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Chapter 1.  INTRODUCTION (From 1991 book Traffic Safety and the Driver)


                 No one who lives in a motorized society can fail to be concerned about the enormous human cost of traffic crashes.  In the United States almost as many young males die as a result of traffic crashes as from all other causes combined.  From 1928 through 1988 more than two and a half million people were killed on US roads; more than half million from 1969.  Traffic deaths from 1977 through 1988 exceeded all US battle deaths in all wars from the revolutionary war through the Vietnam war.  Injuries outnumber deaths by about a factor of 70.  The total annual monetary cost of US motor vehicle crashes is estimated at 70 billion dollars for 1988.  Worldwide, about half a million people are killed annually in traffic crashes.

                 This book describes what has been learned by applying the methods of science to understand better the origin and nature of the enormous human and economic losses associated with automobile-based transportation systems.  The book aims primarily at understanding and illuminating the problem, in, perhaps, the spirit of a microbiologist trying to understand a disease; there is a need to keep some separation between the concern and the science if the science is to succeed.  Understanding and action are different processes; action is more likely to produce the results sought if it is grounded in understanding.  As Haight [1988] comments about efforts to improve traffic safety, "Many of us have heard demands that we `do something', but it is only recently that there have been suggestions that we should `know what we are doing' before we begin to do it." 

                 Before getting into questions about the nature and sources of traffic crashes we summarize some basic facts.  Information from throughout the world will be used in the book, although more from the United States than from any other country.  This is mainly because, with 188 million vehicles in 1988 [National Safety Council 1989, p. 48], the US provides more data than any other single nation.  In addition, the US Department of Transportation maintains data files of magnitude and quality unavailable elsewhere.  Many relationships relating to traffic safety are of a general nature which apply beyond the jurisdiction providing the data from which they were derived.  For example, there is no reason why the effectiveness of occupant protection devices such as safety belts or airbags in preventing fatalities should vary much from jurisdiction to jurisdiction; at the same wearing rates, safety belts are expected to produce a similar percent reduction in fatalities in a nation of one million as in a larger nation providing sufficient data to estimate the percent reduction.  Damask [1987] reports that an attorney's closing remarks to a New Jersey jury included, "The laws of physics are obeyed in the laboratory, but not in rural New Jersey;" the jury, evidently moved by the force of this argument, found in favor of his client [Damask 1988].  When results presented here flow mainly from physics, human physiology and biomechanics, they are likely to apply similarly in jurisdictions other than the one providing the data used to derive them.  Many aspects of traffic safety are, of course, jurisdiction specific.  For example, alcohol plays a quite different role in traffic safety in, for example, Sweden, Saudi Arabia, the United States and Israel.






                 In this book we place considerable emphasis on fatalities, the most serious consequence of a traffic crash.  Fatality data are more complete than data on injuries at other levels, and the definition of fatality involves less uncertainty than for any other type of loss.  This is not to say that fatality data are free from uncertainties and errors.  Hutchinson [1987] documents differences in the total numbers of fatalities indicated in death certificates and in police records in most countries; not all deaths are necessarily known to those responsible for data sets, and missing data can be especially numerous in less economically developed countries.  For a death to be included in any fatality data set it must occur within some specified time of the occurrence of the crash.  While the choice is essentially arbitrary, the longer the period, the more all-inclusive will be the data set.  A one year criterion, as used by the National Safety Council [1989], is a quite common choice.  The disadvantage of so long a period is that the data file is not complete for an entire year after the last crash it documents; thus the theoretically earliest moment at which the data for, say, calender year 1988 could be knowable is January 1990.  The data set we use extensively, described in Chapter 2, defines a death as one that occurs within 30 days of the crash as a result of the crash.

                 Worldwide, more than half a million people are killed each year in traffic crashes [Hutchinson 1987]; about one person in 200 in the world's population dies from injuries received in traffic [Trinca et al. 1988].  These losses are spread among the nations of the world in a far from even way, as indicated in data from 20 illustrative large countries shown in Table 1-1.  This table
shows 154 866 fatalities, less than one third of the world's total.  The first column gives the number of vehicles per thousand inhabitants, which provides a measure of the nation's level of motorization; this is generally linked to the production of economic goods in general.  The 20 countries are listed in order of decreasing degree of motorization; they are selected from the much larger numbers in the cited sources to illustrate the wide variability between countries and the dependence of fatalities on motorization, a dependence captured approximately in relations presented by Smeed [1948; 1968].  The fatality data are not all for the same year -- generally deaths per vehicle declines by about 5% per year, while the other quantities do not change systematically over periods of a few years.


