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3 Overview of traffic fatalities
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The first automobile propelled by an internal combustion engine is generally considered to be a three-wheeled vehicle introduced in 1886 by Germany's Karl Benz. Vehicle development thereafter proceeded rapidly in Europe and in the US. A revolutionary development occurred in 1913 near Detroit, Michigan, when Henry Ford introduced the moving assembly line to mass produce the Ford Model T. The assembly line so reduced production costs that vehicles could be offered at prices that a substantial portion of the US public could afford, leading to rapid growth in vehicle ownership. As the number of vehicles increased, so did the number of crashes and the number of fatalities.
The first known fatal traffic crash killed a 44-year-old female pedestrian on 17 August 1896 in London. The first fatal crash to be well documented and photographed occurred on 25 February in 1899 in Harrow, near London. A detailed account of it appears in the 4 March 1899 issue of the The Autocar, a British weekly started in 1895 and still being published. Six men were traveling in the vehicle shown in Fig. 3-1 when the driver applied maximum braking as the vehicle gained speed on a down hill. This caused the tires to separate from the wheels, with subsequent wheel failure. The vehicle dropped to the ground, coming to an abrupt stop. In accord with well-known physical laws, all six occupants continued to move forward until stopped when their bodies struck the ground or other objects in the roadway environment.
The driver died instantly from head injuries, and one passenger died after spending more than three days unconscious in the hospital. The inquest into the two deaths focused on factors remarkably similar to those that would arise today. Many questions were asked about driver alcohol consumption prior to the crash (no more than modest quantities were consumed, and well prior to the crash). Witnesses attested to the skill of the driver, one stating "he is a splendid driver." However, based on testimony by many witnesses, the coroner advised the jury, "the car appeared to be going at too rapid a pace to be safe, either for the occupants themselves or the public." The quality of the tires and the spokes of the wheel were criticized as contributory factors to the deaths.
In the investigation of this early crash, important themes at the core of traffic safety were already being recognized, including:
· Tension between technology and how it is used
· Tension between driver skill and how it is used
Figure 3-1. The first well documented fatal crash
Long term trends
Figure 3-2 illustrates the rapid growth in fatalities as motorization increased in the US. The general pattern applies to other countries that began to motorize later than the US, and seems likely to occur in the future in countries now in the early stages of motorization. As US vehicle ownership increased rapidly, so did traffic deaths, peaking at 54,589 in 1972, and declining later to a fairly stable rate of just over 40,000 per year.
Annual traffic fatalities are increasing rapidly in China in the same way as happened in the US in the 1920s. There is no way to reliably estimate what the maximum number of fatalities per year will be in China, or when that maximum will occur. However, current trends indicate ongoing increases. Other countries in the midst of rapid motorization are experiencing corresponding increases in traffic deaths.
Deaths for the same distance of travel (distance rate)
The number of traffic deaths per year shows little in the way of an interpretable pattern. However, if we instead examine the number of traffic deaths in the US for the same distance of vehicle travel (the distance rate), the clear trend in Fig. 3-3 emerges. A straight line on the log-linear scale corresponds to a constant percent change each year. Ever since 1921, when data on the total distance traveled by all vehicles were first collected, the distance rate has trended downwards at an average decrease of about 3.5% per year.
Figure 3-4 shows the percent change in the distance rate in a given year compared to the previous year (that is, the percent difference between each of the 82 pairs of consecutive points plotted in Fig. 3-3). Of the 81 resulting differences, 64 are negative, indicating a reduction in the rate from that of the previous year, with an average reduction over all 81 values of 3.5% per year. There is no obvious trend in the data in Fig. 3-4, so that if such a trend-free pattern persists, the number of fatalities for the same distance of travel will continue to decline at about 3.5% per year.
