before–after with comparison sites

California(12)Interstate Total −19 Before–after with comparison sites

Connecticut(13) Limited-access 

roadways

SVROR −32 Before–after with comparison sites

Florida(11) — Fixed object −41 Naive before–after

Florida(11) — Ran-into-water −31 Naive before–after

Illinois and 

California(14)

Freeways SVROR (total) −18 (± 6.8) Before–after with marked 

comparison sites and a comparison 

group

Illinois and 

California(14)

Freeways SVROR (injury) −13 (±11.7) Before–after with marked 

comparison sites and a comparison 

group

Illinois and 

California(14)

Rural freeways SVROR (total) −21.1 (±10.2) Before–after with marked 

comparison sites and a comparison 

group

Illinois and 

California(14)

Rural freeways SVROR (injury) −7.3 (±15.5) Before–after with marked 

comparison sites and a comparison 

group

Kansas (unpublished, 

cited in Stutts(15))

Freeways SVROR −34 Unknown

Maine (16) Rural freeways Total Inconclusive Before–after with comparison sites

Massachusetts 

(unpublished, cited in 

Stutts(15))

— SVROR −42 Unknown

Michigan(17) — SVROR −39 Cross-sectional comparison

8
9

State Type of Facility

Type of Collision 

Targeted

Percent Change in 

Target Collision 

Frequency (Standard 

Deviation) Type of Analysis

Minnesota(18) Rural multilane 

divided highways

Total −16 Naive before–after

Minnesota(18) Rural multilane 

divided highways

Injury −17 Naive before–after

Minnesota(18) Rural multilane 

divided highways

SVROR (total) −10 Naive before–after

Minnesota(18) Rural multilane 

divided highways

SVROR (injury) −22 Naive before–after

Minnesota(18) Rural multilane 

divided highways

Total −21 Before–after with comparison sites

Minnesota(18) Rural multilane 

divided highways

Injury −26 Before–after with comparison sites

Minnesota(18) Rural multilane 

divided highways

SVROR (total) −22 Before–after with comparison sites

Minnesota(18) Rural multilane 

divided highways

SVROR (injury) −51 Before–after with comparison sites

Minnesota(19) Rural two-lane 

roads

SVROR (total) −13 (8) Before–after EB analysis with 

reference group

Minnesota(19) Rural two-lane 

roads

SVROR (injury) −18 (12) Before–after EB analysis with 

reference group

Montana(20)Interstate and 

primary highways

SVROR −14 Before–after with comparison sites

New Jersey 

(unpublished, cited in 

Stutts(15))

— SVROR −34 Unknown

New York(21)Interstate parkway SVROR −65 to 70 Naive before–after

Pennsylvania(22)Interstate SVROR −60 Naive before–after

Tennessee(23)Interstate SVROR −31 Unknown

Utah(24)Interstate SVROR −27 Before–after with comparison sites

9
10

State Type of Facility

Type of Collision 

Targeted

Percent Change in 

Target Collision 

Frequency (Standard 

Deviation) Type of Analysis

Utah(24)Interstate Total −33 Before–after with comparison sites

Virginia(25) Rural freeways SVROR −52 Before–after with comparison sites

Washington(26) — Total −18 Naive before–after

Multistate(11) Rural freeways SVROR −20 Before–after with comparison sites

Note: This table is adapted from table 4 in Torbic et al. (2009).

(10)

—Information was not available.

10
11

Of all the rumble strip crash reduction studies reviewed by Torbic et al., only one (Patel et al.)

specifically addresses rural two-lane roads.(19) That study focused on roads in Minnesota and

used the EB analysis approach, which is generally more accurate than alternative before–after 

analysis types. Therefore, from among the listed sources, the Minnesota study appeared to 

provide the most relevant and reliable indications of the potential safety effects of ELRSs. It 

estimated a crash reduction of 13 percent (standard error (SE) = 8) for all SVROR crashes and 

18 percent (SE = 12) for SVROR injury crashes. It should be noted, however, that these crash 

reduction factors only applied to rural two-lane roads with an AADT greater than 4,000.(27)

Torbic et al. examined the safety effectiveness of SRSs on rural two-lane highways.(10) The EB

before–after results indicated no change in crashes after application of SRSs for total crashes and 

fatal and injury crashes for combined data from Minnesota, Missouri, and Pennsylvania. The 

results indicated a significant 16-percent decrease in SVROR crashes and a significant 

36-percent decrease in SVROR fatal and injury crashes at combined sites. Additional analyses 

indicated that Pennsylvania had a significant 24-percent reduction in total crashes, 44-percent 

decrease in SVROR crashes, and 37-percent decrease in SVROR fatal and injury crashes. In 

consideration of all analytical methods employed, Torbic et al. recommended the following 

CMFs for SRSs on rural two-lane roads based on their research:(10)

• 0.84 for SVROR crashes.

• 0.64 for SVROR fatal and injury crashes.

In addition, Torbic et al. quantified the impact of SRS placement on safety, focusing on SVROR 

fatal and injury crashes. Placement was defined as edge line and non-edge line, which were 

compared with no rumble strips. ELRSs were defined as rumble strips with an offset distance of 

0 to 8 inches, and non-ELRSs were defined as having an offset of 9 inches or more. For two-lane 

rural roadways, there was no significant or practical difference between ELRSs and non-ELRSs. 

Also, there was no evidence that suggested SRSs resulted in a reduction of SVROR crashes 

involving heavy vehicles.(10)

Khan et al. evaluated the safety benefits of SRSs on rural two-lane highways in Idaho.(28) The 

authors conducted an EB before–after analysis using data from 178.63 mi of data from treatment 

sites. The results indicated a 14-percent reduction in ROR crashes. Further analysis indicated a 

33-percent reduction in ROR crashes for sections with an AADT less than 1,000. In addition, 

SRSs were most effective on horizontal tangents and horizontal curves with moderate curvature. 

The study found that SRSs were most effective for paved shoulder widths of 3 ft or more.(28)

Potts et al. evaluated the safety impacts of wider pavement markings with both CLRSs and 

ELRSs with resurfacing on rural two-lane highways in Missouri.(29) The EB analysis indicated 

a significant 47.4-percent reduction in fatal and disabling injury crashes and a significant 

38.3-percent reduction in fatal and all injury crashes. A benefit–cost (B/C) evaluation 

indicated a B/C ratio of 35.6 for wide markings and both CLRSs and ELRSs with resurfacing 

on rural two-lane roadways.(29)

Lyon et al. evaluated the safety impacts of combined SRSs and CLRSs using data from Kentucky, 

Missouri, and Pennsylvania.(30) Kentucky data included SRSs and ELRSs, and the final data 

included sites where SRSs/ELRSs and CLRSs were installed concurrently as part of a resurfacing 
12

effort or where CLRSs had been installed as retrofits. Table 2 provides the dimensions of the 

rumble strips implemented in each of the three States. Note that Pennsylvania had two typical 

applications for CLRSs and an alternative design for bicycle-tolerable rumble strips.

Table 2. Rumble strip dimensions from Lyon et al.(30)

Location Type

Width 

(inches)

Length 

(inches)

Depth 

(inches)

Spacing 

(inches)

Kentucky CLRS 7–7.5 12 1/2–

5

/8 24

Kentucky SRS 7 ± 1/2 16 1/2 ± 1/8 12 ± 1

Missouri CLRS 7 ± 1/2 12 7/16 ± 1/16 12 and 24

Missouri SRS 7 ± 1/2 12 7/16 ± 1/16 12

Pennsylvania CLRS 1 7 ± 1/2 16 1/2 ± 1/16 24 and 48

Pennsylvania CLRS 2 7 ± 1/2 14–18 1/2 ± 1/16 24

Pennsylvania ELRS 5 ± 1/2 6

1

/2 ± 1/16 7

Pennsylvania Bike-tolerable SRS15 ± 1/2 16 3/8 ± 1/16 7

Pennsylvania Bike-tolerable SRS25 ± 1/2 16 3/8 ± 1/16 6

1Roadway’s posted speed limit was greater than or equal to 55 mi/h.

2Roadway’s posted speed limit was less than 55 mi/h.

The EB analysis indicated the following significant CMFs for combined States:(30)

• 0.80 for total crashes (excluding intersection-related and animal crashes).

• 0.77 for fatal and injury crashes.

• 0.74 for ROR crashes.

• 0.63 for head-on crashes.

• 0.77 for sideswipe-opposite-direction crashes.

• 0.70 for head-on and sideswipe-opposite-direction crashes.

• 0.73 for ROR, head-on, and sideswipe-opposite-direction crashes.

Further disaggregate analyses by Lyon et al. indicated significant reductions in Kentucky and 

Missouri but not in Pennsylvania.(30) The authors surmised that earlier installations (which were 

used by Torbic et al.) were higher-crash locations, while more recently treated sites did not have 

a high target crash issue (and therefore no safety benefit).(10) Additional analysis by Lyon et al. 

indicated the following:(30)

• Larger reductions in ROR crashes for higher traffic volumes (greater than 3,200 AADT).

