Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

Safety Evaluation of Improved 

Curve Delineation

Publication No. FHWA-HRT-09-045 september 2009
FOREWORD 

The goal of this research was to evaluate and estimate the effectiveness of improved curve 

delineation on rural two-lane undivided roads as one of the strategies in the Evaluation of LowCost Safety Improvements Pooled Fund Study (ELCSI-PFS), Phase II. This strategy is intended 

to reduce the frequency of crashes related to lack of driver awareness approaching curves 

as well as while navigating through curves by providing more conspicuous signing and lane 

markings. The safety effectiveness of this strategy has not been thoroughly documented 

previously, and this study is an attempt to provide an evaluation through scientifically 

rigorous procedures. However, the estimate of effectiveness for this strategy was determined by 

conducting scientifically rigorous before-after evaluations at sites where this strategy was 

implemented in the United States. 

The above safety improvement and all other targeted strategies in the ELCSI-PFS are identified 

as low-cost strategies in the National Cooperative Highway Research Program (NCHRP) Report 

500 Series. Participating States in the ELCSI-PFS include the following: Arizona, California, 

Connecticut, Florida, Georgia, Illinois, Indiana, Iowa, Kansas, Kentucky, Maryland, 

Massachusetts, Minnesota, Mississippi, Montana, New York, North Carolina, North Dakota, 

Oklahoma, Pennsylvania, South Carolina, South Dakota, Tennessee, Texas, Utah, and Virginia. 

 Chou-Lin Chen 

 Acting Director, Office of Safety 

 Research and Development 

Notice

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

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

the information contained in this document. 

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 DOCUMENTATION PAGE 

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

1. Report No. 

FHWA-HRT-09-045 

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

5. Report Date 

September 2009 

4. Title and Subtitle 

Safety Evaluation of Improved Curve Delineation 

6. Performing Organization Code 

7. Author(s) 

Raghavan Srinivasan, Jongdae Baek, Daniel Carter, Bhagwant Persaud, 

Craig Lyon, Kimberly Eccles, Frank Gross, and Nancy Lefler 

8. Performing Organization Report No. 

9. Performing Organization Name and Address 10. Work Unit No. 

Vanasse Hangen Brustlin, Inc. (VHB) Persaud Lyon, Inc. 

8300 Boone Blvd., Ste. 700 87 Elmcrest Road 

Vienna, VA 22182-2626 Toronto, ON M9C 3R7 

UNC Highway Safety Research Center 

730 Martin Luther King Jr. Blvd 

Chapel Hill, NC 27599-3430 

11. Contract or Grant No. 

DTFH61-05-D-00024 (VHB) 

13. Type of Report and Period 

 Safety Evaluation 

Covered 

12. Sponsoring Agency Name and Address 

U.S. Department of Transportation 

Federal Highway Administration 

1200 New Jersey Avenue SE 

Washington, DC 20590 

14. Sponsoring Agency Code 

FHWA 

15. Supplementary Notes 

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

members were Kimberly Eccles, Nancy Lefler, Dr. Frank Gross, Dr. Forrest Council, Dr. Bhagwant Persaud, Craig Lyon, 

Dr. Raghavan Srinivasan, Dr. Jongdae Baek, Daniel Carter, and Charles Hamlett. The FHWA Office of Safety Research and 

Development Contract Task Order Manager was Roya Amjadi. 

16. Abstract 

The Federal Highway Administration (FHWA) organized a pooled fund study of 26 States to evaluate low-cost safety strategies as 

part of its strategic highway safety effort. One of the strategies chosen to be evaluated for this study was improving curve 

delineation. 

Geometric, traffic, and crash data were obtained at 89 treated curves in Connecticut and 139 treated curves in Washington to 

determine the safety effectiveness of improved curve delineation. Treatments varied by site and included new chevrons, horizontal 

arrows, and advance warning signs as well as the improvement of existing signs using fluorescent yellow sheeting. All sites were 

on two-lane rural roads. To account for potential selection bias and regression-to-the-mean, an Empirical Bayes (EB) before-after 

analysis was conducted. The aggregate results revealed an 18-percent reduction in injury and fatal crashes, a 27.5-percent 

reduction in crashes during dark conditions, and a 25-percent reduction in lane departure crashes during dark conditions. The 

reductions were more prominent at locations with higher traffic volumes and sharper curves (curve radius less than 492 ft) and in 

locations with more hazardous roadsides (roadside hazard rating (RHR) of 5 or higher) compared to locations with less hazardous

roadsides (RHR of 4 or lower). In addition, curves where more signs were either added or replaced (with a more retroreflective 

material) within the curve experienced larger reductions in crashes. An economic analysis revealed that improving curve 

delineation with signing improvements is a very cost-effective treatment with the benefit-cost ratio exceeding 8:1. 

17. Key Words 

Horizontal curves, Curve delineation, Chevrons, Crash reduction factors, 

Lane departure, Countermeasures, Before and after studies, Evaluation and 

assessment, Bayes’ theorem, Empirical methods, Regression analysis, Statistical 

analysis, Traffic volume, Costs, Economic analysis, Dark conditions, Sign 

sheeting, Roadside hazards

18. Distribution Statement 

No restrictions. 

19. Security Classif. (of this report) 

Unclassified 

20. Security Classif. (of this page) 

Unclassified 

21. No. of Pages 

52 

22. Price 
ii 
iii 

TABLE OF CONTENTS 

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

INTRODUCTION..........................................................................................................................3 

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

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

LITERATURE REVIEW .............................................................................................................5

OBJECTIVES ................................................................................................................................7 

STUDY DESIGN............................................................................................................................9 

SAMPLE SIZE OVERVIEW .................................................................................................9 

METHODOLOGY ......................................................................................................................11 

DATA COLLECTION ................................................................................................................13 

CONNECTICUT....................................................................................................................13 

Background....................................................................................................................... 13 

Installation Data................................................................................................................ 14 

Reference Sites.................................................................................................................. 14 

Roadway Data................................................................................................................... 14 

Traffic Data....................................................................................................................... 15 

Crash Data......................................................................................................................... 15 

WASHINGTON .....................................................................................................................15 

Background....................................................................................................................... 15 

Installation Data................................................................................................................ 16 

Reference Sites.................................................................................................................. 16 

Roadway Data................................................................................................................... 16 

Traffic Data....................................................................................................................... 17 

Crash Data......................................................................................................................... 17 

SUMMARY OF DATA .........................................................................................................17 

DEVELOPMENT OF SAFETY PERFORMANCE FUNCTIONS........................................21 

RESULTS .....................................................................................................................................23 

AGGREGATE ANALYSIS ..................................................................................................23 

DISAGGREGATE ANALYSIS............................................................................................26 

ECONOMIC ANALYSIS ...........................................................................................................31 

SUMMARY AND CONCLUSION ............................................................................................33 

APPENDIX: SAFETY PERFORMANCE FUNCTIONS........................................................35 

SAFETY PERFORMANCE FUNCTIONS FOR WASHINGTON SITES .....................38 

ACKNOWLEDGEMENTS ........................................................................................................43 

REFERENCES.............................................................................................................................45 
iv 

LIST OF FIGURES 

Figure 1. Photo. Example of a curve treated with enhanced delineations in Connecticut.............. 4 

Figure 2. Chart. Sign types used in Connecticut horizontal curve treatments from MUTCD...... 13 

Figure 3. Graph. Crashes for 25 site-years of available before period data.................................. 39 

LIST OF TABLES 

Table 1. Minimum required before period mile-years for treated sites ........................................ 10 

Table 2. Data summary for Connecticut (89 curves, 7.08 mi)...................................................... 18 

Table 3. Data summary for Washington (139 curves, 14.06 mi).................................................. 18 

Table 4. Variables considered for inclusion in the SPFs .............................................................. 22 

Table 5. Results from Connecticut sites ....................................................................................... 24 

Table 6. Results from Washington sites ....................................................................................... 25

Table 7. Combined results from Connecticut and Washington .................................................... 26 

Table 8. Results of the disaggregate analysis using curve radius in Connecticut......................... 27 

Table 9. Results of the disaggregate analysis using RHR in Connecticut.................................... 28 

Table 10. Results of the disaggregate analysis using the number of within-curve signs 

added or replaced in Connecticut.................................................................................................. 29 

Table 11. Summary of economic analysis results......................................................................... 32 

Table 12. Crash reduction factors (CRFs) for improving curve delineation through signing 

improvements................................................................................................................................ 33 

Table 13. SPFs from Connecticut ................................................................................................. 36 

Table 14. Yearly factors for Connecticut SPFs ............................................................................ 37 

Table 15. Comparison of EB analysis with the before-after study with comparison 

(based on 5 or more years of before treatment data) .................................................................... 40 

Table 16. SPFs for total crashes from revised statewide reference group in Washington............ 41 

Table 17. Yearly factors for Washington total crash SPF ............................................................ 42 

Table 18. Calibration with well-before treatment data (at least 5 years prior to treatment 

installation) ................................................................................................................................... 42 
v 

