AAA MICHIGAN ROAD IMPROVEMENT 

DEMONSTRATION PROGRAM EVALUATION 

PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN
AAA MICHIGAN ROAD IMPROVEMENT 

DEMONSTRATION PROGRAM EVALUATION 

PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

G.D. Hamilton Associates

Consulting Ltd. 

Prepared by:

Sany Zein, M.Eng., P.Eng. 

Vice President, Transportation 

Adrienne Mairs, EIT 

Transportation Engineer 

August 2002

7499 
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TABLE OF CONTENTS 

1.0 INTRODUCTION 

 1.1 Background 1 

 1.2 Study Objectives 1 

 1.3 Methodology 2 

2.0 SUMMARY OF IMPROVEMENTS 

2.1 Detroit 5 

2.2 Grand Rapids 6 

3.0 SIMPLE-BEFORE-AND-AFTER EVALUATION 

3.1 Methodology 7 

3.2 Simple-Before-and-After Results for Detroit 8 

3.3 Simple-Before-and-After Results for Grand Rapids 11 

4.0 EMPIRICAL-BAYES APPROACH 

4.1 Background 15 

4.2 Calculating the Empirical-Bayes Safety Estimate 16 

4.3 Determining the Treatment Effect 17 

4.4 Detroit Results 19 

4.5 Grand Rapids Results 23 

5.0 ECONOMIC EVALUATION 

5.1 Calculating the Benefit-Cost Ratio 27 

5.2 Economic Evaluation Results, Detroit 28 

5.3 Economic Evaluation Results, Grand Rapids 30 

6.0 OVERVIEW
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APPENDIX A SUMMARY OF SAFETY IMPROVEMENTS IMPLEMENTED 

APPENDIX B SUMMARY OF IMPROVEMENT COSTS 

APPENDIX C SUMMARY OF COLLISION DATA USED FOR SIMPLE BEFORE-ANDAFTER ANALYSIS 

APPENDIX D SUMMARY OF COLLISION PREDICTION MODELS 

APPENDIX E GRAPHICAL ILLUSTRATION OF PREVIOUS COLLISION 

PREDICTION MODELS 

APPENDIX F EB SAFETY ESTIMATES AND VARIANCES 

APPENDIX G ADDITIONAL EMPIRICAL-BAYES ANALYSIS 

LIST OF FIGURES 

FIGURE 4.1 DETERMINATION OF THE TREATMENT EFFECT 19 

FIGURE 4.2 ESTIMATED TREATMENT EFFECTS (TOTAL COLLISIONS) 

DETROIT 20 

FIGURE 4.3 ESTIMATED TREATMENT EFFECTS (TOTAL COLLISIONS) 

GRAND RAPIDS 25 

FIGURE 5.1 ILLUSTRATION OF TYPICAL COST SAVINGS 28 

LIST OF TABLES 

TABLE 3.1 SUMMARY OF SIMPLE-BEFORE-AND-AFTER EVALUATION 

RESULTS, DETROIT 9 

TABLE 3.2 SUMMARY OF DETROIT LOCATIONS WITH STATISTICALLY 

SIGNIFICANT COLLISION REDUCTIONS 10 

TABLE 3.3 SUMMARY OF SIMPLE-BEFORE-AND-AFTER EVALUATION 

RESULTS, GRAND RAPIDS 12 

TABLE 3.4 SUMMARY OF GRAND RAPIDS LOCATIONS WITH STATISTICALLY 

SIGNIFICANT COLLISION REDUCTIONS 13 

TABLE 4.1 ESTIMATED TREATMENT EFFECTS BY LOCATION AND 

COLLISION TYPE, DETROIT 21 

TABLE 4.2 SUMMARY OF TREATMENT EFFECTS, DETROIT 22 

TABLE 4.3 ESTIMATED TREATMENT EFFECTS BY LOCATION AND 

COLLISION TYPE, GRAND RAPIDS 25 

TABLE 4.4 SUMMARY OF TREATMENT EFFECTS, GRAND RAPIDS 25 

TABLE 5.1 AVERAGE SOCIETAL COLLISION COSTS 27 

TABLE 5.2 SUMMARY OF THE ECONOMIC EVALUATION, DETROIT 39 

TABLE 5.3 SUMMARY OF THE ECONOMIC EVALUATION, GRAND RAPIDS 31 
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EXECUTIVE SUMMARY 

Introduction 

As part of a pro-active initiative to reduce the frequency and severity of motor 

vehicle collisions, the Automobile Club of Michigan (AAA Michigan) has developed 

the AAA Michigan Road Improvement Demonstration Program. Under this 

program, AAA Michigan has contributed to road improvement strategies in Detroit 

and Grand Rapids, Michigan since 1997. AAA Michigan now wishes to ascertain 

the effectiveness of its investment. This program evaluation study was therefore 

initiated by AAA Michigan to evaluate the benefits gained from investing in road 

improvement projects throughout the Cities of Detroit and Grand Rapids. 

Methodology 

This program evaluation study was divided into two Phases. The first Phase 

was completed in March 2002, and detailed the development of multivariate 

collision prediction models for both Detroit and Grand Rapids. A separate 

report documenting the findings of Phase 1 was released, under the title 

Program Evaluation Phase 1: Collision Prediction Modeling, Detroit and Grand 

Rapids (Hamilton Associates, 2002). 

This report documents the findings for Phase 2. The second Phase involved 

evaluating the sites where improvements have been impDlemented in Detroit 

and Grand Rapids (referred to as the “treatment sites”). This postimprovement evaluation utilized the collision prediction models developed in 

Phase 1 to predict the number of collisions expected at a treatment site, had 

the improvement not been implemented. This predicted collision frequency 

was refined with an Empirical-Bayes (EB) approach, and compared to the 

actual post-improvement collision frequency to estimate the safety benefits of 

the improvement. 
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Detroit Results 

Of the 35 Detroit treatment sites evaluated using the EB approach, 32

experienced fewer than predicted collisions, while the other three indicate an 

increase. The average treatment effects were -39 percent for total collisions,

and -56 percent for injury collisions. The larger decrease in injury collisions

indicates that the safety improvements have had a greater impact on severe 

collisions than on collisions involving property damage only. The estimated

treatment effects for total collisions at the Detroit sites are illustrated in 

FIGURE ES.1. 

-100%

-80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

100%

120%

140%

Detroit Treatment Site Number (1 to 35)

Estimated Treatment Effect

Sites experienced an

increase in safety

Sites did not experience an

increase in safety

FIGURE ES.1 ESTIMATED TREATMENT EFFECTS USING EB 

APPROACH (TOTAL COLLISIONS) DETROIT

The results of the economic evaluation (in terms of societal costs) for the

Detroit treatment sites are summarized below. 

• Overall, the net present value of the Detroit improvements is $4,792,000 

(two-year life cycle) or $33,720,000 (15-year life cycle). 

• A total of 22 sites (or 65 percent) exceeded a B/C of 2:1 in two years. 

• A total of 33 sites (or 97 percent) exceeded a B/C of 2:1 in 15 years. 

• A total of 32 sites (or 94 percent) reported a positive NPV (benefits) over 

two years. 
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• The Woodward corridor (30 sites) was estimated to have a NPV of 

$3,530,000 and a B/C of 2.8 (two-year life cycle). 

• In terms of the actual before-and-after comparison of societal costs, the 

average annual pre-improvement cost of collisions for the Detroit treatment 

group was $6,563,000. The actual average annual post-improvement cost

of collisions was $3,640,000. This indicates an overall annual cost savings

of $2,923,000. 

Grand Rapids Results 

There were 26 treatment sites evaluated in Grand Rapids. Of the evaluated 

sites, 17 indicate an overall reduction in collision frequency. In terms of total 

collisions, the treatment effects range from -83 percent to +72 percent, with an

average treatment effect of -11 percent. The estimated treatment effects for 

total collisions at the Grand Rapids sites are illustrated in FIGURE ES.2. 

-100%

-80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

100%

Grand Rapids Treatment Site Number (1 to 26)

Estimated Treatment Effect

Sites experienced an

increase in safety

Sites did not experience an

increase in safety

FIGURE ES.2 ESTIMATED TREATMENT EFFECTS USING EB 

APPROACH (TOTAL COLLISIONS) GRAND RAPIDS
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The results of the economic evaluation for the Grand Rapids treatment sites 

(in terms of societal costs) are summarized below: 

• Overall, the net present value of the Grand Rapids improvements is 

$2,635,000 (two-year life cycle) or $17,366,000 (15-year life cycle). 

• A total of 16 sites (or 61 percent) exceeded a B/C of 2:1 in two years. 

• A total of 20 sites (or 77 percent) exceeded a B/C of 2:1 in 15 years. 

• A total of 18 sites (or 69 percent) reported a positive NPV (benefits) over 

two years. 

• In terms of simple-before-and-after societal costs, the average annual preimprovement cost of collisions for the Grand Rapids treatment group was 

$5,711,000 and the post-improvement cost of collisions was $3,305,000, 

indicating an overall annual cost savings of $2,406,000. 

Overview 

In terms of collision reduction, and using the EB refinement approach, the 

program has achieved overall treatment effects of -39 percent in Detroit and 

-11 percent in Grand Rapids, with a combined average treatment effect of 

-27 percent. In both cities, the program has been particularly effective in 

reducing the frequency of high severity collisions. 

The Detroit improvements had a total implementation cost of $2,373,000, and 

a two-year benefit-cost ratio of 3.0 to 1. The Grand Rapids treatments had a 

total implementation cost of $1,014,000 and a two-year benefit-cost ratio of 3.6 

to 1. In terms of societal costs, the net present value of the Detroit and Grand 

Rapids improvements combined was estimated to be $7,427,000, assuming a 

two-year life cycle. 

This evaluation of the AAA Michigan Road Improvement Demonstration 

Program has demonstrated that the program as a whole has achieved a 

positive benefit-cost ratio over two, three, and 15-year life cycles. By 

combining the societal savings and improvement costs for both the two cities, 

the overall benefit-cost ratio of this program was determined to be 3.2:1 over 

two years, 4.6:1 (over three years) and 16.1:1 (over 15 years). 
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1.0 INTRODUCTION 

1.1 Background 

As part of a pro-active initiative to reduce the frequency and severity of motor 

vehicle collisions, the Automobile Club of Michigan (AAA Michigan) has developed 

the AAA Michigan Road Improvement Demonstration Program. Under this 

program, AAA Michigan has contributed to road improvement strategies in Detroit 

and Grand Rapids, Michigan since 1997. AAA Michigan now wishes to ascertain 

the effectiveness of its investment. This program evaluation study was therefore 

initiated by AAA Michigan to evaluate the benefits gained from investing in road 

improvement projects in the Cities of Detroit and Grand Rapids. 

An evaluation study determines whether the expected safety benefits at each 

improved location and for the program as a whole have been achieved. 

Evaluating the impact of investments in traffic safety and road infrastructure is 

essential for AAA Michigan, in order to support continued investment in the 

Road Improvement Demonstration Program. An accurate evaluation ensures 

the effective use of future road improvement funding. 

1.2 Study Objectives 

The objectives of this study were to evaluate the pre- and post-improvement 

collision histories at a sample of the intersections improved under the AAA 

Michigan Road Improvement Demonstration Program, in order to quantify the 

safety benefits and claim cost savings to date. 
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1.3 Methodology 

This program evaluation study was divided into two Phases. The first Phase 

was completed in March 2002, and detailed the development of multivariate 

collision prediction models for both Detroit and Grand Rapids. A separate 

report documenting the findings of Phase 1 was released, under the title 

Program Evaluation Phase 1: Collision Prediction Modeling, Detroit and Grand 

Rapids (Hamilton Associates, 2002). 

This report documents the findings for Phase 2. The second Phase involved 

evaluating the sites where improvements have been implemented in Detroit 

and Grand Rapids (referred to as the “treatment sites”). This postimprovement evaluation utilized the collision prediction models developed in 

Phase 1 to predict the number of collisions expected at a treatment site, had 

the improvement not been implemented. This predicted collision frequency 

was refined with an Empirical-Bayes approach, and compared to the actual 

post-improvement collision frequency to estimate the safety benefits of the 

improvement. 

