As mentioned already, three studies undertaken in the United States more than 25 years ago attempted to quantify the relationship between speed and crash involvement by ascertaining pre-crash speeds for individual vehicles (Solomon, 1964; Cirillo, 1968; Research Triangle Institute, 1970). In each study the essence of the method was to establish pre-crash travelling speeds for vehicles involved in crashes on designated stretches of road, and to compare these speeds with speed measurements for traffic not involved in crashes. The studies were conducted on rural roads, and all reported that the relationship was U-shaped, with crash risk being elevated at both relatively low and relatively high speeds. However, critical appraisal of these studies highlights the possibility that aspects of the way the studies were carried out inadvertently contributed to the apparent increase in risk at relatively low speeds. Thus it is arguable that these studies do not reliably quantify the relationship between speed and crash involvement at the lower end of the speed distribution. By contrast, the estimates of crash risk at the upper end of the speed distribution appear to be free of severe bias and may be taken as indicative, at least for that place and time.

The first and best known attempt to quantify the relationship between speed and crash involvement was that of Solomon (1964), undertaken in the United States in the late 1950s. The aim of Solomon's study was to relate crash involvement to various driver and vehicle factors, including speed. To this end, information from the accident records of nearly 10,000 drivers was compared with speed measurements and interview data from 290,000 drivers not involved in crashes.

Six hundred miles of main rural highway were included in the study, 35 sections in 11 states. The sections were reported to have been representative of main rural highways in the United States: three quarters were two-lane highways, with the remainder being four-lane divided highways; the average section length was 17 miles, although one section was 91 miles long; a daytime speed limit of 55 to 70 mph applied to 28 sections, 45 mph to two sections, and subjective limits (relying on drivers' judgements) to the remainder; on average, there were two entrances to businesses and four intersections per three mile distance. For each section, speed measurements were made using a concealed device at one location, chosen on the grounds that the speeds there were typical of the average for the entire section. Selected drivers were stopped and interviewed after their speeds were registered.

Accident data were obtained from the records of all reported crashes that had occurred on the 35 highway sections during a period of three to four years prior to June 30, 1958. For comparison purposes the 'travel speed' of crash-involved vehicles was required, this being the speed at which the vehicle was moving before the driver became aware of the impending collision. In the accident reports this speed was estimated by drivers, police, or witnesses; about 20 per cent of accident reports did not contain an estimate.

While the information collected enabled the speed distributions of accident-involved and non-involved drivers to be directly compared, the results were also presented in a manner that took into account the amount of travel at a particular speed, that is, in terms of involvements per hundred million vehicle-miles (100 mvm). To achieve these involvement rates, the vehicle-miles for each section were calculated as the product of the section length and the number of vehicles using the section over the period for which accident data were obtained, extrapolated from traffic volume counts. The vehicle-miles were then apportioned to speed categories according to the distribution of speeds obtained for the section; the figures for the different sections were combined to give total vehicle-miles for each speed band. Finally, the number of involvements with reported travel speed in a particular category was divided by the total vehicle-miles for that category.

Solomon found that the daytime involvement rates took the form of a U-shaped curve, being greatest for vehicles with speeds of 22 mph or less (43,238 per 100 mvm), decreasing to a low at about 65 mph (84 per 100 mvm), then increasing somewhat for speeds above this (reaching 139 per 100 mvm for speeds of at least 73 mph); the night-time rates took the same form but, except for that of the lowest speed category, were higher, especially for speeds in excess of 60 mph. These results are reproduced in Figure 2.1.

Solomon also expressed the involvement rates as a function of deviation from mean speed, to overcome irregularities due to the highway sections having a range of speed limits and mean speeds. Under this configuration the involvement rates were again U-shaped, being maximum for vehicles with speeds of more than 35 mph below the average, minimum for speeds of 5 to 10 mph above the average, and somewhat elevated for further deviations above the average. These results are depicted in Figure 2.2.

In addition, severity was taken into account through the presentation of separate involvement rates for crashes with different consequences. The involvement rates for crashes which resulted in injury followed a U-shaped curve that was more symmetric than the curve for all crashes, with a sharper increase evident in the rates at high speeds. This difference was even more prominent for the curve of involvement rates for crashes which resulted in a fatality. Table 2.1 illustrates the differences between the overall and the consequence-specific involvement rates, for day and night combined, and was compiled from data contained in Solomon's report.

Despite the apparent thoroughness of these results, there are several features of the method that are highly likely to have introduced substantial bias, particularly in relation to the estimates of crash risk at the lower end of the speed distribution. Both the numerator (number of crashes in a particular speed band) and the denominator (number of vehicle-miles travelled in that same speed band) may have been quite inaccurate for relatively low speeds.