• Larger reductions in head-on and sideswipe-opposite-direction crashes for lower traffic 

volumes (less than 9,200 AADT).

A B/C analysis found an estimated B/C ratio between 20.2 and 54.7 based on estimated service 

lives of 7 to 12 years and estimated annual costs of $557 to $1,511/mi.(30)

Sayed et al. evaluated the safety effectiveness of CLRSs and SRSs alone and combined on rural 

two-lane and four-lane divided highways in British Columbia using an EB before–after study 

design.(31) The combined application on rural two-lane highways resulted in a 21.4-percent 
13

reduction in off-road right, off-road left, and head-on collisions combined. For rural two-lane 

highways, SRS applications resulted in a 26.1-percent reduction in off-road right collisions, and 

CLRS applications resulted in a 29.3-percent reduction in off-road left and head-on collisions.(31)

Torbic et al. evaluated the effect of combined CLRSs and SRSs using data from approximately 

80 mi of treated roadways in Mississippi.(32) The target crash types evaluated included SVROR

crashes left or right, sideswipe-opposite-direction crashes, and head-on crashes. Crash severities 

evaluated individually included total crashes, fatal and injury crashes, and fatal and serious 

injury crashes. The results of the EB before–after analysis indicated a significant 35-percent 

reduction in total target crashes, significant 40-percent reduction in fatal and injury target 

crashes, and an insignificant 12-percent increase in fatal and serious injury target crashes.(32)

Kay et al. evaluated the safety impacts of CLRSs and combined CLRSs and SRSs on rural twolane highways in Michigan.(33) The EB before–after analysis examined approximately 3,000 mi 

of CLRS applications and 1,075 mi of combined CLRS and ELRS applications. The results for 

CLRSs indicated the following significant reductions (K, A, B, C, and O refer to the KABCO 

scale used to represent injury severity in crash reporting where K is fatal injury, A is 

incapacitating injury, B is non-incapacitating injury, C is possible injury, and O is property 

damage only):

(33)

• 15.8 percent for total crashes.

• 27.3 percent for target crashes. 

• 52.9 percent for target-wet pavement crashes.

• 1.4 percent for target-wintry pavement crashes.

• 42.8 percent for target-passing crashes.

• 28.8 percent for target-impaired driving crashes.

• 44.2 percent for target-K injury crashes.

• 32.0 percent for target-A injury crashes.

• 39.3 percent for target-B injury crashes.

• 27.9 percent for target-C injury crashes.

• 16.2 percent for target-O crashes.

The results for combined CLRSs and SRSs indicated the following significant reductions:(33)

• 17.2 percent for total crashes.

• 32.8 percent for target crashes. 

• 55.6 percent for target-wet pavement crashes.

• 4.6 percent for target-wintry pavement crashes.

• 35.7 percent for target-passing crashes.

• 39.9 percent for target-impaired driving crashes.

• 51.4 percent for target-K injury crashes.

• 32.5 percent for target-A injury crashes.

• 53.7 percent for target-B injury crashes.

• 35.2 percent for target-C injury crashes.

• 28.5 percent for target-O crashes.
14

Target crashes were identified manually as crashes involving a vehicle crossing the center line of 

the roadway. 

Olson et al. conducted a before–after evaluation of combined CLRSs and SRSs on rural two-lane 

highways in Washington.(34) The analyses compared simultaneous installations, installations 

where CLRSs were later added to sections with SRSs, and installations where SRSs were later 

added to sections with CLRSs. In addition, the authors analyzed composite conditions where 

there were no rumble strips in the before period and conditions with both CLRSs and SRSs,

disregarding when they were installed. 

For simultaneous installations, the application resulted in a 63.3-percent reduction in lane 

departure crashes, a 65.4-percent reduction in crossover crashes, and a 61.4-percent reduction in 

ROR right crashes. Installations were noted to be more effective at higher speeds and for sections 

with shoulders greater than 4 ft.(34)

For sections where CLRSs were added to SRSs, the application resulted in a 64.7-percent 

reduction in crossover crashes and an 8.5-percent increase in ROR right crashes, resulting in a 

combined 44.6-percent reduction in lane-departure crashes. For sections where SRSs were added 

to CLRSs, the application resulted in a 47-percent reduction in ROR right crashes and a 

6.8-percent reduction in crossover crashes, resulting in a 37.2-percent reduction in lane-departure 

crashes.(34)

The composite analysis indicated a 66-percent reduction in lane-departure crashes and a 

56-percent reduction in fatal and serious injury crashes. The combined application was noted to 

be slightly more effective for 11-ft lane widths than 12-ft lane widths.

Kubas et al. evaluated the safety effectiveness of CLRSs and SRSs and SRSs only on rural 

two-lane highways in North Dakota.(35) The authors compared before- and after-crash rates to 

estimate the effectiveness of rumble strip applications for various crash types. The installation of 

CLRSs and SRSs resulted in a 2-percent decrease in total crashes, 45-percent decrease in fatal 

crashes, 21-percent increase in injury crashes, 5-percent decrease in property damage only crashes,

and 29-percent decrease in ROR crashes based on a limited sample. The installation of SRSs

resulted in a 15-percent decrease in total crashes, 22-percent decrease in property damage only 

crashes, and 97-percent increase in ROR crashes based on a limited sample. It should be noted that 

no CMFs from this study received more than a two-star rating in the CMF Clearinghouse.(35)
15

CHAPTER 2. OBJECTIVE

The research described in this report examined the safety impacts of ELRSs on rural horizontal 

curves in Kentucky and Ohio with the objective to estimate the safety effectiveness of this 

strategy as measured by crash frequency. Excluding intersection-related and animal crashes, the 

study included the following crash types:

• Total (all types and severities combined).

• Injury (K, A, B, and C injuries on the KABCO scale).

• ROR (all severities combined).

• Nighttime (including dusk and dawn; all severities combined).

• Nighttime ROR (including dusk and dawn; all severities combined).

A further objective was to address questions of interest including the following:

• Do effects vary by level of traffic volumes?

• Do effects vary by posted speed limit?

• Do effects vary by paved shoulder width?

Other questions included the following:

• Are crash migration effects evident?

• Are spillover effects evident?

The evaluation of overall effectiveness included the consideration of the installation costs and 

crash savings in terms of the B/C ratio. 

Meeting these objectives placed some special requirements on the data collection and analysis 

tasks, including the need to do the following:

• Select a large enough sample size to detect, with statistical significance, what may be 

small changes in safety for some crash types.

• Identify appropriate untreated reference sites.

• Properly account for changes in safety due to changes in traffic volume and other 

nontreatment factors.

• Pool data from multiple jurisdictions to improve reliability of the results and facilitate 

broader applicability of the products of the research.

17

CHAPTER 3. STUDY DESIGN

The study design involved a sample size analysis and prescription of needed data elements. The 

sample size analysis assessed the size of sample required to statistically detect an expected 

change in safety and also determined what changes in safety could be detected with likely 

available sample sizes.

Sample size estimations required assumptions of the expected treatment effect and the average 

crash rate at treatment sites prior to treatment. The project team calculated minimum and desired 

sample sizes assuming a conventional before–after with comparison group (C-G) study design, 

as described in Hauer, and a literature review of likely safety effects.

(36) The sample size analysis 

undertaken for this study addressed the size of sample required to statistically detect an expected 

change in safety. The sample size estimates were conservative because the more robust EB 

methodology was actually used in the before–after analysis rather than the C-G methodology. 

Sample sizes were estimated for various assumptions of the likely annual crash rate in the before 

period and likely safety effects of the strategy. Annual crash rates were assumed for five crash 

types (i.e., total, injury, ROR, nighttime, and nighttime ROR) as shown in table 3. Intersectionrelated and animal crashes were not included in these crash rates. 

The horizontal curve site crash rates for the all and injury crash types were obtained directly 

from Torbic et al. (rates A and B) and before-period data from Kentucky (rate C) and Ohio

(rate D).

(10) The crash rates for Washington (rate A) and Minnesota (rate B) were selected in 

particular because they represented the general upper and lower range of national crash rates. For 

instance, estimated crash rates for sites in Pennsylvania and Missouri from the same NCHRP 

report were 1.75 total crashes per mi/yr and 2.11 total crashes per mi/yr, respectively, which 

were both within that range. The before-period crash rates for Washington and Minnesota were 

used for planning purposes during the development of the study design, and the rates for 

Kentucky and Ohio were provided to show the actual rates. The before-period rates for Kentucky 

and Ohio were greater than those assumed during the planning stages, indicating that sufficient 

sample sizes were more achievable.

The Washington and Minnesota crash rates for the ROR crash type were estimated by 

multiplying the total crash rate by the ratio of ROR crashes to total crashes based on data from

Washington between 2001 and 2005. The nighttime crash rates were estimated by multiplying 

the total crash rate by the ratio of nighttime collisions to total collisions based on 2008 Kentucky

crash data. The nighttime ROR crash rates were estimated by multiplying the nighttime crash 

rate by the same ROR crashes ratio.
18

Table 3. Before-period crash rate assumptions.