A systematic approach was taken to conduct Phase 2 of the post-improvement 

evaluation. The methodology included the following components: 

• The necessary data was collected and compiled by AAA Michigan. Care was 

taken to ensure that each treatment site had at least one year of postimprovement collision data available for analysis. Data included the monthly 

frequency of police-reported collisions at each treatment site, traffic volume 

and intersection information, the physical details of the improvements, the total 

cost and date of completion of the improvements, and the AAA Michigan share 

of the costs for each treatment site. 

• The pre- and post-improvement collision data was examined, and a simple 

before-and-after evaluation was done. The change in frequency of total, injury, 

rear-end, side-swipe, angle and left-turn/head-on collision types was 

examined. The T-Test was applied to the results of the simple before-andafter analysis to determine a level of confidence in the results. The simplebefore-and-after analysis is described further in Section 3. 
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• Using the models developed in Phase 1, the predicted collision frequency, 

Empirical-Bayes safety estimate, variance of the EB safety estimate, Odds 

Ratio and treatment effect were calculated. These calculations were repeated 

for each City and for four collision types: total, injury only, rear-end and sideswipe. The Empirical-Bayes approach is described further in Section 4. 

• The average annual cost savings were estimated for the improved locations. 

The benefits were calculated based on the estimated reduction in collision 

frequency at each site, and on the average societal costs for PDO and injury 

collisions. The benefit-cost ratios for each location and for the program as a 

whole were estimated for two, three and 15-year post-improvement periods. 
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2.0 SUMMARY OF IMPROVEMENTS 

This section describes the intersection safety and road infrastructure 

improvements that were implemented in Detroit and Grand Rapids. 

2.1 Detroit 

The treatment sites selected for evaluation included those with at least one 

year of post-improvement collision data and up to three years of preimprovement collision data available. In Detroit, there were 35 treatment 

intersections with at least one year of post-improvement collision data 

available for evaluation. The 35 sites included two intersections along Seven 

Mile Road, 30 intersections along the Woodward Avenue corridor, and three 

other intersections. During the post-improvement period, the average daily 

traffic (ADT) for the Detroit treatment sites ranged from 20,000 to 45,000 

vehicles per day, with an average ADT of 27,000. 

A summary of the safety improvements implemented at each site was 

provided by AAA Michigan, and is provided in APPENDIX A. The costs of the 

improvements are presented in APPENDIX B. 

The types of safety treatments implemented at the Detroit intersections 

included a combination of: 

• Upgrading traffic signals from 8" to 12" diameter lenses; 

• Adding exclusive left-turn lanes; 

• Adding permitted/protected left-turn phasing; 

• Adding far-left low-level traffic signals; 

• Adding an all red interval to the signal timing plan; 

• Adding pedestrian signal displays; 

• Adding additional overhead traffic signals; 

• Improving the traffic signal placement; and 

• Other site-specific improvements. 
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2.2 Grand Rapids 

In Grand Rapids, there were 26 treatment intersections with up to three years 

of pre-improvement collision data and at least one year of post-improvement 

collision data available for evaluation. The 26 sites included nine intersections 

along the Division Avenue corridor, eight intersections along the Burton Street 

corridor, seven intersections along the Eastern Avenue corridor and two other 

intersections. 

AAA Michigan provided traffic volumes counted between 1996 and 1999 for 

each Grand Rapids location. More recent traffic counts were unavailable, and 

therefore it was assumed that traffic volumes have remained relatively stable 

between the pre- and post-improvement periods. The average daily traffic 

(ADT) for the Grand Rapids treatment sites ranged from 15,000 to 59,000 

vehicles per day, with an average ADT of 28,000. 

A summary of the safety improvements implemented at each site was 

provided by AAA Michigan, and is presented in APPENDIX A. The 

implementation date for each treatment intersection is also shown in the same 

appendix. The costs of the improvements are presented in APPENDIX B. 

The types of safety treatments implemented at the Grand Rapids intersections 

included a combination of: 

• Upgrading traffic signals from 8" to 12" diameter lenses; 

• Adding exclusive left-turn lanes; 

• Adding permitted/protected left-turn phasing; 

• Adding far-left low-level traffic signals; 

• Adding an all red interval to the signal timing plan; 

• Adding pedestrian signal displays; and 

• Other site-specific improvements. 
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3.0 SIMPLE-BEFORE-AND-AFTER EVALUATION 

3.1 Methodology

A simple-before-and-after study is a convenient method of identifying 

treatment sites that have experienced changes in collision frequency over

time. This method is relatively easy to undertake and understand, however, it

is acknowledged that this method does not account for three important 

confounding factors: 

1) History of the treatment site (factors other than the treatment may have 

caused the change in safety). 

2) The time trend effect (collision patterns change over time and these

changes should be accounted for). 

3) “Regression-to-the-mean,” or RTM effects. The RTM effects refer to

the phenomenon whereby extreme events are usually followed by less

extreme events, even when no intervention has taken place. The 

failure to account for the RTM effect can lead to an overestimation of 

the safety benefits of an intervention. 

The simple-before-and-after evaluation involved a comparison between the 

annual frequency of collisions recorded at an intersection before the

improvement was implemented and the annual collision frequency after 

implementation. The simple-before-and-after method is summarized below in

equation (1). A reduction in average annual collision frequency was defined

as a negative value, while an increase in average annual collision frequency

was defined as a positive value. 

% Change = (Average Annual Collisions Before – Average Annual Collisions After) 

(Average Annual Collisions Before) 

 (1)
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Significance Testing 

A significance test (T-test) was conducted to determine whether the treatment

effects were significant based on the number of collisions occurring before and 

after the improvements. This derivation of the T-Test was based on research 

conducted at the University of British Columbia and documented in Update to

the Economic Evaluation Methodologies for Road Improvement Programs

(Sayed and Zein, 1997). The T value can be calculated by the following

equation: 

 T (2) x y = x y

−

+ where: 

x = the number of collisions per year observed before the treatment 

y = the number of collisions per year observed after the treatment 

The T value can be compared with the normal distribution Z-value of 1.960 at

the 95 percent significance level. T values greater than or equal to 1.960 are 

considered statistically significant. 

3.2 Simple Before-and-After Results for Detroit 

The simple-before-and-after evaluation methodology was applied to total, 

injury, rear-end, sideswipe, angle and left-turn head-on collision types at the

improved intersections in the City of Detroit. The 35 intersections were 

examined individually, however, the intersections included in the Woodward 

corridor were also examined as a group. 

The simple-before-and-after evaluation indicated that overall collisions

decreased by 34 percent at the Detroit treatment sites. Nine of the 35 sites

recorded an overall increase in average annual collisions during the postimprovement period. Injury collisions decreased by 47 percent, suggesting 

that the safety improvements had a greater impact on severe collisions than 

collisions involving property damage only. The greatest reduction was in 

angle collisions (73 percent). The changes in collision frequency by location 

and collision type are summarized in TABLE 3.1. 
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TABLE 3.1 SUMMARY OF SIMPLE-BEFORE-AND-AFTER EVALUATION 

RESULTS, DETROIT

PERCENT CHANGE BY COLLISION TYPE 

SITE 

# TREATMENT LOCATION 

TOTAL INJURY REAREND 

SIDESWIPE ANGLE LTHO 

1 7 Mile and John R -50% -68% 22% -34% -63% -84% 

2 7 Mile and Ryan -53% -73% -32% -39% -76% -88% 

3 Hubbell and Puritan -64% -72% -50% -56% -86% -82% 

4 Schoolcraft and Evergreen -34% -47% -40% 11% -77% -36% 

5 Linwood and Davison* 115% 176% 189% 80% 129% -77% 

6 Woodward and Adelaide/Sibley 65% n/a -8% -34% n/a -35% 

7 Woodward and Charlotte -50% -38% -100% -39% n/a -8% 

8 Woodward and Eliot/Stimson -31% n/a -100% -56% n/a n/a 

9 Woodward and Mack 55% 62% 115% 11% -50% -31% 

10 Woodward and Parsons 27% 269% -38% n/a n/a n/a 

11 Woodward and Alexandrine -27% -45% -69% -54% -38% 85% 

12 Woodward and Canfield -34% -47% -100% n/a -74% -54% 

13 Woodward and Forest -28% -16% 38% 119% -87% n/a 

14 Woodward and Warren -16% -16% 23% 177% -48% -19% 

15 Woodward and Putnam/Farnsworth -11% -26% -8% -21% -65% -100% 

16 Woodward and Kirby -57% -79% -65% -8% -100% -100% 

17 Woodward and Palmer -25% -26% -21% -20% -54% -54% 

18 Woodward and Antoinette/Medbury -74% -54% -100% -33% -69% n/a 

19 Woodward and Baltimore -34% -54% 13% 85% -100% -31% 

20 Woodward and Milwaukee -69% -74% 131% 85% -96% -100% 

21 Woodward and Bethune 21% 15% -45% 23% -100% n/a 

22 Woodward and Seward -24% -54% 223% n/a -54% n/a 

23 Woodward and Euclid -44% -69% -23% -8% -54% -69% 

24 Woodward and Hazelwood/ Holbrook -12% 11% -31% -54% -8% 85% 

25 Woodward and Clairmont/Owen -57% -85% -69% 85% -93% 177% 

26 Woodward/Chicago -62% -100% -59% -8% -77% -8% 

27 Woodward and Calvert/Towbridge -42% -100% -8% -42% -100% -100% 

28 Woodward and Tux/Tennyson -6% -100% 125% -8% n/a n/a 

29 Woodward and Courtland 50% n/a n/a -8% -50% n/a 

30 Woodward and Glendale/Mclean 41% 29% 58% -82% 88% 275% 

31 Woodward and Buena Vista 50% n/a 69% -8% -25% n/a 

32 Woodward and Gerald 125% 50% 125% -25% n/a n/a 

33 Woodward and Manchester -53% -57% -13% n/a -79% -21% 

34 Woodward and Sears -45% -45% -45% -14% -75% -63% 

35 Woodward and Feris -11% 13% -25% -25% -75% -25% 

INTERSECTIONS 1 TO 4 -51% -65% -26% -34% -77% -79% 

WOODWARD CORRIDOR -25% -35% -10% -14% -70% -10% 

OVERALL -34% -47% -14% -19% -73% -51% 

Notes:

n/a= no collisions recorded during pre-improvement period, therefore calculation not possible 

LTHO = left-turn head-on collision type 

* Treatment site removed from evaluation and not included in overall averages in TABLE 3.1 
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The T-test was applied to each treatment site to determine if the reduction in 

collision frequency may be considered statistically significant. To be 

considered significant, the T value (described previously in Section 3.1) must 

be greater than the normal distribution Z-value of 1.960, at the 95 percent 

confidence level. The T-test results indicated that nine treatment locations 

experienced statistically significant reductions in the frequency of various 

collision types. The Woodward Corridor (a group of 30 intersections) was also 

found to have statistically significant reductions in total, injury and angle 

collisions. The T-test results are summarized in TABLE 3.2. 

TABLE 3.2 SUMMARY OF DETROIT LOCATIONS WITH STATISTICALLY 

SIGNIFICANT COLLISION REDUCTIONS 

COLLISION 

TYPE 

LOCATIONS WITH STATISTICALLY SIGNIFICANT 

REDUCTION IN COLLISION FREQUENCY T-TEST VALUE* 

TOTAL 

7 Mile and John R 

7 Mile and Ryan 

Hubbell and Puritan 

Woodward and Milwaukee 

Woodward and Manchester 

Woodward Corridor (Group) 

3.05 

3.71 

3.29 

2.97 

2.73 

3.74 

INJURY 

7 Mile and John R 

7 Mile and Ryan 

Hubbell and Puritan 

Woodward and Chicago 

Woodward Corridor (Group) 

2.60 

2.78 

2.25 

2.12 

2.77 

ANGLE 

7 Mile and John R 

7 Mile and Ryan 

Schoolcraft and Evergreen 

Woodward and Forest 

Woodward and Milwaukee 

Woodward and Clairmont/Owen 

Woodward and Manchester 

Woodward Corridor (Group) 

3.01 

3.63 

2.07 

3.05 

3.27 

2.29 

2.75 

6.07 

LTHO 7 Mile and John R 

7 Mile and Ryan 

3.41 

3.90 

REAR-END None 

SIDESWIPE None 

* Higher than 1.960 is significant at the 95 percent confidence level
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It was noted that the frequency of collisions at the Linwood/Davison treatment 

site (site #5) increased by 115 percent during the post-improvement period. 