Considering the number of low-speed crashes, this could be biased through making use of pre-crash speed estimates reported by the drivers involved. Solomon was aware of the obvious possibility that drivers might tend to under-estimate their speeds, but maintained it was inconsequential. However, in a discussion of Solomon's work, White and Nelson (1970) insisted that under-estimation of pre-crash speeds by this means was important, and through a type of sensitivity analysis showed that such a bias could contribute to a U-shaped pattern which did not, in fact, represent the true relationship.

In addition, it is possible that crashes at entrances to businesses or intersections accounted for many of the slow moving vehicles. Solomon acknowledged this possibility also, even suggesting that as many as half of the involvements in the 10 to 30 mph category were of this nature, but claimed that excluding such crashes would change the results very little. This claim is somewhat at odds with the explanation offered for the lower involvement rates on four-lane highways compared with two-lane highways, which was in terms of the superior control of access on four-lane highways. It is also clear from Solomon's work that the pattern of involvement rates varied with the type of crash, with rear-end collisions being much more likely to occur at low than at high speeds. Thus it is difficult to accept that removing low-speed crashes associated with particular manoeuvres (rather than low free speeds) would hardly affect the results.

Turning to the denominator, the potential for bias there exacerbates the likelihood that an artifactual U-shaped curve would emerge from the data. Recall that for each section of highway, crashes along the whole length were included in the study, but comparison speeds were measured at only one location at selected times. Although this location was chosen to be in some sense typical of the section, speeds there may not have represented the speed of traffic at crash locations, particularly when driveways or entrances to businesses were proximal to the latter. It is also difficult to comprehend how speeds measured at one location can be considered to be adequately representative of speeds on road sections up to 91 miles in length. Hence it is conceivable that the comparison speed distributions, which formed the basis for the denominator of the crash rates, systematically omitted low speeds that would have been found at crash locations.

A few years later Cirillo (1968) published results of a study similar to Solomon's, but undertaken on interstate highways rather than rural highways. Briefly, twenty state highway departments supplied the data which related to rural and urban sections of interstate highways, with a number of criteria applied to eliminate intersections and to make the sections somewhat homogeneous. Information was obtained on the proportion of traffic in different speed categories and the speeds of vehicles involved in crashes. Only crashes which occurred between 9 am and 4 pm and which were either rear-end, same-direction side-swipe or angle collisions were included. The time restriction was necessary for compatibility with the speed data collected for non-involved vehicles, while the type of collision was restricted as the focus was on the way differences in speeds of vehicles in the same traffic stream contributed to crashes.

Cirillo's results were in terms of deviation from mean speed and were similar to those of Solomon: the accident involvement rates followed a U-shaped curve, being highest for vehicles travelling about 32 mph below the mean speed, falling to a minimum for vehicles travelling around 12 mph above the mean speed, then rising moderately with further deviations from the mean. In addition, the relationship between involvement rates and proximity to an interchange (a connection between major roads) was examined. In urban areas, the involvement rates were highest for sections closest to interchanges and decreased as distance from the interchange increased. There was no obvious pattern for sections in rural areas. In general, the rates at urban interchanges were higher than those for rural interchanges. These results suggested a role for traffic volume as well as speed differences in the occurrence of crashes.

It follows from the similarity in procedures that Cirillo's study suffers from much the same potential for bias as Solomon's work. In addition, Cirillo's results only relate to specific crash types. The Insurance Institute for Highway Safety (1991) pointed out that single vehicle crashes account for more than half of the fatal crashes on interstate highways and such crashes are likely to be associated with high speeds, so the omission of this type of crash means that Cirillo's study almost certainly under-estimated the involvement rates for high speeds. Furthermore, again according to the Insurance Institute for Highway Safety, many of the very slow speeds were probably related to disabled vehicles leaving the road or at the side of the road, rather than to elected travelling speeds of vehicles in the traffic stream.

A third study which aimed to quantify the relationship between speed and the occurrence of a crash was reported by the Research Triangle Institute (1970). It was undertaken a decade after Solomon's study and, while the essential idea was the same, some aspects of the method were different. The study covered all state highways and county roads with a speed limit or a mean speed of at least 40 mph in Monroe County, Indiana, in all about 70 miles of road. A total of 294 crashes were included in the study.

Efforts were made to obtain pre-crash speeds that were more reliable than those abstracted from accident reports, including the use of accident investigation and of a computer-sensor system. For the first eight months of the study an accident investigation team determined the pre-crash speeds on the basis of physical evidence at the crash site and driver and witness reports. In the meantime, a computer-sensor system (basically a series of magnetic loop pairs connected to an on-line computer enabling collection of speeds and traffic volumes) was developed. The sensors were embedded at 16 points along the main highway, Indiana Highway 37. Using this system it was possible to identify accident-involved vehicles or the platoon in which they had been travelling and thereby obtain pre-crash speeds, so accident investigation was replaced by the computer-sensor system for the last few months of the study.