The 2002 rate of 9.4 US traffic deaths per billion km of travel is 94% below the 1921 rate of 150. If the 1921 rate had applied in 2002, the number of US traffic fatalities in 2002 would have exceeded half a million. The downward trend in the distance rate is also observed in other countries. , (p 155)
The variable that is the basis of Figs 3-3 and 3-4 is available only after a nation establishes a procedure to estimate the distance traveled by all of its vehicles. Even when available, estimates of distance of travel differ widely in reliability from country to country. The distance traveled by all US vehicles is estimated by summing estimates obtained in different ways from each of the states. While this process may provide a fairly accurate measure of year-to-year percent changes, the value (estimated at 4.60 billion km for 2002) is of uncertain absolute accuracy. The best estimates are for Great Britain, based on observations at 50 sites supported by the Department of Transport.
Deaths per registered vehicle (the vehicle rate)
The registration, and thereby counting, of vehicles is routinely performed by nearly all jurisdictions for taxation purposes, and is considered fairly reliable even from the earliest days of motorization. Figure 3-5 compares the vehicle and distance rates for the US. Fatalities per vehicle have been declining at an average rate of 3.3% per year since the early 1920s, compared to 3.5% for fatalities for the same distance of travel.
If the average distance traveled per vehicle remained constant from one year to the next, then the two plots in Fig. 3-5 would be identical (apart from a scaling factor). They differ to the extent that they do because the average distance traveled per year per vehicle has been increasing since the early days of motorization (Fig. 4-13, p. 91).
Figure 3-6 shows that not only does the vehicle rate vary by large amounts from country to country, but it also changes at different rates. The fatality rate has been declining in China at 10 percent per year, or halving in 7 years. The US decline of 3.3% per year corresponds to halving in 21 years. One might conclude that the explanation is simply that it is easier to achieve a high rate decline when the absolute value is higher. However, this is not the complete explanation, as the data for Sweden show. Even after achieving a lower absolute value than that for the US, the Swedish rate continued to decline faster than the US rate. We compare changes in rates in different countries in detail
in Chapter 15.
Figure 3-6. Traffic fatalities per thousand registered vehicles for the US, China, and Sweden.
Fatality rates versus degree of motorization. The US vehicle-rate values in Fig. 3-6 are shown again in Fig. 3-7, but plotted versus the number of vehicles per thousand population. The number of vehicles per capita can be regarded as a measure of degree of motorization, and may therefore offer insight into why fatality rates decline. In the US and GB, vehicle registrations per capita in any year have nearly always exceeded the rate in the previous year. Exceptions are related to periods of economic depression or war.
Extended time series as in Fig. 3-7 are not available for many countries. However, nearly all countries have available counts of fatalities, registered vehicles, and human population for some recent years. The number of deaths per thousand vehicles varies greatly between countries - from under 0.13 for Japan, Norway, Sweden, Great Britain, and the Netherlands to 65 for Mozambique, a factor of over 400 (Table 3-1 and Fig. 3-8). The data are
mainly from Refs and , but augmented by personal communications from colleagues in a number of countries. There is a general tendency for the
number of traffic fatalities per vehicle to be lower the higher the degree of motorization, although departures of 50% from the trend occur. The relationship between different countries observed at similar times (Fig. 3-8) has features in common with the relationship for the data for one country observed at different times (Fig. 3-7).
Note that the US, with over three motorized vehicles for every four people, is the most motorized country in the world but has far from the lowest fatality rate, a theme to which we return in Chapter 15.
Who is killed?
All the discussion above has focused on the total numbers killed per year, without regard to category of road user. Although essentially every traffic crash involves at least one driver, Table 3-2 (based on FARS 2001)4 shows that 38% of those killed are not drivers. (Rare crashes with no drivers occur, such as when a child alone in a vehicle sitting in a passenger seat, sets it in motion). The patterns in Table 3-2 change only moderately from year to year (compare with data for 19883(p 45)). However, this pattern should be interpreted to apply specifically to the US. The percent of fatalities that are drivers is much lower in earlier stages of motorization.