ABBREVIATIONS AND SYMBOLS 

Abbreviations 

 A Injury, incapacitating 

 AADT Average annual daily traffic 

 AASHTO American Association of State Highway and Transportation Officials 

ADT Average daily traffic 

 B Injury, non-incapacitating 

 C Possible injury 

 ConnDOT Connecticut Department of Transportation 

DOT Department of Transportation 

EB Empirical Bayes 

FHWA Federal Highway Administration 

 GPS Geographic Positioning System 

HSIS Highway Safety Information System 

KABCO Scale used to represent injury severity in crash reporting 

 K Fatality 

MUTCD Manual on Uniform Traffic Control Devices 

NCHRP National Cooperative Highway Research Program 

NHTSA National Highway Traffic Safety Administration 

 RHR Roadside hazard rating 

SE Standard error 

SPF Safety performance function 

SLOSSS Suggested List of Surveillance Study Sites 

TRB Transportation Research Board 

 WSDOT Washington Department of Transportation 
vi 

Symbols 

β Greek letter beta 

λ Greek letter lambda 

π Greek letter pi 

θ Greek letter theta

C Installation cost 

k Dispersion parameter 

m Expected number of crashes 

N Expected service life (years)

P Sum of annual safety performance function estimates 

R Discount rate (as a decimal)

SPFa The number of crashes predicted in the after period in these sites by the 

SPF estimated with the statewide data 

SPFb The number of crashes predicted in the before period in these sites by the 

same SPF 

w1 Weight for observed crash count used in Empirical Bayes calculation 

w2 Weight for annual SPF estimates used in Empirical Bayes calculation 

x Observed count of crashes in the before period
1 

EXECUTIVE SUMMARY 

The Federal Highway Administration (FHWA) organized a pooled fund study of 26 States to 

evaluate low-cost safety strategies as part of its strategic highway safety effort. The purpose of 

the FHWA Low-Cost Safety Improvements Pooled Fund Study is to evaluate the safety 

effectiveness of several low-cost safety strategies through scientifically rigorous crash-based 

studies. One of the strategies chosen to be evaluated for this study was improved curve 

delineation. This strategy is intended to reduce the frequency of crashes related to lack of driver 

awareness approaching curves as well as while navigating through curves by providing more 

conspicuous signing and lane markings. The safety effectiveness of this strategy has not been 

thoroughly documented, and this study is an attempt to provide an evaluation through 

scientifically rigorous procedures. 

Geometric, traffic, and crash data were obtained at 89 treated curves in Connecticut and 

139 treated curves in Washington to determine the safety effectiveness of improved curve 

delineation through signing improvements and post-mounted delineators. Treatments varied by 

site and included new chevrons, horizontal arrows, advance warning signs, post-mounted 

delineators, and improvements of existing signs using fluorescent yellow sheeting. All curves 

were on two-lane rural roads. To account for potential selection bias and regression-to-the-mean, 

an Empirical Bayes (EB) before-after analysis was conducted, utilizing a reference group of 

untreated curves in each State with similar characteristics to the treated sites. The aggregate 

results revealed an 18-percent reduction in injury and fatal crashes, a 27.5-percent reduction in 

crashes during dark conditions, and a 25-percent reduction in lane departure crashes during dark 

conditions. The reductions were more prominent at locations with higher traffic volumes and 

sharper curves (curve radius less than 492 ft) and in locations with more hazardous roadsides 

(roadside hazard rating (RHR) of 5 or higher) compared to locations with less hazardous 

roadsides (RHR of 4 or lower). In addition, curves where more signs were either added or 

replaced with a more retroreflective material within the curve experienced larger reductions in 

crashes. An economic analysis revealed that improving curve delineation with signing 

improvements is a very cost-effective treatment with the benefit-cost ratio exceeding 8:1.

3 

INTRODUCTION 

BACKGROUND ON STRATEGY 

Statistics from the Fatality Analysis Reporting System indicate that 42,642 people were killed in 

38,588 fatal crashes on the U.S. highway system in 2006. Approximately 27 percent of these 

fatal crashes occurred along horizontal curves.(1) These crashes occurred predominantly on twolane rural highways that were often not part of the State system.(2) Approximately 70 percent of 

curve-related fatal crashes were single-vehicle crashes in which the vehicle left the roadway and 

struck a fixed object or overturned, and 11 percent of curve-related fatal crashes were head-on 

crashes. Thus, run-off-road and head-on crashes accounted for 81 percent of the fatal crashes at 

horizontal curves.(1) Also, the average accident rate for horizontal curves is about three times the 

average accident rate for highway tangents.(3) Hence, implementing strategies designed to 

improve the safety at horizontal curves will help achieve the overall goal of the American 

Association of State Highway and Transportation Officials (AASHTO) Strategic Highway 

Safety Plan.

One such strategy with potential for improving horizontal curve safety is enhancing delineation 

along the curve. According to the National Cooperative Highway Research Program (NCHRP)

Report 500 Series, Volume 7, “A Guide for Reducing Collisions on Horizontal Curves,” 

enhancing delineation along the curve is currently a tried but not proven strategy that can be 

implemented on most curves as well as problem curves.(2) Enhanced curve delineation can serve 

multiple purposes. It allows for better visibility while approaching curves by increasing visual 

cues to drivers when they are approaching a curve. In addition, it provides positive guidance 

while navigating through curves. Improved delineation can be helpful in encouraging drivers to 

decrease their speed into and through curves, reducing the frequency of run-off-road or head-on 

crashes. Last, improving delineation can especially be helpful under low light or dark conditions. 

Options for enhanced delineation include using better pavement markings, such as markings with 

higher durability, all-weather quality, or higher retroreflectivity. Other options include postmounted delineators, chevrons, raised pavement markers, and wider edge lines.(2) An example of 

enhanced curve delineation is shown in figure 1. 
4 

Figure 1. Photo. Example of a curve treated with enhanced delineations in Connecticut. 

Enhanced delineation is a potential treatment for curves that have some form of delineation or 

other safety treatment but continue to experience higher crash rates.(1) The installation or upgrade 

of pavement markings should follow the guidelines in the Manual on Uniform Traffic Control 

Devices (MUTCD).(4) 

BACKGROUND ON STUDY 

In 1997, the AASHTO Standing Committee for Highway Traffic Safety, with the assistance of 

the FHWA, the National Highway Traffic Safety Administration (NHTSA), and the 

Transportation Research Board (TRB) 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 areas that 

affect highway safety. One of these areas focuses on crashes on horizontal curves. 

The NCHRP published a series of guides to advance the implementation of countermeasures 

targeted to reduce crashes and injuries. Each guide addresses 1 of the 22 emphasis areas and 

includes an introduction to the problem, a list of objectives for improving safety in that emphasis 

area, 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. 

The FHWA organized a pooled fund study of 26 States to evaluate low-cost safety strategies as 

part of this strategic highway safety effort. The purpose of the pooled fund study is to evaluate 

the safety effectiveness of several tried and experimental low-cost safety strategies through 

scientifically rigorous crash-based studies. Improving delineation on horizontal curves was 

selected as a strategy to be evaluated as part of this effort.
5 

LITERATURE REVIEW

According to the NCHRP Report 500 Series, Volume 7, “A Guide for Reducing Collisions on 

Horizontal Curves,” although general conclusions can be drawn, no quantitative estimates of the 

effects of the safety effectiveness of enhancing delineation along curves can be made.(2)

Fitzpatrick et al. indicated that post-mounted delineators lower the crash rate at night for 

relatively sharp curves; however, the study did not quantify the effect of the same treatment on 

other curves.(5) Zador et al. conducted a study examining the effect of chevrons, post-mounted 

delineators, and raised pavement markers on the speed and placement of vehicles on two-lane 

rural highways.(6) The study showed that a primary benefit of these treatments is to help drivers 

notice when they are nearing a curve. Studies conducted by Agent and Creasely found that 

pavement markings had a greater effect on drivers than post-mounted delineators and that 

chevrons had a larger influence on speed and encroachments than post-mounted delineators.(7) 

Jennings and Demetsky evaluated three post-mounted delineator systems based on changes in 

speed and lateral placement of vehicles in the travel lanes.(8) They concluded that drivers react 

most favorably to chevron signs on sharp curves greater than or equal to 7 degrees and to 

standard delineators on curves less than 7 degrees. 

A 2004 study conducted by Gates et al. analyzed the impacts of various sign conspicuity 

enhancements on traffic operations and driving behavior.(9) The evaluation was comprised of 

14 sites in Texas. Six different fluorescent applications were chosen for this evaluation, which 

included yellow chevrons, yellow chevron posts, yellow curve signs, yellow ramp advisory 

speed signs, yellow “Stop Ahead” signs, and red stop signs. Two additional applications 

including flashing red light-emitting diode stop signs and standard red borders on speed limit 

signs were studied. Fluorescent yellow chevron signs were found to cause a reduction in edge 

line encroachments as well as curve speed. This investigation yielded valuable results, but the 

study was limited in that it did not examine the possible beneficial impacts on crashes but 

focused on safety surrogates. 

In 2006, FHWA released Low-Cost Treatments for Horizontal Curve Safety, a resource 

providing practical information on low-cost treatments that can address identified or potential 

safety problems at horizontal curves.(10) Although it is a useful resource for horizontal curve 

improvements, it does not contain conclusive quantitative estimates of the safety effectiveness of 

enhancing delineation treatments along curves. 