Crash Type

Rate A 

(Washington) 

(crashes/mi/yr)

Average Site 

Length 0.164 mi

Rate B 

(Minnesota) 

(crashes/mi/yr)

Average Site 

Length 0.142 mi

Rate C 

(Kentucky) 

(crashes/mi/yr)

Average Site 

Length 0.068 mi

Rate D 

(Ohio) 

(crashes/mi/yr)

Average Site 

Length 0.073 mi

Total 3.37 0.84 3.37 4.12

Injury 1.52 0.31 1.25 1.69

ROR 0.94 0.23 2.04 3.15

Nighttime 1.15 0.29 0.97 1.54

Nighttime ROR 0.32 0.08 0.67 1.30

Table 4 through table 8 provide estimates of the required number of before- and after-period 

mile-years for both the 90- and 95-percent confidence levels on horizontal curve sites by crash 

type. The minimum sample indicated the level for which a study seemed worthwhile (i.e., it was

feasible to detect with the level of confidence the largest effect that might reasonably be 

expected based on what was currently known about the strategy). These sample size calculations 

were based on specific assumptions regarding the number of crashes per mile and years of 

available data. Mile-years is the number of miles where the strategy was implemented multiplied 

by the number of years of data before or after implementation. For example, if a strategy was 

implemented at a 9-mi segment and data were available for the 3 years since implementation, 

then a total of 27 mi-years of after-period data would be available for the study.

The sample size values recommended in this study are highlighted with an asterisk in 

table 4 through table 8. These were selected based on the likeliness of obtaining the 

estimated sample size as well as the anticipated effects of the treatment. As noted, the 

sample size estimates provided are conservative in that the state-of-the-art EB 

methodology proposed for the evaluations would require fewer sites than the less robust 

conventional before–after study with a C-G that was assumed for the calculations.

Estimates can be predicted with greater confidence or a smaller reduction in crashes 

would be detectable if there were more site-years of data available in the after period. The 

same holds true if the actual data used for the analysis had a higher crash rate for the 

before period than had been assumed.
19

Table 4. Minimum required before-period mile-years for treated sites—total crashes.

Expected 

Percent 

Reduction 

in Crashes1

Rate A

(Washington)

2

Rate B

(Minnesota)

2

Rate C

(Kentucky)

2

Rate D 

(Ohio)

2

Rate A

(Washington)

3

Rate B

(Minnesota)

3

Rate C

(Kentucky)

3

Rate D

(Ohio)

3

10 550 2,208 550 451 342 1,373 342 280

20 83* 332* 83* 68* 57* 230* 57* 47*

30 28 113 28 23 20 80 20 17

40 12 49 12 9 9 35 9 7

1Assumes equal number of mile-years for treatment and comparison sites and equal length of before and after periods.

295-percent confidence level.

390-percent confidence level.

*Sample size values recommended in this study.

Table 5. Minimum required before-period mile-years for treated sites—injury crashes. 

Expected 

Percent 

Reduction 

in Crashes1

Rate A

(Washington)

2

Rate B

(Minnesota)

2

Rate C

(Kentucky)

2

Rate D 

(Ohio)

2

Rate A

(Washington)

3

Rate B

(Minnesota)

3

Rate C

(Kentucky)

3

Rate D

(Ohio)

3

10 1,220 5,984 1,485 1,100 759 3,719 923 683

20 184* 900* 223* 165* 127* 623* 154* 114*

30 63 306 76 56 44 216 53 40

40 27 132 33 25 19 94 23 17

1Assumes equal number of mile-years for treatment and comparison sites and equal length of before and after periods.

295-percent confidence level.

390-percent confidence level.

*Sample size values recommended in this study.

19
20

Table 6. Minimum required before-period mile-years for treated sites—ROR crashes. 

Expected 

Percent 

Reduction 

in Crashes1

Rate A

(Washington)

2

Rate B

(Minnesota)

2

Rate C

(Kentucky)

2

Rate D 

(Ohio)

2

Rate A

(Washington)

3

Rate B

(Minnesota)

3

Rate C

(Kentucky)

3

Rate D

(Ohio)

3

10 1,973 8,065 910 589 1,227 5,013 565 366

20 297* 1,213* 137* 89* 205* 839* 95* 62*

30 101 413 47 31 71 291 33 22

40 44 178 20 13 31 126 15 10

1Assumes equal number of mile-years for treatment and comparison sites and equal length of before and after periods.

295-percent confidence level.

390-percent confidence level.

*Sample size values recommended in this study.

Table 7. Minimum required before-period mile-years for treated sites—nighttime crashes. 

Expected 

Percent 

Reduction 

in Crashes1

Rate A

(Washington)

2

Rate B

(Minnesota)

2

Rate C

(Kentucky)

2

Rate D 

(Ohio)

2

Rate A

(Washington)

3

Rate B

(Minnesota)

3

Rate C

(Kentucky)

3

Rate D

(Ohio)

3

10 1,613 6,397 1,912 1,207 1,003 3,976 1,190 750

20 243* 962* 287* 181* 168* 666* 199* 125*

30 83 328 98 62 58 231 69 43

40 36 141 42 27 25 100 30 19

1Assumes equal number of mile-years for treatment and comparison sites and equal length of before and after periods.

295-percent confidence level.

390-percent confidence level.

*Sample size values recommended in this study.

20
21

Table 8. Minimum required before-period mile-years for treated sites—nighttime ROR crashes. 

Expected 

Percent 

Reduction 

in Crashes1

Rate A

(Washington)

2

Rate B

(Minnesota)

2

Rate C

(Kentucky)

2

Rate D 

(Ohio)

2

Rate A

(Washington)

3

Rate B

(Minnesota)

3

Rate C

(Kentucky)

3

Rate D

(Ohio)

3

10 5,797 23,188 2,775 1,427 3,603 14,413 1,724 888

20 872 3,488 416 214 603 2,413 287 148

30 297* 1,188* 142* 73* 209* 838* 99* 51*

40 128 513 61 32 91 363 43 22

1Assumes equal number of mile-years for treatment and comparison sites and equal length of before and after periods.

295-percent confidence level.

390-percent confidence level.

*Sample size values recommended in this study.

21
22

Following the data collection for both the before and after periods, the total mile-years of data 

available was 90.38 for the before period and 34.36 for the after period in Kentucky. Ohio had 

217.01 mi-yr for the before period and 120.99 mi-yr for the after period. The States are reported 

separately because Ohio had additional statewide safety treatments (e.g., in-curve and advance 

horizontal curve warning signage) applied at the same time as the ELRS installation. The 

statistical accuracy attainable for a given sample size is described by the standard deviations of 

the estimated percent change in safety. From this, one can estimate P-values for various sample 

sizes and the expected change in safety for a given crash history. A set of such calculations is 

shown in table 9 for Kentucky and table 10 for Ohio. The calculations were based on 

methodology in Hauer.

(36)

For the available data, the minimum percentage changes in crash frequency that could be 

statistically detectable at 5- and 10-percent significance levels were estimated using the same 

crash rates in table 3. The results indicate that the data should allow detection of the anticipated 

crash reduction effects highlighted in table 4 through table 8 (i.e., 20-percent reductions for all 

crash types except for nighttime ROR) in Ohio, if such an effect were present. It might be more 

difficult to use the Kentucky data to detect the crash reduction effects highlighted in table 4

through table 8. However, as noted previously, the values were conservative because the EB 

methodology requires fewer sites than a conventional before–after with C-G methodology.

Using these results, a decision was made to proceed with the evaluation using the data available 

at the time.

Table 9. Analysis for crash effects in Kentucky.

Crash Type

90-Percent 

Confidence Level1

95-Percent 

Confidence Level1

Total 20 25

Injury 30 35

ROR 25 30

Nighttime 35 40

Nighttime ROR 40 45

1Minimum percent reduction detectable for crash rate assumption. Minimum 

percent reduction is rounded to nearest 5 percent.

Note: Mile-years in before period = 90.38; mile-years in after period = 34.36.

Table 10. Analysis for crash effects in Ohio.

Crash Type

90-Percent 

Confidence Level1

95-Percent 

Confidence Level1

Total 15 15

Injury 20 20

ROR 15 15

Nighttime 20 20

Nighttime ROR 20 25

1Minimum percent reduction detectable for crash rate assumption. Minimum 

percent reduction is rounded to nearest 5 percent.

Note: Mile-years in before period = 217.01; mile-years in after period = 120.99.
23

CHAPTER 4. METHODOLOGY

The EB methodology for observational before–after studies was used for the evaluation

conducted in this study. This methodology is considered rigorous in that it accounts for 

regression-to-the-mean using a reference group of similar but untreated sites. In the process, 

safety performance functions (SPFs) were used, which did the following:

• Overcame the difficulties of using crash rates in normalizing for volume differences 

between the before and after periods.

• Accounted for time trends.

• Reduced the level of uncertainty in the estimates of safety effect.