Male fatalities in the US in 2001 totaled 28,878, compared to 13,168 female fatalities, giving a male-to-female ratio of 2.19 to 1 The World Health Organization estimates that of 1,194,115 people killed in 2001 in traffic worldwide, 848,234 were male compared to 345,881 female, giving a male-to-female ratio of 2.34 to 1. The predominance of male fatalities in all types of injury deaths is a universal phenomenon, applying to essentially all types of non-disease deaths, including firearm and other homicides, suicide, drowning, and falling. The preponderance of male over female traffic fatalities persists at all ages (Fig. 3-9). This is not exclusively a driver phenomenon. Figure 3-10 shows that 60% of non-driver (passenger, pedestrian, etc.) road user fatalities in the US were male. (Relationships focusing on ages of drivers are given in Chapter 7).
Trends in pedestrian fatalities
The percent of all traffic fatalities that are pedestrians declines as nations motorize (Fig. 3-11). Note how similar the curves are between the US and Canada on the one hand, and GB and Ireland on the other, reflecting readily observable differences in urban landscape and walking patterns in everyday life. The percent of all fatalities that are pedestrians is much higher in less motorized countries (for example, 80% in Kenya).
Missing values in data sets
Of the 42,116 fatalities coded in FARS 2001, 25,840, or 61.35%, were coded as drivers. The reason why this percent is not identical to the 61.59% in Table 3-2 illustrates features common to all large traffic data sets - nearly all variables have missing (or unknown) values. There were 105 fatalities classified as vehicle occupants, but no information was available identifying whether they were drivers or passengers. Such lack of identification can arise in the case of vehicle fires, or if multiple occupants are ejected from vehicles, and so on. In Table 3-2 these unidentified occupants were distributed among drivers and passengers in the same proportion as identified drivers and passengers so that the distribution would reflect all those killed. This provides a better estimate of the number of driver fatalities than the alternative of assuming that none of the occupants of unknown type was a driver. Likewise, the total numbers of fatalities used to produce Fig. 3-9 is slightly less than the total in Table 3-2 because there are cases for which gender or age is not coded.
Missing values make it impossible to achieve identical totals from one tabulation to another. For variables like age, gender, and vehicle model year, this is no more than an irritating untidiness that has no material effect on results. However, it becomes a major hurdle for analyses using variables, such as alcohol level or belt use, which have a large fraction of missing values.
Drivers rates are usually best measure
In addressing how factors, especially vehicle factors, affect safety, driver rates rather than occupant rates should be used in most cases. Focusing on drivers avoids the confounding influence of occupancy. If vehicle A experienced 50% more occupant fatalities than vehicle B, this does not mean that an occupant of A is at greater risk than an occupant of B. If the average occupancy of A was 1.9, and that of B was 1.1, then the risk to each traveler in A is 13% lower than the risk to each traveler in B. The aim should usually be to determine driver risk. The assumption that passenger risk is proportional to driver risk is generally appropriate.
Number of vehicles
More drivers (and occupants) are killed in single-vehicle crashes than in two-vehicle crashes. Much coverage of traffic safety in the media presumes that the major risk is from two-vehicle crashes, with the characteristics of the other vehicle exercising a more central role in overall risk than is consistent with the pattern in Table 3-3.
Table 3-3. Distribution of number of drivers killed
according to the number of vehicles (any type) involved in
the crash. For single-vehicle crashes
the object struck, or event, associated with most harm is indicated.
Although under two percent of occupants killed are killed
in crashes involving more than 4 vehicles, fatal crashes
involving large numbers of vehicles do occur. In 2001, one
crash involving 56 vehicles killed three drivers and three
passengers. There were also fatal crashes involving 15, 16,
31, and 57 vehicles, each crash killing one driver (one
passenger was also killed in the 15-vehicle crash).
The most harmful event is indicated in Table 3-3 for single-vehicle crashes. If, say, a vehicle strikes a curb, and subsequently overturns leading to occupant ejection, then overturn is likely to be coded in FARS as the most harmful event for that vehicle. This variable is not listed in Table 3-3 for multiple-vehicle crashes because it is associated with vehicles, not crashes. Another variable, the first harmful event, is associated with the crash. The first harmful event might be two vehicles striking each other, leading to one of them subsequently overturning. For this vehicle the most harmful event might be the overturn, and for the other, striking another vehicle.