Table 1-1 about here


                 Motorization took deep roots earlier in the US than in other countries; the relatively low population density of the US has been conducive to developing a roadway system that can accommodate large numbers of vehicles.  In 1988 there were slightly more than three motorized vehicles (mainly cars, but trucks, busses, and motorcycles are also included) for every four members of the US population (188.2 million vehicles for 246 million people).

                 As the degree of motorization increases, there is a decrease in the number of deaths per registered vehicle; the largest rate in Table 1-1 is 140 times the smallest.  This same pattern occurs within an individual nation as its degree of motorization increases (Chapter 13).  It is possible that changes between countries and in time are even greater than the data indicate, because underreporting of fatalities is likely to be greater when less motorized.  As motorization increases, the number of deaths per capita (and also the total
number) may increase if the fatality rates decline at a lower rate than the number of vehicles increases.

                 As degree of motorization increases, not only does the number of fatalities change, but also the types of fatalities.  In the US, 14.6% of all 1988 fatalities were pedestrians.  In only two countries, Canada and the Netherlands, do pedestrian fatalities constitute so low a fraction of all fatalities as this.  In many countries the percentage of fatalities that are pedestrians is much higher (for example, 35% in the UK, 42% in Poland, 45% in Israel, and 60% in Hong Kong) [Hutchinson 1987].  Among the states in the US, the fraction of all traffic fatalities that are pedestrians also varies widely, from a low of 3.2% for Wyoming to a high of 41.7% for the District of Columbia [National Highway Traffic Safety Administration 1989].  Fatality rates vary widely between the states; for example, 97 fatalities per million people in the District of Columbia compared to 324 in Wyoming.  Degree of motorization and degree of urbanization influences the number of fatalities, and the fraction of these that are pedestrians.  Thus, while the data in Table 1-1 show some broad patterns, it is inappropriate to read too much into them, especially as definitions, reliability and completeness also vary from country to country.  Fatalities will be a central consideration in many later chapters.


Non-fatal injuries


                 Non-fatal injury data are not available with the completeness of fatal data.  In contrast to fatal injuries, which conceptually involve only a yes or no discrimination, non-fatal injuries lie along a severity continuum, from minor scratches to nearly fatal.  The question "How many injuries?" has little meaning in the absence of some defined level of injury.  Generally, the less
severe the injury, the greater is its frequency of occurrence, so the total number of injuries is extremely sensitive to, say, whether or not minor scratches are included.  The most widely used injury scale is the Abbreviated Injury Scale (AIS) developed by the Association for the Advancement of Automotive Medicine.  Injuries for each body region are placed into six levels, AIS =1 through AIS = 6.  These are defined in terms of detailed medical examination, and the scale undergoes continuing revision, expansion and enhancement [American Association for Automotive Medicine 1985].  The AIS level is determined based on the level of injury revealed by examination soon after the crash, and not by final outcome.  As a consequence, it is possible for injuries at any AIS level to prove fatal subsequently, although the life- threatening potential of the injury increases steeply with increasing AIS level.  Injured occupants often sustain injuries to more than one body region.  For many analyses it is convenient to use only one measure of injury severity, which is the maximum AIS.  An occupant with three injured regions of the body, all at AIS 1, would have a maximum AIS of 1; an occupant with one region injured at AIS 2 would have a maximum AIS of 2.  The description of the AIS levels presented in Table 1-2 is sufficient for our present purposes.  The probability of death values given are not part of the definitions, nor are they expected to be closely replicated under all conditions.  They are observed values in one study [Malliaris, Hitchcock, and Hedlund 1982] and are presented to indicate more clearly how life-threatening potential increases with AIS.


Table 1-2 about here


                 An estimate of the distribution of traffic injuries by maximum AIS level in the US is available in the National Accident Sampling System (NASS)
[National Highway Traffic Safety Administration 1988].  NASS is based on detailed post-crash examination of a carefully selected sample of crashes.  The sample is chosen according to a probability scheme applied to police- reported crashes -- the more severe the crash, the more likely it is subject to detailed post-crash examination.  National estimates are inferred by scaling up by factors reflecting the probability that a crash of given severity is chosen for investigation.  The information in Table 1-3 is based on data on over 13 000 crashes investigated in the 1986 NASS.  This table, and the next three tables, are from an updating addendum [National Highway Traffic Safety Administration 1987] to an earlier study [National Highway Traffic Safety Administration 1983] which examined in depth the cost of motor vehicle crashes.  Only those who did not die from the injuries at the indicated AIS level are shown in Table 1-3.  If they died they are counted in the fatality total, so the estimates for AIS 5 (and to some extent AIS 4) substantially underestimate the actual numbers sustaining injuries at these levels in view of the probabilities (Table 1-2) that they are counted in the fatality total.  The data in Table 1-3 indicate 74 injuries (of at least AIS = 1) per fatality.  However, note how large a fraction (95.5%) of these injuries are the two lowest AIS levels. 