• Properly accounted for differences in crash experience and reporting practice in 

amalgamating data and results from diverse jurisdictions.

• Provided a foundation for developing guidelines for estimating the likely safety 

consequences of a contemplated strategy.

In the EB approach, the change in safety for a given crash type at a site is given in figure 3.

Figure 3. Equation. Estimated change in safety.

Where:

λ

= expected number of crashes that would have occurred in the after period without the 

strategy.

= number of reported crashes in the after period. 

In estimating , the effects of regression-to-the-mean and changes in traffic volume were 

explicitly accounted for using SPFs, relating crashes of different types to traffic flow and other 

relevant factors for each jurisdiction based on untreated sites (reference sites). Annual SPF 

multipliers were calibrated to account for temporal effects on safety (e.g., variation in weather, 

demography, and crash reporting).

In the EB procedure, the SPF is used to first estimate the number of crashes that would be 

expected in each year of the before period at locations with characteristics similar to the one 

being analyzed (i.e., traffic volume and reference sites). The sum of these annual SPF estimates 

(P) is then combined with the count of crashes (x) in the before period at a strategy site to obtain 

an estimate of the expected number of crashes (m) before installation, as shown in figure 4. 

Figure 4. Equation. EB estimate of expected crashes.

 Safety = λ - π π

λ

m = w(P)+(1-w)(x),
24

Where w is estimated from the mean and variance of the SPF estimate, which is shown in 

figure 5.

Figure 5. Equation. EB weight.

Where k is constant for a given model.

k is estimated from the SPF calibration process with the use of a maximum likelihood procedure. 

In that process, a negative binomial distributed error structure is assumed, with k being the 

overdispersion parameter of this distribution.

A factor is then applied to m to account for the length of the after period and differences in traffic 

volumes between the before and after periods. This factor is the sum of the annual SPF 

predictions for the after period divided by P, the sum of these predictions for the before period. 

The result, after applying this factor, is an estimate of . The procedure also produces an estimate 

of the variance of .

The estimate of is then summed over all sites in a strategy group of interest (to obtain sum) and 

compared with the count of crashes observed during the after period in that group ( sum). The 

variance of is also summed over all sites in the strategy group. 

Figure 6 illustrates the estimate of the index of effectiveness ( ).

Figure 6. Equation. Index of effectiveness.

Figure 7 illustrates the standard deviation of .

Figure 7. Equation. Standard deviation of index of effectiveness.

The percent change in crashes is calculated as 100(1  ); thus, a value of  0.7 with a 

standard deviation of 0.12 indicates a 30-percent reduction in crashes with a standard deviation 

of 12 percent.

w =

1

1+ kP

,

λ

λ

λ λ

π

λ



















2

( )

1

sum

sum

sum

sum

Var













2

2

2 2

2

( )

1

( ) ( )

( )







































sum

sum

sum

sum

sum

sum

Var

Var Var

StDev

















 
25

CHAPTER 5. DATA COLLECTION 

Kentucky and Ohio provided data containing locations and dates of the installation of ELRSs. 

These States also provided roadway geometry, traffic volumes, and crash data for both 

installation and reference sites. This chapter summarizes the data assembled for the analysis.

Additional details about the design, installation, and maintenance of ELRSs, as well as lessons 

learned, can be found in the appendix of this report.

KENTUCKY

This section describes the installation data, reference sites, roadway data, traffic data, crash data,

and treatment cost data for Kentucky sites used in this evaluation.

Installation Data

The Kentucky Transportation Cabinet (KYTC) provided a list of roadway sections where ELRSs

were installed as part of resurfacing projects. The treatment consisted of adding the new 

pavement surface, installing milled rumble strips, and painting the edge line on top of the strip. 

KYTC resurfaced shoulders along with the travel lanes but did not widen shoulders as part of 

this effort. KYTC installed the milled rumble strips with a standard 12-inch width and 1-inch

depth. Installations took place on corridors consisting of both tangents and horizontal curves. 

Kentucky staff identified specific curves for treatment sites for this study using the geographic 

information system (GIS) roadway curve inventory to select moderately to very sharp curves 

(i.e., Highway Performance Monitoring System (HPMS) classes D, E, and F) within these treated 

corridors. The final list of treated sites comprised 229 horizontal curves (15.6 mi) where KYTC

installed ELRSs.

Reference Sites

The treatment applied by KYTC had the potential for crash migration or spillover effects. Crash 

migration occurs when there is “a transfer of crashes resulting from an improvement rather than 

a reduction” (p. 4).

(37) Spillover occurs when the safety benefits of a treatment extend to 

untreated sites downstream of the treated site. 

To detect crash migration and spillover effects, the project team used a two-stage approach

involving two reference groups. In the first stage, the project team selected one reference group 

from a large sample of untreated sites less than 5 mi downstream of treated sites and a second 

group from a limited sample of untreated sites located greater than 5 mi downstream of treated 

sites. Two reference groups were selected in this way to observe potential crash migration or 

spillover effects in the first reference group. According to a simulator study involving drowsy 

drivers and rumble strips, signs of drowsiness return to drivers approximately 5 min after hitting

a rumble strip.

(38) Assuming a 5-min drowsiness-relapse time and vehicle speed equal to or less 

than 60 mi/h, the project team observed crash migration and spillover effects within 5 mi of a 

treated site. By comparing the crash data of these two reference groups, the existence and 

magnitude of the crash migration and spillover could be detected. If no crash migration or 

spillover effects were detected, then the two reference groups were pooled together to form the 

reference group for the EB method.
26

Roadway Data

Roadway data provided by Kentucky staff were in GIS shapefile format. The various road 

characteristics (e.g., shoulder width) were contained in separate shapefiles, each segmented 

differently. GIS files were obtained from the Kentucky Roadway Information and Data website. 

The most useful file segmented the Kentucky road network into curve and tangent sections, 

likely for HPMS purposes. Each curve was denoted along with its degree of curvature and 

HPMS curve classification (A–F). Spatial joining was used to glean the available roadway 

characteristic information: shoulder type and width, traffic volume, and degree of curvature. To 

obtain many other roadway characteristics, such as area type, number of lanes, illumination, 

rumble strip presence, and roadside hazard rating, the data collectors used Google® MapsTM and 

Google® Street ViewTM imagery. To locate and view the curve in Google® MapsTM, the 

coordinates of the curve were extracted from the GIS map, imported to Microsoft® Excel, and 

concatenated into a hyperlink that could be used to quickly find that location in Google®

MapsTM.

Traffic Data

KYTC maintains traffic volume data in the GIS inventory files, specifically the Traffic Flow 

(TF) shapefile. The project team obtained traffic data for the treatment and reference sites by 

spatially joining the TF layer to the site layer to obtain the current and past years’ AADT values.

Crash Data

Crash data for Kentucky are publicly available on the Kentucky State Police’s crash data 

website.(39) The project team used the following specifications for crash queries for each route:

• Crash query dates were from 1/1/2004 to 12/31/2012.

• A crash study area was defined for each horizontal curve, which consisted of up to 

0.05 mi on each approach of the horizontal curve. If two curves were closer than 0.10 mi, 

then the study area was defined as the midpoint between the curves.

• Separate files for collisions, units, and individuals were obtained for each site.

Treatment Cost Data

KYTC provided estimates of the costs and service lives of the treatments for use in conducting a 

B/C analysis of the treatment (table 11).

Table 11. Kentucky treatment cost and service life data.

Countermeasure

Initial Installation 

Cost Maintenance Cost Service Life

Edge-line or shoulder 

rumble strips (installed 

as part of resurfacing)

$2,500/mi for rumble 

strip, $305/mi for 

stripe

No additional 

maintenance cost

12–15 years for 

rumble strip, 

2 years for stripe
27

OHIO

This section describes the installation data, reference sites, roadway data, traffic data, crash data,

and treatment cost data for Ohio sites used in this evaluation.

Installation Data

The Ohio Department of Transportation (ODOT) provided a list of roadway sections where 

ELRSs were installed on nonfreeway highways. The Highway Safety Information System 

(HSIS) provided data identifying rural two-lane segments, and extents of horizontal curves. The 

project team verified installations using ODOT’s video logs as well as Google® StreetviewTM. 

Most installations were confirmed but several treatment sites were noted to have not received the 

ELRS installation. The final list of treated sites comprised 579 horizontal curves (42.3 mi) where 

ELRSs were installed. 

Reference Sites

As with the Kentucky data, the project team used two reference groups in Ohio to account for 

spillover or crash migration effects. The project team selected both reference groups (within 5 mi 

of treatment sites and more than 5 mi downstream of treated sites) from the list of installation 

sites that were not actually treated and were upstream/downstream of installation sites on the 

same corridors. The final list of reference sites comprised 428 horizontal curves (26.1 mi). 

Roadway Data

Roadway data were obtained from the HSIS for each study year. Requisite roadway data for 

identifying study sites included functional classification, number of lanes, and extents of 

horizontal curvature. Additional data included degree of curvature, posted speed limit, and 

shoulder width. The project team used route, beginning milepost, and ending milepost to merge 

roadway data with traffic data and crash data. 