The most harmful event associated with 40% of the drivers killed in single-vehicle crashes is overturn (or rollover). Most of the other most harmful events involve striking objects that are part of the extended roadway environment. The most commonly struck object leading to death is a tree, reflecting the large number of trees adjacent to roadways. The all other category includes more than 30 additional most harmful events listed in FARS. For vehicles involved in multiple-vehicle crashes, striking another vehicle is the most harmful event for 90% of the fatalities.
Fraction of deaths due to rollover and ejection
Figure 3-12 shows the percent of fatalities in light trucks and cars in which overturn was the most harmful event. Given a driver death, rollover is much more likely to be the most harmful event for a driver of a light truck than for the driver of a car. While this likely reflects the typically higher center of gravity of light trucks compared to cars, care must always be exercised in interpreting ratios such as those in Fig. 3-12. Reductions in risk in non-rollover crashes lead to higher values for the percent of all deaths that are from rollover crashes even if the risk of a rollover fatality were to remain unchanged. The age and gender dependence shows how much the probability that a driver death is from rollover depends on driver as well as vehicle characteristics, being about twice as great for 20-year-old drivers as for 70-year-old drivers, and about twice as great for light trucks as for cars. Given a driver death, rollover is as likely to be involved when a 20-year-old is driving a car as when a 70-year-old is driving a light truck.
Alcohol is a large factor in overturn crashes, with 55% of car drivers and 53% of light-truck drivers killed in rollover crashes having blood alcohol concentration levels exceeding 0.8%, the legal limit in most US states. For non-rollovers the corresponding figures are 35% and 35%. All these values are based only on data for which the blood alcohol level was known.
Also, it should be kept in mind how total fatality risk depends on gender and age (Fig. 3-9), so the apparent lack of a major gender dependence in Fig. 3-12 means only that the absolute gender dependence is not materially different from that in Fig. 3-9. Far more male than female drivers are killed in rollover crashes, but given a driver death, the probability it is a rollover is not strongly gender dependent.
For the fatalities represented in Fig. 3-12, 17% of the male drivers of light trucks wore belts (24% of females did). For car drivers the rates were 22% for males and 26% for females. These rates are well below the approximately 50% rates for fatal crashes overall, which are in turn well below rates observed in traffic (p. 52 and Chapter 11).
Many occupants are ejected and killed in non-rollover crashes, so ejection and rollover are separate, although related, factors. Of those killed in rollover crashes, 54% were fully ejected from their vehicles; 59% of fatalities with total ejection resulted from rollover crashes. Fig. 3-13 shows the percent of all drivers killed who were totally ejected from their vehicles.
Figure 3-13. The percent of fatally injured drivers of light trucks and cars who were fully ejected from their vehicles. Belt use by the drivers of light trucks was 1.6% for males and 4.2% for females (for cars, 6.2% and 8.2%). FARS 2001.
Belt use by ejected drivers of light trucks was 1.6% for
males and 4.2% for females. For drivers of cars, it was 6.2%
for males and 8.2% for females. Overall, 96% of the drivers
included in Fig. 3-13 were not wearing belts. Properly worn
lap/shoulder belts make ejection exceedingly improbable.
Being ejected increases fatality risk three to four times
compared to remaining in the vehicle in a same severity
crash . The effectiveness of safety belts in reducing
fatality risk when rollover is the first crash event is 82%
Fatalities according to seating position
Figure 3-14 shows the percent of occupants killed according to the seat they occupied. The data are for car occupants only as the six seats represented do not apply to vehicles in general. Indeed, many of the cars included have only four seats, and those with six seats tend to be older model year cars. This figure reflects the mix of cars on the roads in 2001 by type and model year. All the occupants in Fig. 3-14 are fatalities - so the pattern does not represent occupancy patterns for vehicles on the road that do not crash, for which reliable data do not seem to be available.