Further information on the operation and output of the computer-sensor system was provided by West and Dunn (1971). In order to test the reliability of the system, measures of pre-crash speed for a group of 36 crashes were obtained using both available methods. It was found that in a quarter of the cases the speed of the accident-involved vehicle or the platoon in which it had been travelling could be identified confidently from the computer output (a result which seemed to be regarded as an achievement rather than as a cause for misgivings about the quality of the data). Some information was retrievable for the remaining crashes, but it was not made clear how these less certain estimates were gained or treated.

The findings of the Research Triangle Institute for state highways were only presented in terms of accident involvement rates for categories of deviation from the mean speed, calculated in a similar manner to those of Solomon. However, in recognition of the distorting influence of vehicles executing turning manoeuvres, crashes in which such a manoeuvre occurred (44% of the total cases) were excluded from the analysis. Based on data for 154 vehicles, the pattern of involvement rates was a U-shaped curve, as shown in Table 2.2, but the elevated rates at low speeds were not nearly as pronounced as those of Solomon.

For a subset of the Research Triangle Institute data, West and Dunn elaborated on the exclusion of crashes which involved a turning vehicle: the involvement rate for vehicles with speeds of more than 15.5 mph below the mean speed was reduced by a factor of seven when such crashes were excluded, while the other rates changed only a little. This result and the high involvement rate for intersections were interpreted as evidence of the large potential for conflict when vehicles enter or exit a traffic stream and where traffic streams intersect. It was suggested that this increase in risk was largely inevitable, although the provision of special lanes for turning vehicles was one way the situation could be improved.

This research design was used again recently in a small study undertaken in Adelaide by Moore, Dolinis and Woodward (1995) which served as a pilot study for the present work. Briefly, speeds of 45 vehicles involved in severe crashes in the Adelaide metropolitan area were compared with speeds of other vehicles passing through the crash locations at the same time of day, day of week, and season. Travelling speeds of vehicles involved in crashes were determined using accident reconstruction techniques, and sensitivity analyses were conducted to examine effects of errors in these estimates of pre-crash speed. Overall, crash-involved vehicles were relatively more frequent than controls in the highest speed categories, as shown in Figure 2.3.

The relative risk of involvement in a severe crash was calculated for vehicles in 60 km/h zones. With 55-64 km/h used as the reference category, the risk of involvement in a severe crash appeared to be elevated for vehicles travelling in excess of 75 km/h, as shown in Table 2.3.

Interest in relating a driver's speed on some occasion to his or her accident history has been evident from at least the 1930s (Tilden, 1936). Early studies indicated that fast drivers, defined variously, had greater experience of (recorded) crash involvement than relatively slow drivers (DeSilva, 1940; Lefeve, 1956; Cleveland, 1959). However, this dichotomous classification of speed behaviour meant that the relationship between speed and crash risk was not depicted over a range of speeds.

From the early 1960s, the notion that an individual's manner of driving on one occasion would be linked to their past accident involvement was pursued in a series of studies using a device known as a drivometer. This mechanical device could be fitted to a car to record information such as the trip time, steering actions that changed the direction of the vehicle, accelerator and brake applications, and vehicle speed. At least two studies that searched for differences in drivometer variables between accident-free and accident-involved drivers found no difference in the case of speed (Greenshields, 1963; Johns and Bundy, 1974).

This vein of research was taken up again by Wilson and Greensmith (1983). These authors used the drivometer to record various aspects of driving behaviour of 100 volunteers. Males and females differed in their manner of driving, taking into account the number of miles driven per year (exposure). With regard to accident history, the overall suggestion from the data was that accident-involved drivers had higher speeds and moved more continually in traffic during the drivometer tests than other drivers. In particular, among males and females with moderate exposure to driving, mean preferred speed on a clear stretch of road was lower among those with no history of accidents than those who had been involved in accidents in the past. Among males with high exposure to driving, mean clear speed did not distinguish between those with and without prior accident-involvement, but the accident-free males appeared to adjust their speeds to changing conditions more than the accident-involved males. However, as this summary of results shows, there was no attempt to describe the full functional form of the relationship between speed and crash involvement.

A study which compared the crash involvement of slow, moderate and fast drivers was conducted by Munden (1967). It covered 31,000 vehicles travelling on rural main roads in the south-east of England during 1962. At each of ten locations, speeds and registration numbers were recorded in the evening peak flow of traffic, to try to identify regular travellers and gain repeated measurements of their speeds.