AAA Michigan noted that this large increase in collision frequency is likely 

related to a new commercial development that opened during the postimprovement period. This new development is situated near the treatment 

intersection, and the increase in collision frequency may be attributed to the 

increase in turning manoeuvres at nearby site access points. These changes 

in nearby traffic patterns were determined to be unique to this treatment site, 

and it was therefore removed from the analysis to avoid skewing the overall 

evaluation results. 

3.3 Simple Before-and-After Results for Grand Rapids 

There were 26 treatment intersections evaluated in the City of Grand Rapids. 

The simple-before-and-after evaluation methodology was applied to determine 

the decrease (or increase) in total, injury, rear-end, sideswipe, angle and leftturn head-on collision types. 

The simple-before-and-after evaluation indicated that overall collisions 

decreased by 22 percent at the Grand Rapids treatment sites. Of the 26 

treatment sites, 19 recorded an overall decrease in collisions during the postimprovement period, six recorded an increase, and one site experience no 

change in collision frequency. Injury collisions decreased by 47 percent, 

suggesting that the safety improvements had a greater impact on severe 

collisions than collisions involving property damage only. The most notable 

drop by collision type was angle collisions (decreased by 59 percent). Overall, 

there were no notable changes in rear-end or sideswipe collision types (both 

experienced a one percent increase in collision frequency). The changes in 

collision frequency by location and type are summarized in TABLE 3.3. 
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The T-test was applied to each Grand Rapids treatment site to determine if the 

reduction in collision frequency may be considered statistically significant. The 

T-test results indicated that nine treatment locations experienced statistically 

significant reductions in the frequency of various collision types. These 

locations are summarized in TABLE 3.4. 

TABLE 3.3 SUMMARY OF SIMPLE-BEFORE-AND-AFTER EVALUATION 

RESULTS, GRAND RAPIDS

PERCENT CHANGE BY COLLISION TYPE 

SITE 

# TREATMENT LOCATION 

TOTAL INJURY REAREND 

SIDESWIPE ANGLE LTHO 

1 Leonard and College -74% -69% -47% -93% -56% -91% 

2 Ottawa and Michigan 40% 22% 117% 47% 127% 77% 

3 Division and Oakes -52% -100% 9% -45% -100% n/a 

4 Division and Cherry 55% 100% 52% 138% -27% -100% 

5 Division and Weston 47% 60% -4% 60% -71% n/a 

6 Division and Wealthy -36% -56% 71% 17% -77% -65% 

7 Division and Delaware -59% -100% -65% -42% -45% n/a 

8 Division and Franklin -6% -27% 17% 29% -84% 43% 

9 Division and Cottage Grove 0% -77% 31% -100% 129% n/a 

10 Division and Hall -36% -67% -39% 11% -38% -74% 

11 Division and Burton -23% -52% 19% 4% -61% -71% 

12 Burton and Raybrook -42% -17% -38% -84% -100% 20% 

13 Burton and Breton -33% -50% -14% 29% -100% -72% 

14 Burton and Plymouth -20% -54% -40% 71% -51% -62% 

15 Burton and Sylvan -2% -22% 88% -100% -70% 140% 

16 Burton and Kalamazoo -16% -66% 19% 125% -60% -85% 

17 Burton and Madison -37% -77% -28% 71% -41% -70% 

18 Burton and Jefferson 74% 60% 112% -43% 14% 243% 

19 Burton and Buchanan -10% -10% 8% -22% -89% -25% 

20 Eastern and Lake -64% -56% 9% -100% -75% -40% 

21 Eastern and Cherry -83% -100% -73% -100% -80% -100% 

22 Eastern and Wealthy 43% -100% 173% 87% -64% 45% 

23 Eastern and Sherman -27% 64% -33% -69% 45% 191% 

24 Eastern and Hall -23% -31% -8% -80% -9% -66% 

25 Eastern and Oakdale 20% 17% 27% 145% 255% -40% 

26 Eastern and Franklin -42% -69% -31% -45% -42% -64% 

OVERALL -22% -47% 1% 1% -59% -50% 

Notes:

n/a= no collisions recorded during pre-improvement period, therefore calculation not possible 

LTHO = left-turn head-on collision type 
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TABLE 3.4 SUMMARY OF GRAND RAPIDS LOCATIONS WITH 

STATISTICALLY SIGNIFICANT COLLISION REDUCTIONS 

COLLISION 

TYPE 

LOCATIONS WITH STATISTICALLY SIGNIFICANT 

REDUCTION IN COLLISION FREQUENCY T-TEST VALUE* 

TOTAL 

Leonard and College 

Burton and Breton 

Eastern and Lake 

Eastern and Cherry 

3.49 

2.08 

2.11 

2.78 

INJURY Division and Hall 

Burton and Madison 

2.24 

2.43 

ANGLE 

Division and Wealthy 

Division and Franklin 

Eastern and Lake 

2.40 

2.51 

1.98 

LTHO 

Leonard and College 

Division and Hall 

Division and Burton 

Burton and Breton 

2.21 

2.52 

2.64 

1.96 

REAR-END None 

SIDESWIPE None 

* Higher than 1.960 is significant at the 95 percent confidence level
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4.0 EMPIRICAL-BAYES APPROACH 

The Empirical-Bayes approach comprised two steps. First, the EB safety 

estimate (a prediction of the collision frequency at the treatment site, had the 

treatment not been implemented) was calculated for each site and for each 

collision type. Secondly, the treatment effect in terms of a percent decrease 

(or increase) in collision frequency, was calculated. 

4.1 Background 

The Empirical-Bayes (EB) approach to before-and after evaluations is 

considered statistically more robust than the simple-before-and-after 

approach. The EB process uses a reference group to help account for the 

RTM effect described in Section 3.1. Previous research documented in 

Update to the Economic Evaluation Methodologies for Road Improvement 

Programs (Hamilton Associates, 1997) compared the EB approach to classical 

statistical techniques (such as simple-before-and-after). The comparison 

indicated a potentially significant difference in the estimated treatment 

effectiveness measurement. The difference was lower for sites with high 

exposure and higher for low exposure sites. 

According to Hauer1

, there are two kinds of clues to the safety of a location: 

(1) characteristics of the location such as geometry and traffic conditions, and 

(2) the collision history of the location. In an EB analysis, the collision 

prediction for a site is based on the two clues: the historical collision 

experience for similar intersections (a reference group) as well as the collision 

experience at the treatment site. 

 

1

 Hauer, E. (1997). “Observational Before-After Studies in Road Safety,” Department of Civil 

Engineering, University of Toronto. 
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The EB approach makes use of the multivariate collision prediction models 

that were previously developed in Phase 1 of the evaluation study. These 

models were developed based on the characteristics of reference groups. The 

expected number of collisions at each treatment site (had no improvement 

taken place) was predicted by using the collision prediction models. The EB

refinement process involved combining the predicted collision frequency (as 

determined by model output) with the historical collision data at each site to 

predict the expected number of collisions that would have occurred at an 

intersection, had the treatment not been implemented. 

A more detailed description of the collision prediction model development may

be found in the Phase 1 report. A summary of the models used for this

evaluation is provided in APPENDIX D. 

4.2 Calculating the EB Safety Estimate 

The process of determining the EB safety estimate is described in detail in

Hauer (1997), and is summarized below in equation (3). 

EB Safety Estimate = ∀ x (Predicted) + (1-∀) x (Counted) (3)

Where: ∀ = 1 (4) 

 1+Var(Predicted)

 Predicted

And: Predicted = number of collisions predicted from a model 

Counted = number of collisions counted at the treatment site 

Var (Predicted) = variance of the model’s estimate 
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According to Hauer (1997), the variance of the EB Safety Estimate never

exceeds the EB Safety Estimate and is almost always smaller. The variance

of the EB Safety Estimate can be calculated using equation (5): 

Var(EB Safety Estimate) =(1-∀) x EB Safety Estimate (5) 

In the case of the negative binomial distribution, the variance of the predicted

collision frequency is defined by equation (6): 

Var(Predicted) = (Predicted)

2 (6)



Where is a parameter of the negative binomial distribution, provided by 

the GLIM model. 

Therefore, when using collision prediction models based on the negative 

binomial assumption, equations (3) and (5) can be rearranged to yield 

equations (7) and (8): 

EB Safety Estimate = (Predicted) x (+Counted) (7) 

 (+Predicted) 

Var(EB Safety Estimate) = (Predicted)2 x (+Counted) (8) 

 (+Predicted) 

4.3 Determining the Treatment Effect 

The treatment effect of a safety improvement is ideally expressed as an

estimated percent reduction (or increase) in collision frequency. In the context 

of the EB approach, the treatment effect may be defined as the difference 

between the estimated collision frequency at the treatment site, had the 

treatment not been implemented and the actual post-improvement collision

frequency at the treatment site. 

The EB refinement process accounts for the RTM effect. In order to account 

for the other two confounding factors (history and the time trend effect), a 
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18 HAMILTON ASSOCIATES

comparison group was defined. The comparison group comprised a small 

group of non-treatment sites (approximately 10) considered to be similar to the 

treatment sites. The comparison group accounts for unrelated changes in 

collision frequency over time. By combining the simple before-and-after

change in collision frequency within the comparison group, the change of 

collision frequency at the treatment site and the EB safety estimate, an Odds

Ratio (O.R.) was calculated as shown in equation (9). 

(B / D)

( A/ C) O.R.= (9)

Where A = Pre-improvement collision frequency of comparison group 

B = EB safety estimate 

C = Post-improvement collision frequency of comparison group 

D = Post-improvement collision frequency at treatment site 

Finally, the treatment effect was calculated as shown in equation (10). The 

treatment effect was converted to a percentage to indicate either a percent 

decrease in collision frequency (a negative value) or an increase (a positive 

value). 

Treatment Effect = O.R. – 1 (10)

FIGURE 4.1 graphically illustrates how, in theory, the treatment effect is

calculated for a typical intersection. In reality, depending on the actual

characteristics of the treatment and comparison group data being analyzed,

the points on the graph fluctuate. 
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100

200

300

400

0 1 2 3 4 5 6 7 8

Annual Collision Frequency

BEFORE AFTER

Treatment Sites (actual)

EB Estimate

Actual Treatment Site Data 

Comparison Sites (actual)

Treatment Sites (had no

treatment taken place)

Actual Comparison Group

Treatment Effect

B

C

D A

FIGURE 4.1 DETERMINATION OF THE TREATMENT EFFECT 

4.4 Detroit Results 

Of the 35 Detroit treatment sites evaluated, 32 indicate an overall reduction in 

collisions, while the other three indicate an increase. The average treatment 

effects were -39 percent for total collisions, and -56 percent for injury 

collisions. The larger decrease in injury collisions indicates that the safety 

improvements have had a greater impact on severe collisions than on 

collisions involving property damage only. The average treatment effects for 

rear-end and sideswipe collisions were -42 and -48 percent, respectively. The 

relatively low pre- and post-improvement frequencies of rear-end and sideswipe collisions make a site-by-site comparison between the simple-beforeand-after results and EB analysis results difficult. 

Changes in left-turn/head-on and angle collisions were not examined as part 

of the EB evaluation. Collision prediction models for left-turn/head-on and

angle collision types developed in Phase 1 were not found to be statistically 

meaningful (see the Phase 1 report). 
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The Woodward corridor sites were also examined as a group to determine the 

corridor-wide treatment effect. The average Woodward corridor treatment 

effects were noted to be greater than or equal to the overall Detroit average

treatment effects for each collision type evaluated. A 39 percent reduction in

total collision frequency along this corridor was estimated, with an even

greater (57 percent) reduction in injury collisions. The estimated treatment 

effects for total collisions at the Detroit sites are illustrated in FIGURE 4.2. 