The restrained category includes the use of lap and shoulder belt, shoulder belt only, lap belt only, child safety seat or unknown type of restraint. Those coded as not using the devices properly are excluded. Ninety percent of restrained drivers and right-front passengers were using the familiar integrated lap/shoulder belt combination that became standard for all 1974 and later model year cars. The restraint use variable is, in general, not all that reliable because many occupants who survive tell police officers that they were belted when they were not. However, as all occupants included in Fig. 3-14 are fatalities, the coded restraint use is considered reliable. The cells show the percent relative to the 18,216 occupants with known restraint use killed as occupants of cars - all 12 values sum to 100%.
Belt use by fatalities compared to observed belt rates
The data in Fig. 3-14 show 49% of driver and right-front passengers killed in cars were belted. The corresponding value for light trucks is 31%. For all fatalities in cars and light trucks, 43% were unbelted. In 2001, the observed belt use for drivers and passengers was 73%.
The difference between the wearing rates of those killed and those observed in traffic has been incorrectly attributed exclusively to the reduction in fatality risk produced by belts, and the reduction incorrectly used to estimate the effectiveness of safety belts in reducing fatality risk in crashes. The erroneous calculation proceeds along the following lines. If one had a population of identical drivers experiencing random crashes, with 73% using a protective device, then a finding of 43% of fatalities using the device would imply that the device reduced fatality risk by 1 - (27 43)/(73 57) = 72%. This is not even an approximate estimate of safety-belt effectiveness, but rather a value that is necessarily substantially higher than the true value because three effects bias the estimate upwards:
1. The belt wearing estimates are based on daytime observations. It is difficult to see if people are wearing their belts in the dark! Also, nighttime traffic is too sparse to collect observational data efficiently, yet this is when many fatal crashes occur (Fig. 3-19, p. 58). Nighttime wearing rates are expected to be lower than daytime rates.
2. Drivers who wear belts have lower crash rates than non-wearers, so some of the reduction in deaths attributed to the belt's effectiveness is due instead to the avoidance of crashes.
3. When belt wearers do crash, they have lower severity crashes than wearers.
The effects listed above are treated in detail in Chapter 11.
Relative fatality risk in different seats
The data in Fig. 3-14 do not address the relative risk of sitting in different seats, because the number of fatalities in a seat is determined mainly by the occupancy of that seat. Even if we could correct for different occupancy rates, other factors that affect fatality risk would still make it difficult to isolate the influence of the seating position. Cars with only one occupant are involved in crashes of different types and severity than those with more than one occupant. Occupants in different seats have different distributions by gender and age, factors that influence fatality risk in a crash (Chapter 6). We thus encounter another example of the problem of exposure referred to in Chapter 1.
The risk associated with different seating positions was addressed by selecting, from 1975-1985 FARS data, cars containing drivers and passengers in specified seats. In order to avoid confounding gender and age effects, only cases in which the driver and passenger were of the same gender, and had ages the same to within three years, were included. Also, occupants coded as using any restraint system, or who were less than 16 years old, were excluded from the analysis. Data restricted in this way were used to compute the ratio
R provides a largely assumption-free estimate of the difference in risk due to differences in the physical environment of the different seating positions. It is essentially free from the confounding effects that arise from occupant characteristics being correlated with different seating positions because all occupants for Eqn 3-1 were killed in crashes in which the other occupant was also present in the same car involved in the same crash, and both occupants were of the same gender and similar age.
Raw data and computed values of R are shown in Fig. 3-15. Because all values are relative to the driver, there is no computed relative risk for the driver, for whom, by definition, R = 1.
For cars containing a driver and a right-front passenger, there were 15,880 right-front passenger fatalities compared to 15,793 driver fatalities, for a right-front passenger relative fatality risk of R = 1.006 ± 0.011. The error is computed assuming that the fatalities arise from a Poisson process (p. 14). Thus, to high precision, no difference is found in fatality risk to drivers and right-front passengers. The center-front seat R = 0.78 ± 0.04 indicates that this position is associated with a (22 ± 4)% lower fatality risk than the outboard (driver or right-front passenger) front positions. The outboard-rear seats have a composite R = 0.739 ± 0.015. That is, for unrestrained occupants in outboard seating positions, rear seats are associated with a fatality risk (26.1 ± 1.5)% lower than for front seats. The safest seat of all is the center rear, where risk is (37 ± 3)% lower than in the driver seat. The earlier FARS data used in this study documented a fleet of larger cars with larger numbers of center seats than the 2001 data used for Fig. 3-14.12 Another study using more recent vehicles reports a 39% lower risk of fatality and 33% lower risk of injury in rear compared to front seats.