Traffic Data

The project team obtained traffic data from the HSIS for each study year. Traffic data were 

obtained for the treatment and reference sites to obtain current and past years’ AADT values. 

While data have not been collected every year, HSIS data included AADT information for each 

year in the study.

Crash Data

The project team obtained Ohio crash data from the HSIS for each study year. The project team

used the following specifications for crash queries for each route:

• Crash query dates were from 1/1/2005 to 12/31/2013.

• A crash study area was defined for each horizontal curve, which consisted of up to 

0.05 mi on each approach of the horizontal curve. If two curves were closer than 0.10 mi, 

then the study area was defined as the midpoint between the curves.
28

Treatment Cost Data

ODOT provided estimates of the costs and service lives of the treatment for use in conducting a 

B/C analysis of the treatment (table 12).

Table 12. Ohio treatment cost data.

Countermeasure

Initial Installation 

Cost Maintenance Cost Service Life

Edge-line or shoulder 

rumble strips (installed 

as part of resurfacing)

$850/mi for one side 

of roadway

No additional 

maintenance cost

Time until next 

resurfacing

DATA CHARACTERISTICS AND SUMMARY

Table 13 defines the crash types used by each State. The project team attempted to make the 

crash type definitions consistent. In all States, intersection-related and animal-related crashes 

were excluded.

Table 13. Definitions of crash types.

Crash Types Kentucky Ohio

Total Identified as non-intersection and nonramp and excluding those where 

“Event Collision With” indicated an 

animal or deer involvement

Identified as non-intersection and nonanimal related

Injury Resulted in an injury or possible injury Resulted in a fatal injury, 

incapacitating injury, nonincapacitating injury, or possible injury

ROR “Event Collision With” indicates an 

object off roadway was struck, and 

“Pre-Collision Action” is “avoiding 

object in roadway,” “going straight 

ahead,” or “slowing or stopped”

“Accident Type” described as other 

non-vehicle, fixed object, other object, 

other non-collision

Night Identified including “Dusk,” “Dawn,”

“Dark” (light), or “Dark (no light)”

Identified including “Dusk,” “Dawn,”

“Dark-No-Lights,” or “Dark-Lighted.”

Nighttime ROR Identified as being nighttime and ROR Identified as being nighttime and ROR

Table 14 provides summary information for the data collected for the treatment sites. The 

information in table 14 should not be used to make simple before–after comparisons of crashes 

per mile-year because it does not account for factors (other than the strategy) that might cause a 

change in safety between the before and after periods. Such comparisons were properly done 

with the EB analysis, as presented later. Table 15 and table 16 provide summary information for 

the reference site data for Kentucky and Ohio, respectively. As discussed previously, separate 

reference groups were established to identify potential spillover and crash migration effects.
29

Table 14. Data summary for treatment sites.

Variable Kentucky Ohio

Number of miles 15.59 42.25

Mile-years before 90.38 217.01

Mile-years after 34.36 120.99

Total crashes/mile/year before 3.37 4.12

Total crashes/mile/year after 2.50 3.35

Injury crashes/mile/year before 1.25 1.69

Injury crashes/mile/year after 0.76 1.36

ROR crashes/mile/year before 2.04 3.15

ROR crashes/mile/year after 1.46 2.52

Nighttime crashes/mile/year before 0.97 1.54

Nighttime crashes/mile/year after 0.61 1.19

Nighttime ROR crashes/mile/year before 0.67 1.30

Nighttime ROR crashes/mile/year after 0.49 0.94

AADT before Average 1,589

Minimum 412

Maximum 4,268

Average 2,784

Minimum 240

Maximum 15,670

AADT after Average 1,500

Minimum 400

Maximum 4,443

Average 2,659

Minimum 240

Maximum 14,660

Average paved shoulder width (ft) Average 1.36

Minimum 0.00

Maximum 2.00

Average 3.46

Minimum 0.00

Maximum 10.00

Average degree of curve Average 23.38

Minimum 8.50

Maximum 221.50

Average 10.03

Minimum 3.00

Maximum 58.00
30

Table 15. Data summary for Kentucky reference sites.

Variable <5 mi >5 mi

Number of miles 2.69 5.47

Mile-years 24.19 49.27

Total crashes/mile/year 5.13 1.12

Injury crashes/mile/year 1.53 0.43

ROR crashes/mile/year 2.94 0.57

Nighttime crashes/mile/year 1.24 0.28

Nighttime ROR crashes/mile/year 0.87 0.24

AADT Average 1,475

Minimum 224

Maximum 7,960

Average 403

Minimum 101

Maximum 2,450

Average paved shoulder width (ft) Average 1.46

Minimum 0.00

Maximum 4.00

Average 1.11

Minimum 0.00

Maximum 2.00

Average degree of curve Average 22.47

Minimum 8.50

Maximum 173.62

Average 21.80

Minimum 8.70

Maximum 124.4

Table 16. Data summary for Ohio reference sites.

Variable Ohio

<5 mi >5 mi

Number of miles 8.45 17.67

Mile-years 76.05 159.03

Total crashes/mile/year 6.14 4.42

Injury crashes/mile/year 2.41 1.97

ROR crashes/mile/year 4.21 3.56

Nighttime crashes/mile/year 2.25 1.65

Nighttime ROR crashes/mile/year 1.66 1.44

AADT Average 3,383

Minimum 240

Maximum 15,670

Average 2,819

Minimum 250

Maximum 11,460

Average paved shoulder width (ft) Average 2.23

Minimum 0.00

Maximum 10.00

Average 3.09

Minimum 0.00

Maximum 10.00

Average degree of curve Average 9.57

Minimum 3.00

Maximum 23.00

Average 10.20

Minimum 3.00

Maximum 27.00
31

CHAPTER 6. DEVELOPMENT OF SAFETY PERFORMANCE FUNCTIONS

This chapter presents the SPFs developed for each crash type. The SPFs were used in the EB 

methodology to estimate the safety effectiveness of this strategy.(36) Generalized linear modeling 

was used to estimate model coefficients assuming a negative binomial error distribution, which is 

consistent with the state of research in developing these models. In specifying a negative 

binomial error structure, the dispersion parameter, k, was estimated iteratively from the model 

and the data. For a given dataset, smaller values of k indicate relatively better models.

CRASH SPILLOVER AND MIGRATION 

Before developing SPFs, the project team analyzed the separate reference groups to identify 

potential crash migration and spillover effects. An SPF was developed using data from both 

reference groups in order to develop yearly multipliers for each group. The form of the SPF is

provided in figure 8, with parameter estimates presented in table 17.

Figure 8. Equation. SPF model form for crash migration or spillover effects.

Where:

AADT = annual average daily traffic volume.

L = segment length (mi).

invradius = inverse of the horizontal curve radius (ft).

right_shoulder = right shoulder width (ft).

a, b, c, d, e = parameters estimated in the SPF calibration process.

k = overdispersion parameter of the model.

Table 17. Reference group SPF for total crashes—parameter estimates.

State a (SE) b (SE) c (SE) d (SE) e (SE) k

Kentucky −9.063

(0.843)

1.288

(0.111)

0.391

(0.219)

27.738

(37.716)

−0.298

(0.159)

2.183

Ohio −5.226

(0.442)

0.634 

(0.046)

0.390 

(0.057)

206.883 

(47.521)

−0.069

(0.019) 1.022

Table 18 presents the observed crashes versus predicted crashes for each of the two reference 

groups in Kentucky. Group 1 was the reference group more than 5 mi downstream, and group 2 

was the reference group immediately downstream of the treatment sites. Group 1 also included 

reference sites that were on different roadways than the treatment sites. The yearly factors were 

the ratio of observed crashes to predicted crashes for the given group within the given year. 

Spillover and crash migration effects would be apparent if the yearly factors became drastically 

different between group 1 and group 2 after treatment application (2010 for most sites). These 

effects would also become apparent if the yearly factor for group 2 increased or decreased

markedly after treatment application. However, neither of these scenarios appeared to be the 

case. Figure 9 provides a graphical representation of the yearly factors from table 18.

Crashes/mile/year = e

a

∗ AADT

b

∗ L

c

∗ e

(invradius ∗d+right_shoulder ∗e)
32

Table 18. Observed and predicted crashes for reference groups in Kentucky.

Year

Group 1

Observed

Group 2

Observed

Group 1

Predicted

Group 2

Predicted

Group 1

Factor

Group 2

Factor

2004 5 9 6.072 12.806 0.823 0.703

2005 4 13 6.074 12.817 0.659 1.014

2006 5 14 6.077 12.827 0.823 1.091

2007 8 11 6.103 12.875 1.311 0.854

2008 5 12 6.166 12.928 0.811 0.928

2009 5 12 6.265 13.001 0.798 0.923

2010 7 14 6.368 13.065 1.099 1.072

2011 3 23 5.875 12.515 0.511 1.838

2012 13 16 5.446 12.007 2.387 1.333

Source: FHWA.

