U.S. Department 

of Transportation 

National Highway 

Traffic Safety 

Administration 

 DOT HS 809 540 March 2003 

 

Technical Report 

DRIVER ATTRIBUTES AND 

REAR-END CRASH INVOLVEMENT 

PROPENSITY 

 

Published By: 

National Center for Statistics and Analysis 

Advanced Research and Analysis

This document is available to the public from the National Technical Information Service, Springfield, Virginia, VA 22161
 

 

This publication is distributed by the U.S. Department of Transportation, National Highway 

Traffic Safety Administration, in the interest of information exchange. The opinions, findings 

and conclusions expressed in this publication are those of the author(s) and not necessarily 

those of the Department of Transportation or the National Highway Traffic Safety 

Administration. The United States Government assumes no liability for its contents or use 

thereof. If trade or manufacturers' names are mentioned, it is only because they are considered 

essential to the object of the publication and should not be construed as an endorsement. The 

United States Government does not endorse products or manufacturers. 
 

 

 Technical Report Documentation Page 

1. Report No. 

DOT HS 809 540

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

5. Report Date 

March 2003

1. Title and Subtitle 

Driver Attributes and Rear-end Crash Involvement Propensity 6. Performing Organization Code 

NPO-121 

7. Author(s) 

Santokh Singh, Ph.D.

8. Performing Organization Report No. 

9. Performing Organization Name and Address 10. Work Unit No. (TRAIS) 

Rainbow Technology Inc. 

17106 Thatcher Court 

Olney, MD 20832

11. Contract or Grant No.

13. Type of Report and Period Covered 

NHTSA Technical Report 

12. Sponsoring Agency Name and Address 

Mathematical Analysis Division, National Center for Statistics and Analysis 

National Highway Traffic Safety Administration 

U.S. Department of Transportation 

NRD-31, 400 Seventh Street, S.W. 

Washington, D.C. 20590

14. Sponsoring Agency Code 

15. Supplementary Notes 

Discussions with Mr. Dennis Utter (Mathematical Analysis Division, NHTSA) and Dr. Mike Goodman (Driver Vehicle 

and Simulation Division, NHTSA) were useful, as were the comments made by them. Author wishes to thank Ms. Ellin 

Ramsey (NHTSA) for proofreading this technical report. 

16. Abstract

Rear-end crashes are one of the frequently occurring types of crashes. It is becoming increasingly apparent that in order to 

develop effective rear-end crash countermeasures, it is important to understand the driving behavior and performance of a 

driver prior to a rear-end crash. The study compiled in this report is one of the attempts in this direction. The driver 

attributes age and sex were considered as two of several factors that might be contributing to crash involvement of drivers 

and possibly associated with the role that a driver would assume in a rear-end crash. Due to the random nature of rear-end 

crashes and unpredictability of age and sex of the driver who would be involved in such a crash, statistical treatment of the 

data was considered as the most reasonable means of drawing conclusions regarding the occurrence of these crashes and 

the involvement of drivers therein. 

Two databases, the General Estimates System (GES) and the Fatality Analysis Reporting System (FARS), compiled by 

the National Highway Traffic Safety Agency (NHTSA), were used for the statistical analysis that supports the results 

presented in this study. The frequency distributions based on driver’s age and sex gave a fairly good idea about the crash 

involvement profile of drivers, thereby providing directions for further analysis. The statistic, Crash Involvement 

Propensity Index, proposed in this research, was used to compare the crash involvement propensity of drivers belonging to 

different age groups. This enabled identification of the age group that is likely to be most vulnerable to crashes. 

Narrowing the study to rear-end crashes, the contingency analysis was used to establish an association between driver’s 

age and his/her role (striking/struck) as well as between driver’s sex and his/her role in a rear-end crash. In fact, statistical 

evidence of a strong association between age of the driver and the type of rear-end crash (striking/struck) in which he/she 

is involved was provided. Similarly, it was statistically inferred that there is a strong association between sex of the young 

driver and his/her role in a rear-end crash. The joint, marginal, and conditional probability distributions brought out 

differences in the tendencies of drivers in assuming striking or struck role in rear-end crashes The conclusions of this 

study can provide useful guidelines for future data collection and further studies aimed at developing crash 

countermeasures.

17. Key Words 

age, association, crash involvement propensity, 

rear-end, sex, striking, struck 

18. Distribution Statement 

Document is available to the public through the National Technical 

Information Service, Springfield, VA 22161 

http//:www.ntis.gov

19. Security Classif. (of this report) 

Unclassified

20. Security Classif. (of this page) 

Unclassified

21. No. of Pages 22. Price 

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

EXECUTIVE SUMMARY ............................................................................ ii

1. Introduction. ................................................................................... 1 

2. Driver attributes and crash involvement ................................................ 2 

2.1. Driver’s age and crash involvement. ................................................ 2 

2.2. Driver’s sex and crash involvement ................................................. 4 

2.3. Crash involvement propensity of drivers ............................................. 6 

3. Association between driver attributes and his/her role in a rear-end crash ......... 9 

4. Driver attributes and likelihood of his/her role in a rear-end crash. ................. 10 

4.1. Driver’s age and likelihood of rear-end crash involvement ........................ 11 

4.2. Sex of young driver and likelihood of rear-end crash involvement ............... 13 

5. Conclusions and recommendations. ................................. ...................... 15 

6. Appendix A. Tables. ........................................................................... 17 

7. Appendix B. Analytical details of Crash Involvement Propensity Index ............ 19 

8. References. ....................................................................................... 21 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 ii

EXECUTIVE SUMMARY 

Background and objectives 

Rear-end crashes are not only one of the frequently occurring types of crashes, but also are 

responsible for a large number of injuries and fatalities and substantial property damage 

every year. In order to develop effective rear-end crash countermeasures, a better 

understanding of the driving behavior and performance associated with the response to 

driving conflicts or imminent crash situations is needed. However, it is clear that the 

involvement of a driver in a crash depends on his/her perception of the complex scenario 

that emerges prior to a crash and that resolution of the driving conflicts, that have occurred, 

depends on driver’s pre-crash behavior and performance. These facts suggest that the driver 

attributes, such as age and sex, could possibly be two of several factors that contribute to a 

driver’s involvement in a crash, in general, and in determining the role (striking/struck) 

he/she assumes in a rear-end crash, in particular. The objective of this study is to investigate 

if there is a crash involvement profile of drivers of different age groups and of young drivers 

based on driver’s sex. Narrowing the study to rear-end crashes, the study aims at providing 

statistical evidence of the association between the driver attributes and his/her role in a rearend crash. 