Seating position and direction of impact
FARS data contain a principal impact point variable, defined as the impact that is judged to have produced the greatest personal injury or property damage for a particular vehicle. The impact refers to the location on the vehicle sustaining damage, so that principal impact point at 12 o'clock means that the damage is in the center-front of the vehicle (Fig. 3-16). The region damaged does not necessarily indicate the direction of impact, because the center front could be damaged by, say, an oblique impact into a tree. A detailed post-crash investigation is necessary to determine the actual direction of impact. However, principal impact point 12 o'clock may be approximately interpreted as indicating, on average at least, head-on impacts.
Figure 3-16. Regions corresponding to impact clock points.
Figure 3-17 shows relative risk for the five passenger
seating positions versus principal impact point displayed in
the same bird's eye view of the vehicle traveling up the
page used in Figs 3-14 and 3-15. All values are relative to
a value one for drivers.
Focusing on the right-front passenger data (top-right circle) shows that when the impact is from the right, the right-front passenger is 2.74 times as likely to die as is the driver (as before, both occupants are of the same gender, and ages not different by more than three years). When the impact is from the left, the right-front passenger is 0.38 times as likely to die as the driver. This can be expressed equivalently by saying that the driver is 1/0.38 = 2.63 times as likely to die as is the right-front passenger. The essential symmetry (reflected in the closeness of the ratios 2.74 and 2.63) is to be expected on physical grounds, and increases confidence in the estimates. For principal impact point 12 o'clock the value of R for right-front passengers is R = 0.988 ± 0.019. Thus the similarity of fatality risk to drivers and right-front passengers applies also to the frontal case. Drivers and right-front passengers are at similar fatality risks from rear impacts (R = 1.00 ± 0.10).
The safety advantage of sitting in a rear seat compared to the corresponding front seat is larger for frontal crashes than for all crashes without regard to direction of impact (Fig. 3-16). The general pattern in Fig. 3-17 shows that occupants near the point of impact are at greater fatality risk than those far from the point of impact. Although rear occupants are at much greater risk than front occupants in rear impact crashes, such crashes account for less than 5% of all fatalities. The overall 26% lower fatality risk in rear than in front seats reflects that frontal crashes account for most fatalities. The lower risk in center seats is likely reflecting greater distance from the highest risk points of impact, as well as protective cushioning from other passengers.
A corresponding phenomenon occurs for motorcyclists, where it is found that fatality risk in the driver seat is (26 ± 2)% greater than that in the passenger seat; for frontal crashes the difference is (40% ± 6)%, again demonstrating the greater risk associated with being nearer the impact. Also, the motorcycle driver probably helps cushion the impact for the passenger. For non-frontal motorcycle crashes, drivers and passengers are at similar risk (R = 1.01 ± 0.04).
An additional finding in the car occupant risk study is that there are 38% more impacts of high severity from the right than from the left, a result possibly reflecting asymmetries resulting from driving on the right.12 It would be informative to know if countries that drive on the left experience more severe impacts from the left than from the right.
Variation throughout year and day
Fatalities occur at a far from uniform rate, varying systematically throughout the year, as shown in Fig. 3-18. In each of the 8 years plotted, the lowest number of fatalities was recorded for February, and by an amount larger than due to the fewer number of days in February. In all cases, the highest number of fatalities was recorded for July or August, a pattern similarly stable in 1983-1988 data.3(p 86) The pattern occurs largely because more difficult driving conditions in winter months reduce speeds (see also Chapter 5).