Figure 9. Graph. Yearly multiplier by year for reference groups in Kentucky.

The sample sizes for reference sites were too small to make a statistical observation of difference 

between the groups (i.e., fewer than 20 crashes per year were observed). However, both groups 

experienced an abnormally large number of total crashes in 2011 or 2012, and group 1 observed 

an abnormally low number of crashes in 2011. Therefore, data for 2011 and 2012 were removed 

for the reference sites for SPF development. Before-period data from treatment sites were 

combined with reference-site data to bolster sample size, and the project team estimated an 

interaction term for the pretreatment site indicator and AADT to determine whether there was a 

difference in the effect of traffic volume at treatment sites in the before period versus at the 

references sites. The results indicated that the reference data and pretreatment data could be 

combined for SPF estimation. 
33

In addition, because of the lack of data at the reference curves in this dataset, the project team 

sought an alternative reference group for developing annual factors. The Kentucky reference data 

from Lyon et al. provided a robust dataset for estimating annual factors for the before and after 

periods from combined horizontal curves and tangents.(30) This reference set included sections 

that were eligible for resurfacing but had not yet received resurfacing and had texturing; this was 

consistent with the treatment group. The reference set also included those identified by Lyon et 

al. to be “resurfacing effort” sites but excluded sites that had SRSs in the prior condition.(30)In 

total, the reference group consisted of 401.21 roadway mi. The project team used the reference 

segments to develop predicted crashes, which were compared with observed crashes to develop 

annual factors. The after-period factor was 1.034 for 2009 installations, 0.993 for 2010 

installations, and 0.982 for 2011 installations. Table 19 presents the observed crashes versus 

predicted crashes for each of the two reference groups in Ohio. As with Kentucky, group 1 

represents the reference group more than 5 mi downstream, and group 2 represents the reference 

group immediately downstream of the treatment sites. Figure 10 provides a graphical 

representation of the yearly factors from table 19. The annual factors show that the reference 

sites, particularly those not adjacent to treatment sites, observed a substantial reduction,

beginning in 2011, relative to the before period. This possibility was expected for group 2 but not 

for group 1. 

The project team explored this finding further with statewide data for rural two-lane roadways 

and for horizontal curves on rural two-lane highways. Consistently, the trends showed an 

approximate 10- to 15-percent reduction in crashes beginning in 2011. The project team 

contacted ODOT to gain further insight into this finding to determine why this systematic 

reduction was observed statewide. ODOT noted that in 2010, the systemic program focused on 

upgrading signage for horizontal curves statewide. This included upgrading hundreds of curves. 

The upgraded signage included chevrons, curve ahead signs, and speed advisory signs, among 

others. Therefore, the project team considered using horizontal tangent sections as a potential 

reference group for developing annual factors to mitigate the impact of signage upgrades on the 

overall findings. Spillover effects were observed for short tangents; the annual multipliers for 

short tangents (i.e., tangents less than 0.5 mi in length) were found to match those of horizontal 

curves within 1.0 percent for each installation year. Tangents longer than 1.0 mi were used as a 

reference group for developing annual factors because no spillover effects were observed. The 

reference segments were used to develop predicted crashes, which were compared with observed 

crashes to develop annual factors. The after-period factor was 1.040 for 2010 installations, 1.043 

for 2011 installations, and 1.038 for 2012 installations.
34

Table 19. Observed and predicted crashes for reference groups in Ohio.

Year

Group 1

Observed

Group 2

Observed

Group 1

Predicted

Group 2

Predicted

Group 1

Factor

Group 2

Factor

2005 81 49 84.82 46.24 0.954963 1.059689

2006 83 60 85.75 45.87 0.96793 1.308044

2007 72 38 84.47 45.37 0.852374 0.837558

2008 79 66 83.64 43.95 0.944524 1.501706

2009 87 49 81.15 44.11 1.072089 1.110859

2010 90 68 90.33 44.56 0.996347 1.526032

2011 58 52 90.33 44.61 0.64209 1.165658

2012 67 47 88.88 44.13 0.753825 1.065035

2013 86 38 89.71 43.88 0.958645 0.865998

Source: FHWA.

Figure 10. Graph. Yearly multiplier by year for reference groups in Ohio.

SAFETY PERFORMANCE FUNCTIONS

Figure 11 shows the form of the SPFs for combined reference groups, which are presented in 

table 20. 

Figure 11. Equation. SPF model form for Kentucky and Ohio.

Where:

posted = posted speed.

f = parameter estimated in the SPF calibration process.
35

The Kentucky SPF was estimated using treatment site before period data and 2004 to 2010 

reference site data. The Ohio SPFs were estimated using reference site data from 2005 to 2010.

Table 20. SPFs by crash type.

Parameters

Kentucky 

Total (SE)

Ohio 

Total

(SE)

Ohio 

ROR

(SE)

a −10.338

(0.573)

−6.962

(0.813)

−6.443

(0.927)

b 1.249

(0.072)

0.697

(0.060)

0.553

(0.066)

c 0.128

(0.100)

0.365

(0.069)

0.433

(0.078)

d N/A 236.022

(58.139)

282.222

(63.957)

e N/A −0.063

(0.024)

−0.099

(0.028)

f N/A 0.021

(0.011)

0.0319

(0.013)

k 0.738 1.083 1.289

N/A = not applicable.

In addition, the project team considered crash sample size for reference sites in the development 

of SPFs. In Kentucky, total crashes per year ranged from 65 to 77. Other crash types had smaller 

sample sizes. The Highway Safety Manual recommends a minimum of 100 crashes per year to 

produce reliable SPFs.(40) Therefore, an SPF was developed for total crashes, and proportion 

factors relating other crash types to total crashes were used in place of separate SPFs. In Ohio, 

total crashes ranged from 110 to 158. There were sufficient crashes to develop separate SPFs for 

total crashes and ROR crashes. To relate other crash types to total crashes, proportion factors

were used in place of separate SPFs. The prediction from the SPF was multiplied by the 

proportion factor to determine the number of predicted crashes of each specific crash type. The 

following is a list of crash type proportions for Kentucky:

• Fatal and injury crashes = 0.370.

• ROR crashes = 0.603.

• Nighttime crashes = 0.289.

• Nighttime ROR crashes = 0.200.

The following is a list of crash type proportions for Ohio:

• Fatal and injury crashes = 0.403.

• Nighttime crashes = 0.373.

• Nighttime ROR crashes = 0.314.

In addition, observed crashes and predicted crashes were used to develop annual factors for timebased trends at reference sites. Factors were used as multipliers for predicted crashes at treatment 
36

sites in the after period. Factors greater than 1.00 indicate an increase in crashes at reference 

sites, and factors less than 1.00 indicate a decrease in crashes at reference sites. Table 21

provides the annual factors based on total crashes in Kentucky and Ohio for each installation 

year. 

Table 21. Time trend factors for predicted crashes.

Year

Kentucky

Total

Ohio

Total

2009 1.034 N/A

2010 0.993 1.040

2011 0.982 1.043

2012 N/A 1.038

N/A = not applicable.
37

CHAPTER 7. BEFORE–AFTER EVALUATION RESULTS

This chapter presents the results of the before–after evaluation, including aggregate analysis for 

both Kentucky and Ohio and disaggregate analysis of the Ohio data. Disaggregate analysis of the 

Kentucky data was not conducted because the sample size was too small.

AGGREGATE ANALYSIS

Table 22 provides the estimates of expected crashes in the after period without treatment, the 

observed crashes in the after period, and the estimated CMF and its SE for all crash types 

considered in Kentucky. Table 23 presents the results for Ohio.

Table 22. Aggregate analysis results for Kentucky.

Statistic Total Injury ROR Nighttime

Nighttime 

ROR

EB estimate of crashes expected 

in the after period without 

strategy

113.9 40.8 67.6 33.1 22.5

Count of crashes observed in the 

after period

86 26 50 21 17

Estimate of CMF 0.75* 0.64* 0.74* 0.63* 0.75

SE of estimate of CMF 0.09 0.14 0.11 0.14 0.19

*Statistically significant results at the 95-percent confidence level.

Table 23. Aggregate analysis results for Ohio.

Statistic Total Injury ROR Nighttime

Nighttime 

ROR

EB estimate of crashes expected 

in the after period without 

strategy

514.2 208.6 392.7 191.6 160.1

Count of crashes observed in the 

after period

405 165 305 144 114

Estimate of CMF 0.79* 0.79* 0.78* 0.75* 0.71*

SE of estimate of CMF 0.04 0.07 0.05 0.07 0.07

*Statistically significant results at the 95-percent confidence level.