To indicate a driver's speed in relation to other traffic at the same time and location, the absolute speed measurement for each vehicle was converted to a speed ratio, calculated as the measured speed divided by the mean of the four preceding and the four following recorded speeds. When data for the ten sites were combined, these speed ratios were also standardised. In addition, adjustments were made for the likelihood of over-estimating the characteristic speed deviation of the slowest and fastest drivers. The repeated measurements of speed enabled the assumption that a driver has a characteristic relative speed to be examined, and there was a reasonable degree of correlation between pairs of relative speeds for the same vehicle from different locations.

Registration numbers were matched to those in about 14,000 accident records, where the accident occurred in 1961 or 1962 but not necessarily on the roads surveyed. This allowed the proportion of accident-involved drivers to be calculated for different categories of standardised speed ratio (SSR). The main result, for drivers whose speeds were recorded at least twice, was that the proportions took the form of a U-shaped curve: 10 per cent of drivers with SSR less than -1.0 were accident-involved, around 5 per cent of drivers with SSR between -1.0 and 0.59 were accident-involved, while almost 7 per cent of drivers with SSR of at least 0.6 were accident-involved. It should be noted that the U-shaped pattern did not emerge consistently in other groupings of the data, there was a large degree of variability in the proportions for even the middle SSR categories, and small numbers hampered much of the analysis. Munden interpreted these results with caution, recognising that speed per se may not have had a causal role in the observed relationship, but that other characteristics of drivers who chose to travel relatively fast or slowly might have been responsible for the elevated accident-involvement at these extremes.

Another study which related drivers' typical speeds and accident rates is that of Wasielewski (1984). The aim was to examine factors which predicted risky driving, where speed was taken as an indicator of risky driving. Speeds were recorded for vehicles using a two-lane road in Michigan. Vehicles were photographed and some 2,600 registration numbers were matched with state files. Repeated measurements of speed were obtained for about half of the sample; the correlations between pairs of speeds for the same vehicle were relatively weak. However, a positive correlation was found between the number of crashes a vehicle had been involved in during the preceding seven years and the mean speed of vehicles in each crash-frequency group.

A study was conducted in Australia by Fildes, Rumbold and Leening (1991) with the aim of examining relationships between speed behaviour and a large number of possible contributory factors, including driver, vehicle and trip characteristics, and driver attitudes. In addition, the relationship between speed behaviour and five year accident history of the driver was assessed.

Unobtrusive measurements of vehicle speeds were made on two urban arterial roads and on two rural undivided highways in Victoria during 1989 and 1990. It is noteworthy that an urban sample was obtained, since little work of this kind has been undertaken in an urban setting. More than 700 drivers were stopped and interviewed after their speeds were recorded; these drivers were asked whether they had been involved in a crash in the past five years and, if so, to give details of when and how severe the crash was. As noted earlier, a problem with this research design is that only drivers who have survived past crashes are able to be studied, and since high-speed crashes are least likely to be survivable, it is possible that involvement rates for high speeds may be systematically under-estimated.

Speed behaviour was found to be associated with many of the variables on which information was collected when considered separately. Multivariate analyses for the urban data suggested that the following factors were the most important indicators of a speeding driver: being aged less than 34 years and having a high accident history; reporting a safe travelling speed that was high; having a vehicle less than five years old; travelling on business and doing a large amount of such travel each week. However, only a third of the variance in speed behaviour was able to be explained.

For the urban sample a linear relationship between characteristic speed and crash involvement was found. Drivers with speeds above the 85th percentile were more likely to have been involved in a crash, than were drivers with speeds in the middle range, while drivers with speeds below the 15th percentile were less likely. In addition, fast drivers were more likely to have experienced multiple and more severe crashes than relatively slow drivers. Results for the rural sample were consistent with those of the urban sample.

Fildes, Rumbold and Leening (1991) contrasted their results with those of Solomon (1964), drawing attention to the fact that they found no evidence of elevated crash involvement for drivers who travelled slowly, rather the reverse, but noting that their sample size was relatively small and that few extreme speeds were recorded. It was also acknowledged that self-reports of crash involvement were probably subject to error, however, it was pointed out that another study had demonstrated self-reports to be more reliable than official records.

The results of Fildes, Rumbold and Leening (1991) are consistent with those of a study carried out in England at about the same time. West, et al. (1993) recruited 48 drivers, ostensibly to test an automated in-car route guidance system. Assessors recorded aspects of the subject's driving, including maximum and preferred speed, over a 50 mile test drive. A high preferred speed was found to be positively associated with self-reported involvement in at least one accident during the past three years. The models developed indicated that for each 1 km/h increase in preferred speed on the motorway, the odds of having had a crash in the past 3 years increased by a factor of between 1.27 and 1.55.