Table 1-3 about here


                 The National Highway Traffic Safety Administration [1987] reports that a 1981 survey they conducted indicates that there might be as many as 0.27 injury crashes not reported to the police for each NASS police-reported injury crash, with essentially all of the additional injuries being AIS 1.  This suggests 4.34 million (rather than 3.42 million) injuries per year, and 94, rather than 74, injuries per fatality.

                 The above discussion of injuries has focused on the US, and shown the difficulties associated with injury measurements.  Trinca et al. [1988] write that about 15 million people per year are injured in traffic crashes, and estimate that the average citizen of the world consequently has about a one in seven chance of being injured in a traffic crash sometime during his or her life.


Property damage only


                 The most common type of crash involves property damage only, without any personal injury.  Estimates of the total number of vehicles involved in crashes are particularly uncertain, because as the value of the property loss  becomes less, so does the probability that authorities will know that the crash has occurred.  One report [National Highway Traffic Safety Administration 1983, p. II-14] estimates the total number of vehicles involved in crashes in 1980, based on two separate approaches.  In one approach, 34 million reported incidents (to police, insurance, or other authorities) of vehicles involved in property damage only crashes are augmented by an estimate of an additional 11 million unreported incidents, to give 44 million.  In another approach, an estimated number of reported and unreported crashes of 24 million is multiplied by an average of 1.7 vehicles per crash to give 41 million vehicles involved in all types of crashes.  The National Safety Council [1989, p. 48] provides comparable, but lower estimates of 19.4 million property damage only crashes involving 36.2 million vehicles for 1988.  These values indicate that the average vehicle has about a 20% probability of being involved in some type of crash per year, or is likely to be involved in some type of crash about every five years.

                  Given that the number of property damage only crashes depends critically on the definition of a crash, and that there is much uncertainty in the number of minor crashes, it is more appropriate to consider the total monetary cost.  In doing so, not counting large numbers of very minor incidents will have less effect.




                 In discussing economic losses, we confine our attention to specifically identifiable monetary losses.  We do not delve into the question of how much a life is worth, which is steeped in problems of the type discussed by Broome [1978] and others, and by Adams [1981, p. 245] in his essay ".... And how much for your grandmother?"   Nor do we address the emotional effects on families and associates of traffic victims, additionally ignoring their personal additional medical costs [Miller and Luchter 1988].

                 Estimates of monetary costs associated with different levels of injury are shown in Table 1-4.  The costs attributed to death and injury include estimates of costs associated with lost earnings, medical, legal, and property damage costs; although property damage costs increase with injury severity, they become a smaller fraction of the total cost of the crash.  The traffic crash costs for uninvolved vehicles reflect various fixed costs that are relatively unaffected by the number of crashes, such as the administrative costs of insurance and other activities concerned with safety.


Table 1-4 about here


                 The largest single economic cost of traffic crashes is property damage (29.6 billion dollars for the US in 1986).  This arises because of the
enormous number of property damage only crashes, even though the cost of each such crash is very small compared to that for an injury-producing crash.  The next highest monetary cost is fatalities (16.5 billion dollars for the US in 1986).  The divisions of cost amongst the various AIS levels depend on the definitions of these levels, and therefore do not have the same clear-cut meaning as the fatality or property damage only categories.  The total monetary cost of all non-fatal injury-producing crashes is similar to the cost for fatalities.

                 Fig. 1-5 shows an estimate of where the 74.2 billion dollar cost of traffic crashes in the US in 1986 went.  The second largest cost, insurance expenses, includes only costs spent to maintain and operate the insurance system, including marketing, administrating, adjusting, and so on.  A large proportion of all the costs are paid directly, or reimbursed, by insurance; such transfer payment processes do not, in idealized form, add to the cost.


Table 1-5 about here





                 The word "accident" is avoided in this book; Doege [1978], Langley [1988], and others have reasoned persuasively that the conceptual ambiguities encompassed by this term are sufficient to disqualify it for technical use, notwithstanding its near universal general use.  Accident conveys a sense that the losses incurred are due to fate and devoid of predictability; this book is devoted to examining the factors that influence the likelihood of occurrence and resulting harm from "crashes", the preferred term that we have been using.  Some crashes are purposeful acts for which the term "accident" would be quite
inappropriate even in popular use.  Philipps [1979] and Bollen and Philipps [1981] indicate that suicide may contribute to traffic fatalities.  Although the use of vehicles for homicide may be less frequent than in the movies, such use is certainly not zero.  The chosen word, crash, indicates in a simple factual way what is observed in nearly all cases, while accident seems to additionally suggest a general explanation of why it occurred.  There are very few traffic fatalities (the small fraction of drownings and fire-deaths not initiated by crashes) for which the term crash is inappropriate.