A 2006 study by Opiela et al. evaluated the effectiveness of roadway delineation at a variety of 

curves.(11) Sixteen research participants drove an instrumented FHWA test vehicle for a 

consecutive 8-night period. Each night, various curves were treated with different combinations 

of pavement markings, pavement markers, and horizontal signage. The research participants 

rated the effectiveness of the roadway delineation on each curve. The study recorded positive 

results for increasing retroreflectivity of pavement markings and horizontal signage. Wider edge 

lines along with the installation of horizontal curve warning signage also achieved desirable 

results. While this investigation yielded valuable results, it did not investigate the impacts on 

crashes. 
6 

A 2007 study by Charlton tested two groups of curve treatments using a driving simulator.(12)

One group consisted of treatments to warn drivers before driving through the curve, and the other 

group focused on treatments to reduce driver speed while driving through the curve. The results 

indicated that advance warning signs by themselves were not as effective at reducing driver 

speeds as when they were used in conjunction with chevron sight boards and/or repeater arrows. 

However, this study focused on attention, perceptual, and lane placement factors. It did not 

include effects on crashes. 

A 2009 study by Montello evaluated the safety effectiveness of treatments aimed at improving 

horizontal curve delineation on 15 curves on the A16 Naples-Canosa motorway in Italy.

Montello indicated that all the curves are characterized by low radius and high deflection angle, 

limited sight distance, and limited super elevation.(13) Treatments involved installation of 

chevron signs, curve warning signs, and sequential flashing beacons along the road. An EB 

observational before-after study was performed. There was a statistically significant reduction in 

total, nighttime, daytime, rainy, non-rainy, run-off-road, and property damage only crashes. Total 

crashes decreased by 39.4 percent. The treatment was more effective in curves with radii less 

than or equal to 984 ft and with deflection angles greater than 54 degrees. The results of this 

study clearly indicate that improving curve delineation can provide significant benefits, although 

it is not clear if these results can be translated to conditions in the United States. In addition, the 

focus of Montello’s study was on access-controlled four-lane divided roads, unlike the two-lane 

rural roads that are investigated in this low-cost pooled fund effort.(13)

The results of this literature review support the NCHRP Report 500 Series statement that this 

strategy cannot be considered proven because there were no truly valid estimates of the 

effectiveness based on sound before-after crash-based studies in the United States. More research 

is needed to substantiate these and other evaluations for highway agencies implementing the 

strategy to be confident that they are applying their resources effectively.
7 

OBJECTIVES

This study examined the safety impacts of improved delineation through signing improvements 

on horizontal curves using the EB method. Target crash types included the following: 

• Total non-intersection crashes. 

• Non-intersection lane departure crashes. 

• Injury and fatal non-intersection crashes (K, A, B, and C injuries on KABCO scale, 

which is used to represent injury severity in crash reporting). 

• Non-intersection crashes during dark conditions. 

• Non-intersection lane departure crashes during dark conditions. 

A second objective was to determine whether the effects varied by the following: 

• Traffic volume. 

• Curve radius. 

• Type of treatment, e.g., installation of new signs versus replacement of old signs. 

The final objective was to estimate the overall effectiveness of the strategy. Meeting these 

objectives placed some special requirements on the data collection and analysis tasks including 

the following: 

• The need to select a large enough sample size to detect, with statistical significance, what 

may be small changes in safety for some crash types. 

• The need to identify appropriate reference sites. 

• The need to properly account for traffic volume changes. 

• The need to pool data from multiple jurisdictions to improve reliability of the results and 

facilitate broader applicability of the products of the research.

9 

STUDY DESIGN 

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

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

in safety, and it also determined what changes in safety could be detected with likely available 

sample sizes. 

SAMPLE SIZE OVERVIEW 

Minimum and desired sample sizes were calculated assuming a conventional before-after study 

with a comparison group, as described in Hauer.(14) The sample size estimates were conservative 

because the EB methodology was incorporated in the before-after analysis rather than applied in 

a conventional before-after analysis with a comparison group. 

Sample sizes were estimated for assumptions of likely safety effects and crash frequencies in the 

before period. Based on information from the horizontal curves without the treatment in 

Connecticut, average crash rates were calculated for three crash types, which included the 

following: 

• Non-intersection crashes: 6.96 crashes per mile per year. 

• Non-intersection lane departure crashes: 4.86 crashes per mile per year. 

• Non-intersection crashes during dark conditions: 2.56 crashes per mile per year. 

To facilitate the analysis, it was also assumed that the number of reference sites was equal to the 

number of strategy sites. The sample size estimates provided would be conservative in that stateof-the-art EB methodology proposed for the evaluations would require fewer sites. 

Table 1 provides estimates of the required number of before and after period mile-years for both 

the 90-percent and 95-percent confidence levels. Mile-years are the number of miles of roadway 

on which the strategy was applied multiplied by the number of years the strategy was in place. 

For example, if a strategy is applied on 9 mi of roadway and has been in place for 3 years on all 

9 mi, there are 27 mile-years. 

The minimum sample indicates the level for which a study seems worthwhile; that is, it is 

feasible to detect with 90-percent confidence the largest effect that may reasonably be expected 

based on what is currently known about the strategy. In this case, a 20-percent reduction in 

crashes was assumed as this upper limit on safety effectiveness. The desirable sample assumes 

that the reduction could be as low as 10 percent for total crashes, and this is the smallest benefit 

that one would be interested in detecting with 90-percent confidence. The logic behind this 

approach is that safety managers may not want to implement a measure that reduces crashes by 

less than 10 percent, and the sample size required to detect a reduction smaller than 10 percent 

would likely be prohibitively large. The sample size calculations for this study were based on 

specific assumptions regarding the number of crashes per mile-year. 
10 

The minimum and desirable sample size depends on the target crash type that is selected. The 

two primary target crash types are total number of non-intersection lane departure crashes and 

non-intersection crashes during dark conditions. Depending on which crash type is selected, the 

minimum sample size is either 37 or 71 mile-years, and the desirable sample size is either 

183 or 348 mile-years (shown in bold in table 1). As mentioned earlier, the calculations assume 

an equal number of mile-years for the strategy and reference sites and an equal length of before 

and after periods. These selections assume that the reduction in crashes in each case could be as 

low as a 10-percent reduction in all crashes and that this is the smallest benefit that one would be 

interested in detecting with 90-percent confidence. Estimates may be predicted with greater 

confidence, or a smaller reduction in crashes may be detectable if it turns out that there are more 

mile-years of data available in the after period. The same holds true if there is a higher crash rate 

than expected in the before period. 

Table 1. Minimum required before period mile-years for treated sites. 

Type of Crash 

Expected 

Reduction 

in Crashes 

(Percent) 

95-Percent 

Confidence 

90-Percent 

Confidence 

10 183 128 

20 37 26 Non-intersection 

crashes 

30 13 19 

10 262 183 

20 53 37 

Non-intersection 

lane departure 

crashes 30 19 13 

10 498 348 

20 102 71 

Non-intersection 

crashes during 

dark conditions 30 36 25 

Note: The bold numbers denote the desirable sample size. 
11 

METHODOLOGY 

The EB methodology for observational before-after studies was used for the evaluation.(14) This 

methodology is rigorous in that it addresses the following: 

• It properly accounts for regression-to-the-mean. 

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

between the before and after periods. 

• It reduces the level of uncertainty in the estimates of safety effect. 

• It provides a foundation for developing guidelines for estimating the likely safety 

consequences of contemplated strategy. 

• It properly accounts for differences in crash experience and reporting practices in 

amalgamating data and results from diverse jurisdictions. 

In the EB approach, the change in safety for a given crash type at a site is given by the following: 

Δ Safety = λ - π (1)

Where: 

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

strategy. 

π = The number of reported crashes in the after period. 

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

explicitly accounted for using safety performance functions (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 the temporal effects 

(e.g., variation in weather, demography, and crash reporting) on safety. 

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 traffic volumes and other 

characteristics similar to the one being analyzed (i.e., 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 strategy. This 

estimate of m is as follows: 

( ) ( ) m = w1 x + w2 P (2)
12 

Where the weights w1 and w2 are estimated from the mean and variance of the SPF, estimate as 

follows: 

1 1+ = Pk

Pk

w (3)

1

1

2

+ = Pk

w (4)

Where: 

k = A constant for a given model, and it 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 dispersion 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. 

After applying this factor, the result is an estimate of λ. The procedure also produces an estimate 

of the variance of λ. 

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

compared with the count of crashes during the after period in that group (πsum). The variance of λ

is also summed over all sites in the strategy group. 

The Index of Effectiveness (θ) is estimated as follows: 

⎟

⎠

⎞ ⎜

⎝

⎛ +

=

2

( ) 1 sum

sum

sum

sum

Var

λ

λ

λ

π

θ

(5) 

The standard deviation of θ is given by the following:

2

2

2 2

2

( ) 1

( ) ( )

( )

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

=

sum

sum

sum

sum

sum

sum

Var

Var Var

StDev

λ

λ

λ

λ

π

π θ

θ

(6) 

The percent change in crashes is calculated as 100(1−θ). Thus, a value of θ = 0.7 with a 

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

of 12 percent.
13 

DATA COLLECTION 

CONNECTICUT 

Background

Connecticut provided installation data, including locations and dates for installations of 

improved signing on horizontal curves. It also provided roadway characteristics data, traffic 

volumes, and crash data for both the installation and reference sites. This section provides a 

summary of the data assembled for the analysis. 

The Connecticut Department of Transportation (ConnDOT) used fluorescent yellow sheeting 

to improve signing at horizontal curves between 2002 and 2006. These curves were selected 

through a regular program called the Suggested List of Surveillance Study Sites (SLOSSS). 