The treatment effects are summarized by location and collision type in TABLE 

4.1. 

-100%

-80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

100%

120%

140%

Detroit Treatment Site Number (1 to 35)

Estimated Treatment Effect

Sites experienced an

increase in safety

Sites did not experience an

increase in safety

FIGURE 4.2 ESTIMATED TREATMENT EFFECTS USING EB APPROACH 

(TOTAL COLLISIONS) DETROIT

It should be emphasized that the average treatment effects determined by the 

EB approach (shown in the bottom row of TABLE 4.1) are calculated simply by

summing the treatment effects and dividing by the total number of treatment 

sites. A comparison between the overall average EB treatment effect and the 

overall results of the simple-before-and-after analysis (shown in the bottom 

row of TABLE 3.1) should be done, as they have different meanings. The EB 

averages shown in the bottom row of TABLE 4.1 are not weighted, whereas 

the simple-before-and-after reductions are calculated based on an overall 

change in magnitude of collisions in the treatment group. 
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TABLE 4.1 ESTIMATED TREATMENT EFFECTS USING EB APPROACH 

BY LOCATION AND COLLISION TYPE, DETROIT 

TREATMENT EFFECT BY COLLISION TYPE 

SITE # LOCATION 

TOTAL INJURY REAR-END SIDE-SWIPE 

1 7 Mile and John R -38% -47% 62% -14% 

2 7 Mile and Ryan -43% -58% 24% -13% 

3 Hubbell and Puritan -57% -57% -48% -53% 

4 Schoolcraft and Evergreen -29% -28% -39% -41% 

5 Linwood and Davison 126% 125% 140% 27% 

6 Woodward and Adelaide/Sibley -60% -65% -86% -77% 

7 Woodward and Charlotte -65% -68% -100% -81% 

8 Woodward and Eliot/Stimson -77% -82% -100% -100% 

9 Woodward and Mack 47% 5% 13% 49% 

10 Woodward and Parsons -34% -39% -75% -39% 

11 Woodward and Alexandrine -28% -65% -67% -26% 

12 Woodward and Canfield -40% -61% -100% -18% 

13 Woodward and Forest -24% -27% 5% -6% 

14 Woodward and Warren -6% -8% 8% -29% 

15 Woodward and Putnam/Farnsworth -5% -43% -16% 3% 

16 Woodward and Kirby -60% -80% -67% -29% 

17 Woodward and Palmer -31% -57% -35% -37% 

18 Woodward and Antoinette/Medbury -88% -85% -100% -100% 

19 Woodward and Baltimore -44% -64% -7% -62% 

20 Woodward and Milwaukee -68% -74% -52% -68% 

21 Woodward and Bethune -20% -38% -71% -41% 

22 Woodward and Seward -33% -55% -24% -69% 

23 Woodward and Euclid -51% -74% -56% -52% 

24 Woodward and Hazelwood/ Holbrook -31% -46% -53% -78% 

25 Woodward and Clairmont/Owen -60% -86% -83% -69% 

26 Woodward/Chicago -67% -100% -64% -88% 

27 Woodward and Calvert/Towbridge -60% -100% -53% -72% 

28 Woodward and Tuxedo/Tennyson -64% -100% -65% -83% 

29 Woodward and Courtland -75% -100% -88% -100% 

30 Woodward and Glendale/Mclean 26% -6% 30% -39% 

31 Woodward and Buena Vista -17% -29% -9% -84% 

32 Woodward and Gerald -10% -65% -19% -63% 

33 Woodward and Manchester -48% -41% -18% -49% 

34 Woodward and Sears -45% -41% -31% -7% 

35 Woodward and Feris -26% -30% -23% -44% 

INTERSECTIONS 1 TO 4* -42% -47% -0.4% -30% 

WOODWARD CORRIDOR AVERAGE* -39% -57% -47% -52% 

AVERAGE TREATMENT EFFECT* -39% 56% -42% -48% 

* Averages are calculated based on the sum of treatment effects divided by the number of treatment sites 

** Treatment site removed from evaluation and not included in overall averages shown in TABLE 4.1 

TABLE 4.2 provides an overview of the evaluation results. 
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TABLE 4.2 SUMMARY OF TREATMENT EFFECTS USING EB 

APPROACH, DETROIT

COLLISION 

TYPE 

TOTAL 

TREATMENT 

SITES 

NUMBER OF SITES WITH 

ESTIMATED COLLISION 

REDUCTION 

PERCENT OF SITES 

WITH ESTIMATED 

COLLISION 

REDUCTION 

AVERAGE 

TREATMENT 

EFFECT 

TOTAL 35 32 91% -39% 

INJURY 35 33 94% -56% 

REAR-END 35 28 80% -42% 

SIDE-SWIPE 35 31 89% -48% 

The total collision treatment effects for the Detroit intersections range from -88 

percent (Woodward and Antoinette/Medbury) to +126 percent 

(Linwood/Davison). As indicated earlier in the simple-before-and-after 

analysis, the notably high increase in collision frequency at Linwood/Davison 

was attributed to a new commercial development located adjacent to the 

intersection. The treatment effect at this intersection has been obscured by 

the unrelated changes in traffic patterns. Therefore, as was done for the 

simple-before-and-after analysis, this treatment site was removed from the 

analysis to avoid skewing the overall evaluation results. 

The EB safety estimates and their variances are provided in APPENDIX F. 

The variance of each EB safety estimate was found to be in the expected 

range, according to the definition provided by Hauer (1997). 

In Phase 1 of the evaluation study, two additional models were developed to 

predict the frequency of total collisions at an intersection: (1) a model 

incorporating the presence of large diameter signal displays and the total 

number of left-turn lanes, and (2) a model incorporating the sum of all-red 

intervals. The inclusion of intersection layout variables in a collision prediction 

model helps correlate collision frequency to existing intersection features such 

as geometry and traffic signal characteristics. These two models are included 

in APPENDIX D. A more detailed discussion of the models incorporating 

layout variables, including an examination of the coefficients for these models, 

is provided in the Phase 1 report. 
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The EB evaluation was repeated for total collisions using the two models that 

incorporate layout variables. The results of this additional evaluation are very 

similar to the results of the previously discussed evaluation, and are presented 

in APPENDIX G. 

4.5 Grand Rapids Results 

There were 26 treatment sites evaluated in Grand Rapids. Of the evaluated 

sites, 17 indicate an overall reduction in collision frequency. In terms of total 

collisions, the treatment effects range from -83 percent to +72 percent, with an 

average treatment effect of -11 percent. 

In Phase 1 of the evaluation study, it was determined that a statistically 

significant injury collision prediction model could only be developed for 

intersections with a total average daily traffic (ADT) of 28,000 or greater. Of 

the 26 treatment sites, 11 have an ADT greater than 28,000. Therefore, the 

EB evaluation for injury collisions only examined 11 treatment sites in Grand 

Rapids. Of these sites, nine indicate a reduction in injury collision frequency, 

with an average treatment effect of -36 percent. 

Of the 26 treatment sites, seven indicate a reduction in rear-end collisions, and 

13 indicate a reduction in side-swipe collisions. However, the average 

treatment effects for rear-end and sideswipe collisions were +35 and +8 

percent, respectively, indicating an overall increase in the risk of these 

collision types. It should be noted that the relatively low pre- and postimprovement frequencies of rear-end and side-swipe collisions make a 

comparison between the simple-before-and-after results and EB analysis 

results difficult. 

The treatment effects are summarized by location and collision type in TABLE 

4.3. Changes in left-turn/head-on and angle collisions were not examined as 

part of the EB evaluation. Collision prediction models involving left-turn/headon and angle collision types were developed in Phase 1 of the evaluation 

study, but were not found to be statistically meaningful. 
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24 HAMILTON ASSOCIATES 

The EB safety estimates and their variances are provided in APPENDIX F. 

The variance of each EB safety estimate was found to be in the expected 

range, according to the definition provided by Hauer (1997). 

TABLE 4.3 ESTIMATED TREATMENT EFFECTS USING EB APPROACH 

BY LOCATION AND COLLISION TYPE, GRAND RAPIDS

TREATMENT EFFECT BY COLLISION TYPE 

SITE # LOCATION 

TOTAL INJURY REAR-END SIDE-SWIPE 

1 Leonard and College -68% n/a -47% -100% 

2 Ottawa and Michigan 72% 4% 101% 165% 

3 Division and Oakes -53% n/a 10% -42% 

4 Division and Cherry 54% n/a 81% 172% 

5 Division and Weston 9% n/a -17% 45% 

6 Division and Wealthy -18% -47% 90% 53% 

7 Division and Delaware -66% n/a -73% -47% 

8 Division and Franklin 12% -8% 97% 39% 

9 Division and Cottage Grove 7% n/a 92% -100% 

10 Division and Hall -10% -50% 20% 46% 

11 Burton and Division 12% -35% 131% 72% 

12 Burton and Raybrook -21% 7% 68% -79% 

13 Burton and Breton -14% -53% 40% 59% 

14 Burton and Plymouth -30% -56% -10% 37% 

15 Burton and Sylvan -11% n/a 26% -100% 

16 Burton and Kalamazoo -5% -61% 75% 134% 

17 Burton and Madison -25% -66% -5% 69% 

18 Burton and Jefferson 52% n/a 88% -65% 

19 Burton and Buchanan 8% n/a 60% -6% 

20 Eastern and Lake -61% n/a -21% -100% 

21 Eastern and Cherry -83% n/a -63% -100% 

22 Eastern and Wealthy -6% n/a 32% 81% 

23 Eastern and Sherman -10% n/a 28% -58% 

24 Eastern and Hall -28% -32% 6% -78% 

25 Eastern and Oakdale 34% n/a 66% 129% 

26 Eastern and Franklin -26% n/a 23% -18% 

AVERAGE TREATMENT EFFECT* -11% -36% 35% 8% 

* Averages are calculated based on the sum of treatment effects divided by the number of treatment s es it

n/a = not applicable: EB analysis for injury collisions only conducted for intersections with ADT>28,000

The estimated treatment effects for total collisions at the Grand Rapids sites 

are illustrated in FIGURE 4.3. TABLE 4.4 summarizes the evaluation results 

by collision type. 
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-100%

-80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

100%

Grand Rapids Treatment Site Number (1 to 26)

Estimated Treatment Effect

Sites experienced an

increase in safety

Sites did not experience an

increase in safety

FIGURE 4.3 ESTIMATED TREATMENT EFFECTS USING EB APPROACH 

(TOTAL COLLISIONS) GRAND RAPIDS

TABLE 4.4 SUMMARY OF TREATMENT EFFECTS USING EB 

APPROACH, GRAND RAPIDS

COLLISION 

TYPE 

TOTAL 

TREATMENT 

SITES 

NUMBER OF SITES WITH 

ESTIMATED COLLISION

REDUCTION 

PERCENT OF SITES 

WITH ESTIMATED 

COLLISION 

REDUCTION 

AVERAGE 

TREATMENT 

EFFECT 

TOTAL 26 17 65% -11% 

INJURY 11 9 82% -36% 

REAR-END 26 7 27% 35% 

SIDE-SWIPE 26 13 50% 8% 
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26 HAMILTON ASSOCIATES 

In Phase 1 of the evaluation study, one additional model was developed to 

predict the frequency of total collisions at an intersection. This model (shown 

in APPENDIX D) was developed based on a Grand Rapids reference group, 

and incorporates the total number of existing signal heads at a treatment 

intersection. A more detailed discussion of the model incorporating layout 

variables, including an examination of the coefficients for this model, is 

provided in the Phase 1 report. The results from this model are included in 

APPENDIX G, and are very similar to the results of the EB evaluation using 

the total collision prediction model. 
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5.0 ECONOMIC EVALUATION 

5.1 Calculating the Benefit-Cost Ratio 

A benefit-cost ratio (B/C) was calculated for each treatment site and was used 

as an indicator to assess the cost effectiveness of the safety improvements, in 

terms of societal savings. Several steps were involved in calculating the 

benefit-cost ratios. First, the cost savings related to the reduction in collisions 

were determined. The difference between the EB expected annual collision 

frequency (the number of collisions that would have occurred had the 

treatment not been implemented) and the actual post-improvement collision 

frequency was calculated for both total and injury collisions. These values 

indicated the collisions reduced by the treatment effect. 