                 Collections of observed numbers are referred to as "data" and not "statistics".  Since this latter term is the name of a branch of mathematics dealing with hypothesis testing and confidence limits, using it to also mean "data" invites needless ambiguity. 

                 We follow common usage in indicating ages; age 20 means people with ages equal to or greater than 20 years, but less than 21 years.  Strictly speaking, age 20 means those who have been alive for, on average, 20.5 years; 40-year olds are not quite twice as old as 20-year olds, which might come as good news to some!

                 We use the term car, in preference to more cumbersome terms such as motor car, or passenger automobile.  Stationwagons are considered to be cars. Persons travelling in vehicles are referred to as occupants, and all occupants are either drivers or passengers.  We follow customary usage in referring to the device that controls the fuel to a vehicle's engine as the accelerator pedal, although this is an unfortunate designation.  The accelerator must be pressed to impart zero acceleration to a vehicle in motion, and its non-use generates an acceleration, albeit a negative one, to a vehicle in motion.  Indeed, it must be applied to decelerate a vehicle at a lower level of deceleration than the vehicle's coast-down deceleration.  The use of "throttle", rather than "accelerator", is technically incorrect for vehicles
not equipped with carburetors, which now constitute the majority of all vehicles.  The term decelerate is also enshrined in common usage, and will be used rather than the more technically coherent term negative acceleration, although the negative and positive values of variables are not usually given different names.

                 It is assumed in the text that the driver sits on left side of the vehicle and that traffic drives on the right, as in America and Europe.  Those from countries which drive on the left, including Japan, the UK, Ireland, Australia, and Hong Kong, should make the necessary transformation.

                 We use the terms "safety" and "risk" throughout the book without confining them any narrow technical definition, so that their meaning will be context dependent.  In accord with common usage, increased safety generally implies reductions in such quantities as the numbers of crashes, injuries or deaths.




                 Given the high level of uncertainty intrinsic in many traffic safety studies, it is important to avoid needless confusion and ambiguity from other sources.  Accordingly, when questions of units arise, I have been at some pains to be as explicit as possible.  The workings of nature are, of course, independent of units.  An intelligent Martian visitor would correctly predict when a dropped object would strike the ground, even though the numerical values used in his, her, or its calculation would have nothing in common with numerical values we would use, because the Martian would use Martian units.  However, the underlying equation would be the same as ours.  Although units never affect the answer, they do impact all numerical steps in calculations, and mistakes will lead to incorrect results.

                 The core of science is quantification, which requires measuring the values of specific quantities, or variables.  In traffic safety such concepts as fatalities per unit distance of travel should, to the extent that is practicable, be conceived of as variables defined without regard to units of measurement, rather than thought of as, say, fatalities per hundred million miles of travel.  The quantitative statement that fatalities per unit distance of travel tends to decline by about 5% per year is independent of the units in which the variable is measured.  Different units may be used in different circumstances, but the variable remains the same variable.  Thinking about variables without regard to the units in which they are measured is universal in science, and common in general usage.  For example, one asks for a person's height and age, which are appropriate variable names; one does not ask for their inchage and yearage.  The units are a crucial component of the answer, but should not appear in the question.  Sometimes it is impractical to avoid the inappropriate use of units in table column headings or in names of quantities, such as fatalities per year; here the unit of time is so universal in this application that little inelegance results.

                 Another reason why throughout the book I am particularly explicit about units is the hope that by doing so I might help encourage a more unified and rational practice [Evans 1978].  Such optimism probably merits the same dismissal as Dr. Samuel Johnson's description of a second marriage as "the triumph of hope over experience."  In presenting material original to this book I have nearly always used the SI system, the internationally agreed upon metric system of units which is universally accepted, if not always correctly used, throughout the world outside the US and the UK.  (Their contiguous majority-English-speaking neighbors, Canada and Ireland, have embraced the SI system).  Even in the US, the SI system has been adopted in some industries,
such as soft drinks, photographic, pharmaceutical, and automobile manufacturing.