SLOSSS uses crash data, traffic volumes, and roadway characteristics to identify intersections 

and road segments with higher than expected crash rates. District engineers were asked to 

indicate which of the SLOSSS were located on horizontal curves, and these curve locations 

were then treated with improved signing. After these were implemented, the ConnDOT 

received positive feedback from enforcement officials who then asked to have these installed 

at additional curves.

The treatments used in Connecticut consisted of improved signing using fluorescent yellow 

sheeting. This included installing new signs or replacing existing signs. The signs in question 

were either warning signs (e.g., curve ahead or suggested speed limit) and/or curve delineation 

signs (e.g., chevrons or horizontal arrows). Figure 2 shows the types of signs used in the 

treatment. Signs W1-1, W1-2, W1-3, W1-4, W1-5, and W1-10 were classified as warning 

signs in this study. Signs W1-6 and W1-8 were classified as curve delineation signs. 

Figure 2. Chart. Sign types used in Connecticut horizontal curve treatments from MUTCD. 

The unit cost of a fluorescent yellow sign in Connecticut ranged from $30 to $160 depending on 

the size of the sign. Smaller signs such as chevrons and advisory speed signs were cheaper than 

larger signs such as curve warning signs. 
14 

Installation Data 

ConnDOT provided information on 34 curve treatment projects; each project had between 1 and 

16 individual horizontal curves, providing a total of 91 treated horizontal curves. Two curves 

were excluded from the analysis because their curve radii could not be obtained. This resulted in 

a sample of 89 curves for further analysis. Service memorandums for each project gave details 

on the treatment description, installation date, treatment cost, and the number of warning and 

curve delineation signs that were replaced or newly installed. 

Reference Sites 

In order to account for biases in treatment site selection, the study analysis required the 

identification of reference sites. Reference sites were curves that were similar to the treatment 

sites but did not receive the improved signing treatment. Reference sites were identified in this 

study by first identifying curves that were located within 1.55 mi of the treatment curves. These 

curves were then filtered down based on certain exclusion criteria. These criteria ensured that the 

final list of reference sites would be an appropriate match to the group of treatment sites. Curves 

that were not included in the final group of reference sites contained the following 

characteristics: 

• Right-turn lane. 

• Left-turn lane. 

• Center-turn lane (two-way left-turn lane). 

• Median. 

• More than two travel lanes. 

• Radius under 32.8 ft or over 3,280 ft. 

• Heading change of less than 2 degrees. 

The final group of reference sites included 334 horizontal curves. The total length of the curves 

in the reference group was 23.6 mi. 

Roadway Data

Roadway characteristics data were collected by an instrumented vehicle that drove the entirety of 

the Connecticut State highway system. One of the most useful pieces of data from this vehicle 

was the photolog. The vehicle took photos every 32.8 ft along the route in each direction. The 

photolog was used to visually obtain data on the following items: 

• Number of lanes (through, right-turn, left-turn, and center-turn lanes). 

• Number of driveways and public street access points. 
15 

• Median presence and type. 

• Shoulder type and width. 

• RHR (1–7 scale). 

• Speed limit (regulation). 

• Suggested curve speed (if any). 

• Cable barrier/guardrail. 

Another key piece of data collected by the vehicle was horizontal alignment data. Geographic 

positioning system (GPS) coordinates taken at regular intervals allowed the vehicle to track the 

horizontal alignment of the road. An algorithm was later run on the GPS data to divide the road 

into segments and determine where tangents, arcs, and spirals began and ended. It also calculated 

the curve radius and degree of heading change from one tangent to the next. 

The vehicle also took readings for super-elevation and grade at regular intervals. For unknown 

reasons, super-elevation data were only available for 40 out of 91 treatment sites and 194 out of 

334 reference sites. Grade data were available for all sites. 

Traffic Data 

Traffic volume counts are performed once every 3 years for each Connecticut road. These 

average daily traffic (ADT) values are recorded on ADT maps. Maps from 1997 to 2005 were 

made available to the research team in addition to an electronic file of 2006 ADT data. Team 

members located each treatment site on the map and took the reading of the nearest ADT count 

point. In the case of a site lying between two ADT count points, the average value was taken. 

Since reference sites were chosen in close proximity to treatment sites, any particular reference 

site was assumed to have the same ADT as its treatment site. 

Crash Data 

Connecticut crash data from 1995 to 2006 were obtained from the University of Connecticut. 

Crash data for 2007 were not available at the time of this study. 

WASHINGTON 

Background

Unlike Connecticut, the treatments in Washington only involved the installation of chevrons 

(W1-8 signs) on horizontal curves. This included both installation locations where there were 

previously no chevrons and where the number of chevrons was increased. The Washington State 

Department of Transportation (WSDOT) provided information on the location of chevrons. 

Information on traffic volume, roadway characteristics, and crashes were obtained from the 

Highway Safety Information System (HSIS). The following section of this report provides a 
16 

summary of the data assembled for the analysis. The cost of each chevron sign was estimated 

to be $100. 

Installation Data

WSDOT provided the research team with information about locations where chevrons were 

installed in the last 15 years. The milepost information for the chevrons was from a different 

milepost system than the roadway inventory. WSDOT provided information on converting 

between the two systems. The project team used these converted mileposts to tie the location of 

the chevrons with the beginning and ending mileposts of horizontal curves in the HSIS system. 

The project team identified 139 curves on rural two-lane roads where chevrons were installed 

sometime between 1994 and 2006. 

Reference Sites 

HSIS data were used to identify curves on rural two-lane roads that could serve as reference 

sites. The initial set of reference sites included about 4,000 curves that experienced 

approximately 8,000 crashes between 1993 and 2007. Several alternative reference groups were 

examined to obtain the reference group most similar to the treatment group in its characteristics. 

Further detail about the different reference groups is available in the appendix. 

Roadway Data

From HSIS, the following information was compiled for each reference curve over the study 

period: 

• Average annual daily traffic (AADT). 

• Curve length. 

• Curve radius. 

• Shoulder width. 

• Lane width. 

• Percent grade. 

• Terrain. 

In situations where a particular characteristic (e.g., shoulder width) varied within a curve, an 

average value was computed for each curve. There is some evidence to indicate that curves 

separated by short tangent sections may have more accidents compared to curves that are 

separated by long tangent sections. Therefore, the distance between consecutive curves was 

desired. The initial effort to obtain the distance between curves found a large number of long 

tangent sections (tangent sections exceeding 5 mi). Further review indicated that this 

counterintuitive result was because of gaps in the data due to coinciding routes. Coinciding 

routes are two routes that share the roadway section, but the roadway inventory and crash 
17 

information is available only for one of the routes. Identifying the coinciding routes required 

the project team and HSIS staff to review individual roadway sections from the raw data 

provided by WSDOT. 

Traffic Data

AADT data were obtained from HSIS for the treatment and reference sites. AADT data were not 

available from 1999 to 2001. To fill in the missing data, an algorithm developed by Lord was 

utilized.(19) Upon a cursory review of the AADT, there were several curves where AADT 

changed dramatically from year to year (for example, one site had an AADT of 138 in 2005 and 

7,325 in 2006). The project team only included curves where the difference between the AADT 

of 2 consecutive years was less than 20 percent to exclude any sites with unreliable AADT. 

Crash Data

Crash data were requested from HSIS for the study period starting in 1993 and ending in 2007. 

Crash data for 1997 and 1998 were not provided to HSIS by WSDOT; therefore, it was not 

available for analysis in this effort. 

SUMMARY OF DATA 

In both States, data were compiled for the following crash types: 

• Total non-intersection crashes: A non-intersection crash was defined based on the 

information by the police officer on the location of the crash. 

• Non-intersection injury and fatal crashes: This included all non-intersection crashes 

where there was at least one non-fatal injury or one fatal injury. 

• Non-intersection lane departure crashes: Lane departure crashes included sideswipe, 

overturn, head-on, jackknife, and run-off-road. 

• Non-intersection crashes during dark conditions: This category included crashes for 

which the light condition was coded as “dark-not lighted” or “dark-lighted.” 

• Non-intersection lane departure crashes during dark conditions: This category included 

crashes that were lane departure but with the light condition coded as “dark-not lighted” 

or “dark lighted.” 

Table 2 shows the summary of the data collected in Connecticut. Table 3 shows the summary of 

the data collected in Washington. 
18 

Table 2. Data summary for Connecticut (89 curves, 7.08 mi). 

Variable Before After 

Mile-years 45.80 21.60 

AADT (minimum) 895 920 

AADT (average) 4,381 4,741 

AADT (maximum) 19,945 20,479 

Non-intersection crashes per mile per year 

(average) 9.01 7.19 

Non-intersection lane departure crashes per 

mile per year (average) 7.66 6.08 

Non-intersection crashes that are injury or fatal 

(K, A, B, or C) per mile per year (average) 3.43 1.95 

Non-intersection crashes during dark conditions 

per mile per year (average) 3.99 2.18 

Non-intersection lane departure crashes during 

dark conditions per mile per year (average) 3.54 1.86 

Table 3. Data summary for Washington (139 curves, 14.06 mi). 