Average collision costs were then applied to convert the reduced collisions to 

an estimated cost savings. The National Safety Council has developed 

average societal costs relating to motor vehicle collisions. These estimates 

include the calculable costs of collisions (wage and productivity losses, 

medical expenses, administrative expenses, motor vehicle damage and 

employer costs), as well as an estimated value of the reduced quality of life 

resulting from the collision. These costs are summarized in TABLE 5.1. 

TABLE 5.1 AVERAGE SOCIETAL COLLISION COSTS 

COLLISION TYPE AVERAGE COLLISION COST 

Property Damage Only $1,800 

High Severity Injury: $153,500 

Medium Severity Injury: $39,500 

Low Severity Injury: $18,800 Injury 

Average Injury (Weighted): $34,000 

Source: National Safety Council 

A graphical illustration of the estimated cost savings at a typical intersection is 

shown in FIGURE 5.1. 
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28 HAMILTON ASSOCIATES

$10,000

$20,000

$30,000

$40,000

$50,000

$60,000

$70,000

0 1 2 3 4 5 6 7 8

Annual Insurance Cost at Typical Intersection

BEFORE AFTER

Estimated cost if no

improvement had been

implemented

Estimated Cost Using Empirical-Bayes Approach

Actual Cost

Estimated Annual 

Savings

Actual preimprovement cost

Actual postimprovement cost

FIGURE 5.1 ILLUSTRATION OF TYPICAL COST SAVINGS 

The annual cost savings at each intersection were converted to 2, 3, and 15-

year cost savings by assuming an annual discount rate of 7 percent. The 

benefit-cost ratio for these improvement life cycles was then calculated for

each intersection by dividing the discounted cost savings by the total cost of 

improvement implementation. 

The expected net present value (NPV) of each improvement was also 

determined. The NPV is determined by subtracting the implementation cost 

from the discounted savings over the payback period (2, 3 or 15 years). 

5.2 Economic Evaluation Results, Detroit 

An overall benefit-cost ratio of 3.0:1 (over two years) was calculated for the

improved Detroit locations. With the 15-year life cycle assumption, the benefitcost ratio was estimated to be approximately 15.2:1. The results of the 

economic evaluation for the Detroit treatment sites are presented in TABLE 

5.2. 
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TABLE 5.2 SUMMARY OF THE ECONOMIC EVALUATION, DETROIT 

BENEFIT-COST RATIO NET PRESENT VALUE SITE 

# LOCATION 2-

YEAR 

3-

YEAR 

15-

YEAR 2-YEAR 3-YEAR 15-YEAR 

1 7 Mile and John R 12.1 17.5 60.7 $390,000 $581,000 $2,103,000 

2 7 Mile and Ryan 15.1 21.9 76.0 $509,000 $755,000 $2,709,000 

3 Hubbell and Puritan 12.5 18.1 63.0 $349,000 $520,000 $1,878,000 

4 Schoolcraft and Evergreen 1.1 1.5 5.3 $16,000 $146,000 $1,178,000 

6 Woodward and Adelaide/Sibley 1.8 2.7 9.3 $57,000 $113,000 $555,000 

7 Woodward and Charlotte 2.2 3.2 11.1 $81,000 $147,000 $673,000 

8 Woodward and Eliot/Stimson 2.3 3.3 11.4 $84,000 $152,000 $691,000 

9 Woodward and Mack -0.3 -0.4 -1.4 ($86,000) ($94,000) ($161,000) 

10 Woodward and Parsons 1.4 2.0 6.9 $25,000 $66,000 $392,000 

11 Woodward and Alexandrine 2.7 4.0 13.8 $116,000 $199,000 $853,000 

12 Woodward and Canfield 3.2 4.6 16.0 $145,000 $241,000 $999,000 

13 Woodward and Forest 2.3 3.3 11.6 $87,000 $156,000 $706,000 

14 Woodward and Warren 1.6 2.4 8.3 $43,000 $93,000 $486,000 

15 

Woodward and 

Putnam/Farnsworth 1.5 2.2 7.5 $33,000 $77,000 $431,000 

16 Woodward and Kirby 3.9 5.6 19.6 $193,000 $310,000 $1,238,000 

17 Woodward and Palmer 2.7 3.9 13.4 $112,000 $192,000 $829,000 

18 

Woodward and 

Antoinette/Medbury 2.9 4.2 14.7 $128,000 $216,000 $913,000 

19 Woodward and Baltimore 3.6 5.2 18.2 $175,000 $283,000 $1,146,000 

20 Woodward and Milwaukee 5.8 8.4 29.3 $322,000 $497,000 $1,888,000 

21 Woodward and Bethune 1.6 2.3 8.1 $41,000 $90,000 $474,000 

22 Woodward and Seward 1.9 2.7 9.3 $58,000 $113,000 $557,000 

23 Woodward and Euclid 4.3 6.3 21.7 $221,000 $351,000 $1,383,000 

24 

Woodward and Hazelwood/ 

Holbrook 2.6 3.8 13.3 $110,000 $190,000 $824,000 

25 Woodward and Clairmont/Owen 5.9 8.6 29.9 $330,000 $509,000 $1,929,000 

26 Woodward/Chicago 5.0 7.2 25.0 $265,000 $414,000 $1,600,000 

27 

Woodward and 

Calvert/Towbridge 3.9 5.7 19.7 $195,000 $313,000 $1,249,000 

28 

Woodward and 

Tuxedo/Tennyson 3.2 4.7 16.3 $149,000 $247,000 $1,020,000 

29 Woodward and Courtland 2.9 4.2 14.5 $126,000 $212,000 $900,000 

30 Woodward and Glendale/Mclean 0.6 0.8 2.9 ($28,000) ($11,000) $129,000 

31 Woodward and Buena Vista 1.2 1.8 6.2 $15,000 $52,000 $345,000 

32 Woodward and Gerald 1.9 2.7 9.4 $58,000 $115,000 $561,000 

33 Woodward and Manchester 5.2 7.6 26.4 $283,000 $440,000 $1,692,000 

34 Woodward and Sears 3.5 5.0 17.5 $165,000 $269,000 $1,098,000 

35 Woodward and Feris 1.6 2.3 8.0 $40,000 $87,000 $466,000 

INTERSECTIONS 1 TO 4 4.4 6.4 22.1 $1,262,000 $2,001,000 $7,866,000 

WOODWARD CORRIDOR 2.8 4.0 13.9 $3,530,000 $6,026,000 $25,855,000 

OVERALL (ROUNDED) 3.0 4.4 15.2 $4,792,000 $8,027,000 $33,720,000 

The results of the economic evaluation for the Detroit treatment sites are 

further summarized below. 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

30 HAMILTON ASSOCIATES 

• Overall, the net present value of the Detroit improvements is $4,792,000 

(two-year life cycle) or $33,720,000 (15-year life cycle). 

• A total of 22 sites (or 65 percent) exceeded a B/C of 2:1 in two years. 

• A total of 33 sites (or 97 percent) exceeded a B/C of 2:1 in 15 years. 

• A total of 32 sites (or 94 percent) reported a positive NPV (benefits) over 

two years. 

• The Woodward corridor (30 sites) was estimated to have a NPV of 

$3,530,000 and a B/C of 2.8 (two-year life cycle). 

• In terms of simple-before-and-after societal costs, the average annual preimprovement cost of collisions for the Detroit treatment group was 

$6,563,000. The actual average annual post-improvement cost of 

collisions was $3,640,000. This indicates an overall annual cost savings of 

$2,923,000. 

5.3 Economic Evaluation Results, Grand Rapids 

The societal savings related to the treatment effect were estimated for the 

Grand Rapids treatment sites. An overall benefit-cost ratio of 3.6:1 (over two 

years) was calculated for the improved Grand Rapids locations. With the 15-

year life cycle assumption, the benefit-cost ratio was estimated to be 

approximately 18.1:1. The results of the economic evaluation for the Grand 

Rapids treatment sites are presented in TABLE 5.3, and are summarized 

below: 

• Overall, the net present value of the Grand Rapids improvements is 

$2,635,000 (two-year life cycle) or $17,366,000 (15-year life cycle). 

• A total of 16 sites (or 61 percent) exceeded a B/C of 2:1 in two years. 

• A total of 20 sites (or 77 percent) exceeded a B/C of 2:1 in 15 years. 

• A total of 18 sites (or 69 percent) reported a positive NPV (benefits) over 

two years. 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES 31 

• In terms of simple-before-and-after societal costs, the average annual preimprovement cost of collisions for the Grand Rapids treatment group was 

$5,711,000. The actual average annual post-improvement cost of 

collisions was $3,305,000. This indicates an overall annual cost savings of 

$2,406,000. 

TABLE 5.3 SUMMARY OF THE ECONOMIC EVALUATION, 

GRAND RAPIDS

BENEFIT-COST RATIO NET PRESENT VALUE 

SITE # LOCATION 2-

YEAR 

3-

YEAR 

15-

YEAR 2-YEAR 3-YEAR 15-YEAR 

1 Leonard and College 4.6 6.6 23.0 $233,000 $367,000 $1,433,000 

2 Ottawa and Michigan n/a n/a n/a n/a n/a n/a 

3 Division and Oakes 8.9 13.0 45.0 $172,000 $259,000 $950,000 

4 Division and Cherry -5.2 -7.5 -26.0 ($133,000) ($184,000) ($583,000) 

5 Division and Weston -1.6 -2.4 -8.2 ($57,000) ($73,000) ($200,000) 

6 Division and Wealthy 14.0 20.3 70.5 $281,000 $417,000 $1,500,000 

7 Division and Delaware 6.2 8.9 31.0 $112,000 $172,000 $649,000 

8 Division and Franklin 1.1 1.6 5.6 $7,000 $36,000 $266,000 

9 Division and Cottage Grove 5.2 7.6 26.3 $91,000 $142,000 $546,000 

10 Division and Hall 4.2 6.0 21.0 $254,000 $404,000 $1,599,000 

11 Burton and Division 3.7 5.4 18.7 $177,000 $287,000 $1,154,000 

12 Burton and Raybrook 0.5 0.8 2.6 ($15,000) ($8,000) $50,000 

13 Burton and Breton 5.6 8.2 28.4 $330,000 $510,000 $1,945,000 

14 Burton and Plymouth 4.9 7.1 24.6 $169,000 $265,000 $1,024,000 

15 Burton and Sylvan 1.6 2.3 8.1 $17,000 $36,000 $193,000 

16 Burton and Kalamazoo 4.0 5.9 20.4 $234,000 $373,000 $1,484,000 

17 Burton and Madison 5.7 8.3 28.8 $312,000 $482,000 $1,834,000 

18 Burton and Jefferson -3.4 -5.0 -17.3 ($133,000) ($180,000) ($550,000) 

19 Burton and Buchanan 0.5 0.8 2.7 ($32,000) ($16,000) $114,000 

20 Eastern and Lake 4.4 6.5 22.4 $88,000 $139,000 $542,000 

21 Eastern and Cherry 6.1 8.8 30.5 $129,000 $198,000 $748,000 

22 Eastern and Wealthy 10.6 15.4 53.5 $244,000 $365,000 $1,330,000 

23 Eastern and Sherman -2.7 -3.9 -13.5 ($94,000) ($124,000) ($368,000) 

24 Eastern and Hall 3.2 4.6 16.0 $90,000 $149,000 $617,000 

25 Eastern and Oakdale -0.8 -1.2 -4.2 ($68,000) ($82,000) ($192,000) 

26 Eastern and Franklin 12.0 17.5 60.7 $280,000 $418,000 $1,511,000 

OVERALL (ROUNDED) 3.6 5.2 18.1 $2,635,000 $4,283,000 $17,366,000 

Note:

n/a = improvement cost not available 

PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES 33 

6.0 OVERVIEW 

In terms of collision reduction, and using the EB refinement approach, the 

program has achieved overall treatment effects of -39 percent in Detroit and 

-11 percent in Grand Rapids, with a combined average treatment effect of 

-27 percent. In both cities, the program has been particularly effective in 

reducing the frequency of higher severity collisions. 