Data and methodology 

Two databases, the General Estimates System (GES) and the Fatality Analysis Reporting 

System (FARS), compiled by the National Highway Traffic Safety Administration 

(NHTSA), were used in the analysis. Statistical methods were used to arrive at the 

conclusions drawn in this report. Simple statistics, such as percent frequencies, were used 

for the purpose of preliminary analysis. The statistic Crash Involvement Propensity Index, 

proposed in this study, proved to be a useful tool for comparison between different age 

groups with respect to their propensity of being involved in a crash. In addition, the 

contingency analysis was used to test hypotheses about the association between driver’s 

attributes and driver’s role in a rear-end crash. Finally, the joint, marginal, and conditional 

probabilities were used to bring out the differences among categories of drivers with respect 

to driver’s role in a rear-end crash. 

Results and conclusions 

Based on GES and FARS data for the year 2000, it was found that drivers younger than 18 

years were most vulnerable to roadway crashes, followed by 18 to 24 year old drivers. In 

fact, the propensity of drivers involved in crashes showed a decreasing trend with increasing 

age. This, however, was observed up to the age of 69, after which the drivers again showed 

a higher crash involvement propensity as compared to the drivers who were 25 to 69 year 

old. Young (18 to 24 year old) drivers were treated as a special group in this study. So far as 

driver’s attribute sex is concerned, among this group of drivers, male drivers were found to 

be more prone to crash involvement as compared to their female counterparts. 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 iii

Narrowing the study to rear-end crashes, it could be established that there was strong 

evidence of an association between age of the driver and driver’s role (striking/struck) in a 

rear-end crash, as was of an association between sex of the young driver and driver’s role. It 

was also found that in rear-end crashes drivers up to the age of 25 years or so are more 

likely to be in the striking role than in the struck role. In fact, as drivers get older, they tend 

to be in the striking role less often than in the struck role. Furthermore, young male drivers 

are more likely to be in the striking role as compared to young female drivers. 

 

The results of this study strongly support the use of driver attributes, age and sex, as 

stratification variables in data collection and analysis that are directed towards the 

development of effective rear-end crash countermeasures. 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 1

1. Introduction 

A rear-end crash refers to a crash in which the front of one vehicle collides with the rear of 

another vehicle. Thus, a driver involved in such a crash may be the driver of a striking 

vehicle, of the struck vehicle, or of the vehicle that both struck and was struck. Rear-end 

crashes are not only one of the frequently occurring types of crashes, but also are 

responsible for a large number of injuries and fatalities and substantial property damage 

every year. In fact, based on the General Estimates System (GES) of the National 

Automotive Sampling System (NASS) and the Fatality Analysis Reporting System (FARS) 

data, compiled by the National Highway Traffic Safety Administration (NHTSA), 

approximately 29.7% of all crashes in the year 2000 were rear-end crashes. These crashes 

were responsible for 30% of all injuries and 29.7% of the property damage. So far as the 

involvement of drivers in rear-end crashes is concerned, of the 190,625,023 licensed drivers 

(Federal Highway Administration (FHWA)) in 2000, approximately 2.2% were involved in 

rear-end crashes. Further, of the 6% of licensed drivers involved in all types of crashes, 36% 

were involved in rear-end crashes alone. 

This significant involvement of drivers in rear-end crashes alone is a matter of great 

concern. It is becoming increasingly apparent that in order to develop effective rear-end 

crash countermeasures, a better understanding of the driving behavior and performance 

associated with response to driving conflict or imminent crash situations is needed. The 

present study is an attempt to identify some of the driver-related factors to which crash 

involvement and driver’s role (striking/struck) in a rear-end crash can be attributed. This 

information can subsequently be used, for example, in stratifying the population of drivers 

for the purpose of designing a sample for data collection on driver related parameters in 

rear-end crashes. 

In general, the involvement of a driver in a crash depends on his/her perception of the 

complex scenario that has emerged prior to a crash. Equally important are the driver’s precrash behavior and performance to resolve the driving conflicts that have occurred. These 

facts suggest that the driver attributes, such as age and gender, could possibly be the factors, 

among others, that contribute to a driver’s involvement in a crash, in general, and in 

determining his/her role in a rear-end crash, in particular. Given a rear-end crash, the 

questions that immediately and naturally come to one’s mind are: Who struck and who was 

struck and what was the age/gender of the striking and the struck drivers? The answers to 

these questions lie in GES and FARS databases, which contain a great deal of information 

about crashes, including the role (striking/struck) of vehicles and hence of the drivers 

involved in rear-end crashes as well as about their age and gender. What needs to be done, 

however, from the point of view of driving behavior and performance of a driver prior to a 

crash, is to find out if the driver attributes, such as age and gender have any impact on 

his/her involvement in a crash. Pertinent to this study is to further determine if there is an 

association between these attributes and his/her role (striking/struck) in a rear-end crash. 

The tendencies of drivers of different age groups and gender, with respect to the role they 

are likely to assume in rear-end crashes, will also be brought out. Complying with the 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 2

variables naming convention of GES and FARS databases, the driver attributes age and 

gender will henceforth be referred to as age and sex of the driver. 