The results for Kentucky indicated statistically significant reductions for all crash types except 

nighttime ROR crashes at the 95-percent confidence level. Nighttime crashes had the smallest 

CMF (which translates to the greatest reduction) with a value of 0.63. Total, injury, and ROR

crashes had CMFs of 0.75, 0.64, and 0.74, respectively. The CMF for nighttime ROR crashes 

was 0.75 and was consistent with the same CMF from Ohio; however, it was significant only at 

the 80-percent level, suggesting that sample size was the reason for the lack of statistical 

significance at the 95-percent confidence level. The CMFs were smaller than—but consistent 

with—those found in the most comprehensive and reliable study of SRSs to date.(10) Based on a 

before–after EB analysis, the project team found that milled SRSs had a crash reduction of 
38

16 percent (SE = 8) for all SVROR crashes and 36 percent (SE = 10) for SVROR injury 

crashes.

(10) However, the analysis results for SRSs in Torbic et al. considered segments with both 

horizontal tangents and curves; therefore, a direct comparison of results cannot be made.(10)It is 

also important to remember that all crash types considered in this research excluded intersectionrelated and animal crashes. 

The results for Ohio indicated statistically significant reductions for all crash types. Nighttime 

ROR crashes had the smallest CMF with a value of 0.71. Total, injury, ROR, and nighttime 

crashes had CMFs of 0.79, 0.79, 0.78, and 0.75, respectively. As with the Kentucky results, the 

CMFs were smaller than but consistent with those found in Torbic et al.

(10) The resulting Ohio 

installation CMFs reflected the installation of ELRSs on horizontal curves as well as the impact 

of the statewide signing program.

A subset of both treatment and reference curves received sign upgrades, including chevrons, 

curve ahead signs, and speed advisory signs, all of which target crash types (i.e., nighttime and 

ROR) similar to those targeted by ELRSs but through a different mechanism (i.e., rumble strips 

target distracted or drowsy drivers through a haptic alert). The initial set of reference sites 

accounted for the impact of the signing upgrades. Additional analyses of the reference sites

indicated a spillover effect of the horizontal curve signing program on curves that did not receive 

treatments as well as shorter tangents; therefore, longer tangent segments were used to determine 

the expected trend in the after period had no treatment (i.e., the signing program or ELRS 

installation) occurred. Owing to the spillover effects of the signing program, further analyses 

involving curves that specifically received new or additional signs were not fruitful (i.e., the 

resulting CMFs could not separate the effects of the signing program from those resulting from 

ELRS installation). 

DISAGGREGATE ANALYSIS OF OHIO DATA

The disaggregate analysis sought to identify those conditions under which the treatment was

most effective. Because ROR, nighttime, and nighttime ROR crashes were the focus of this 

treatment, the project team focused on these crash types for the disaggregate analysis. In 

addition, disaggregate results are presented for total crashes and fatal and injury crashes. The 

data sample for Kentucky was too small to perform disaggregate analyses; therefore, 

disaggregate analyses focused only on Ohio data.

Several variables were identified as being of interest and available for both States, including 

degree of curve, posted speed limit, paved shoulder width, lane width, AADT, and before-period 

expected crash frequency. Disaggregate results are provided by AADT in table 24 and beforeperiod expected crash frequency in table 25. The number of crashes in the after period is 

presented for each CMF to indicate the sample size available. Several of the estimated CMFs 

rely on small samples, especially for nighttime crashes and nighttime ROR crashes. 
39

Table 24. Ohio results by AADT.

Crash Type

<4,000

Observed

<4,000

CMF (SE)

4,000+

Observed

4,000+

CMF (SE)

Total 289 0.82* (0.06) 116 0.72* (0.08)

Injury 118 0.82* (0.08) 47 0.72* (0.12)

ROR 239 0.82* (0.06) 66 0.64* (0.09)

Nighttime 105 0.79* (0.08) 39 0.66* (0.12)

Nighttime ROR 88 0.78* (0.09) 26 0.54* (0.11)

*Statistically significant results at the 95-percent confidence level.

Table 25. Ohio results by before-period expected crash frequency.

Crash Type

Expected 

Crash 

Frequency

Less Than 

Value—

Observed

Less Than 

Value—

CMF (SE)

Greater Than 

or Equal to 

Value—

Observed

Greater Than 

or Equal to 

Value—

CMF (SE)

Total 0.25 136 1.09 (0.11) 269 0.69* (0.05)

Injury 0.10 63 1.00 (0.14) 102 0.70* (0.08)

ROR 0.20 111 1.13 (0.12) 194 0.66* (0.05)

Nighttime 0.15 85 0.93 (0.11) 59 0.59* (0.08)

Nighttime 

ROR 0.075 38 0.85 (0.15) 76 0.66* (0.08)

*Statistically significant results at the 95-percent confidence level.

As shown in table 24, smaller CMFs (i.e., larger safety benefits) were found for all crash types 

for sites with an AADT of 4,000 or more vehicles per day; however, the 95-percent confidence 

intervals overlap for each crash type. At AADTs lower than 4,000 vehicles per day, for example,

an ROR crash CMF of 0.82 was estimated versus a CMF estimate of 0.64 for AADTs of 

4,000 vehicles per day or greater. A similar difference was found for all other crash types. The 

4,000 vehicles per day AADT cutoff is consistent with previous research by Patel et al. and 

Lyon et al.(19,30)

For the before-period expected crash frequency, as shown in table 25, the project team found 

larger safety benefits for all crash types for higher before-period expected crash frequency. The 

95-percent confidence intervals did not overlap for total crashes and ROR crashes. Owing to the 

differences in the frequencies of different crash types, the before-period expected crash 

frequency cutoff varied for each crash type. For example, an ROR crash CMF of 1.13 was 

estimated for horizontal curves with an ROR before-period expected crash frequency of less than 

0.20 crashes/yr. This can be compared with a CMF of 0.66 for horizontal curves with 0.20 or 

more before-period expected crashes/year. Note that the CMF of 1.13 for an ROR before-period 

expected crash rate less than 0.20 is not statistically significant. Similar results were found for all 

other crash types. 

Caution should be used in interpreting and applying these disaggregate CMF results because of 

correlation among variables and because they were not robust enough to develop crash 

modification functions. A crash modification function is a formula used to compute the CMF for 

a specific site as a function of its site-specific characteristics. For example, crash modification 
40

functions would allow the estimation of CMFs for different levels of AADT and before-period 

crash frequency. In addition, the disaggregate analysis results used the EB analysis data, which

include the effects of the statewide horizontal curve signing program. However, the disaggregate 

analysis CMF results can be used to inform the process of prioritizing treatment sites for ELRSs. 

For example, sites with a high proportion of ROR crashes and high AADTs could have high 

priority for receiving this treatment because those are the sites likely to benefit the most.
41

CHAPTER 8. ECONOMIC ANALYSIS

The project team conducted an economic analysis to estimate the B/C ratio for this strategy on 

rural two-lane horizontal curves. For the purposes of the economic analysis, the assumed 

treatment was the application of ELRSs. The project team used the recommended CMFs of 

0.75 for Kentucky and 0.79 for Ohio to estimate the benefit of this treatment strategy. The Ohio 

results likely included the impact of additional sign upgrades, which were not provided or 

considered in this analysis. In addition, the cost of pavement markings was not considered in the 

study because these markings were already present on the roadway and the ELRSs did not affect 

the lifespan of edge-line pavement markings. Treatment costs ranged from $1,700/mi for Ohio to 

$2,500/mi for Kentucky. For Kentucky, service life was estimated as 12 to 15 years. For Ohio, 

ODOT noted that the service life was as long as the pavement life, which was assumed as 7 to 

10 years. A conservative value of 12 years was assumed for Kentucky and 7 years for Ohio.

The FHWA Office of Safety Research and Development suggested using the Office of 

Management and Budget’s Circular A-4 to determine the conservative real discount rate of 

7 percent.

(41) This value was applied to calculate the annual cost of the treatment for 12- and 7-year 

service lives in Kentucky and Ohio, respectively. With this information, the capital recovery factor 

was computed to be 7.94 for a 12-year service life and 5.39 for a 7-year service life. 

At the time of this report, the most recent FHWA mean comprehensive crash costs disaggregated 

by crash severity, location type, and speed limit were based on 2001 dollar values.(42) The 

2001 unit costs for property damage only and fatal and injury crashes from the FHWA report 

($7,428 and $158,177, respectively) were multiplied by the ratio of the 2014 (when the analysis 

was performed) value of a statistical life of $9.2 million to the 2001 value of a $3.8 million.(43,44)

The project team applied this ratio of 2.42 to the unit costs for property damage only and fatal 

and injury crashes. The results were weighed by the frequencies of these two crash types in the 

after period to obtain aggregate 2014 unit costs for total crashes for Kentucky and Ohio. The 

resulting values were $128,268 and $166,603, respectively.

The total crash reduction was calculated by subtracting the actual crashes in the after period from 

the expected crashes in the after period had the treatment not been implemented. The number of 

crashes saved per mile-year was 0.812 in Kentucky and 0.913 in Ohio. These numbers were 

obtained by dividing the total crash reduction by the number of after period mile-years per site.