Variable Before After 

Mile-years 71.50 95.09 

AADT (minimum) 261 354 

AADT (average) 3,305 3,700 

AADT (maximum) 11,567 14,790 

Non-intersection crashes per mile per year 

(average) 4.39 3.80 

Non-intersection lane departure crashes per 

mile per year (average) 3.57 3.07 

Non-intersection crashes that are injury or fatal 

(K, A, B, or C) per mile per year (average) 2.45 1.88 

Non-intersection crashes during dark conditions 

per mile per year (average) 1.68 1.36 

Non-intersection lane departure crashes during 

dark conditions per mile per year (average) 1.47 1.22 
19 

Connecticut has more crashes per mile per year than Washington. The average AADT is also 

about 30 percent higher in Connecticut. Looking at the injury and the total crash numbers in both 

States, a higher percentage of crashes in Washington are injury as compared to crash types in 

Connecticut. 

The total available sample of 117.3 mile-years in the before period and 116.6 mile-years in the 

after period are higher than the minimum sample of 37 mile-years for non-intersection lane 

departure crashes and the minimum sample size of 71 mile-years for non-intersection crashes 

during dark conditions but less than the desirable sample sizes for both these crash types. 

However, it is important to note that actual crash rates in the before period are higher in 

Connecticut (for both non-intersection lane departure crashes and non-intersection crashes during 

dark conditions) and lower in Washington (for the same crash types) than the rates assumed in 

the study design. The average crash rates from the two States for the two crash types are slightly 

higher than the rates assumed in the study design. Hence, it is safe to assume that the sample size 

is adequate for both these two crash types and to proceed with the analysis. 

21 

DEVELOPMENT OF SAFETY PERFORMANCE FUNCTIONS 

This section presents the methodology used to estimate the SPFs. The SPFs are used in the EB 

methodology to estimate the safety effectiveness of this strategy.(14) Generalized linear modeling 

was used to estimate model coefficients using the software package SAS® assuming a negative 

binomial error distribution, which is consistent with the state of research in developing these 

models.(15) The over-dispersion parameter, k, is also estimated by SAS® in the model calibration 

process. The over-dispersion parameter relates the mean and variance of the SPF estimate and is 

such that the smaller its value, the better a model it is for a given set of data. Thus, it is a useful 

criterion in comparing candidate models. 

The form of the SPFs is as follows: 

 

Crashes/year = exp( )

1

0 ∑=

+

n

i

β β i Xi

 (7)

Where: 

X = The independent variables. 

β = Parameters to be estimated. 
22 

Table 4 shows the independent variables that were available for the models in the two States. 

Table 4. Variables considered for inclusion in the SPFs. 

Variable Name Connecticut Washington

Annual average daily traffic (AADT) X X 

Section length X X 

Radius of the curve X X 

Grade X X 

Average distance to the next curve X X 

Lane width X 

Shoulder width X 

Terrain X 

Presence of transition curve (indicator variable with 1 coded for 

yes, and 0 for no) X 

RHR—based on Zegeer et al., it varies from 1 through 7, with 1 

corresponding to the least hazardous roadside and 7 corresponding 

to the most hazardous roadside.(16) X 

Presence of curb and gutter (indicator variable with 1 coded for 

yes and 0 for no) X 

Presence of cable barrier (indicator variable with 1 coded for yes 

and 0 for no, coded separately for inside and outside of the curve) X 

Presence of guardrail (indicator variable with 1 coded for yes and 

0 for no, coded separately for inside and outside of the curve) X 

Number of driveways on the curve X 

The developed SPFs are presented in the appendix. While estimating the SPFs, if a variable did 

not significantly improve the model, it was eliminated. To account for the effect of changes in 

factors such as weather, crash reporting practices, and demography over time, annual factors 

were estimated for each year. The annual factor for a particular year is defined as the ratio of 

observed to predicted crashes for that year. Annual factors for all five models were estimated 

based on the SPFs developed for total crashes.
23 

RESULTS 

Two sets of results are provided below: aggregate and disaggregate. The aggregate analysis 

provides evidence for the general effectiveness of the strategy, while the disaggregate analysis 

provides insight on the situations where the strategy may be most effective. 

AGGREGATE ANALYSIS 

The aggregate results are present in table 5 through table 7 for Connecticut, Washington, and the 

two States combined, respectively. The tables provide the EB estimate of the crashes expected in 

the after period if the treatment had not been installed, the actual number of crashes in the after 

period, and two measures of change. The first measure of safety effect is the estimated percent 

reduction due to the strategy along with the standard error (SE) of this estimate—a negative 

value would indicate an increase in crashes. If the magnitude of the percent change is at least 

1.96 times higher than the SE, then the change is statistically significant at the 95-percent 

confidence level. Those safety effects that are significant at the 95-percent confidence level are 

denoted by bold text. The second measure of safety effect is the change in the number of crashes 

per mile-year, which is calculated as the difference between the EB estimate of crashes expected 

in the after period and the count of observed crashes in the after period divided by the number of 

mile-years in the after period. 

In Connecticut, there was a statistically significant reduction at the 95-percent confidence level 

in all the crash types that were evaluated. Total non-intersection and non-intersection lane 

departure crashes were reduced by approximately 18 percent. Injury and fatal non-intersection 

crashes were reduced by about 25 percent. The percentage reduction was larger (35 percent) for 

the crashes that occurred during dark conditions. 

In Washington, there was a statistically significant reduction in crashes during dark conditions 

and lane departure crashes during dark conditions. The reduction for these two crash types 

exceeded 20 percent. The combined results presented in table 7 for the two States indicate a 

statistically significant reduction in injury and fatal crashes, crashes during dark conditions, and 

lane departure crashes during dark conditions. 
24 

Table 5. Results from Connecticut sites. 

NonIntersection

NonIntersection 

Lane 

Departure 

Injury and 

Fatal (K, A, 

B, and C) 

NonIntersection

NonIntersection 

During 

Dark 

Conditions 

NonIntersection 

Lane 

Departure 

During 

Dark 

Conditions 

EB estimate of 

crashes expected in 

the after period 

without strategy 188.1 158.8 55.9 72.2 60.4

Count of crashes 

observed in the after 

period 155 131 42 47 40

Estimate of percent 

reduction 17.8 17.7 25.2 35.3 34.2

SE 7.7 8.4 12.7 10.5 11.5

Estimate of reduction 

in crashes per 

mile-year 1.54 1.29 0.64 1.17 0.95

Note: Bold denotes results that are statistically significant at the 95-percent confidence level. 
25 

Table 6. Results from Washington sites. 

NonIntersection

NonIntersection 

Lane 

Departure 

Injury and 

Fatal (K, A, 

B, and C) 

NonIntersection

NonIntersection 

During 

Dark 

Conditions 

NonIntersection 

Lane 

Departure 

During 

Dark 

Conditions 

EB estimate of 

crashes expected in 

the after period 

without strategy 374.8 308.6 211.8 169.5 147.7

Count of crashes 

observed in the after 

period 361 292 179 129 116

Estimate of percent 

reduction 4.3 5.9 16.4 24.5 22.1

SE 8.9 8.8 10.4 9.5 10.1

Estimate of reduction 

in crashes per 

mile-year 0.15 0.18 0.35 0.43 0.33

Note: Bold denotes results that are statistically significant at the 95-percent confidence level. 
26 

Table 7. Combined results from Connecticut and Washington. 

NonIntersection

NonIntersection 

Lane 

Departure 

Injury and 

Fatal (K, A, 

B, and C) 

NonIntersection

NonIntersection 

During 

Dark 

Conditions 

NonIntersection 

Lane 

Departure 

During 

Dark 

Conditions 

EB estimate of 

crashes expected in 

the after period 

without strategy 562.9 467.4 267.7 241.7 208.1

Count of crashes 

observed in the after 

period 516 423 221 176 156

Estimate of percent 

reduction 8.6 9.7 18.0 27.5 25.4

SE 6.4 6.4 8.6 7.3 7.8

Estimate of reduction 

in crashes per mileyear 0.40 0.38 0.40 0.56 0.45

Note: Bold denotes results that are statistically significant at the 95-percent confidence level. 

DISAGGREGATE ANALYSIS 

The disaggregate results are presented in table 8 through table 11. The disaggregate analysis 

focused on the following factors: 

• Average AADT at a site before treatment. 

• The radius of the curve where the treatment was implemented. 

• The RHR at the treatment site. 

• The number of signs in advance of the curve that were added or replaced. 

• The number of within-curve signs that were added or replaced. 

AADT and curve radius were available from both Washington and Connecticut. The RHR and 

the number of signs were available only in Connecticut. 

Curve radius was examined with combined data from Washington and Connecticut. There were 

no clear trends regarding the effectiveness of the treatment with respect to the radius of the 

curve. Curve radius was also examined in the two States separately. In Washington, there were 
27 

no clear trends regarding the effectiveness of the treatment with respect to the radius of the 

curve. However, in Connecticut, the treatments seem to have been more effective in sharper 

curves (radius less than 0.093 mi) compared to flatter curves (radius equal to or exceeding 

0.093 mi; see table 9). 

When the RHR was examined using data from Connecticut, the results indicated that the 

treatments were more effective at sites with more hazardous roadsides (RHR of 5 or 6) compared 

to less hazardous roadsides (RHR between 2 and 4) for crashes during dark conditions and lane 

departure crashes during dark conditions (see table 10). 