In order to seek directions for investigating into the possible relationship between driver 

attributes and rear-end crash involvement, this study first conducts a preliminary analysis to 

look at the crash involvement profile of drivers belonging to different groups based on 

driver’s age and sex. Some studies in this direction have been done in the past (e.g., [1], [2], 

[3]). An important point that needs to be borne in mind, in this regard, is that the crash 

involvement rates for such groups with reference to the entire population of licensed drivers 

do not give a true picture. The smallest number of drivers of a category involved in crashes 

may not mean that this category of drivers is least prone to crash involvement, as this may 

merely be due to the smallest size of the category in question. The idea is to see which 

groups contribute disproportionately to crash involvement and hence the rates should have 

reference to the respective groups rather than to the entire population. Based on this fact, a 

frequency approach is used for developing the methodology used in this study. 

The statistical analysis conducted and the resulting conclusions drawn in this study are 

based on the information/data retrieved from the following sources: 

1. Age/sex distribution of licensed drivers for 2000, reported by the FHWA 

2. Drivers involved in all crashes and those involved in rear-end crashes in 2000, reported 

in GES (excluding fatal crashes that have been considered through FARS) 

3. Drivers involved in fatal crashes in 2000, reported in FARS. 

2. Driver attributes and crash involvement 

As a first step, a preliminary analysis of GES and FARS data for the year 2000 was 

conducted to obtain an idea of the incidence of crashes and the role that the driver attributes 

age and sex might have played in driver’s involvement in a crash. In the following analysis, 

several subpopulations will be defined based on certain criteria so as to look at the problem 

of crash involvement from various angles. 

2.1. Driver’s age and crash involvement 

Based on a pilot study conducted for the development of rear-end crash countermeasures, 

the population of drivers was partitioned into five age groups: drivers under 18 (Age group 

1), 18 to 24 (Age group 2), 25 to 49 (Age group 3), 50 to 69 (Age group 4), and 70 and older 

(Age group 5), to be also referred to as A1, A2, A3, A4, and A5. The frequencies of crashinvolved drivers from each age group (category) were calculated using GES and FARS 

databases. The results, including the frequencies of licensed drivers falling in each category, 

are summarized in Table A.1 (Appendix A) and are presented in the Venn diagram (Figure 

1). This figure represents the population of Licensed Drivers: D (universal set) as a union of 

the subpopulations A1, A2, A3, A4, and A5 (subsets of D) and their intersections with the 

subpopulation C of crash-involved drivers. It may be noted that the areas (with different 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 3

types of hatching) in this figure are merely representative of the population/subpopulation 

and not of the magnitudes of their sizes. 

The statistics presented in Figure 1 show that the crash-involved drivers from age groups A1, 

A2, A3, A4, and A5, respectively, made up 0.4%, 1.2%, 3.1%, 0.9%, and 0.3% of the 

population of all licensed drivers, D. So far as their representation in the subpopulation, C, 

of crash-involved drivers is concerned, these age groups, respectively, contributed 6.6%, 

20.7%, 51.8%, 15.7%, and 5.1% to various types of crashes. 

A comparison of the statistics in Figure 1 further shows that although only 2% of the 

licensed drivers were in age group A1, 19.6% of them were involved in various types of 

crashes. Similarly, of the 11.5% of drivers belonging to A2, 10.8% were involved in crashes. 

On the other hand, of the 51.4% of drivers who were in A3, only 6.0% were involved in 

various types of crashes as compared to those in A4 who made up 29.1% of the driver 

population with 3.2% involved in crashes. The drivers from age group A5 made up 6% of 

the licensed drivers, while 5.1% of them were involved in various types of crashes. It can 

Age group1 

(<18) 

Age group 2 

(18 to 24 ) 

 Age group 3 

 (25 to 49 ) 

 Age group 4 

 (50 to 69 ) 

 Age group 5 

 (> 69) 

Crash-involved 

drivers 

Percent of all 

drivers 

Percent of 

crash-involved 

Percent crash-involved 

in Age group

 Source: National Center for Statistics and Analysis, NHTSA, GES 2000 and FARS 2000, FHWA 

Figure 1. Percent of licensed drivers and crash-involved drivers in five age groups, 

 with reference to the population D and subpopulations A1, A2, A3, A4, A5, and C. 

also be seen in this figure that drivers of both Age group 1 and Age group 2 have much 

higher representation (6.6% and 20.7%, respectively) among the crash-involved drivers (C) 

as compared to their overall representation (2.0% and 11.5%, respectively) in the population 

of licensed drivers (D). On the other hand, drivers of Age group 4 had much lower (15.7%) 

contribution to C as compared to their representation (29.1%) in D, while drivers of Age 

group 3 have almost the same contribution (51.8%) to the subpopulation C as to the 

population D (51.7%). The contribution of Age group 5 drivers to C (5.1%) is slightly less 

than their representation in D (6.0%). The representations, in terms of percent frequencies, 

%

%

%

2.0 11.5 51.4 29.1 6.0

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

1.2 3.1 1.0 0.3 0.4

6.6 20.7 51.8 5.1 15.7

3.2 5.1 10.8 6.0 19.6

... 

...
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 4

of different age groups in the population D and their contribution to the subpopulation C are 

shown in Fig 1(a). This figure shows crash involvement profile of drivers belonging to five 

age groups: lower age group drivers (younger than 24) have lower representation in the 

population D of licensed drivers, but have higher representation in the subpopulation C of 

crash-involved drivers, while higher age group drivers (50 and above) have higher 

representation in D with lower representation in C. The drivers in Age group 3 have almost 

the same representation both in D and C. 

 Source: National Center for Statistics and Analysis, NHTSA, GES 2000 and FARS 2000, FHWA 

 Figure 1(a). Representation of five age groups in the population of licensed 

 drivers D and subpopulation of crash-involved drivers C 

2.2. Driver’s sex and crash involvement 

GES and FARS data for the year 2000 were also analyzed to investigate if sex of a driver 

plays a role in his/her involvement in a crash. The frequencies and other statistics of the 

crash-involved and licensed drivers belonging to different categories based on driver’s sex 

are summarized in Table A.2 (Appendix A). These results are presented in Figure 2 and 

Figure 3. 