Studies which are not based on speeds of specific vehicles but rather relate some aggregate indicator of speed to crash frequency are much more common than either of the preceding study designs. This approach has the longest history of use to describe the role of speed in crash causation (although, as will be discussed, it is not well-suited to this task). For example, an article in the June 1931 issue of "The American City" with the title "Are traffic accidents caused by speed?" reported that a correlation between monthly average speed and number of crashes had been established from technical observations made on Rhode Island since 1924.

Studies based on group characteristics generally provide weaker evidence than studies based on individual data. They are subject to further sources of bias and confounding, making the results more open to interpretation, and there is a fundamental difficulty in attributing to individual events (a single crash) a characteristic that was assessed at the group level (mean speed or speed limit). As well as this inherent weakness, such studies have limited ability to provide a complete description of the relationship between speed and crash involvement because they are usually concerned with a selected part of the continuum of speeds. For example, when correlational studies are used to examine the change in accident frequency following a change in speed limit, the information obtained is restricted to a difference in crash risk under two speed scenarios. Furthermore, in this circumstance mean speed is not usually measured. It is presumed to have changed, but by an unknown amount, likely to have been much less than the difference in the two posted limits (Finch, et al., 1994). Thus it is very difficult to know precisely what the results of such correlational studies imply for the speed and crash involvement relationship.

In addition to evaluating changes in accident frequency following changes in speed limits, correlational designs are the basis for studies which model differences in accident rates across sites or states or countries (sometimes called cross-sectional studies). The common aim is to link variation in speed (limit) to variation in crash rate. In the first case this is done using (a minimum of) one site and information from different time points, whereas in the latter instance there are multiple sites but it is only necessary to have crash data from one time interval. (By extension, complex models can be used to consider multiple sites and time intervals.) All configurations suffer from similar problems with interpretation. In speed limit evaluation studies relating to certain sites, the site characteristics are fixed, but other factors which affect the crash rate may have varied (for example, traffic volume and season). In models built on data from different places, there may be systematic differences between site characteristics as well as differences in all of the other factors which affect the crash rate. To appreciate the magnitude of this problem, consider that Fridstrom, et al. (1995) showed that randomness and exposure accounted for 80 to 90 per cent of the observed variation in accident counts from 68 provinces in four Nordic countries. Against this backdrop, effects of speed limit or mean speed differences are likely to be hard to detect in the first place, as well as being difficult to indisputably separate from other factors. The capacity of a model to provide insights relevant to the real world is limited both by theoretical knowledge of influential factors and the data that can actually be collected. Most correlational studies take into account only a few potentially influential variables. This may be adequate when assessing whether, for example, a change in speed limit made any difference to the accident rate, but is not a sound basis for elucidating the relationship between speed and crash risk.

Hillman and Plowden (1986, cited in Finch, et al., 1994) identified at least two dozen evaluations of speed limits dating back to 1935. Almost all studies indicated that the imposition or lowering of a speed limit was accompanied by a reduction in accident frequency. Most of this work contributes little to a detailed description of the relationship between speed and crash risk, particularly where a speed limit was imposed without documentation of what speeds actually were to begin with. The benefits claimed in many of the studies reviewed by Hillman and Plowden are much larger than those suggested by recent experience, perhaps reflecting an overly simple approach to analysis (see Lloyd, 1990), or publication bias (Dickersin, 1990). During the past decade it has been increasingly recognised that quite sophisticated techniques are required to confidently identify changes in accidents associated with changes in speed limits. A good example is the work of Johansson (1996) which included a time series analysis using both Poisson and negative binomial distributions for accident frequency.

In one of the largest exercises of its type, Fieldwick and Brown (1987) modelled fatality counts from 21 countries with different urban and rural speed limits. Most of the variation in fatalities could be attributed to population size, although the fit of the model developed was improved by including speed limit variables. Predictions from the model were that a reduction in the urban limit from 60 km/h to 50 km/h, with the rural limit constant at 100 km/h, would lead to a 28 per cent reduction in the fatality rate (per million population). A reduction in the rural limit from 100 km/h to 90 km/h, with the urban limit constant at 60 km/h, was expected to produce an 11 per cent decrease in the fatality rate. A 10 km/h reduction in both the urban and rural limits, originally set at 60 km/h and 100 km/h, respectively, was predicted to result in a 36 per cent decline in the fatality rate.