                 I have advocated [Evans 1987] that the SI system should be used exclusively in all technical work, a practice to which I have adhered in my own research.  However, I have departed from exclusive SI use in this book because work performed and described in one set of units may not readily translate into another.  If an instruction was given to drive at about 30 mph (miles per hour), then that was the instruction.  It was not to drive at about 50 km/h, and it was certainly not to drive at about 48 km/h, because the concept of about 48 km/h (let alone 48.28 km/h) does not exist in the context of humans attempting to produce vehicle speeds.  So, when describing studies reporting material in customary US/English units that do not convert readily, I quote as in the original work, without adding any distracting, and generally unneeded, conversions in parenthesis.  Hopefully, the reader who wants the values in the other units system will have little difficulty performing the conversions, which rarely require knowing more than that one mile is approximately 1.6 km (in fact, one mile is exactly 1.609 344 km, because US customary units are now defined as multiples of SI standard units).  Similarly, Y fatalities per 100 million miles is equivalent to 6.213 71 times Y fatalities per billion km (one billion = one thousand million), and Z fatalities per billion km is equivalent to 0.160 933 4 times Z fatalities per hundred million miles.

                 In writing numbers with more than four digits, as in the last two sentences, I follow the SI practice of inserting a space between each group of three, as in 1 000 000 for a million; for four digits the space is optional, as in 1 000 or 1000.  The customary US/English use of the comma is avoided, because the same symbol is used by others to denote the decimal point.




                 The position of a scientist trying to understand traffic safety has more in common with that of an astronomer than with that of a more terrestrially- oriented physical or biological scientist.  The traffic safety scientist must try to devise ways to extract information from a system that is to a large extent given.  This is done mainly using data collected by public authorities for purposes other than addressing the specific question the scientist has in mind.  The luxury of varying input variables and observing what happens, and then repeating until reliability is established is not available.  Some research relating to traffic safety is done in laboratories, and on test tracks and public roads using volunteer subjects and instrumented vehicles.  This provides more experimenter control, but a question arises regarding how the results relate to normal driving.  Studies have also been conducted in which the behavior of drivers in actual traffic has been observed.  Studies using a variety of experimental and observational methods will be described throughout the book.  Although such studies can illuminate road-user behavior, they cannot address the matter of most interest -- the crash.  While there were an estimated 20.6 million crashes [National Safety Council, p. 48] in the US in 1988, these occurred in 3200 billion km of travel, so that there was one crash per 150 000 km.  If one imagined photographically observing or instrumenting a 50 m section of "random" roadway, then one would expect about one out of every three million observed vehicles to crash, most likely into another vehicle.  At a typical flow of 10 000 vehicles per day, you would expect about one crash (typically involving no injury and only minor property damage) per year; the same calculation indicates one fatal crash per 400 years.  Given this, it is not surprising that most of what we know about crashes is based on crash data collected by public authorities.


The problem of exposure


                 Knowledge about the numbers of persons injured at some level is rarely sufficient to answer specific traffic safety questions without some measure of "exposure", or the numbers exposed to the risk of being injured.  The difficulties of estimating exposure in traffic safety research can be illustrated by a non-traffic example.  Although fewer people are killed by crocodile bites than by dog bites, one cannot conclude that it is safer to have a pet crocodile around the house than a pet dog.  Even after recognizing this, the way to proceed is not all that clear.  Fatalities per animal appears a better measure than a simple count of fatalities, yet this is also flawed.  Dogs, unlike crocodiles, tend to be close to people.  Even if one normalized for proximity, the problem remains that people, even without the benefit of carefully controlled studies, exercise more care near crocodiles.  So, all in all, it would be very difficult to answer the question "Is it safer to keep a pet crocodile or a pet dog?" based on comparing fatalities due to dog and crocodile bites.

                 Comparable difficulties surround some questions in traffic safety, such as the influence of occupant age and car size on fatality risk in a crash, and the effectiveness of safety belts in preventing fatalities.  The approaches used to address these problems are described in Chapters 2, 4, and 9.

                 There is no all-purpose definition of exposure [Evans 1984]; it always depends on the question being addressed.  If we want to know if more males or females are killed in traffic crashes in the US, the answer is simply the count of the number of deaths; the answer is unmistakably clear -- more males are killed.  We may want to know how the risk per capita depends on sex -- then again, using population data to normalize, or correct for exposure, we
find an equally clear difference, but one which does not address the risk of crashing for the same amount of travel.  To do this we compute the number of deaths per unit distance of travel, and find only a small difference depending on sex remains.  This provides a measure of the rate per unit distance of driving, but not per unit of driving under identical driving conditions.  As it is likely that males do more driving under more risky conditions (while intoxicated, at night, in bad weather, etc.), these additional factors would have to be incorporated into the measure of exposure. 