The statistics presented in the Venn diagram (Figure 2) show that sex of the driver is 

possibly one of the contributing factors in driver’s crash involvement. For instance, in the 

year 2000, although there was a marginal difference in the number of male (50.3%) and 

female (49.7%) drivers in the entire population of licensed drivers, the percentage of male 

drivers (60.2) among the crash-involved drivers was significantly higher than that of the 

female drivers (39.8). Figure 2 also shows that of the 6% of all licensed drivers who were 

involved in crashes, 3.6% were male and 2.4% female. Further, 7.1% of the male drivers 

were involved in all crashes as compared to 4.8% of the female drivers. 

Referring back to Figure 1, it can be seen that leaving aside drivers younger than 18 (who 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 5

Male drivers 

Female drivers

Crash-involved 

divers

Percent of all 

drivers 

Percent of crashinvolved drivers

Percent of Crashinvolved drivers 

in group or 

 Source: National Center for Statistics and Analysis, NHTSA, GES and FARS 2000, FHWA 

 Figure 2. Percent of drivers: male, female, and crash-involved drivers, with reference 

 to the population D and subpopulations M, F, and C. 

made up only 2% of the population of licensed drivers), 18 to 24 year old drivers (to be 

referred to as young drivers in the subsequent discussion) have the highest crash 

involvement among drivers who are 18 and older. We will now focus our attention on the 

group of young drivers and find out the extent to which crash involvement of these drivers 

can be attributed to the attribute sex. The statistics (from Table A.2, Appendix A) presented 

in the Venn diagram (Figure 3) answer this question to a large degree and bring some other 

facts to light as well. 

Male drivers 

Female drivers 

Crash-involved 

drivers 

Percent of all 

licensed drivers 

Percent of crashinvolved drivers 

Percent of crashinvolved drivers in 

subpopulation 

 or 

Percent of 

drivers in

 Source: National Center for Statistics and Analysis, NHTSA, GES and FARS 2000, FHWA 

Figure 3. Percent of drivers: young (male and female) and crash-involved drivers, with 

reference to the population D and subpopulations Y, M, F, and C. 

%

%

% 

%

%

% 

... 

...

...

... 50.3 49.7 

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.6 2.4

60.2 7.1 4.8 39.8

5.9 5.6 

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.7

59.9 12.4 40.1

0.5

8.3

51.3 48.7

20.7 

%
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 6

The statistics in Figure 3 show that the young male and female drivers, respectively, 

accounted for 5.9% and 5.6% of the licensed drivers. So far as the crash involvement 

profile of young drivers is concerned, it can be noticed in this figure that of the 20.7% of 

them, who were involved in crashes, 59.9% were male as compared to 40.1% female 

drivers. Further, 12.4% of the young male drivers were involved in crashes, accounting for 

0.7% of all the licensed drivers, while 8.3% of the young female divers were crash-involved, 

making up 0.5% of the population of licensed drivers. 

The representation of male and female drivers in the population of licensed drivers, 

subpopulation of young drivers, and subpopulation of crash-involved young drivers is 

displayed in Figure 3(a), where outer rectangles represent male drivers and inner rectangles 

female drivers. It can be clearly seen in this figure that the slight difference between the 

percentages 50.3 and 49.7 of male and female drivers, respectively, in the population 

 

Source: National Center for Statistics and Analysis, NHTSA, GES and FARS 2000, FHWA 

Figure 3(a). Representation of male and female drivers in the population of 

 licensed drivers D, young drivers Y, and young crash-involved drivers. 

of licensed drivers was reflected in their representations 51.3% and 48.7%, respectively, in 

the subpopulation of young drivers. This figure also depicts that male to female ratio in the 

subpopulation of young drivers (100:98.8) does not differ as much from that in the 

population of all licensed drivers (100:95) as it does in the subpopulation of crash-involved 

young drivers (100:67). 

2.3. Crash involvement propensity of drivers

Consider a situation in which, based on a certain criterion (e.g., age), drivers are subdivided 

into K categories (subpopulations) and our interest is in comparing these categories with 

respect to their propensity of being involved in a crash. This information can, for instance, 

be useful in stratifying the population for data collection so that maximum information 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 7

could be acquired not only in terms of the occurrences of crashes but also in terms of certain 

driver-related parameters across the driver categories. In order to develop a measure of the 

crash involvement propensity of a driver belonging to a category as compared to other 

categories, it is important to consider the occurrence of crashes in this category relative to 

the occurrence of its drivers in the entire population of drivers. The important information 

that one needs in this context is an answer to the question: Given that a driver selected at 

random is from a certain category, what is the probability that he/she would be involved in a 

crash? In other words, what one needs to look for is the likelihood of a driver of each 

category being involved in a crash. These likelihoods can then be combined into the statistic 

φ , called Crash Involvement Propensity Index (CIPI), to provide a reasonable measure of 

for comparing crash involvement propensities of different categories considered in a given 

situation. This statistic is given by (for analytical details refer to Appendix B) 

 i 1 2 K

S

C

S

C

K

j 1

2

j

j

2

i

i

i , = , , . . . ,















 =

∑

=

φ (1) 

where 

Ci is the number of crash-involved drivers belonging to the ith category (Ai), 

Si is the number of drivers in the ith category, i.e., the size of the ith category Ai, Si > 0 , 

S1 + S2 + . . . + SK = N (size of the population of licensed drivers), 

K is the number of mutually exclusive categories that are exhaustive of the entire 

population of licensed drivers. 