When the effect of the number of signs in advance of the curve (added or replaced) was 

examined using data from Connecticut, there was no clear trend in terms of safety. However, 

when the number of within-curve signs (added or replaced) was examined, sites with more signs 

added or replaced (more than seven per curve) seemed to have experienced a larger reduction in 

crashes compared to sites where fewer signs were added or replaced (less than or equal to seven 

per curve). 

Finally, there were indications that the treatment was more effective for sites with higher AADT 

compared to sites with lower AADT. 

Table 8. Results of the disaggregate analysis using curve radius in Connecticut. 

Crash Type 

Radius 

Category (m)

EB Estimate 

of Crashes 

Expected in the 

After Period 

Without Strategy 

Count of 

Crashes 

Observed in 

the After 

Period 

Estimate of 

Percent 

Reduction in 

Crashes (SE) 

Lane departure < 150 92.5 70 24.7 (10.4)

crashes 

≥ 150 66.3 61 8.6 (13.7)

Crashes during dark < 150 44.6 26 42.3 (12.5)

conditions 

≥ 150 27.6 21 24.8 (18.1)

< 150 38.6 22 43.6 (13.2) Lane departure 

crashes during dark 

conditions ≥ 150 21.8 18 18.4 (21.2)

1 m = 3.28 ft 

Note: Bold denotes results that are statistically significant at the 95-percent confidence level. 
28 

Table 9. Results of the disaggregate analysis using RHR in Connecticut. 

Crash Type RHR 

EB Estimate 

of Crashes 

Expected in the 

After Period 

Without Strategy 

Count of 

Crashes 

Observed in 

the After 

Period 

Estimate of 

Percent 

Reduction in 

Crashes (SE) 

Lane departure 2, 3, 4 74.6 64 14.7 (12.3)

crashes 

5, 6 84.2 67 20.9 (11.3)

Crashes during dark 2, 3, 4 29.5 27 9.5 (19.4)

conditions 

5, 6 42.7 20 53.6 (11.2)

2, 3, 4 26.7 22 18.6 (19.2) Lane departure 

crashes during dark 

conditions 5, 6 33.7 18 47.2 (13.6)

Note: Bold denotes results that are statistically significant at the 95-percent confidence level. 
29 

Table 10. Results of the disaggregate analysis using the number of within-curve signs 

added or replaced in Connecticut. 

Crash Type 

Number of 

WithinCurve Signs 

Added or 

Replaced 

EB Estimate 

of Crashes 

Expected in the 

After Period 

Without Strategy 

Count of 

Crashes 

Observed in 

the After 

Period 

Estimate of 

Percent 

Reduction in 

Crashes (SE) 

≤ 7 per curve 79.6 77 3.9 (13.0)

Lane departure 

crashes Greater than 

7–28 per 

curve 79.2 54 32.2 (10.5)

≤ 7 per curve 35.4 27 24.5 (16.1)

Crashes during dark 

conditions Greater than 

7–28 per 

curve 36.8 20 46.3 (13.1)

≤ 7 per curve 29.2 24 18.6 (18.5) Lane departure 

crashes during dark 

conditions 

Greater than 

7–28 per 

curve 31.2 16 49.4 (13.7)

Note: Bold denotes results that are statistically significant at the 95-percent confidence level.

31 

ECONOMIC ANALYSIS 

Table 11 summarizes the results of the economic analysis. A combined economic analysis is 

provided, but separate analyses are also provided for each State, as each State has its own 

variation of the treatment. The annualized cost of the treatment is first computed based on 

information provided by Connecticut and Washington. Connecticut provided costs based on the 

type of treatment, ranging from $30 to $160 for a fluorescent yellow sign with a service life of 

5 years. The unit cost varied depending on the size of the sign; smaller signs such as chevrons 

and advisory speed signs were less expensive than larger signs such as curve warning signs. 

Washington provided an estimate of $100 for chevrons. The lower and upper limits from 

Connecticut were used to provide a range of cost estimates, but the cost may vary for other 

States depending on the size of the sign and installation and maintenance practices. 

The formula to calculate the annual cost is as follows: 

- N 1- (1 R)

C*R Annual Cost

+ = (8) 

Where: 

C = Installation cost. 

R = Discount rate (as a decimal). 

N = Expected service life (years). 

Based on information from the Office of Management and Budget, a discount rate of 2.4 percent 

was used to determine the annual cost of the strategy.(17) Assuming installation costs of $30 per 

sign, this equates to an annualized cost of $6.44 per sign. Although the number of warning signs 

per curve may vary, it was assumed that 10 chevron signs were installed per curve, resulting in 

an annual treatment cost per curve of $64. Assuming installation costs of $160 per sign, the 

annualized cost is $34.34 per sign and an annual treatment cost of $343 per curve. Consequently, 

the required annual crash savings ranges from $128 to $686 per curve to achieve a 2:1 benefitcost ratio. 

The most recent FHWA mean comprehensive crash costs were used to estimate the cost for 

a lane departure crash based on 2001 dollar values.(18) The FHWA crash cost document does 

not directly report the cost for a lane departure crash, so the cost was estimated based on the 

cost of lane departure-related crashes and the percentage of these crashes. Lane departurerelated crashes include head-on, sideswipe, single-vehicle rollover, and single-vehicle fixed 

object crashes. Based on Washington crash data, these crashes represent 2.6, 1.6, 25.9, and 

69.9 percent, respectively. The mean comprehensive crash costs for these crash types are 

$60,451, $16,019, $147,629, and $67,353, respectively, assuming a speed limit less than 

45 mi/h. A weighted average was computed by combining the crash costs with the percentage 

of each crash type, resulting in a cost of $87,143 per lane departure crash. 

Crash savings were computed based on the results for non-intersection lane departure crashes 

during dark conditions. The total crash reduction was calculated for each State by subtracting the 

actual crashes in the after period from the expected crashes in the after period had the treatment 
32 

not been implemented. Crashes per site-year were calculated by dividing the total crash reduction 

by the number of site-years for each State. Site-years, which are computed similarly to mileyears, are the number of sites multiplied by the number of years of installation. The benefit 

(i.e., crash savings) is the product of the total crash reduction per site-year and the cost of a lane 

departure crash (i.e., $87,143). The benefit-cost ratio indicates a range for which the lower and 

upper limits represent assumed installation costs of $160 and $30 per sign, respectively. 

Table 11. Summary of economic analysis results. 

State Sites Years 

Total Crash 

Reduction 

(Per Year) 

Total Crash 

Reduction 

(Per Site-Year)

Crash Savings 

(Per Site-Year) 

Benefit-Cost 

Ratio 

All 228 4.58 11.373 0.050 $4,347 12.7 to 67.9

Connecticut 89 3.05 6.686 0.075 $6,546 19.1 to 102.3

Washington 139 6.76 4.687 0.034 $2,938 8.6 to 45.9

Even with the conservative assumptions made, a very modest reduction in crashes is required 

to justify this strategy economically. The benefit-cost ratios reported in table 11 far exceed a 

2:1 benefit-cost ratio. While the cost of the strategy may vary by State, it is likely that the 

annualized costs will not exceed the annual crash savings. Therefore, this strategy is justified 

economically. 
33 

SUMMARY AND CONCLUSION 

The objective of this study was to evaluate the safety effectiveness of improved delineation on 

horizontal curves through signing improvements. The results of the aggregate analysis using data 

from Connecticut and Washington indicated a statistically significant reduction in injury and 

fatal crashes (18-percent reduction), crashes during dark conditions (27.5-percent reduction), and 

lane departure crashes during dark conditions (25.4-percent reduction). Table 12 presents the 

recommended crash reduction factors and SEs. Based on the limited data from Connecticut, the 

reductions in crashes were more prominent on sharper curves (curve radius less than 492 ft) and 

in locations with more hazardous roadsides (RHR of 5 or higher) compared to locations with less 

hazardous roadsides (RHR of 4 or lower). In addition, curves where more within-curve signs 

were either added or replaced (with a more retroreflective material) experienced larger 

reductions in crashes. In both States, the reductions appeared to be more prominent at locations 

with higher traffic volumes. An economic analysis revealed that improving curve delineation 

with signing improvements is a very cost-effective treatment with the benefit-cost ratio 

exceeding 8:1. 

Table 12. Crash reduction factors (CRFs) for improving curve delineation through 

signing improvements. 

Crash Type 

Recommended 

CRF Point 

Estimate 

(Percent) SE 

Injury and fatal 

curve crashes 18 8.6

Curve crashes 

during dark 

conditions 27.5 7.3

Lane departure 

crashes on curves 

during dark 

conditions 25.4 7.8

 

35 

APPENDIX: SAFETY PERFORMANCE FUNCTIONS 

This appendix provides the SPFs estimated in Connecticut and Washington. As mentioned 

previously, the form of the SPFs is as follows: 

Crashes/year = exp( )

1

0 ∑=

+

n

i

β β i Xi (9) 

Where: 

X = The independent variables. 

β = Parameters to be estimated. 

The tables in the appendix show the independent variable, β , the SE for β , the over-dispersion 

parameter, k, some summary statistics, and goodness-of-fit information. The yearly factors 

derived from the observed crash counts and predicted crash counts are also shown. For 

Washington, there is also a discussion of the alternative reference groups that were considered. 
36 

Table 13. SPFs from Connecticut. 