                 None of the above measures is in any basic sense more "correct" than any other.  Each validly measures something important; it is crucial to always understand clearly what is measured and what it means.  Crashes per year, or "accident liability", determines insurance premiums for which it is not relevant whether increased liability arises from increased driving or increased risk while driving; because of its ready availability in data sets, this same measure is used in many studies [Peck, McBride, and Coppin 1971].  If one is interested in how fatal traffic crashes impact population projections, the appropriate measure is the simple count of fatalities.  If the aim were to examine if one sex is more likely to crash under the same driving conditions, then all the discussed factors, and more, would have to be incorporated in the exposure measure, a task of such difficulty that the answer to this question remains unknown.

                 To help clarify thinking on this further, consider that it turned out that one sex did have a higher crash rate under identical driving conditions, but that it is suggested that this is due to faster driving under the same conditions, and that this should be incorporated into the measure of exposure.  Suppose that when this is done, a difference in fatality rate is now thought to be due to one sex being more vulnerable to death from the same impact, and that this also should be normalized.  It should be apparent that this process
must end in the rates being identical, and the vacuous conclusion that when you correct for everything that is different, there cannot be any differences! 

                 Because of the above considerations, it is inadvisable to think of exposure as some narrow concept; one should not say that any measure is corrected for exposure.  Throughout the book various measures and rates are used; if we are discussing, say, crashes per unit distance of travel, this will be stated explicitly, and all inferences will apply explicitly only to crashes per unit distance of travel.


Poisson distribution


                 Probability, statistics, and mathematics are kept to a minimum in this book.  However, there are a number of occasions in which we use the Poisson distribution.  This can be explained in an example in which we assume that drivers have some average crash rate, say x, per some unit of time.  If x were 0.1 crashes per year, this would mean that drivers have, on average, 1 crash per 10 years.  The underlying assumption for Poisson processes is that the observed risk of crashing is the result of a uniform risk of crashing at all times (a 0.1 probability of crashing per year, or equivalently a 1/120 probability of crashing each month, and so on).  If a group of drivers have the same probability of crashing each month, at the end of a year all will not have the same number of crashes because of randomness.  The Poisson distribution enables us to compute the probability, P(n), that a driver will have precisely n crashes as


                 P(n) = exp (-x)(x)n/n! , Eqn 1-1


where n! (factorial n) means 1 x 2 x 3...x n.  For more details see, for example, Haight [1967].  Rather than thinking of P(n) as referring to the probability that an individual driver will have n crashes, we can think of it as the fraction, or percent, of drivers from a population of identical drivers who will have n crashes.  Substituting x= 0.1 into Eqn 1-1 gives that at the end of one year 90.48% of drivers are crash free, 9.05% have one crash, 0.45% have two crashes, and 0.02% have more than two crashes.  If we encountered some driver with more than two crashes, this would strongly suggest that the driver is from a different, and more crash involved, population than the one with drivers whose average risk is 0.1 per year.  After 20 years, if everything remained the same, the average number of crashes would be 2.0, which, when substituted for x in Eqn 1-1 gives that 13.53% of drivers would be expected to be crash free, 27.07% to have one crash, 27.07% to have two, 18.04% to have three, 9.02% to have four, 3.61% to have five, and 1.66% to have more than five.  Note how the most likely values are close to the average of 2.0.  What is indicated is purely statistical variation -- we are assuming here that all the drivers are identical, so the drivers with zero crashes were lucky and those with more than two were not.

                 An illustrative actual distribution of data for 148 006 California drivers in 1963 with an average police-reported crash rate of 0.0626 crashes per year [from Peck, McBride, and Coppin 1971] is compared to the Poisson distribution below:


           Number of crashes        Observed      Poisson distribution

                  0                  94.135%            93.932%

                  1                   5.500              5.880

                  2                   0.341              0.184

                  3 or more           0.024              0.004


While there is broad agreement, the differences between observed and calculated distributions, which are well above what is expected by chance in so large a sample, reflect that some drivers do indeed have higher crash rates than others [Peck, McBride, and Coppin 1971].  The California rate for police-reported crashes has remained close to about 0.05 crashes per year [Gebers and Peck 1987].  In various examples we use a larger rate of 0.1 crashes per year, which is considered more reflective of other US states, as indicated in, for example, the data of Evans and Wasielewski [1982] for Michigan.  The police-reported crash rate is of course critically dependent on the threshold criterion for reporting, and on levels of police enforcement; it should not be interpreted to reflect safer driving in one jurisdiction compared to another.