Note that the numerator in equation (1) takes into account the likelihood or conditional 

probability (conditional on category) of a driver belonging to the ith category being involved 

in a crash, while the denominator is the normalizing quantity. As the name suggests, CIPI 

(equation (1)) can be used to assess the propensity of drivers belonging to a certain category 

being involved in crashes, relative to that of the drivers of other categories. 

The statistic CIPI was used to compare the five age groups (defined in Section 2.1) of the 

population of licensed drivers for the year 2000 (FHWA) for their crash involvement 

propensity. Based on GES and FARS data, φ in equation (1) was calculated for each of the 

five age groups as shown in Table 1. The results presented in this table show that Age group 

1 has the highest crash involvement propensity (φ1 = 0.8299), indicating that among all 

licensed drivers, drivers under 18 are most vulnerable to roadway crashes. Age group 2 has 

the next highest crash involvement propensity (φ2 = 0.0794), though this is far lower than 

that of Age group 1. However, among drivers older than 18, the Age group 2 drivers are 

most prone to crash involvement. The drivers of Age group 5 are slightly less prone 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 8

(φ5 = 0.0714) as compared to Age group 2, while Age group 3 and Age group 4 have very 

low and almost the same crash involvement propensity (φ3 = 0.0099 and φ4 = 0.0094, 

respectively). 

 Table 1. Crash involvement propensity of licensed drivers belonging to five 

 age groups 

Age group i Subpopulation Size of 

subpopulation

Number of 

crash-involved 

drivers 

Crash Involvement 

Propensity 

Index 

(interval in years) (Ai) (Si) (Ci) (φi ) 

Age group 1 

(<18) A1 3,827,438 751,667 0.8299 

Age group 2 

(18 to 24) A2 21,881,758 2,351,971 0.0794 

Age group 3 

(25 to 49) A3 98,046,947 5,861,801 0.0099 

Age group 4 

(50 to 69) A4 55,396,514 1,775,570 0.0094 

Age group 5 

(>69) A5 11,472,366 581,312 0.0714 

 Source: National Center for Statistics and Analysis, NHTSA, GES 2000, FARS 2000, FHWA. 

The crash involvement propensities for the five age groups are plotted in Figure 4. This 

figure clearly depicts that as the drivers get older, their propensity of being involved in 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Age group

Crash Involvement Propensity Index

Age group 1 Age group 2 Age group 3 Age group 4 Age group 5

 Source: National Center for Statistics and Analysis, NCSA, GES 2000, FARS 2000, FHWA 

 Figure 4. Crash involvement propensity of drivers belonging to five 

 age groups, as measured by CIPI.
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 9

crashes keeps decreasing (with a noticeably sharp decrease from Age group 1 to Age group 

2). It can also be noticed in this figure that the crash involvement propensity increases again 

when the drivers get older (70 and above). In fact, it reaches almost the same level as of the 

young (18 to 24) drivers. 

3. Association between driver attributes and his/her role in a rear-end 

crash

The statistics presented thus far provide a clear idea about the variation that exists in the 

crash involvement propensity of drivers belonging to different age and sex groups. We now 

focus our attention on rear-end crashes and seek statistical justification to the possible 

association between age/sex of the driver and his/her role (striking/struck) in a rear-end 

crash. As a first step, based on the preliminary analysis conducted in the previous sections, 

the population of drivers was classified with respect to three factors: Age of the driver, Sex 

of the young driver, and Role of the driver in a rear-end crash. 

Specifically, the following modes of classification were used in the subsequent analysis. 

• Classification of drivers based on Age of the driver: 

▪ Age group 1 (younger than 18) 

▪ Age group 2 (18 to 24 ) 

▪ Age group 3 (25 to 49 ) 

▪ Age group 4 (50 to 69 ) 

▪ Age group 5 (70 and older) 

• Classification of drivers based on Sex of the young driver: 

▪ Young male (18 to 24 male drivers ) 

▪ Young female (18 to 24 female drivers) 

• Classification of drivers based on driver’s Role in a rear-end crash: 

▪ Rear-end striking (drivers involved as striking drivers in rear-end crashes) 

▪ Rear-end struck (drivers involved as struck drivers in rear-end crashes) 

The contingency analysis [4] was carried out to test the hypothesis: 

H1: There is no association between Age of the driver and his/her Role in a rear-end crash. 

Contingency analysis is one of the useful statistical techniques for testing independence 

between two or more factors and can be performed on the data that may be meaningfully 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 10

classified in a contingency table, such as Table A.3 (Appendix A).

Since GES data are based on three-stage sampling, the statistical software SUDAAN 8.01 

was used for carrying out the contingency analysis, which takes into account the underlying 

sampling design. The contingency analysis of GES data for the year 2000 was carried out to 

test the hypothesis H1. The results are presented in the contingency table (Table A.3, 

Appendix A.) that yield 2 χ = 169.7 with 4 degrees of freedom. Since 95th percentile, 9.49, 

of 2 χ distribution with 4 degrees of freedom is far less than 169.7, there is strong evidence 

of the association between Age of the driver and his/her Role in a rear-end crash. 

As seen earlier in Section 2.1, drivers under the age of 18 made up only 2% of the total 

population of licensed drivers, and among drivers older than 17, drivers of age 18 to 24 were 

most prone to crash involvement (Section 2.3). Based on this profile, we will now focus our 

attention on the age group: 18 to 24 (young drivers) and test the hypothesis: 

H2: There is no association between Sex of the young driver and his/her Role as striking or 

struck driver. 

The contingency analysis was carried out to test the hypothesis H2, using the statistical 

software SUDAAN 8.01 for the same reason as in testing the hypothesis H1. The results are 

presented in the contingency table, Table A.4, (Appendix A) which yield 2 χ = 33.1 with 1 

degree of freedom. Since 95th percentile, 3.84, of 2 χ distribution with 1 degree of freedom 

is much less than 33.1, we would reject the hypothesis of independence between Sex of the 

young driver and his/her Role in a rear-end crash and conclude that there is an association 

between these two factors. 