The annual benefit (i.e., crash savings) of $104,165 in Kentucky and $150,368 in Ohio was the 

product of the crash reduction per mile-year and the aggregate cost of a crash (all severities 

combined). The B/C ratio was calculated as the ratio of the annual benefit per mile to the annual 

cost per mile. The B/C ratio was estimated as 331:1 in Kentucky and 477:1 in Ohio. USDOT 

recommended a sensitivity analysis be conducted by assuming values of a statistical life of 0.57 

and 1.41 times the recommended 2014 values.(43) These factors were applied directly to the 

estimate B/C ratios to obtain a range of 189:1 to 467:1 for Kentucky and 272:1 to 672:1 for 

Ohio. On first inspection, the B/C ratios were larger than would reasonably be expected for an 

installation of this type. However, the installations took place on corridors, while the analysis 

only examined the safety effects on horizontal curves. Horizontal curves have higher crash rates 

than overall corridors, and the cost per mile of installation would not be representative for 
42

installations only on horizontal curves. As a curve-specific treatment, the B/C ratio would likely 

be reduced owing to the higher installation cost; however, these results suggest that the 

treatment can be highly cost effective. 
43

CHAPTER 9. SUMMARY AND CONCLUSIONS

The objective of this study was to perform a rigorous before–after evaluation of the safety 

effectiveness, as measured by crash frequency, of ELRSs applied on rural two-lane horizontal 

curves. The study used data from Kentucky and Ohio to examine the effects for specific crash 

types, including total, fatal and injury, ROR, nighttime, and nighttime ROR crashes. Crashes 

occurring at or related to intersections, as well as animal-related crashes, were not included. Based 

on the aggregate results, table 26 and table 27 show the recommended CMFs for the various crash 

types. Note that the results for Kentucky were based on smaller sample sizes and that the results 

for Ohio included the effects of a statewide horizontal curve warning sign upgrade program.

Table 26. Recommended CMFs for ELRSs based on Kentucky data.

Statistic Total Injury ROR Nighttime

Nighttime

ROR

Estimate of CMF 0.75* 0.64* 0.74* 0.63* 0.75

SE error of estimate of CMF 0.09 0.14 0.11 0.14 0.19

*Statistically significant results at the 95-percent confidence.

Table 27. Recommended CMFs for ELRSs and curve signage based on Ohio data.

Statistic Total Injury ROR Nighttime

Nighttime

ROR

Estimate of CMF 0.79* 0.79* 0.78* 0.75* 0.71*

SE of estimate of CMF 0.04 0.07 0.05 0.07 0.07

*Statistically significant results at the 95-percent confidence.

To date, the most comprehensive and reliable study of SRSs was published by Torbic et al.

(10)

Compared with the results of that study for ELRSs, the results of the current study suggest that 

greater reductions in all crash types may be found by placing rumble strips on or near the edge

line for horizontal curves. 

A disaggregate analysis of the results of the current study indicated that larger safety benefits 

were found for horizontal curves with AADT greater than 4,000 for all crash types; however, the 

differences by AADT were not statistically significant at the 95-percent confidence level. The 

disaggregate analysis further indicated larger safety benefits for horizontal curves with a higher 

before-period expected crash frequency. The results suggested no benefit for curves with low 

before-period expected crash frequencies for all crash types. The difference in CMFs that were 

dependent on before-period expected crash frequency were statistically significant for total and 

ROR crashes. Caution should be used in interpreting and applying these disaggregate results; 

however, the disaggregate analysis CMFs may be used in prioritizing treatment sites.

Estimated B/C ratios range from 189:1 to 467:1 for Kentucky and from 272:1 to 672:1 for Ohio.

On first inspection, the B/C ratios were larger than would reasonably be expected for an 

installation of this type. However, the installations took place on corridors, while the analysis 

only looked at the safety effects on horizontal curves. Horizontal curves have higher crash rates 

than overall corridors, and the cost per mile of installation would not be representative for 

installations only on horizontal curves. For a curve-specific treatment, the B/C ratio would 
44

likely be reduced owing to the higher deployment cost for spot-specific installations. 

Regardless, these results suggest that the treatment, even in its most expensive variation, can be 

highly cost effective. 
45

APPENDIX: ADDITIONAL INSTALLATION DETAILS

The following appendix presents additional details provided by Kentucky and Ohio. The States 

were asked to provide responses to the following questions:

1. What was the “before-period” condition for the treatment sites with respect to center-line 

and edge-line rumble strips? (No rumble strips? Center-line rumble strips only? Edge-line 

rumble strips only? Or some combination of these?)

2. Do you know whether the treatment sites analyzed by this study were installed as a 

RETROFIT, through RESURFACING, or by a combination of these?

3. The installation dates for the treatment sites on our list range from 2009 to 2011. What 

type of rumble strip was installed at these treatment sites? (If there is more than one, 

please indicate all that apply.)

a. Milled.

b. Rolled.

c. Formed.

d. Raised.

e. Other.

4. We would like to provide a summary of the rumble strip characteristics below. Would 

you have any standard drawings—dated 2009/2010—that applied to all of the treatment 

sites considered in this study? If not, would you be able to identify the following 

characteristics for the edge-line rumble strips at the study sites?

a. Width.

b. Length.

c. Depth.

d. Spacing.

e. Pavement marking type.

f. Pavement marking width.

5. Were there any other requirements (e.g., minimum paved shoulder width, pavement 

structure, etc.) for the installation of rumble strips at the study sites?

6. Were any other safety countermeasures (besides RESURFACING, if that was your 

answer to no. 2 above) installed in conjunction with the rumble stripes at the treatment 

sites evaluated by this study?

7. Please describe any notable challenges related to the rumble stripe installation and how 

you overcame them.

8. Please describe any notable challenges related to the rumble stripe maintenance and how 

you overcame them.
46

9. What lessons learned or recommendations would you share with another States interested 

in the widespread application of edge-line rumble stripes?

RESPONSES FROM KENTUCKY

Kentucky staff responded to all questions. Their responses are listed in numeric order. 

1. The “before condition” had no rumble strips.

2. The treatment sites analyzed by this study were a combination of RETROFIT and 

RESURFACING.

3. The installations were all milled rumble strips.

4. The following dimensions were used for the ELRS based on the pavement cross section 

in the ELRS Standard Drawings provided by Kentucky:

a. Width: 7 inches to 7.5 inches.

b. Length: 6, 8, and 12 inches, based on pavement width.

c. Depth: 0.5 to 0.625 inches.

d. Spacing: 12 inches center-to-center.

5. The pavement width was required to be at least 20 ft minimum (lanes and shoulders), and 

the speed limit was 50 mi/h and greater.

6. No (that I am aware of). There may be sites that received updated signs but not in 

conjunction with this treatment.

7. Communication with the field personnel through meetings to alleviate any 

misconceptions and trepidation.

8. Minor issues with rumbles installed at the edge of the mat may cause accelerated 

pavement edge degradation.

9. Communicate the intentions. Initially target overrepresented crash routes to convey safety 

improvements. Provide experience from other public agencies as testimony. Leave room 

for flexibility in design and implementation. Track crash statistics of comparative routes 

that do not have rumbles to indicate missed opportunities for crash reductions.

RESPONSES FROM OHIO

Ohio staff responded to all questions. Their responses are listed in numeric order. 

1. The “before condition” had no rumble strips.

2. They were installed on routes meeting the minimum requirements (i.e., shoulder width, 

acceptable PCR....and not just resurfacing). They may have been added to district 
47

pavement marking contracts as well as resurfacing in the year or two when they were 

installed through the systematic program.

3. The installations were all milled rumble strips.

4. The following dimensions were used for the ELRS based on the pavement cross section 

in the ELRS Standard Drawings provided by Kentucky:

a. Width: 5 inches ± 0.5 inches.

b. Length: 6, 10, and 16 inches, based on shoulder width.

c. Depth: 0.375 inches.

d. Spacing: 12 inches center-to-center.

5. The treatment sites were installed as a combination of adequate shoulder (2 ft or greater), 

acceptable pavement condition (PCR rating of 80 or higher), minimum lane widths (11 

ft), two-lane routes outside of urban areas and locations where the speed limit is 45 mi/h 

or greater.

6. No. Sites were gathered if they met the criteria shown in question 5.

7. After surveying a few of the ODOT Districts, no notable challenges were encountered 

upon installation.

8. After surveying a few of the ODOT Districts, no notable challenges were mentioned in 

regard to the maintenance of the rumble stripes.

9. The recommendation would be to have some sort of policy set that governs where they 

will/can be installed. We all know that they provide a safety benefit; however, we are still 

selective of where they can be placed depending on shoulder width and pavement 

condition. The goal is to uphold the condition of the roadway system as best we can 

while continuing to improve safety.

49

ACKNOWLEDGEMENTS

This report was prepared for the FHWA Office of Safety Research and Development under 

Contract DTFH61-13-D-00001. The FHWA Program and Task Manager for this project was 

Roya Amjadi. 

The project team gratefully acknowledges the participation of the following organizations for 

their assistance in this study:

• Kentucky Transportation Cabinet.

• Ohio Department of Transportation.

51

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HRDS-20/12-17(200)E