The Detroit improvements had a total implementation cost of $2,373,000, and 

a two-year benefit-cost ratio of 3.0 to 1. The Grand Rapids treatments had a 

total implementation cost of $1,014,000 and a two-year benefit-cost ratio of 3.6 

to 1. In terms of societal costs, the net present value of the Detroit and Grand 

Rapids improvements combined was estimated to be $7,427,000, assuming a 

two-year life cycle. 

This evaluation of the AAA Michigan Road Improvement Demonstration 

Program has demonstrated that the program as a whole has achieved a 

positive benefit-cost ratio over two, three, and 15-year life cycles. By 

combining the societal savings and improvement costs for both the two cities, 

the overall benefit-cost ratio of this program was determined to be 3.2:1 over 

two years, 4.6:1 (over three years) and 16.1:1 (over 15 years). 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

34 HAMILTON ASSOCIATES 

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PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES A - 1 

APPENDIX A 

SUMMARY OF SAFETY IMPROVEMENTS IMPLEMENTED
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

A - 2 HAMILTON ASSOCIATES 

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PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES A - 3 

Appendix A Summary of Safety Improvements and 

Implementation Dates (Provided by AAA Michigan) 

TABLE A.1 WOODWARD AVENUE CORRIDOR IMPROVEMENTS, DETROIT 

SITE # INTERSECTION YEAR 

COMPLETED 12" LTL LTP LL AR P AO ISP 

1. Woodward at Alexandrine 1999 X X X X X 

2. Woodward at Antoinette/Medbury 1999 X X X X X 

3. Woodward at Baltimore 1999 X X X X X 

4. Woodward at Bethune 1999 X X X X X 

5. Woodward at Buena Vista 1999 X X X X X X 

6. Woodward at Calvert/Trowbridge 1999 X X X X X 

7. Woodward at Canfield 1999 X X X X 

8. Woodward at Charlotte 1999 X X X X 

9. Woodward at Chicago/Arden Park 1999 X X X X X 

10. Woodward at Clairmont/Owen 1999 X X X X 

11. Woodward at Cortland 1999 X X X X 

12. Woodward at Euclid 1999 X X X X X 

13. Woodward at Farnsworth/Putnam 1999 X X X X 

14. Woodward at Forest 1999 X X X X 

15. Woodward at Gerald 1999 X X X 

16. Woodward at Glendale/McLean 1999 X X X X 

17. Woodward at Hazelwood/Holbrook 1999 X X X X X 

18. Woodward at Kirby 1999 X X X 

19. Woodward at Mack/MLK 1999 X X X 

20. Woodward at Manchester 1999 X X X 

21. Woodward at Milwaukee 1999 X X X X X 

22. Woodward at Palmer 1999 X X X X X X 

23. Woodward at Parsons 1999 X X X 

24. Woodward at Pilgrim/Ferris 1999 X X X X 

25. Woodward at Sears/Ford 1999 X X X X 

26. Woodward at Seward/Marston 1999 X X X X X 

27. Woodward at Sibley/Adelaide 1999 X X X 

28. Woodward at Stimson/Eliot 1999 Signal Removed 

29. Woodward at Tuxedo/Tennyson 1999 X X X X X 

30. Woodward at Warren 1999 X X X 

LEGEND

12" - Upgraded traffic signals from 8" to 12" diameter lenses 

LTL - Added exclusive left-turn lanes 

LTP - Added permitted/protected left-turn phasing 

LL - Added low level traffic signals 

AR - Added an all red interval to the signal timing 

P - Added pedestrian signals 

AO - Added additional overhead traffic signals 

ISP - Improved the traffic signal placement 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

A - 4 HAMILTON ASSOCIATES 

TABLE A.2 OTHER DETROIT INTERSECTION IMPROVEMENTS 

SITE 

# INTERSECTION YEAR 

COMPLETED 12" LTL LTP LL AR P AO ISP 

1. Seven Mile at Ryan 1997 X X X X X 

2. Seven Mile at John R 1997 X X X X X 

3. Hubbell at Puritan 1997 X X X X 

4. Schoolcraft at Evergreen 1998 X X X X 

5. Linwood at Davison 1999 X X X X X X 

TABLE A.3 GRAND RAPIDS INTERSECTION IMPROVEMENTS 

SITE # INTERSECTION YEAR 

COMPLETED 12" LTL LTP LL AR 

1. Leonard at College 1998 X X X 

2. Michigan at Ottawa 1998 X X 

3. Division at Franklin 1998 X X X 

4. Division at Hall 1998 X X X X X 

5. Division at Burton 1999 X X X X 

6. Division at Cottage Grove 1999 X X X 

7. Division at Weston 1999 X X 

8. Division at Oakes 1999 X X 

9. Division at Wealthy 1999 X X X 

10. Eastern at Hall 2000 X X X X 

11. Eastern at Oakdale 2000 X X X X 

12. Burton at Buchanan 2000 X X X X 

13. Burton at Jefferson 2000 X X X 

14. Burton at Madison 2000 X X X X X 

15. Burton at Plymouth 2000 X X X X X 

16. Burton at Breton 2000 X X X 

17. Burton at Kalamazoo 2000 X X X X 

18. Burton at Raybrook 2000 X X X 

19. Burton at Sylvan 2000 X X X 

20. Division at Cherry 2000 X X 

21. Division at Delaware 2000 X X X 

22. Eastern at Cherry 2001 X X X X 

23. Eastern at Franklin 2001 X X X X X 

24. Eastern at Lake 2001 X X X X X 

25. Eastern at Sherman 2001 X X X X 

26. Eastern at Wealthy 2001 X X X X X 

LEGEND

12" - Upgraded traffic signals from 8" to 12" diameter lenses 

LTL - Added exclusive left-turn lanes 

LTP - Added permitted/protected left-turn phasing 

LL - Added low level traffic signals 

AR - Added an all red interval to the signal timing 

P - Added pedestrian signals 

AO - Added additional overhead traffic signals 

ISP - Improved the traffic signal placement 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES B - 1 

APPENDIX B 

SUMMARY OF IMPROVEMENT COSTS
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

B - 2 HAMILTON ASSOCIATES 

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PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES B - 3 

Appendix B Summary of Improvement Costs (Provided by AAA Michigan) 

TABLE B.1 DETROIT IMPROVEMENT COSTS 

TREATMENT LOCATION TOTAL COST OF IMPLEMENTATION 

Seven Mile-John R $35,200 

Seven Mile-Ryan $36,100 

Hubbell-Puritan $30,300 

Schoolcraft-Evergreen $272,000 

Linwood-Davison $157,000 

Woodward Corridor (30 intersections) $2,000,000 

ROUNDED TOTAL $2,531,000 

TABLE B.2 GRAND RAPIDS IMPROVEMENT COSTS 

SITE # TREATMENT LOCATION TOTAL COST OF IMPLEMENTATION* 

1 Leonard and College $65,000 

2 Ottawa and Michigan not available 

3 Division and Oakes $21,589 

4 Division and Cherry $21,589 

5 Division and Weston $21,589 

6 Division and Wealthy $21,589 

7 Division and Delaware $21,589 

8 Division and Franklin $58,000 

9 Division and Cottage Grove $21,589 

10 Division and Hall $80,000 

11 Division and Burton $65,000 

12 Burton and Raybrook $30,061 

13 Burton and Breton $70,986 

14 Burton and Plymouth $43,340 

15 Burton and Sylvan $27,227 

16 Burton and Kalamazoo $76,596 

17 Burton and Madison $65,872 

18 Burton and Jefferson $29,925 

19 Burton and Buchanan $67,239 

20 Eastern and Lake $25,314 

21 Eastern and Cherry $25,314 

22 Eastern and Wealthy $25,314 

23 Eastern and Sherman $25,314 

24 Eastern and Hall $41,050 

25 Eastern and Oakdale $37,175 

26 Eastern and Franklin $25,314 

ROUNDED TOTAL $1,014,000 

*Note: Intersection cost estimates for Burton/Eastern Corridor improvements based on overall implementation cost 

of approximately $670,000 (not all improvements are currently being evaluated). Intersection cost 

estimates for Division Corridor improvements based on overall implementation cost of approximately 

$380,000 (not all improvements are currently being evaluated). 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

B - 4 HAMILTON ASSOCIATES 

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PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES C - 1 

APPENDIX C 

SUMMARY OF COLLISION DATA USED FOR SIMPLE 

BEFORE-AND-AFTER ANALYSIS
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

C - 2 HAMILTON ASSOCIATES 

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PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES C - 3 

TABLE C.1 SUMMARY OF DETROIT COLLISION DATA USED FOR 

SIMPLE BEFORE-AND-AFTER ANALYSIS 

PRE-IMPROVEMENT POST-IMPROVEMENT 

SITE # LOCATION 

YEARS COLLISIONS YEARS COLLISIONS 

1 7 Mile and John R 2.0 111 4.3 120 

2 7 Mile and Ryan 2.0 142 4.6 152 

3 Hubbell and Puritan 3.0 108 4.2 54 

4 Schoolcraft and Evergreen 2.0 69 3.3 76 

5 Linwood and Davison 2.0 66 1.8 124 

6 Woodward and Adelaide/Sibley 2.0 2 2.2 5 

7 Woodward and Charlotte 2.0 11 2.2 6 

8 Woodward and Eliot/Stimson 2.0 4 2.2 3 

9 Woodward and Mack 2.0 38 2.2 64 

10 Woodward and Parsons 2.0 8 2.2 11 

11 Woodward and Alexandrine 2.0 29 2.2 23 

12 Woodward and Canfield 2.0 28 2.2 20 

13 Woodward and Forest 2.0 58 2.2 45 

14 Woodward and Warren 2.0 102 2.2 93 

15 Woodward and Putnam/Farnsworth 2.0 27 2.2 26 

16 Woodward and Kirby 2.0 26 2.2 12 

17 Woodward and Palmer 2.0 27 2.2 22 

18 Woodward and Antoinette/Medbury 2.0 7 2.2 2 

19 Woodward and Baltimore 2.0 25 2.2 18 

20 Woodward and Milwaukee 2.0 48 2.2 16 

21 Woodward and Bethune 2.0 13 2.2 17 

22 Woodward and Seward 2.0 17 2.2 14 

23 Woodward and Euclid 2.0 28 2.2 17 

24 Woodward and Hazelwood/ Holbrook 2.0 21 2.2 20 

25 Woodward and Clairmont/Owen 2.0 32 2.2 15 

26 Woodward/Chicago 2.0 24 2.2 10 

27 Woodward and Calvert/Towbridge 2.0 16 2.2 10 

28 Woodward and Tuxedo/Tennyson 1.5 4 2.0 5 

29 Woodward and Courtland 1.0 1 2.0 3 

30 Woodward and Glendale/Mclean 1.5 24 2.0 45 

31 Woodward and Buena Vista 1.5 8 2.0 16 

32 Woodward and Gerald 1.5 4 2.0 12 

33 Woodward and Manchester 1.6 61 2.0 36 

34 Woodward and Sears 1.5 33 2.0 24 

35 Woodward and Feris 1.5 16 2.0 19 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

C - 4 HAMILTON ASSOCIATES 

TABLE C.2 SUMMARY OF GRAND RAPIDS COLLISION DATA USED FOR 

SIMPLE BEFORE-AND-AFTER ANALYSIS

PRE-IMPROVEMENT POST-IMPROVEMENT 

SITE # LOCATION 

YEARS COLLISIONS YEARS COLLISIONS 

1 Leonard and College 3 83 3.3 23 

2 Ottawa and Michigan 3 96 3.1 138 

3 Division and Oakes 2 18 0.9 4 

4 Division and Cherry 3 28 0.9 13 

5 Division and Weston 2 12 1.3 11 

6 Division and Wealthy 2 87 1.1 30 

7 Division and Delaware 3.2 25 0.9 3 

8 Division and Franklin 3 101 2.3 74 

9 Division and Cottage Grove 2 24 1.8 21 

10 Division and Hall 3 126 2.1 56 

11 Burton and Division 2 126 2.0 97 

12 Burton and Raybrook 3 68 1.7 22 

13 Burton and Breton 3 199 1.7 74 

14 Burton and Plymouth 3 49 1.8 23 

15 Burton and Sylvan 2 18 1.7 15 

16 Burton and Kalamazoo 3.5 108 1.7 44 

17 Burton and Madison 3 81 1.8 30 

18 Burton and Jefferson 2 19 1.8 29 

19 Burton and Buchanan 3 80 1.8 42 

20 Eastern and Lake 2 30 0.9 5 

21 Eastern and Cherry 2 26 0.9 2 

22 Eastern and Wealthy 3 32 0.9 14 

23 Eastern and Sherman 2 27 0.9 9 

24 Eastern and Hall 4 68 1.8 24 

25 Eastern and Oakdale 3 30 1.8 22 

26 Eastern and Franklin 2 56 0.9 15 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES D - 1 

APPENDIX D 

SUMMARY OF COLLISION PREDICTION MODELS 

DEVELOPED FOR DETROIT AND GRAND RAPIDS
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