Thus, the above analysis justifies partitioning of the population of drivers into 

subpopulations based on (i) age of the driver, and (ii) sex of the driver. A finer analysis 

conducted in the following sections can provide more insight into the likelihood of the role 

that a driver of a category (based on age/sex) would assume in a rear-end crash. 

4. Driver attributes and likelihood of his/her role in a rear-end crash

Considered as events, a rear-end crash, and age and sex of the driver involved in a crash 

cannot be predicted in advance and hence are random events. The phenomenon of the 

occurrence of rear-end crashes and the involvement of drivers, therefore, submits itself to a 

probabilistic treatment. For that purpose, we define discrete random variables: X1 that 

assumes values, depending on the driver’s age; X2 that assumes values, depending on sex of 

the driver (with focus on young drivers); and Y that assumes values, depending on the 

driver’s role in a rear-end crash. Specifically, these random variables were defined as: 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 11

X1 {driver’s Age} 

= 1, if driver’s age is younger than 18, 

= 2, if driver’s age is 18 to 24, 

= 3, if driver’s age is 25 to 49, 

= 4, if driver’s age is 50 to 69, 

= 5, if driver is older than 69. 

X2 {driver’s Sex} 

 = 1, if young (18 to 24) driver is male, 

= 2, if young (18 to 24) driver is female, 

= 3, otherwise (if driver of either sex is under 18 or is older than 24). 

Y {driver’ Role} 

= 1, if driver is striking in the rear-end crash, 

= 2, if driver is struck in the rear-end crash, 

= 3, otherwise (i.e., if the driver is either involved in a crash other than rear-end or not at 

all). 

Based on GES and FARS data for the year 2000, the joint, marginal, and conditional 

probability distributions of the random variables X1, X2, and Y were evaluated, in order to 

look at the crash involvement profile of drivers categorized on the basis of age and sex 

4.1. Driver’s age and likelihood of rear-end crash involvement

Table 4 shows the conditional probability distributions: (i) of X1, given Y, i.e., of age group, 

conditional on driver’s role (striking/struck) in a rear-end crash (Table 4(a)), (ii) of Y given, 

X1, i.e., of driver’s role in a rear-end crash, conditional on driver’s age group (Table 4(b)). 

These probability distributions provide useful information about the crash involvement 

profile of drivers belonging to different age groups in rear-end striking and struck crashes. 

The conditional probabilities of driver’s age groups, given driver’s role, as shown in Table 

4(a), are plotted in Figure 5. This figure also shows the probability distribution of licensed 

drivers over different age groups. By comparing the distributions of licensed drivers (Figure 

5(a)), of the striking drivers (Figure 5(b)), and of the struck drivers (Figure 5(c)) with the 

normal distribution (dotted line), it can be seen that all these distributions are in close 

proximity to each other. 

 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 12

 Table 4. Conditional probability distributions of the discrete random variables 

 X1 and Y 

(a) Conditional probability distribution of Driver’s age group, given Driver’s role 

P(X1=i / Y=j)

Y X1 (Driver’s age group) 

(Driver’s role) 1 2 3 4 5 

1 0.08168 0.229445 0.523402 0.12792 0.03755 

2 0.04298 0.16352 0.56647 0.18819 0.03884 

3 0.01907 0.11283 0.51360 0.29379 0.06071 

 (b) Conditional probability distribution of Driver’s role, given Driver’s age group 

P( Y=j / X1=i )

Y X1 (Driver’s age group) 

(Driver’s role) 1 2 3 4 5 

1 0.04786 0.02352 0.01197 0.00518 0.00734 

2 0.02502 0.01666 0.01288 0.00757 0.00755 

3 0.92711 0.95983 0.97515 0.98725 0.98511 

 Source: National Center for Statistics and Analysis, NHTSA, GES 2000, FARS 2000, FHWA 

 Source: National Center for Statistics and Analysis, NHTSA, GES 2000, FARS 2000, FHWA 

Figure 5. Probability distributions of All, Rear-end striking, and Rear-end struck 

drivers over Age groups. 

Also, the conditional probabilities of driver’s roles: striking (thick line) and struck (dotted 

line), given his/her age group, as shown in Table 4(b), are plotted in Figure 6. This figure 

shows that among five age groups, the incidence of rear-end striking crashes is most 

probable for drivers of Age group 1 (younger than 18). The tendency of drivers of Age 

group 2 (18 to 24) is no different from that of Age group 1 drivers, i.e., of being in the 

striking role more often than in the struck role, though comparatively Age group 2 drivers 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 13

0

0.01

0.02

0.03

0.04

0.05

0.06

Driver's age group 

Crash involvement likelihood

Age group 1 Age group 2 Age group 3 Age group 4 Age group 5

 Source: National Center for Statistics and Analysis, NHTSA, GES2000, FARS 2000 

 Figure 6. Rear-end (striking and struck) crash involvement likelihood 

of drivers belonging to five age groups.

tend to get involved in rear-end striking crashes less often. Additionally, Figure 6 shows that 

as the drivers get older, they tend to be in the striking role less often than in the struck role. 

It is also interesting to note in this figure that drivers of Age group 5 (70 and above) are 

likely to get involved in striking crashes as often as in struck crashes. 

4.2. Sex of young driver and likelihood of rear-end crash involvement

We now focus our attention on the subpopulation of young drivers and compare the 

likelihood of rear-end crash involvement of male and female drivers of this subpopulation. 

Of special interest will be to bring out the difference between the tendencies of male and 

female drivers in this group, if any, in assuming the role (striking/struck) in a rear-end crash. 