Evaluations of speed limit changes were recently revisited by Finch, et al. (1994). These authors updated the work of Hillman and Plowden (1986, cited in Finch, et al., 1994) and undertook a meta-analysis to ascertain the overall expected effect of a change in speed limit. Only studies in which there was an initial speed limit were suitable for this analysis. Finch and colleagues did not state the number of studies that were included in their data synthesis, although they mentioned that the data set was sparse and dealt mainly with rural roads. Overall, the percentage change in accidents was estimated to be 1.0 to 2.5 times the change in speed limit (in mph). In other words, a 10 km/h reduction in (rural) speed limit was expected to confer a 6 to 16 per cent decrease in the number of fatal accidents.

In an Australian context, Sliogeris (1992) analysed a change of speed limits on Melbourne's rural and outer freeway network. On 1 June 1987, the speed limit on these roads was raised from 100 km/h to 110 km/h and in September 1989 the limit was lowered again to 100 km/h. Analysis of crash data showed an increase in injury accident rate per kilometre travelled of 24.6 per cent in the 'before 110' to 'during 110' period and a decrease of 19.3 per cent in the 'during 110' to 'after 110' period in comparison with a control group.

These overviews indicate that the relationship between speed and crash risk is positive, at least for that part of the spectrum of speeds considered, typically 80 to 100 km/h. However, they quantify the relationship fairly crudely and cannot clarify whether successive increments in speed (of 10 km/h, for example) are associated with a fixed or an escalating increase in risk.

A noteworthy exception is the work of Nilsson (1990) in which a number of evaluations of changes to speed limits in Sweden were amalgamated. The ratio of the fatality rates before and after a change in speed limits was found to be proportional to the fourth power of the ratio of the corresponding median speeds. The ratio of rates of casualty crashes before and after a change in speed limit was proportional to the third power of the median speed ratio. Most of this work related to roads outside built-up areas, and the limits concerned were high (90 to 110 km/h), which suggests some bounds on the extent to which these relationships may be generalised.

A substantial body of work has been undertaken in relation to recent increases in speed limits in the United States. An interest in effects of speed limits in that country has continued since the nationwide 55 mph maximum speed limit was introduced in 1974, in response to the Arab oil embargo rather than concern for safety. That year, however, the number of highway fatalities was 16 per cent less than the previous year, an unprecedented drop outside of wartime. The Transportation Research Board (1984) reviewed studies of the 55 mph limit and concluded that after factors such as reduced travel and improved medical services were taken into account, the new limit probably accounted for 5 to 10 per cent of the remarkable reduction in fatalities.

In 1987 the United States Congress voted to allow states to increase the limit on rural interstate highways to 65 mph, and subsequently, in November 1995, authorised states to set their own speed limits. The most recent increases in limits have not been in place long enough for sound evaluations to emerge (Graham, 1996), but the prior 65 mph limit was adopted by 40 states and effects were scrutinised in a number of studies. As summarised by Godwin (1992), many of these studies found that road traffic fatalities tended to be higher following the increase in the maximum limit, but very few could demonstrate a statistically significant change, not surprising in view of the relative rarity of fatal crashes and hence the small sample sizes available in single states. Congress also exempted the 65 mph roads from speed monitoring, which is another reason why these studies provide uncertain information as to the speed and crash involvement relationship.

Through the Transportation Research Board, Godwin (1992) obtained some speed data from 18 states that had moved to the 65 mph limit, as well as information on fatalities and comparable data from 7 states that did not change their maximum limit. These data suggested that average speeds had increased by 3 mph under the 65 mph limit (less than the 10 mph difference in the maximum limit, as lack of compliance with the 55 mph limit was widespread). Also, on roads to which the increased limit applied, fatalities had increased by 35 per cent, against a background trend of a 9 per cent increase on rural interstate highways where the limit remained at 55 mph. An increase in fatalities was also evident when the rate for rural interstate highways was compared with that for other roads within the same states. Godwin also discussed four studies that had considered longer-term national trends: despite different methodologies, all found evidence of a higher fatality rate on rural interstate highways after the 65 mph limit was introduced.

There is a dissenting view, however. Lave and Elias (1994) argued that the 65 mph limit saved lives when the change was evaluated at a system level. In their model, Lave and Elias considered not the fatality rate for particular roads or collections of roads, but fatalities rates for states as a whole. They argued that the increased speed limit might confer a safety benefit through encouraging more traffic to use the interstate highways which were of superior design and therefore safer than other roads, and through allowing police resources to be directed elsewhere resulting in improved safety on other roads. This is not the place for a full discussion of the potential pitfalls of the approach of Lave and Elias, suffice to say that as the outcome variable used (in this case, statewide fatality rate) becomes more distant from the event of interest (changes to speed limit on only a few roads), it is increasingly difficult to interpret results of a model which inevitably over-simplifies a complex situation. The point to be made in the context of the current review is that Lave and Elias do not argue that the 65 mph limit roads themselves became safer than they were when the limit was 55 mph.