Fatalities follow the regular daily pattern shown in Fig. 3-19. The hour with the fewest number of fatalities is from 4 am to 5 am on the normal workdays Monday through Friday. The hour with the largest number of fatalities - about four times the lowest - is from 2 am to 3 am on Saturday and Sunday mornings, with weekend drinking playing a key role.
Someone does NOT get killed every 13 minutes
If the 42,116 US fatalities in 2001 are divided by the number of minutes in the year the result is an average rate of one per 12.5 minutes. This has led to many statements like, "There is a death caused by a motor vehicle crash every 13 minutes and a disabling injury every 14 seconds." This is far from being strictly correct. No fatal crash occurred between 3:30 am and 7:00 am on Tuesday 6 March 2001, or between 3:00 am and 6:30 am on Tuesday 27 November 2001. In both these cases, three and a half hours elapsed without anyone being killed. Note how these extreme values relate to the hourly and monthly dependencies in Figs 3-18 and 3-19. On the other hand, there are many occurrences of three, four, and five crashes being coded as occurring at the same time. Indeed, if crashes were a perfectly random Poisson process, more would be coded as occurring at the same time than separated by any other time interval.
The distribution of the times between crashes coded in FARS 2001 is plotted in Fig. 3-20. All crash times are converted to Eastern time, so a crash occurring at 1:00 pm California time is converted to 4:00 pm Eastern time, and is therefore correctly interpreted as occurring at the same time as a 4:00 pm crash in New York.
Figure 3-18. The distribution of the times between
consecutive fatal crashes in the US in 2001.
If the data were a perfect representation of reality, the largest number of occurrences listed above would be for time zero between crashes. As the smallest time unit in the data is one minute, a recording of no time difference between a pair of crashes implies that they occurred within a minute of each other. The probability that two crashes in fact occur at exactly the same time (or are separated by any specified time) is, of course, zero. Compelling statistical reasoning implies that the number of occurrences should decline systematically with increasing time since the previous crash. Thus fewer crashes are expected to occur 5 minutes after the previous crash than to occur 4 minutes after the previous crash. The prominent peak at 5 minutes results from the tendency to record times in multiples of 5 minutes, a tendency reinforced by traditional mechanical analogue devices which display time using circular dials marked in five-minute intervals. This tendency (it may disappear when the digital revolution is complete) also leads to the prominent cyclical pattern of peaks at multiples of five minutes evident in Fig. 3-20. If one assumes that about 20% of readings are rounded to the nearest five minutes, a smoother pattern results.
The straight line in Fig. 3-20 is the theoretical prediction based on assuming that crashes are a Poisson process with an average risk of crashing per minute, l = 0.07133 (calculated as 37,490 crashes divided by the number of minutes in 2001). This corresponds to fatal crashes occurring at an average rate of one every 14.02 minutes. The number of crashes reflects the exclusion of 372 for which the time of crash was not adequately coded (see p. 45 on missing values).
The open symbols in Fig. 3-20 represent averaging over five minutes rather than one minute as data become sparse due to few occurrences of crash-free periods of more than a couple of hours. The greater number of crash-free periods of more than an hour or so observed compared to the Poisson process prediction reflects major departures from the assumption of a constant rate of crashing, as is clearly apparent in the monthly and hourly variations in Fig. 3-18 and Fig. 3-19. However, even if the crashes were perfectly random, the relationship in Fig. 3-20 still predicts that in a year we should expect one period of 110 minutes to elapse with no crashes anywhere in the US.
Caution in interpreting averages
Much of the material in this and other chapters relates to averages. Averages do not apply to individuals. As shown for the case of the claim that someone gets killed every 13 minutes, averages can convey a misleading impression. Averages should be interpreted with a caution well captured in the quip: An average is like a bikini swimsuit - what it reveals is interesting, but what it conceals is crucial. It has also been remarked that the average human has approximately one breast and one testicle.
Summary and conclusions (see printed text)
References for Chapter 3 - Numbers in [ ] refer to superscript references in book that do not correctly show in this html version. To see how they appear in book see the pdf version of Chapter 1.
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