For that purpose, the joint, marginal, and conditional probability distributions of the random 

variables X2 and Y were evaluated using GES and FARS data for the year 2000. The results 

are presented in Table 5. The joint and marginal probabilities (Table 5(a)) for young male 

and young female drivers are also displayed in Figure 7. The important conclusion that one 

can draw from this figure is that relative to the likelihood of a driver being male or female in 

the population of licensed drivers, the likelihood of involvement of young male drivers in 

rear-end striking crashes was 1.5 times greater than that of the young female drivers, while 

the likelihood of involvement of young male drivers in rear-end struck crashes was only 

slightly greater (1.1 times) than that of young female drivers. 

 

Striking 

Struck 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 14

Table 5. Joint and conditional distributions of the discrete random 

 variables X2 and Y and marginal distribution of X2

(a) Joint Probability Distribution: P( X2=i, Y=j ) and Marginal distribution of X2

X2 (Driver’s Age/Sex) Y (Driver’s role) 

1 2 3 

1 0.00162 0.00108 0.00907 

2 0.00100 0.00091 0.00978 

3 0.05623 0.05395 0.86637 

Marginal 

distribution of X2

0.05885 0.05594 0.88522 

(b) Conditional Probability Distribution: P( Y=j / X2=i )

X2 (Driver’s Age/Sex) Y (Driver’s role) 

1 2 3 

1 0.02751 0.01932 0.01024 

2 0.01698 0.01632 0.01105 

3 0.95552 0.96437 0.97871 

 Source: National Center for Statistics and Analysis, NHTSA, GES 2000, FARS 2000 

 

 Source: National Center for Statistics and Analysis, NHTSA, GES and FARS 2000 

Figure 7. Rear-end crash involvement of young male and young female drivers. 

The conditional probabilities of driver’s Role, conditional on driver’s Age/Sex (from Table 

5) for young male and young female drivers are plotted in Figure 8. This figure shows that 

young male drivers are more likely to get involved in striking crashes as compared to young 

female drivers, though both of them have a higher tendency to be in the role of a striking 

driver than that of the struck driver. 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 15

0

0.005

0.01

0.015

0.02

0.025

0.03

Male(18-24) Female(18-24) Others(<18&>24)

Driver's age/sex 

Crash-involvement likelihood

Striking

Struck

 Source: National Center for Statistics and Analysis, NHTSA, GES 2000, FARS 2000

Figure 8. Comparison of young male, young female and others (male/female 

under 18 and above 24) with respect to rear-end crash involvement likelihood. 

5. Conclusions and recommendations

The present study was initiated with the descriptive statistical analysis. The rates (percent 

frequencies) calculated with reference to the population and subpopulations of drivers 

indicate crash involvement profiles of drivers of different age/sex groups. The use of the 

statistic CIPI, proposed in this study, further enabled a comparison of the crash involvement 

propensity of drivers belonging to different age groups. In fact, based on propensity, the 

population of licensed drivers in 2000 can be classified into four categories: (i) drivers under 

18 (with highest propensity), (ii) 18 to 24 year old drivers (with the next highest propensity, 

though much lower than the previous age group), (iii) 25 to 69 year old drivers (with the 

minimum propensity), and (iv) drivers 70 and above (with the same propensity as of 18 to 

24 year old drivers). This information provided useful guidelines for further analysis 

conducted in the context of rear-end crashes. 

The contingency analysis of GES and FARS data for 2000 shows that both driver’s age and 

sex are strongly associated with driver’s role (striking/struck) in a rear-end crash. Some 

important inferences could be made about the occurrence of rear-end crashes, on the basis of 

joint, marginal, and conditional probability distributions. Based on driver’s age and role in a 

rear-end crash, these distributions indicate that drivers under 18 have the highest incidence 

of rear-end striking crashes. These probability distributions also show that the likelihood of 

involvement in rear-end striking crashes, rather than in struck, decreases with age. Similarly, 

based on the young driver’s sex and role in rear-end crash, the probability distributions show 

that young male drivers are more prone to rear-end striking crashes as compared to their 

female counterparts. 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 16

The statistics presented in this study show that the involvement of drivers in crashes, in 

general, and the role that a driver may assume in a rear-end crash, can be attributed to driver 

attributes age and sex. This, in turn, strongly supports the use of these attributes as 

stratification factors in data collection and analysis that are directed towards development of 

effective rear-end crash countermeasures. 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 17

6. Appendix A. Tables

Table A.1. This table shows the results presented in Figure 1 (Venn diagram), partitioning the 

population of licensed drivers in subpopulations, based on age of drivers. 

Table A.1. Distribution (in terms of frequency and percent) of drivers classified according 

 to driver’s age and the corresponding crash involvement statistics

Licensed drivers D 

(190,625,023) 

Involved in crashes C 

Subpopulation (11,322,321) 

(Age group) 

Ai Frequency 

Si 

Percent of 

D 

Frequency Percent of 

D 

Percent of 

C 

Percent of 

Ai 

Age group 1: A1

(younger than 18) 3,827,438 2 751,667 0.39 6.64 19.64 

Age group 2: A2 

(18 to 24) 21,881,758 11.5 2,351,971 1.23 20.77 10.75 

Age group 3: A3 

(25 to 49) 98,046,947 51.4 5,861,801 3.08 51.77 5.98 

Age group 4: A4 

(50 to 69) 55,396,514 29.1 1,775,570 0.93 15.68 3.21 

Age group 5: A5 

(70 and older) 11,472,366 6 581,312 0.30 5.13 5.07 

Total 190,625,023 100 11,322,321 5.94 100.00 5.94 

 Source: National Center for Statistics and Analysis, NHTSA, GES 2000, FARS 2000, FHWA 

Table A.2. This table shows the results presented in Figure 2 (Venn diagram), partitioning the 

population of licensed drivers in subpopulations, based on sex of drivers and sex of the young 

drivers. 