Another theme in the literature, addressed sporadically by correlational studies, is that variation in traffic speed is also a determinant of crash risk. This idea appears to be in a large part derived from the work of Solomon (1964), particularly the results in terms of deviation from mean speed which also had the U-shaped form. As discussed earlier, there are a number of reasons why Solomon's estimates of the crash risk associated with low speeds (deviations below the mean) are unreliable. Nonetheless, the speed variation idea gained weight, more through successive restatements than through good research, it would seem.

Conceptually it is possible to separate speed variance from mean speed, but practical demonstrations of separate effects are difficult. This is because, in reality, both factors are strongly tied to characteristics of the road which are fundamental determinants of the local accident rate. (In theory, the role of speed variation would best be addressed by examining accident rates for a set of roads that were matched for geometry and other characteristics, but which had a different degree of speed variation for the same mean speed. While this is unlikely to be feasible, the point is that any less rigorous approach will entail major problems with interpretation of the underlying cause of differences in the accident rate. This point seems not to have been fully appreciated by some researchers.)

In early research reflecting a version of the speed variation idea, Taylor (1965) sought criteria for the allocation of speed zones, and proposed that non-normal variation in speed between drivers at a particular location was due to some drivers being unable to evaluate the situation properly. Taylor argued that the speed distribution itself provided information as to where speed zones would be useful. He then examined changes in accident rates upon the introduction of 51 speed zones on two-lane rural highways in Ohio during 1958 to 1962. Taylor found that the greatest reductions in accident rates occurred where the speed distribution changed from non-normal to normal, as indicated by skewness, after the introduction of a speed zone. However, not all non-normal distributions became normal upon the introduction of a speed zone. On the whole, this study raises more questions than it answers. It was not stated whether the skewness that characterised non-normal distributions was positive or negative, nor how mean speeds were affected. In the absence of such information, the results cannot be fully interpreted and it remains possible that speed dispersion was unduly credited with influence.

A decade later, Krzeminski (1976) re-examined the proposal that at locations where a relatively large number of crashes had occurred the speed distribution was more likely to be skewed than at sites with few crashes. This proposal was supported by data for 12 sites on low-volume rural highways in Tippecanoe County, Indiana. Although it was reasoned that skewness of the speed distribution indicated that drivers experienced perceptual difficulties at that location, no demonstration of underlying causes was attempted.

A study to examine factors which influence speed variation and to quantify the relationship between speed variation and accident rates was conducted by Garber and Gadirau (1988). The underlying hypothesis was that the difference between design and posted speeds was the major factor that influenced speed variation and thereby accident rates. Data for the study were obtained from 36 sections of interstate highway in Virginia. Seven types of interstate highway were covered and each section included was considered to represent its type and had a posted speed limit of 55 mph. The design speeds for the sections varied from 40 mph to 70 mph, where this speed was (presumably judged to be) the maximum safe speed under favourable conditions, and was used as a summary of the geometric characteristics of the section.

The results of Garber and Gadirau indicated that the different types of highways had different average speeds and variations in speed, despite having the same posted speed limit. Average speed was found to increase with increasing design speed, that is, with better road geometry, while speed variance decreased with increasing average speed. In addition, it was reported that speed variance was a U-shaped function of the difference between design and posted speeds, being minimum when this difference was 6 to 12 mph.

A negative correlation between accident rate and average speed was reported. Garber and Gadirau recognised that this was unlikely to be a causal relationship and was most probably due to the fact that the roads with the highest average speeds were better roads. It was also found that accident rates increased as speed variance increased but, by contrast, this relationship was implicitly regarded as causal. It was concluded that since accident rates increased with increasing speed variance, and since speed variance was minimum when the posted speed limit was some 5 to 10 mph below the design speed, changing posted speed limits to within this band would minimise accident rates.

There are a number of grounds on which the appropriateness of the conclusions drawn by Garber and Gadirau are questionable. To begin with, the measure of speed variation appears to be extremely dependent on the number of very slow vehicles at a site; for example, at one location the slowest 2 per cent of vehicles accounted for 47 per cent of speed variance. Thus speed variance would seem to indicate the relative frequency of very slow vehicles at a site. Furthermore, as far as it is possible to judge (visually and by partial re-analysis), the data which supposedly showed a U-shaped relationship between speed variance and the difference between design and posted speeds could equally well support a linear relationship. A linear form would be readily interpretable: given that all speed limits were 55 mph, this form could simply mean that highways with low design speeds have more slow moving vehicles since they do not have good provision for passing slow vehicles and slow platoons develop, whereas these are less common on highways with high design speeds. In any case, there was no indication of how much of the fluctuation in speed variance was accounted for by design speed, and within the data there is a suggestion that other factors over-ride this influence, in that for rural and urban interstate highways with similar design speeds, the measures of speed variation are markedly different. Thus it is possible that the results relating to speed variance merely confirm what was deduced from the relationship between average speed and accident rates, that better roads have lower accident rates, not directly through speed variation but through features which produce this, such as ease of overtaking and special provision for turning vehicles.