D - 2 HAMILTON ASSOCIATES 

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PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES D - 3 

TABLE D.1 SUMMARY OF DETROIT COLLISION PREDICTION MODELS 

COLLISION TYPE MODEL* kvalue 

Total Collisions 

(All Traffic Volumes) Predicted = 0.0313 x V1

0.3849 x V20.3304 7.9 

TOTAL 

COLLISIONS 

Total Collisions 

(Low Volume Reference 

Group – ADT<30,000) 

Predicted = 0.0013 x V1

0.7047 x V20.3425 8.7 

INJURY 

COLLISIONS 

Injury Collisions 

(All Traffic Volumes) Predicted = 0.0221 x V1

0.3147 x V20.3039 10 

Rear-end Collisions 

(All Traffic Volumes) Predicted = 0.000004 x (V1+V2)

1.404 12.8 

Rear-end Collisions 

(High Volume Reference 

Group - ADT>30,000) 

Predicted = 0.0000004 x (V1+V2)

1.625 10.9 

REAR-END COLLISIONS 

Rear-end Collisions 

(Low Volume Reference 

Group – ADT<35,000) 

Predicted = 0.0001 x (V1+V2)

1.078 22.1 

Sideswipe Collisions 

(All Traffic Volumes) Predicted = 0.0008 x (V1+V2)

0.8130 n/a 

SIDESWIPE 

COLLISIONS 

Sideswipe Collisions 

(High Volume Reference 

Group - ADT>30,000) 

Predicted = 0.00008 x (V1+V2)

1.024 n/a 

Total Collisions 

(Incorporating signal lens 

size and number of leftturn phases) 

Predicted = 0.0719 x V1

0.2841 x V20.3658 x eΓbixi 

Where: 

Γbixi = (-0.1185 x "large lenses")+(0.0894 x number of left-turn phases) 

And:

"large lenses" = 1 if 12-inch lenses present at intersection, or 2 if not present

10.2 

TOTAL COLLISIONS WITH 

LAYOUT VARIABLES 

Total Collisions 

(Incorporating the length 

of all-red intervals) 

Predicted = 0.0226 x V1

0.2953 x V20.4508 x eΓbixi 

Where: Γbixi = 0.0772 x sum of all-red intervals

8.8 

Notes: Predicted annual collisions = a0 x V1

a1 x V2a2 x eΓbixi

V1 and V2 denote major and minor street ADT, 

a0, a1, a2 and bi are model parameters 

n/a denotes poisson model (k is a GLIM parameter relating to negative binomial distribution only) 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

D - 4 HAMILTON ASSOCIATES 

TABLE D.2 SUMMARY OF GRAND RAPIDS COLLISION PREDICTION MODELS 

COLLISION TYPE MODEL* k-value 

Total Collisions 

(All Traffic Volumes) Predicted = 0.0058 x V1

0.4582 x V20.4037 14.8 

TOTAL 

COLLISIONS 

Total Collisions 

(High Volume Reference 

Group - ADT>28,000) 

Predicted = 0.0047 x V1

0.5397 x V20.3374 25.5 

INJURY 

COLLISIONS 

Injury Collisions 

(High Volume Reference 

Group - ADT>28,000) 

Predicted = 0.00008 x V1

0.6319 x V20.5293 n/a 

Rear-end Collisions 

(All Traffic Volumes) Predicted = 0.000009 x (V1+V2)

1.304 16.7 

REAR-END 

COLLISIONS 

Rear-end Collisions 

(High Volume Reference 

Group - ADT>28,000) 

Predicted = 0.00001 x (V1+V2)

1.262 20.6 

Sideswipe Collisions 

(All Traffic Volumes) Predicted = 0.0015 x (V1+V2)

0.7367 n/a 

SIDESWIPE 

COLLISIONS 

Sideswipe Collisions 

(High Volume Reference 

Group - ADT>28,000) 

Predicted = 0.00007 x (V1+V2)

1.020 n/a 

Predicted = 0.0346 x V1

0.4088 x V20.3215 x eΓbixi

TOTAL 

COLLISIONS 

WITH LAYOUT 

VARIABLES 

Layout Variables 

 (All Traffic Volumes) Where: Γbixi = -0.0698 x total number of signal heads 

44.7 

Notes: Predicted annual collisions = a0 x V1

a1 x V2a2 x eΓbixi

V1 and V2 denote major and minor street ADT, 

a0, a1, a2 and bi are model parameters 

n/a denotes poisson model (k is a GLIM parameter relating to negative binomial distribution only) 

Notes

As illustrated in the Phase 1 report, some of the prediction models may underestimate 

collisions at high frequency locations, and overestimate collisions at low frequency locations. 

This pattern appears to be typical of models developed using generalized linear interactive 

modeling, and has been documented in previous studies. 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES D - 5 

For comparison purposes, graphical results from three previous collision prediction modeling 

studies are provided in APPENDIX E, along with graphical results of a model prepared for the 

Phase 1 report. Hamilton Associates did not research the reasons for this apparent trend. 

However, we ensured that all the models used for this study met the rigid significance criteria, 

as documented in the Phase 1 report. 

Several of the collision prediction models were determined to have k-values (parameters of 

the Negative Binomial distribution) larger than typical for models based on data that follows 

this distribution. This trait may be attributed to several factors, including the use of a relatively 

small reference group, and that the dispersion of the data cannot be described completely by 

one error structure. For example, the Poisson distribution for these models was examined, 

and found to be a satisfactory assumption based on the magnitude of the coefficients 

estimated for these models. 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

D - 6 HAMILTON ASSOCIATES 

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PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES E - 1 

APPENDIX E 

GRAPHICAL ILLUSTRATION OF 

PREVIOUS COLLISION PREDICTION MODELS 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

E - 2 HAMILTON ASSOCIATES 

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PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES E - 3 

APPENDIX E GRAPHICAL ILLUSTRATION OF COLLISION PREDICTION MODELS 

The graphs presented in this Appendix (FIGURES E.1 to E.4) provide a simple comparison of 

collision prediction models developed in Program Evaluation Phase 1: Collision Prediction 

Modeling, Detroit and Grand Rapids (Hamilton Associates, 2002) to models developed in 

previous studies. Each of the four graphs illustrates a relationship between observed 

collisions and predicted collisions within a reference group. A well-fitted model should have 

the plotted points clustered near the 45 degree line. All four graphs were developed using 

generalized linear modeling techniques, and have the common trait of “over-predicting” 

collisions at low frequency locations and “under-predicting” collisions at high frequency 

locations. The impact of this model trait is mitigated by the use of the Empirical-Bayes 

refinement process, which combines collision prediction modeling results with historical 

collision data to refine the predicted values. 

FIGURE E.1 PLOT OF PREDICTED COLLISIONS VS. OBSERVED COLLISIONS FOR 

DETROIT TOTAL COLLISION PREDICTION MODEL 

SOURCE: PROGRAM EVALUATION PHASE 1: COLLISION PREDICTION MODELING, 

DETROIT AND GRAND RAPIDS (HAMILTON ASSOCIATES, 2002) 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

E - 4 HAMILTON ASSOCIATES 

FIGURE E.2 PLOT OF PREDICTED COLLISIONS VS. OBSERVED COLLISIONS FOR 

TOTAL COLLISION PREDICTION MODEL 

SOURCE: ADVANCE WARNING FLASHERS-DO THEY IMPROVEMENT SAFETY? 

(SAYED AND SAWALHA, 1999)
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES E - 5 

FIGURE E.3 PLOT OF PREDICTED COLLISIONS VS. OBSERVED COLLISIONS FOR 

TOTAL COLLISION PREDICTION MODEL 

SOURCE: MICROSCOPIC COLLISION PREDICTION MODELS FOR SIGNALIZED 

INTERSECTIONS (M. QUINTERO, 1999)
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

E - 6 HAMILTON ASSOCIATES 

FIGURE E.4 PLOT OF PREDICTED COLLISIONS VS. OBSERVED COLLISIONS FOR 

TOTAL COLLISION PREDICTION MODEL 

SOURCE: PREDICTING THE SAFETY OF URBAN SIGNALIZED INTERSECTIONS IN 

BRITISH COLUMBIA (SAYED, RODRIGUEZ AND FENG, 1998)
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

DETROIT AND GRAND RAPIDS, MICHIGAN 

HAMILTON ASSOCIATES F - 1 

APPENDIX F 

EB SAFETY ESTIMATES AND VARIANCES 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