Variable 

NonIntersection 

Crashes 

NonIntersection 

Lane 

Departure 

Crashes 

NonIntersection 

Injury and 

Fatal 

Crashes 

NonIntersection 

Crashes 

During 

Dark 

Conditions 

NonIntersection 

Crashes Lane 

Departure 

During Dark 

Conditions 

Intercept 

2.8479 

(0.3757)

2.3637 

(0.3091)

1.5232 

(0.403)

2.4234 

(0.5973) 

1.4829 

(0.4295)

Ln (section length 

in mi) 

0.8161 

(0.06768)

0.9898 

(0.09439)

0.8531 

(0.12)

0.9412 

(0.115) 

0.9994 

(0.1329)

Ln (AADT/10,000) 

1.0047 

(0.05998)

0.7003 

(0.07719)

1.294 

(0.09779)

0.9542 

(0.09782) 

0.872 

(0.1161)

Radius (in m) 

-0.00147 

(0.00018)

-0.00206 

(0.00024)

-0.00141 

(0.00028)

-0.00125 

(0.00027) 

-0.00172 

(0.00034)

1 if RHR is 1–4, 

0 otherwise 

-0.9917 

(0.5247) 

1 if RHR is 5, 

0 otherwise 

-0.7919 

(0.5182) 

1 if RHR is 1–5, 

0 otherwise 

-0.7523 

(0.3313) 

1 if RHR is 6, 

0 otherwise 

-0.7386 

(0.3478) 

-0.6146 

(0.5423) 

RHR = 7 

(reference case) 

Number of driveways 

in the arc portion of 

the section 

0.04011 

(0.01946) 

0.06047 

(0.03102) 

1 if there is a cable 

barrier in the inside of 

the curve, 0 otherwise 

0.2219 

(0.09202)

0.3343 

(0.1136) 

0.2741 

(0.1642)

1 if there is a cable 

barrier on the outside 

of the curve, 0

otherwise 

-0.3005 

(0.1649) 

1 if there is a guardrail 

in the inside of the 

curve, 0 otherwise 

0.2077 

(0.04093)

0.2446 

(0.05538)

0.2625 

(0.05517)

0.2164 

(0.05444) 

0.1827 

(0.06614)
37 

1 if there is a guardrail 

on the outside of the 

curve, 0 otherwise 

-0.5141 

(0.1511) 

Average distance to 

next curve (km) 

-0.8101 

(0.4666)

-1.2513 

(0.5683)

-0.7954 

(0.5548) 

-1.4775 

(0.6586)

1 if there is a curb and 

gutter in the shoulder, 

0 otherwise 

0.4138 

(0.1187) 

0.3532 

(0.1826) 

Grade in the middle of 

the arc portion of the 

section 

0.04583 

(0.02629)

k 

0.8535 

(0.09992)

1.3859 

(0.1732)

0.9321

 (0.23)

1.2365 

(0.2413) 

1.6375 

(0.3594)

Observations in the 

reference group 3,290 3,020 3,020 3,020 3,020

Crashes in the 

reference group 1,400 843 438 487 350

Freeman Tukey 

R-square 0.163 0.079 0.130 0.069 0.047

1 m = 3.28 ft 

1 km = 0.621 mi 

Note: The estimate value is shown first with the SE following in parentheses. Blank cells indicate that the variable was 

not included in the particular model (i.e., for a specific crash type). 

Table 14. Yearly factors for Connecticut SPFs. 

Year Yearly Factor 

1997 0.982 

1998 0.846 

1999 0.936 

2000 1.152 

2001 1.130 

2002 0.949 

2003 0.927 

2004 1.061 

2005 1.066 

2006 0.970 
38 

SAFETY PERFORMANCE FUNCTIONS FOR WASHINGTON SITES 

In Washington, a special procedure was required to ensure that the reference group was 

representative of and comparable to the treatment group. Initially, a large reference group of 

curves on rural two-lane roads from all over the State was used to estimate the SPFs. When the 

results of these SPFs were used to predict the number of crashes in the treatment group before 

the installation of the treatment, the predicted crashes were unexpectedly much lower compared 

to the actual number of crashes before treatment (144 crashes were predicted compared to 

314 crashes that actually occurred during that period). This difference is much larger than might 

be expected due to regression to the mean, especially considering that the before period averaged 

about 5 years. Next, the research team sought to ensure that the reference group was indeed 

similar to the treatment group in terms of characteristics that were available (e.g., AADT, curve 

radius, and terrain) and characteristics that were not available (e.g., roadside characteristics and 

climate). To this end, the help of HSIS staff was sought to identify curves on the same route in 

close proximity to the treatment curves. This investigation lead to two additional potential 

reference groups: one group with curves within 5 mi of treatment curves and the other within 

2 mi of the treatment curves. By selecting curves in close proximity to the treatment group, it 

was determined that the characteristics such as roadside characteristics and climate would be 

similar in the treatment and reference groups. SPFs were developed with data from these two 

additional reference groups; however, the results from these SPFs did not produce better 

predictions. In fact, 135 crashes were predicted, which was slightly lower than the 144 crashes 

that were predicted by the larger statewide reference group. 

The next step was to explore the possibility of matching the distribution of critical independent 

variables in the reference and treatment groups. Although these critical variables were included 

in the SPFs, it was concluded that matching the distributions would provide better predictions, 

considering that the functional form of these independent variables in the SPFs may not always 

correspond to their true functional form. AADT and curve radius were considered the most 

critical variables in the models. 

The distribution of AADT was similar in the treatment and reference groups. However, the 

median and mean curve radii were much lower in the treatment group compared to the reference 

groups, indicating that the reference groups had a larger percentage of curves with a higher 

radius (the range of curve radius was the same in all groups). Curve radius was divided into 

seven categories, which included the following: 

• Radius less than or equal to 500 ft. 

• Radius is between 501 ft and 1,000 ft. 

• Radius between 1,001 ft and 1,500 ft. 

• Radius between 1,501 ft and 2,000 ft. 

• Radius between 2,001 ft and 2,500 ft. 
39 

• Radius between 2,501 ft and 3,000 ft. 

• Radius between 3,001 ft and 4,000 ft. 

Curves were randomly selected by using a random number generator and removed from the 

statewide reference group so that the percentage of curves within the seven categories was 

similar in the treatment and statewide reference group. The revised statewide reference group 

was used to estimate the SPFs. The predicted number of crashes was marginally higher (153 

versus 144 from the original statewide reference group), but it was still substantially lower than 

the 314 crashes that actually occurred during the same period. WSDOT was contacted regarding 

this apparent anomaly, but they were not able to provide further insight. 

This exercise seemed to indicate that the treatment curves were unique for some unknown factors 

that were not reflected in the reference group data. To proceed with an analysis that would 

recognize this uniqueness and be defendable, the SPFs developed using the revised statewide 

reference group were calibrated to be more representative of the treatment group. The total 

number of crashes in the treatment group in the first year before treatment through the sixth year 

before treatment were plotted to identify if there was any evidence of randomly high crashes 

during any of these periods. Only those sites that had data for 6 consecutive years before the 

treatment were included in this plot. In Washington, crash data were not available in 1997 and 

1998, and hence, only sites where the treatment was implemented in 2006 or 2005 provided 

6 consecutive years before the implementation of the treatment. Data from 25 sites (out of 

139 sites) were included in the plot in figure 3. 

Figure 3. Graph. Crashes for 25 site-years of available before period data. 

This plot suggests that crash counts in the 5 years before treatment may have been randomly 

high, but this apparent selection bias seemed to disappear for curves with 5 or more years before 

treatment. Based on this observation, it was decided that using curves with 5 or more years of 

data before treatment for the calibration would minimize the possibility of bias due to regression 

to the mean. This decision was also supported by anecdotal evidence that there was a tendency to 
40 

follow the rule of thumb of selecting high crash sites for treatment based on no more than the 

most recent 5 years of data. 

To further examine whether regression to the mean may have influenced the results of the 

evaluation, the research team conducted a before-after study (with a comparison group) where 

data for 5 years before the treatment, which were likely subject to regression to the mean bias, 

were excluded from all the sites. Consequently, sites with less than 6 years of before data were 

excluded from this examination. In this before-after study with a comparison group, the expected 

crashes in the after period were computed as follows: 

Expected crashes in the after period = (Observed crashes in the before period)*

b

a

SPF

SPF

 (10)

Where: 

SPFa = The number of crashes predicted in the after period in these sites by the SPF estimated 

with the statewide data. 

SPFb = The number of crashes predicted in the before period in these sites by the same SPF. 

Thus, the actual SPF calibration factor is immaterial since it is in both the numerator and 

denominator of the above equation. Table 15 compares the results of the EB analysis (reported in 

the main body of the report) with the before-after study with a comparison group based on before 

periods 5 or more years before treatment. 

Table 15. Comparison of EB analysis with the before-after study with comparison 

(based on 5 or more years of before treatment data). 

Crash Type 

Percent Reduction 

Reported From 

Before-After 

EB Study 

(139 Sites) 

Percent Reduction 

From Before-After 

Study with 

Comparison Group 

(70 Sites) 

Total 4.3 (8.9) -1.4 (20.3) 

Lane departure 5.9 (8.8) 2.9 (22.6) 

Injury and fatal 16.4 (10.4) 26.2 (20.3) 

Crashes during 

dark conditions 24.5 (9.5) 30.0 (19.9) 

Lane departure 

crashes during dark 

conditions 22.1 (10.1) 32.1 (22.0) 

Note: The standard errors are presented in parentheses after the percent reduction. 

