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Kloeden et al Critique Assumption is the mother of all screw-ups - Wethern's Law 
Fact LTSA & Police Myth
Australian traffic researchers assumed far too much, proved nothing significant or unexpected, yet their extravagant claims led to draconian laws and enforcement policies. Each 5 km/h increase in speed doubles the risk of a casualty crash!

In the publication Speed, Factsheet 33, LTSA states:

    For urban roads, research in Australia has demonstrated that the risk of involvement in a casualty crash increases exponentially. This means that with each 5 km/h increase in travelling speed above a 60 km/h speed limit, the risk of involvement in a casualty crash approximately doubles.

The source for this, and many other confident pronouncements on the risks of speed is a paper: Travelling Speed and the Risk of Crash Involvement, by Kloeden CN, McLean AJ, Moore VM, and Ponte G, Adelaide University Road Accident Research Unit, November 1997.

 A fair and accurate summary of that study is this:

  • From 997 dry-weather, working-day crashes attended by the study team in the Adelaide metropolitan area 60 kph zone during 1996, 148 cases (14.8%) were selected for study based on these criteria:
    • ambulance was required,
    • vehicle was a car,
    • vehicle speed was not constrained,
    • driver was not manoeuvring illegally,
    • driver medically fit and sober,
    • no rollover,
    • information was available to estimate the vehicle pre-crash speed.
  • The pre-crash speed was estimated from crash site observations using a computer package.
  • The crash site was revisited at the same time of day, day of week and weather conditions within a period usually of several weeks, occasionally up to several months, and, using a laser gun from a range of at least 200 metres, the speeds of four “randomly chosen” cars with unconstrained speed were measured at the crash site.
  • The proportions of vehicles traveling at different speeds were compared from the two groups – the non-crash measurements and the crash estimates – and the ratios of these were used as estimates of the relative risks of travel at varying speeds.

 The paper leads with this bold, unqualified statement in summary of their findings:

 “In a 60 km/h speed limit area, the risk of involvement in a casualty crash doubles with each 5 km/h increase in travelling speed above 60 km/h”

But how was this conclusion reached and was it justified?

 To reach this conclusion, Kloeden et al implicitly make the following heroic assumptions with neither recognition nor justification: 

  1. their non-random selection of less than one crash out of six biases neither the results nor the risk calculation (only some of these exclusions are justifiable - see below), 
  2. drivers do not adjust speed according to conditions, 
  3. all drivers traveling at a particular speed have the same risk profile,
  4. drivers on average perceived the same risk level and had the same visibility in the control conditions as pertained when the crashes occurred, and
  5. the pre-crash speed estimates are unbiased and the variance in the estimates are consistent with those of the control measurements.

 The last two assumptions are unknowable after the fact – at least they deserved to have been given serious consideration prior to the study so that some attempt could have been made to assess their significance.

 However that is only an academic concern, since the first three assumptions are demonstrably false and invalidate the conclusions of the study regarding relative risk at different speeds.

 First, examine the cases excluded from the analysis:

(adapted from Kloeden et al, Table 4.1)

Crashes Attended and Reasons for Exclusion from the Study
Crashes Attended Number of Crashes
Total number of crashes attended 1015
Crashes excluded 867
1.  No ambulance transport required 325
2.  Case vehicle was not a car or car derivative 148
3.  Case vehicle did not have a free travelling speed 148
4.  No evidence of crash remained at scene 63
5.  Case vehicle doing illegal manoeuvre 26
6.  Crash due to medical condition of driver 23
7.  Site not in a 60 km/h zone 18
8.  Not a vehicle accident 8
9.  Case driver had a positive blood alcohol concentration 5
10.  Case vehicle rolled over 4
11.  Insufficient information for crash reconstruction 99
Valid crashes 148

These reasons are not necessarily exclusive but there is no information of how the reasons were classified when more than one reason applied.

The exclusions of cases 1, 7 and 8 are unexceptional given the objectives of the study.

However, all the other exclusions, totalling 501 cases, affect at least the accuracy of the risk analysis. For every case included, the study excluded 3.4 possibly relevant casualty crashes.

It may be argued that exclusion 2 is unexceptional given the objective of studying homogeneous vehicles (cars and car derivatives). There are two problems with this.