                 Many of the results derived involve combinations of observed frequencies, such as numbers of driver fatalities, numbers of pedestrian fatalities, etc.  By assuming that these arise from Poisson processes we can estimate errors.  Suppose there is on average one crash per day, so that after n days we would expect n crashes.  However, a rate of one crash per day, on average, is not going to lead to exactly n crashes because of randomness, but to a distribution with an average value of n.  The standard deviation of this distribution is equal to n, and for n reasonably large (say, more than about 6), the distribution is close to the normal distribution, which has particularly convenient properties.  Thus, an observed n fatalities implies that the process generating them, if replicated many times, would produce
(n + n) fatalities, where the error is one standard error.  The fractional error is n/n = 1/n.  Applying this simple formula enables one to compute errors in quantities formed by combining observed quantities which may be assumed to arise from Poisson-like processes.


Statistical inference


                 We shall not often make reference to whether something is "statistically significant", a phrase of ubiquitous occurrence in the literature.  It is generally used to discriminate between the competing hypotheses that an observed difference is likely to have occurred by chance, or had a probability less than some specified low level (written p < 0.05, say) to have occurred by chance.  While answering such questions may sometimes be important in that grey area between knowing nothing about a subject, and the first glimmers of information, it is but a first step on the road of the scientific goal of quantification.  There is rarely any scientific, let alone practical, interest in knowing whether one variable affects another.  Basically, just about everything in the universe influences everything else to some extent, especially the variables investigated in most reported studies.  For sufficiently large samples, every effect, no matter how small or unimportant, becomes statistically significant.  On the other hand, for sufficiently small samples, no effect, no matter how large or important, will be found to be statistically significant.  Thus statistical significance measures are really more commentaries on the experiment than on the phenomenon being studied.

                 To illustrate, suppose studies investigated whether two alternative paints, B and C, covered more area than a presently-used paint A.  Assume results report no statistically significant difference between A and B, but that C covers more area than A, this difference being statistically
significant at p < 0.001.  Such results provide no guidance on which paint to select to minimize the cost of painting the same area.  If all three cost the same per can, the results presented might mislead a decision maker to choose C.  If B and C cost more per can than A, then the results do not invite any decisions, which is perhaps better than inviting an incorrect one.  If the results are presented in terms of interval estimates, for example that B covered (20 + 25)% more area than A, and C covered (4 + 1)% more area than A, then the likely most economical paint can be identified.  If all cost the same, B is expected to minimize cost, but with some uncertainty.  If both new paints cost 10% more than A, then the results indicate clearly that the statistically significantly better C is almost certainly the most costly choice, while B is still likely the least costly, with A still an option for the risk-averse.  Assuming that the errors are one standard error arising from an underlying normal distribution, one can compute that there is a 66% chance that paint B will cover a given area at less cost than paint A (compared to a 34% chance that paint A is the more economical choice).

                 While academic statisticians might consider the above comments and illustration trivial (a clear exposition is presented by Mood and Graybill [1963]), many papers in traffic safety publish levels of statistical significance as if they are of paramount importance.  The problem illustrated in the example has an analogue in traffic safety literature, in which it is often implied that the finding that some intervention has a statistically significant effect is sufficient reason to favor it over an equally costly intervention whose effect has not been shown to be statistically significant.  The goal in this book will be to express estimates quantitatively with associated errors which convey immediately the magnitude and reliability of estimates.  I follow the common practice in science of quoting plus or minus one standard error, as in (X + DX); the approximate interpretation is that the
true value of X has a 68% chance of being within the indicated range, a 16% chance of being lower than X - DX and a 16% chance of being higher than X + DX.  In some cases the indicated error will include contributions from other than randomness in data, in analogue with experimental errors in the physical sciences.  It is simply not true that collecting more and more data in the same way will eventually provide a numerical value of some property of nature to whatever precision is desired.  In much literature 95% confidence intervals, which correspond to 1.96 standard errors, are given.  Provided it is clear which is used, the choice is arbitrary.  The computation of confidence intervals and of whether something is statistically significantly different from zero (or some other value) are essentially identical, but as discussed above, presenting an interval estimate is nearly always more illuminating.




                 Because the goal of quantification with specified error limits is not always attainable, it is helpful to distinguish three levels of knowledge:


                 1.                 Not based on observational data.


                 2.                 Hinted at by observational data.


                 3.                 Quantified by observational data.


                 It might seem surprising that the first level should appear at all in any effort focused on technical understanding.  Yet there are many cases in traffic safety, and even more in other aspects of life, in which we have
confident knowledge not based on scientific investigation.  One crucial example in traffic safety is advising pedestrians to look both ways before crossing the road.  There are no observational data showing that it is safer to look than not to look, nor is it likely that the question will ever be addressed experimentally.  Even in the absence of a shred of empirical verification, I nonetheless look both ways myself, and consider it good public policy to vigorously encourage everyone to do likewise.  Such a conclusion is based on reason and logic alone, and most people agree that it would be foolish to suspend judgment until a study satisfying strict standards of rigor is published in the scientific literature.  There are other important traffic safety problems where reason is our only guide.  When this is all that is available, there is nothing shameful about using it, provided that the basis for the belief is stated clearly.  A major problem is of course that what is reasonable to one might not be reasonable to others.  Claims not supported by firm evidence are naturally less satisfactory, other factors being equal, than those supported by objective data.