Table 15 shows that the results from the before-after EB study were very close to (and actually 

on the conservative side) the results of the before-after study with a comparison group where 

crashes for 5 years before treatment were eliminated. The similarity between the results provides 
41 

further evidence that the approach adopted in recalibrating the SPFs using well-before treatment 

data was a reasonable one. 

Having rationalized the calibration of the SPFs to the treatment site data 5 or more years before 

treatment, this calibration was done for the five different crash types. The SPFs, calibration 

factors, and estimated over-dispersion parameters are shown in table 16 through table 18. 

Table 16. SPFs for total crashes from revised statewide reference group in Washington. 

Variable Estimate (SE) 

Intercept 2.4666 (0.3462) 

Ln (section length in mi) 1.1539 (0.0465) 

Ln (AADT/10,000) 1.1995 (0.0776) 

AADT/10,000 -0.7667 (0.1983) 

Ln (1/radius in mi) 0.6106 (0.0480) 

Shoulder width (ft) -0.0565 (0.0131) 

Lane width (ft) -0.0701 (0.0218) 

Percent grade (percent) 0.0249 (0.0124) 

Terrain is mountainous 

(coded as 1 for mountainous, 

0 for level or rolling) 0.2477 (0.0774) 

k 0.7583 (0.1027) 

Table 16 is based on 17,078 observations and 1,971 crashes in the reference group. The 

calculated Freeman Tukey R-square value is 0.099. Note that for this SPF, two AADT terms 

were included to capture the more complex relationship between crash frequency and AADT. 

The coefficients for one of the AADT terms was negative, indicating that for high values of 

AADT, crash frequency may start decreasing, which is a counterintuitive result. In the dataset 

used for the estimation, the maximum AADT was 15,000, and for AADT not exceeding 15,000, 

the predicted crash frequency continuously increased with AADT. This model should not be 

used to predict crashes for sections with AADT exceeding 15,000. SPFs using a similar 

functional form were estimated by Hauer et al. for four-lane undivided road segments.(20) 
42 

Table 17. Yearly factors for Washington total crash SPF. 

Year Yearly Factor 

1993 1.197 

1994 1.023 

1995 0.936 

1996 0.983 

1999 0.972 

2000 1.033 

2001 0.974 

2002 0.838 

2003 1.097 

2004 0.998 

2005 0.973 

2006 0.980 

2007 0.998 

Table 18. Calibration with well-before treatment data 

(at least 5 years prior to treatment installation). 

Crash Type 

Crashes 

Predicted by 

the SPF from 

the Statewide 

Group 

Actual Crash 

Counts in the 

Well-Before 

Years 

Calibration 

Factor 

Calibrated 

Over-Dispersion 

Parameter, k

Total crashes 49.003 96 1.9591 1.2500

Lane departure 

crashes 37.119 74 1.994 0.7634

Injury and fatal 

crashes 22.102 57 2.579 1.7857

Crashes during 

dark conditions 19.044 42 2.205 1.0101

Lane departure 

crashes during dark 

conditions 15.066 36 2.389 0.9091
43 

ACKNOWLEDGEMENTS 

This report was prepared for the FHWA. The current FHWA Contract Task Order Manager for 

this project was Roya Amjadi. Kimberly Eccles, P.E., was the study Principal Investigator. 

Dr. Raghavan Srinivasan was the lead analyst for this strategy and was the primary author of the 

report. Dr. Bhagwant Persaud and Craig Lyon developed the study design and provided general 

oversight of the analysis. Dr. Jongdae Baek was the lead programmer on this effort and prepared 

the data sets for analysis. Nancy X. Lefler and Daniel Carter led the data collection for the study 

and also contributed sections to the draft report. Charles Hamlett also participated in the data 

collection. Other significant contributions to the study were made by Dr. Hugh McGee, 

Dr. Forrest Council, Michelle Scism, and Yusuf Mohamedshah. 

The project team gratefully acknowledges the participation of the following organizations and 

individuals for their assistance in this study: 

• The ConnDOT, particularly John F. Carey, Al Iallonardo, and Brad Overturf. 

• The University of Connecticut, particularly Hongmei Zhou and John Ivan. 

• The WSDOT, particularly Rick Mowlds, Dan Davis, Mark Finch, and John Milton. 

45 

REFERENCES 

1. National Center for Statistics and Analysis of the National Highway Traffic Safety 

Administration. (2006). Fatality Analysis Reporting System, Washington, DC. Obtained 

from: http://www-fars.nhtsa.dot.gov/Main/index.aspx. Last accessed June 21, 2008. 

2. Torbic, D.J., Harwood, D.W., Gilmore, D.K., Pfefer, R., Neuman, T.R., Slack, K.L., and 

Hardy, K.K. (2004). “Guidance for Implementation of the AASHTO Strategic Highway 

Safety Plan: A Guide for Reducing Collisions on Horizontal Curves,” NCHRP Report 500 

Series, Vol. 7, Transportation Research Board, Washington, DC. 

3. Glennon, J.C., Neuman, T.R., and Leisch, J.E. (1983). Safety and Operational 

Considerations for Design of Rural Highway Curves, FHWA/RD-86/035, Federal Highway 

Administration, Washington, DC. 

4. Federal Highway Administration. (2003). The Manual on Uniform Traffic Control Devices 

(MUTCD), Washington, DC. Obtained from: http://mutcd.fhwa.dot.gov/pdfs/2003r1r2/ 

pdf_index.htm. Last accessed June 18, 2008. 

5. Fitzpatrick, K., Balke, K., Harwood, D.W., and Anderson, I.B. (2000). “Accident Mitigation 

Guide for Congested Rural Two-Lane Highways,” NCHRP Report 500 Series, Vol. 44, 

Transportation Research Board, Washington, DC. 

6. Zador, P.H., Stein, S., Wright, P., and Hall, J. (1987). “Effects of Chevrons, Post-Mounted 

Delineators, and Raised Pavement Markers on Driver Behavior at Roadway Curves,” 

Transportation Research Record 1114, Transportation Research Board, Washington, DC. 

7. Agent, K.R. and Creasey, T. (1986). Delineation of Horizontal Curves, Interim Report

UKTRP-86-4, University of Kentucky, Lexington, KY. 

8. Jennings, B.E. and Demetsky, M J. (1985). “Evaluation of Curve Delineation Sign,”

Transportation Research Record 1010, Transportation Research Board, Washington, DC. 

9. Gates, T.J., Carlson, P.J., and Hawkins Jr., G.H. (2004). “Field Evaluations of Warnings and 

Regulatory Signs with Enhanced Conspicuity Properties,” Transportation Research Record 

1862, Transportation Research Board, Washington, DC. 

10. McGee, H.W. and Hanscom, F.R. (2006). Low-Cost Treatments for Horizontal Curve Safety, 

FHWA-SA-07-002, Federal Highway Administration, Washington, DC. 

11. Opiela, K.S., Donnell, E.T., Katz, B.J., Molino, J., and Moyer, M. (2006). Field Ratings of 

Nighttime Delineation Enhancements For Curves, Transportation Research Board Annual 

Meeting 2006 Paper No. 06-2698, Transportation Research Board, Washington, DC. 

12. Charlton, S.G. (2007). “The Role of Attention in Horizontal Curves: A Comparison of 

Advance Warning, Delineation, and Road Marking Treatments,” Accident Analysis & 

Prevention, 39(5), 873–885. 
46 

13. Montello, A. (2009). “Safety Evaluation of Curve Delineation Improvements: an Empirical 

Bayes Observational Before-After Study,” Presented at the 2009 Annual Meeting of the 

Transportation Research Board, Washington, DC. 

14. Hauer, E. (1997). Observational Before-After Studies in Road Safety: Estimating the Effect of 

Highway and Traffic Engineering Measures on Road Safety, Pergamon Press, Elsevier 

Science Ltd, Oxford, U.K. 

15. SAS®, SAS Institute Inc., Cary, NC. 

16. Zegeer, C.V., Hummer, J., Reinfurt, D., Herf, L., and Hunter, W. (1986). Safety Effects of 

Cross-Section Design for Two-Lane Roads, FHWA-RD-87-008, Federal Highway 

Administration, Washington, DC. 

17. Office of Management and Budget. (2008). Discount Rates for Cost-Effectiveness, 

 Lease Purchase, and Related Analyses: No. A-94 (01/08/2008). Obtained from: 

http://www.whitehouse.gov/omb/circulars/a094/dischist.pdf. Last accessed March 7, 2009. 

18. Council, F., Zaloshnja, E., Miller, T., and Persaud, B. (2005). Crash Cost Estimates by 

Maximum Police-Reported Injury Severity Within Selected Crash Geometries, FHWA-HRT05-051, Federal Highway Administration, McLean, VA. 

19. Lord, D. (2000). “Procedure to Estimate Missing Year-to-Year Traffic Counts at 

Intersections,” 3rd Transportation Specialty Conference of the Canadian Society of Civil 

Engineering, London, ON. 

20. Hauer, E., Council, F.M., and Mohammedshah, Y. (2004). “Safety Models for Urban FourLane Undivided Road Segments,” Transportation Research Record 1897, 96–105, 

Transportation Research Board, Washington, DC. 

HRDS-06/09-09(WEB)E