 Table A. 2. Distribution (in terms of frequency and percent) of drivers classified according 

 to driver’s age/sex and the corresponding crash involvement statistics

Licensed drivers D 

(190,625,023) 

Involved in crashes C 

(11,322,321) 

Subpopulation 

Di 

Frequency 

Si

Percent of 

D 

Frequency Percent of 

D 

Percent of 

C 

Percent of 

Di 

Male: M 95,796,069 50.25 6,815,502 3.58 60.20 7.11 

Female: F 94,828,953 49.75 4,506,125 2.36 39.80 4.75 

Young (18 to 24) 

Male: 

Y∩ M 

11,218,354 5.89 1,407,710 0.74 12.43 12.55 

Young (18 to 24) 

Female: Y∩ F 10,663,404 5.59 944,261 0.50 8.34 8.86 

 Source: National Center for Statistics and Analysis, NHTSA, GES 2000, FARS 2000, FHWA 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 18

Table A.3. This table shows sample size and weighted size for each category (age group) 

that were computed by SUDDAN while carrying out the contingency analysis for testing the 

association between driver’s Age and driver’s Role in a rear-end crash (Section 3). 

 Table A.3. Contingency table: Driver’s Age vs. Driver’s Role in a rear-end crash 

Driver’s role 

Driver’s age group Statistics 

Rear-end striking Rear-end struck 

Total 

Age group 1 

(younger than 18) 

Sample size 

Weighted size 

1079 

147982 

471 

66179 

1550 

214161 

Age group 2 

(18 to 24) 

Sample size 

Weighted size 

3418 

437657 

2204 

292887 

5622 

730544 

Age group 3 

(25 to 49) 

Sample size 

Weighted size 

7484 

896980 

8621 

1053726 

16105 

1950705 

Age group 4 

(50 to 69) 

Sample size 

Weighted size 

1954 

219596 

2935 

357328 

4889 

576924 

Age group 5 

(70 and older) 

Sample size 

Weighted size 

1337 

200681 

937 

118743 

2274 

319424 

Total Sample size 

Weighted size 

15272 

1902896 

15168 

1888863 

30440 

3791758 

 Source: National Center for Statistics and Analysis, NHTSA, GES 2000, FARS 2000, FHWA 

Table A.4. This table shows sample size and weighted size for each category (sex of young 

driver), that were computed by SUDDAN while carrying out the contingency analysis for 

testing the association between Sex of the young driver and driver’s Role in a rear-end crash 

(Section 3).

Table A.4. Contingency table: Young driver’s Sex vs. Driver’s Role in a 

 rear-end crash 

Driver’s role 

Young driver’s 

Sex 

Statistics 

Rear-end striking Rear-end struck 

Total 

Young 

(18 to 24) 

Male 

Sample size 

Weighted size 

2185 

271079 

1198 

153791 

3383 

424870 

Young 

(18 to 24) 

Female 

Sample size 

Weighted size 

1233 

166578 

1006 

139096 

2239 

305674 

Total Sample size 

Weighted size 

3418 

437657 

2204 

292887 

5622 

730544 

 Source: National Center for Statistics and Analysis, NHTSA, GES 2000, FARS 2000, FHWA 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 19

7. Appendix B. Analytical details of Crash Involvement Propensity Index

B.1. Crash Involvement Propensity Index (CIPI) 

This appendix supplies the analytical details of the statistic called Crash Involvement 

Propensity Index in Section 2.3. 

In order to develop a measure of the crash involvement propensity of a driver belonging to a 

category as compared to other categories, it is important to consider the occurrence of crashes 

in that category relative to the occurrence of its drivers in the entire population of drivers. For 

this purpose, we consider the space Ω of all drivers belonging to a category and the subspace 

Ω C of those drivers of this category who are involved in crashes. 

Let 

L(Ω) be the probability that a driver selected at random belongs to the category Ω , 

( ) L Ω C be the probability that a driver selected at random is involved in a crash, given that 

he/she belongs to the category Ω . 

Let N be the number of drivers in the entire population of drivers that has been subdivided 

into K categories, based on a certain criterion, Si the number of drivers belonging to category i 

(Si>0), and Ci the number of drivers belonging to category i who are involved in crashes, i= 1, 

2,...,K. Then the Crash Involvement Propensity of category i drivers can be defined as 

 i 1 2 K

L

L

i

i

i

C

, , , . . . , ( )

( )

( )

( )

= Ω

Ω

λ = (B.1) 

where 

 

i

i i

C S

C L ( Ω ) = ( ) 

and 

 N

S L i i ( Ω ) = ( ) , 

so that λi defined in (B.1) becomes 

 i 1 2 K

S

C

N 2

i

i

i , = , , . . . , 













 λ = . (B.2) 

Note that λi in (B.2) is basically, the conditional probability of a driver being involved in a 

crash, given that he/she belongs to that ith category. In order to compare the crash 

involvement propensity of mutually exclusive categories A1, A2,...,AK into which the 

population of all drivers is subdivided, these probabilities can be combined to define the CIPI 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 20

i 1 2 K K

j 1

j

i

i = , = , , . . . ,

∑=

λ

λ φ . 

Using λi from (B.2), the CIPI can be derived in the usable form 

 i 1 2 K

S

C

S

C

K

j 1

2

j

j

2

i

i

i , = , , . . . ,















 =

∑=

φ . (B.3) 
 

 

 National Center for Statistics and Analysis ♦ 400 Seventh St., S.W., Washington, D.C. 20590 21

8. References

[1] NHTSA, Crash Data and Rates for Age-Sex Groups of Drivers, Research Note, US 

Department of Transportation, Washington DC, 1992. 

[2] NHTSA, Crash Data and Rates for Age-Sex Groups of Drivers, Research Note, US 

Department of Transportation, Washington DC, 1996. 

[3] NHTSA, Crash Data and Rates for Age-Sex Groups of Drivers, Research Note, US 

Department of Transportation, Washington DC, 1998. 

[4] Rohatgi, V. K., An Introduction to Probability Theory and Mathematical Statistics, 

 John Wiley and Sons, New York (1976). 

DOT HS 809 540

March 2003