The Transportation Research Board (1984) of the United States discussed the issue of mean speed versus speed variance in its review of the effects of the nationwide 55 mph speed limit. The improvements in safety associated with that speed limit were considered to have resulted from both slower speeds and a more uniform pace of travel. It was suggested that the persistence of reduced fatality rates over the decade following the implementation of the 55 mph limit, despite some increases in mean speeds, may have been due in part to the maintenance of reduced variation in speeds. However, this was largely conjecture, as mean speeds increased on urban interstates, by a few miles per hour only, but were stable on other types of highway. Also, precise comparisons of speed variation over time were not possible as there were major changes to the way the measurements were obtained. Furthermore, significant changes to other factors influencing fatality rates, such as vehicle crashworthiness, occurred over the same period. It was concluded that it was not clear to what extent speed variation and mean speed independently influenced crash involvement and it was uncertain how much weight should be given to each factor.

While this conclusion would seem reasonable, an alternative view has been put forward by Lave (1985), who claimed to have separated the influences of mean speed and speed variation on fatality rates and to have found no effect related to mean speed alone. For six types of highway, multiple regression analyses were performed on data from up to 50 states. Data points included the average speed for that type of highway, the number of fatalities per 100 million vehicle miles, and the 85th percentile speed. Except possibly for rural interstates, the model which was used to demonstrate the superior influence of speed variation (in this case, the difference between the mean speed and the 85th percentile speed) does not actually fit the data very well. Furthermore, as pointed out by Godwin and Kulash (1988), the data for each state are extremely aggregated and, rather than depicting speeds on single roads at certain times, relate to many roads and many times, so that the meaning of the variance measure is uncertain. Lastly, judging the relative causal influence of a factor from its impact within a regression model is a very dubious practice (Neter, et al., 1990). A model may prefer one variable over another very closely related variable (speed variance over mean speed) for pragmatic mathematical reasons that give no insight as to which is the primary causal variable.

Baruya and Finch (1994) recently investigated the role of speed variance and other aspects of the speed distribution on accidents on rural roads in Britain. Results suggested effects of both mean speed and the coefficient of variation of the speed distribution (a measure of speed dispersion) on the occurrence of accidents. These relationships were exponential rather than linear. On roads where mean speed was relatively high, the coefficient of variation tended to be comparatively low. This pattern was seen in cross-sectional data (a snap-shot of the current situation) and does not necessarily imply that changing the mean speed will actually influence the variance. Assuming that it did, however, Baruya and Finch showed that the increase in the accident rate associated with a certain increase in mean speed would overwhelm any reduction that might accrue through a reduced coefficient of variation.

Recent work by Schmidt (1996) provides further context for the speed variation idea. Accidents rates on two-lane rural roads in Germany were modelled. The accident rate decreased as the quality of the construction of the stretch of road increased. The dominant influences on the accident rate were alignment and width of the carriageway. Together with median speed, these variables explained about half the variation in accident rates, with the speed variable accounting for approximately 7 per cent of the total variance. The standard deviation of the speed distribution did not contribute additional predictive capacity to the model.

Evidence from correlational studies suggests there is a positive association between speed and crash involvement. This type of study is unable to provide full details of the relationship, however.

Three studies conducted in the United States more than 25 years ago attempted to enumerate the relationship between speed and crash involvement using data from individual crashes. These studies concluded that crash involvement was a U-shaped function of vehicle travelling speed. The studies were subject to methodological problems, with the consequence that the meaning of the results is not certain. In particular, it is debatable as to whether the elevated involvement rates found at low speeds were due to bias, to vehicles undertaking slow manoeuvres, or to drivers genuinely electing to travel slowly.

Studies which have linked drivers' speeds and accident histories have, on the whole, not supported a U-shaped relationship between speed and crash involvement. In particular, a recent Australian study found that the slowest drivers had the least experience of crashes, while the fastest drivers had the greatest experience of crashes.

Progress in determining the nature of the relationship in question would appear to require further use of the most direct study design, bearing in mind and attempting to overcome past deficiencies. Estimates of pre-crash speed are a potential weakness of the approach, but this could be improved using contemporary accident reconstruction methods and computer programs (in the absence of a representative and valid cohort study using 'black box' speed recorders). In addition, care should be taken to ensure that all vehicles contributing to the data set were actually travelling at a free speed and that controls are truly comparable.