                 The second level occurs when there are data, but for various reasons the data do not support clear-cut quantitative findings.  The problem is generally that using the data to make inferences requires assumptions of such uncertainty that more than one interpretation is possible.  Another problem may be that the data are so few that they do not lead to definitive conclusions.

                 The firmest knowledge flows from the third level, the one to which we always aspire, and in many cases successfully.  The goal is captured in the often quoted words of Lord Kelvin, for whom the absolute temperature unit, degrees K, one of the seven basic units in the SI system, is named:

                      I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot
express it in numbers, your knowledge is a meagre and unsatisfactory kind.  It may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the stage of science, whatever the matter may be.




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Table 1-1.               Fatality rates for various countries based on data in Hutchinson [1987], Trinca et al. [1988], National Highway Traffic Safety Administration [1989], and International Road Federation [1984].


               Vehicles per   Deaths per     Deaths per    Fatalities     Data

Country         1000 people    1000 veh.   million people   per year      year


United States                  766                 0.25                  192             47 093              1988

Canada      561                 0.28                  158              4 120              1984

Australia     540                 0.34                  186              2 821              1984

Japan         403                 0.26                  103             12 456              1985

Netherlands                  355                 0.32                  113              1 625              1984

United Kingdom    322                 0.32                  103              5 788              1984

Greece       176                 1.20                  211              2 091              1984

Israel          147                 0.74                  109                  436              1981

South Africa                  123                   2.5                  305              9 621              1984

Chile            74                   1.8                  133              1 552              1983

Colombia     35                   2.6                    89              2 383              1981

Turkey         27                   4.4                  118              5 677              1984

Egypt           19                   6.0                  114              5 092              1982

Thailand       17                   5.0                    84              4 315              1985

Kenya          12                 11.3                  134              2 228              1980

Nigeria           7                 14.5                  107              9 150              1980

South Korea  5                   5.2                  171              6 834              1983

India              4                 10.9                    42             30 471              1983

Ethiopia          1                    17                    25              1 016              1983

Liberia           1                    36                    39                    97              1981

Table 1-2. The Abbreviated Injury Scale and probability of fatality reported in the study of Malliaris, Hitchcock, and Hedlund [1982].



AIS                         Injury                            Fraction of those

Level                     description                         injured who died



                      0          No injury                   --


                      1 Minor (may not require professional treatment) 0.0%


                      2        Moderate (nearly always require professional treatment, but

                                     are not ordinarily life-threatening or permanently disabling) 0.1%


                      3            Serious (potential for major hospitalization and

                                 long-term disability, but not normally life-threatening)              0.8%


                      4      Severe (life threatening and often permanently disabling,

                           but survival is probable) 7.9%


                      5 Critical (usually require intensive medical care;

                                    survival uncertain)            58.4%


                      6        Maximum (untreatable; virtually unsurvivable)             100%

Table 1-3.               Estimates of the number of people injured at different maximum AIS levels who did not die, and fatalities, for the US in 1986.  Data from National Highway Traffic Safety Administration [1987].



Maximum AIS                 Number            Percent



                      1        2 895 000               84.7


                      2           370 200               10.8


                      3           127 400                3.7


                      4             15 500                0.5


                      5               9 500                0.3


Total injured survivors 3 417 600       100.0


Fatalities      46 056


Table 1-4.               Estimates of costs of US motor-vehicle crashes in 1986 according to the maximum level of injury in the crash.  Data from National Highway Traffic Safety Administration [1987].



   Maximum AIS      $ (billions)         Percent



   1             9.39   12.7


   2             2.47   3.3


   3             1.88   2.5


   4             1.01   1.4


   5             2.71   3.7



Fatalities  16.50   22.2



Property damage   29.59   39.9

only (vehicles)



Uninvolved    10.64    14.3




Total             74.20 100.00

Table 1-5.               Estimates of where the total 74.2 billion dollars in Table 1-4 went.  Data from National Highway Traffic Safety Administration [1987].



Cost category             $ (billions)               Percent


Property losses                       27.37              36.9

Insurance expenses 20.86              28.1

Productivity losses      16.38              22.1

Legal and court costs        4.32                 5.8

Medical costs  4.12          5.6

Emergency costs         0.70                 0.9

Other       0.45                 0.6


    Totals  74.20             100.0