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HAMILTON ASSOCIATES F - 3 

TABLE F.1 EB SAFETY ESTIMATES AND VARIANCES, DETROIT 

COLLISION TYPE 

TOTAL INJURY REAR-END SIDESWIPE 

SITE 

# LOCATION EB 

ESTIMATE VAR EB 

ESTIMATE VAR EB 

ESTIMATE VAR EB 

ESTIMATE VAR 

1 7 Mile and John R 48.2 46.1 12.1 5.1 5.7 1.1 6.7 3.3 

2 7 Mile and Ryan 62.2 61.3 12.8 5.7 8.0 1.8 9.4 4.7 

3 Hubbell and Puritan 32.1 27.7 9.0 3.6 4.5 0.8 4.4 2.2 

4 Schoolcraft and Evergreen 34.7 28.1 13.0 6.4 10.1 5.0 7.1 3.6 

5 Linwood and Davison 33.7 26.8 7.9 3.9 11.0 6.3 10.7 5.3 

6 Woodward and 

Adelaide/Sibley 6.2 1.8 2.8 0.8 3.7 0.6 2.1 1.1 

7 Woodward and Charlotte 8.5 3.5 3.1 0.8 4.1 0.7 2.6 1.3 

8 Woodward and 

Eliot/Stimson 6.5 2.0 2.8 0.8 3.8 0.6 2.1 1.1 

9 Woodward and Mack 21.6 14.4 6.6 3.1 6.2 2.7 6.3 3.2 

10 Woodward and Parsons 8.2 3.0 3.2 1.0 3.9 0.6 2.4 1.2 

11 Woodward and 

Alexandrine 15.9 9.7 4.2 1.4 4.6 0.8 4.0 2.0 

12 Woodward and Canfield 16.4 9.7 5.1 1.9 4.3 0.8 4.2 2.1 

13 Woodward and Forest 29.3 22.4 6.8 3.0 5.7 1.2 6.8 3.4 

14 Woodward and Warren 49.0 43.7 10.8 5.5 11.0 6.1 13.2 6.6 

15 Woodward and 

Putnam/Farnsworth 13.5 8.2 3.5 1.0 4.1 0.7 2.9 1.4 

16 Woodward and Kirby 14.8 8.6 4.9 1.6 4.5 0.8 2.8 1.4 

17 Woodward and Palmer 15.8 9.2 4.6 1.7 4.6 0.8 3.2 1.6 

18 Woodward and 

Antoinette/Medbury 8.2 2.9 3.4 1.0 4.9 1.0 2.8 1.4 

19 Woodward and Baltimore 16.1 8.9 5.5 2.2 5.9 1.3 3.9 1.9 

20 Woodward and Milwaukee 25.1 18.4 7.5 3.3 5.1 2.2 6.1 3.1 

21 Woodward and Bethune 10.6 4.6 4.0 1.3 5.1 1.0 3.4 1.7 

22 Woodward and Seward 10.3 5.1 3.3 0.8 4.6 0.9 3.2 1.6 

23 Woodward and Euclid 17.3 10.0 5.8 2.3 5.6 1.2 5.2 2.6 

24 Woodward and 

Hazelwood/ Holbrook 14.4 7.7 5.5 2.4 6.4 2.7 4.6 2.3 

25 Woodward and 

Clairmont/Owen 18.8 11.8 7.1 3.1 6.0 2.6 4.8 2.4 

26 Woodward/Chicago 14.9 8.2 5.1 1.8 5.6 1.2 4.2 2.1 

27 Woodward and 

Calvert/Towbridge 12.2 5.7 4.1 1.5 5.2 1.1 3.5 1.7 

28 Woodward and 

Tuxedo/Tennyson 7.5 2.4 3.4 1.0 4.6 0.9 3.1 1.6 

29 Woodward and Courtland 6.4 1.8 3.0 0.9 4.5 0.9 2.8 1.4 

30 Woodward and 

Glendale/Mclean 19.2 12.0 6.9 3.2 7.9 3.6 7.1 3.5 

31 Woodward and Buena 

Vista 10.4 4.2 3.8 1.4 5.3 1.1 3.4 1.7 

32 Woodward and Gerald 7.1 2.3 3.1 0.9 4.0 0.7 2.9 1.5 

33 Woodward and 

Manchester 36.9 31.5 10.9 5.0 7.2 3.0 8.4 4.2 

34 Woodward and Sears 23.5 16.4 7.3 3.1 6.2 1.3 4.6 2.3 

35 Woodward and Feris 13.8 7.3 4.6 1.7 4.9 0.9 3.8 1.9 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

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F - 4 HAMILTON ASSOCIATES 

TABLE F.2 EB SAFETY ESTIMATES AND VARIANCES, GRAND RAPIDS 

COLLISION TYPE 

TOTAL INJURY REAR-END SIDESWIPE 

SITE 

# LOCATION EB 

ESTIMATE VAR EB 

ESTIMATE VAR EB 

ESTIMATE VAR EB 

ESTIMATE VAR 

1 Leonard and College 22.0 7.9 n/a n/a 5.0 1.2 3.7 1.8 

2 Ottawa and Michigan 24.0 9.4 5.0 2.5 5.0 1.0 9.0 4.5 

3 Division and Oakes 11.4 2.2 n/a n/a 3.2 0.5 2.0 1.0 

4 Division and Cherry 10.2 1.9 n/a n/a 3.3 0.5 2.2 1.1 

5 Division and Weston 10.7 1.9 n/a n/a 3.1 0.5 1.8 0.9 

6 Division and Wealthy 33.9 16.4 9.3 4.7 6.8 1.7 4.5 2.3 

7 Division and Delaware 12.3 2.4 n/a n/a 4.3 0.9 2.2 1.1 

8 Division and Franklin 28.5 11.9 8.5 4.2 7.3 1.7 3.3 1.7 

9 Division and Cottage 

Grove 10.6 2.1 n/a n/a 5.1 1.1 2.5 1.3 

10 Division and Hall 29.2 13.6 10.2 5.1 6.0 1.1 3.5 1.8 

11 Burton and Division 41.2 24.8 10.8 5.4 8.8 2.1 7.5 3.8 

12 Burton and Raybrook 18.7 5.9 3.6 1.8 6.5 1.1 3.1 1.6 

13 Burton and Breton 42.3 26.3 11.0 5.5 14.3 4.8 6.1 3.0 

14 Burton and Plymouth 21.0 6.2 5.5 2.8 5.5 1.1 2.2 1.1 

15 Burton and Sylvan 12.4 2.5 n/a n/a 4.0 0.8 1.7 0.9 

16 Burton and Kalamazoo 28.3 11.4 8.1 4.0 6.9 1.6 3.2 1.6 

17 Burton and Madison 23.7 8.6 8.9 4.5 5.1 1.0 2.5 1.3 

18 Burton and Jefferson 15.1 3.4 n/a n/a 4.3 0.9 1.7 0.9 

19 Burton and Buchanan 22.3 7.9 n/a n/a 6.5 1.6 3.3 1.6 

20 Eastern and Lake 15.1 3.8 n/a n/a 2.9 0.5 1.8 0.9 

21 Eastern and Cherry 14.3 3.4 n/a n/a 3.1 0.5 2.5 1.2 

22 Eastern and Wealthy 19.3 5.0 4.5 2.2 4.4 0.9 2.6 1.3 

23 Eastern and Sherman 12.2 2.7 n/a n/a 3.7 0.6 2.8 1.4 

24 Eastern and Hall 20.4 6.0 5.2 2.6 4.4 0.8 2.6 1.3 

25 Eastern and Oakdale 10.6 2.0 n/a n/a 2.5 0.3 1.5 0.8 

26 Eastern and Franklin 21.5 7.7 n/a n/a 5.7 1.3 4.3 2.1 

Note:

n/a = no EB safety estimate possible for low volume intersections (ADT<28,000) due to collision prediction model traits. 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

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HAMILTON ASSOCIATES G - 1 

APPENDIX G 

ADDITIONAL EMPIRICAL-BAYES ANALYSIS 

(USING COLLISION PREDICTION MODELS THAT 

INCORPORATE INTERSECTION LAYOUT VARIABLES
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

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HAMILTON ASSOCIATES G - 3 

APPENDIX G 

ADDITIONAL EMPIRICAL-BAYES ANALYSIS 

(USING COLLISION PREDICTION MODELS THAT INCORPORATE INTERSECTION 

LAYOUT VARIABLES 

The additional collision prediction models developed in Phase 1 were used to repeat the EB 

analysis. These models incorporated the intersection characteristics present at each 

treatment site prior to the improvement implementation. The EB safety estimates calculated 

with these additional models were found to be very similar to the EB safety estimates using 

the total collision models, and are presented in TABLES G.1 and G.2. 

The EB safety estimate is a prediction of what would have happened at the treatment site, had 

the safety improvements not been done. Each treatment site had multiple improvements 

done, causing a combined treatment effect. The effects of each individual safety improvement 

are not possible to separate. Therefore, due to the combined treatment effect at each site, it 

was not possible to determine a “cause and effect” relationship between the individual 

improvements by using a layout variable model. 

The collision prediction models incorporating layout variables models have several 

applications outside of evaluation studies, including the following. 

• The identification of collision-prone locations. Collision-prone locations are sites that 

exhibit a significant number of collisions compared to the norm. The layout variable 

models can be used to identify collision-prone locations in cases where intersection layout 

information is known. 

• Collision prediction models may be used in safety planning to identify the geometric 

variables that have the most impact (positive or negative) on the safety performance of 

signalized intersections. 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

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G - 4 HAMILTON ASSOCIATES 

TABLE G.1 SUMMARY OF ADDITIONAL EMPIRICAL-BAYES EVALUATION FOR 

DETROIT TREATMENT SITES 

TREATMENT EFFECT 

Collision Prediction Model Used to Determine EB 

Safety Estimate SITE # LOCATION 

Total Layout Variable All-red 

1 7 Mile and John R -38% -35% -36% 

2 7 Mile and Ryan -43% -40% -41% 

3 Hubbell and Puritan -57% -56% -56% 

4 Schoolcraft and Evergreen -29% -28% -28% 

5 Linwood and Davison 126% 132% 133% 

6 Woodward and Adelaide/Sibley -60% -60% -52% 

7 Woodward and Charlotte -65% -63% -57% 

8 Woodward and Eliot/Stimson -77% -76% -72% 

9 Woodward and Mack 47% 45% 47% 

10 Woodward and Parsons -34% -32% -23% 

11 Woodward and Alexandrine -28% -24% -19% 

12 Woodward and Canfield -40% -37% -34% 

13 Woodward and Forest -24% -21% -20% 

14 Woodward and Warren -6% -4% -5% 

15 Woodward and Putnam/Farnsworth -5% 5% 16% 

16 Woodward and Kirby -60% -57% -54% 

17 Woodward and Palmer -31% -28% -24% 

18 Woodward and Antoinette/Medbury -88% -87% -85% 

19 Woodward and Baltimore -44% -41% -38% 

20 Woodward and Milwaukee -68% -68% -67% 

21 Woodward and Bethune -20% -15% -6% 

22 Woodward and Seward -33% -22% -9% 

23 Woodward and Euclid -51% -48% -46% 

24 Woodward and Hazelwood/ Holbrook -31% -33% -30% 

25 Woodward and Clairmont/Owen -60% -60% -59% 

26 Woodward/Chicago -67% -64% -61% 

27 Woodward and Calvert/Towbridge -60% -57% -54% 

28 Woodward and Tuxedo/Tennyson -64% -62% -56% 

29 Woodward and Courtland -75% -74% -69% 

30 Woodward and Glendale/Mclean 26% 24% 28% 

31 Woodward and Buena Vista -17% -14% -7% 

32 Woodward and Gerald -10% -7% 9% 

33 Woodward and Manchester -48% -46% -46% 

34 Woodward and Sears -45% -43% -42% 

35 Woodward and Feris -26% -23% -18% 

Woodward Corridor Average* -39% -32.0% -28.1% 

AVERAGE TREATMENT EFFECT* -39% -37% -33% 

Notes:

Total = Collision prediction model that predicts total collisions (previously discussed in main body of report) 

Layout Variable = Collision prediction model that predicts total collisions, incorporating intersection layout variables 

(refer to APPENDIX D for description) 

All-red = Collision prediction model that predicts total collisions, incorporating intersection layout variables (refer to 

APPENDIX D for description) 
PROGRAM EVALUATION PHASE 2: EVALUATION RESULTS 

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HAMILTON ASSOCIATES G - 5 

TABLE G.2 SUMMARY OF ADDITIONAL EMPIRICAL-BAYES EVALUATION FOR 

GRAND RAPIDS TREATMENT SITES 

TREATMENT EFFECT 

Collision Prediction Model Used to Determine 

EB Safety Estimate SITE # LOCATION 

Total Layout Variable 

1 Leonard and College -68% -65% 

2 Ottawa and Michigan 72% 100% 

3 Division and Oakes -53% -59% 

4 Division and Cherry 54% 52% 

5 Division and Weston 9% -12% 

6 Division and Wealthy -18% -12% 

7 Division and Delaware -66% -71% 

8 Division and Franklin 12% 20% 

9 Division and Cottage Grove 7% 22% 

10 Division and Hall -10% -1% 

11 Burton and Division 12% 27% 

12 Burton and Raybrook -21% -24% 

13 Burton and Breton -14% 13% 

14 Burton and Plymouth -30% -33% 

15 Burton and Sylvan -11% -23% 

16 Burton and Kalamazoo -5% -2% 

17 Burton and Madison -25% -22% 

18 Burton and Jefferson 52% 18% 

19 Burton and Buchanan 8% 16% 

20 Eastern and Lake -61% -61% 

21 Eastern and Cherry -83% -84% 

22 Eastern and Wealthy -6% -15% 

23 Eastern and Sherman -10% -13% 

24 Eastern and Hall -28% -31% 

25 Eastern and Oakdale 34% 21% 

26 Eastern and Franklin -26% -18% 

AVERAGE TREATMENT EFFECT* -11% -10% 

Notes:

Total = Collision prediction model that predicts total collisions (previously discussed in main body of report) 

Layout Variable = Collision prediction model that predicts total collisions, incorporating intersection layout variables 

(refer to APPENDIX D for description) 
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HAMILTON ASSOCIATES H - 1