  • Firstly, vehicle weight is an important contributor to casualty figures – especially with the very high proportion of side-impact crashes in this study. A light car may be only one-third the weight of a heavy 4WD “car-derivative”. Given that there is substantial variation in the vehicles studied it is arbitrary to exclude other vehicles of varying weights – all of which contribute to speed profiles and accident risks.
  • Secondly, the study conclusion purports to cover the entire risk of travel at varying speeds. But that includes the risk of colliding with all other vehicles on the road. By systematically excluding such a large number of crashes with other vehicles the study fails to do what it claims.

Furthermore, the study does not examine the risk of having a casualty crash when driving at different speeds. It discards almost all cars involved in casualty crashes except when they were the faster vehicle.  (In only three cases did the study include two vehicles from a single crash.  These were all median cross-over head-on crashes.  In two cases a driver lost control and in the other swerved to avoid a crash.)

Through this filtering of case vehicles, the study effectively examines risks only for the faster vehicle in a casualty crash when traveling at different speeds immediately approaching a crash zone in dry weather and mostly in working hours. 

When the risk being studied is stated accurately in this way, it is obvious that the study is limited to estimating a risk component which inevitably rises with increased speed in high risk locations.  It does not give any indication of the significance of this risk component relative to all other circumstances that occur while driving.

This result is neither unexpected nor applicable to other circumstances. In particular, the estimated risk from this study is only a limited subset of the total road travel risks and the relativities obtained do not apply either generally overall or specifically in lower risk locations.

Next, examine the crash event causes:

Crash Type and Average Travelling Speed
(adapted from Kloeden et al, Table 4.4)
Crash Type Number of Cases Proportion of Cases Average Case Speed (km/h) Average Control Speed (km/h)
Case Vehicle Had Right of Way
1.  Oncoming vehicle turned right across path 55 36.4% 68.9 59
2.  Vehicle entering from left turned right across path 23 15.2% 63 58.6
3.  Vehicle doing U turn in front 8 5.3% 65.1 60.6
4.  Vehicle crossing in front from left to right 7 4.6% 62.7 60.3
5.  Hit by an out of control vehicle 7 4.6% 66.4 65
6.  Vehicle on right turned right into path 1 0.7% 66 61.3

Case Vehicle At Fault
7.  Loss of control followed by collision  14 9.3% 82.6 63.3
8.  Rear end collision with vehicle in front 14 9.3% 63.5 60.4
9.  Side swiped vehicle travelling in the same direction 1 0.7% 92 58

Fault Indeterminate
10.  Hit pedestrian or bicyclist 12 7.9% 62.8 61.6
11.  Vehicle crossing in front from right to left 9 6% 65.2 56.4

151 100% 67.6 59.9

Note: 3 crashes yielded 2 case vehicles each giving a total of 151 total cases

75% of crashes were at intersections (e.g. see Types 1,2,4,6,11: 63%).  In the majority of crashes the other vehicle failed to give way (Types 1-6: 67%).

For most of the accident types, the differences in average speeds between the control and case vehicles were small – less than 5 kph.   Therefore even a small bias in the case accident speed estimates would have a major impact on the calculated risk profiles.

The crash types with highest average speeds for the control vehicles had low accident frequencies (see Types 5,7).  This directly refutes the stated study claim that higher speeds cause much higher risks.  It is also further evidence that assumption (b) is invalid and that drivers generally had increased speed in relatively low risk locations.  It reflects the fact that drivers modify their speed for the environment and that these crashes were on straight roadways remote from intersections.

Good drivers do vary their speeds according to the perceived risk in the conditions.  Apart from being pure common sense, the study cites the finding of Wilson and Greensmith (1983):

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.

That finding also shows that assumption (c) is invalid.  Drivers traveling at the same speed in various conditions do not have the same risk profiles.  Again, this is simple common sense.  Good drivers are vigilant, cautious and adjust both speed and line of travel with consideration for due clear separation from risks.  Bad and dangerous driving occurs at all speeds.

About three-quarters of the cases cited involved a failure to anticipate and avoid a mistake made by the other driver.  The remainder were due to errors by the case vehicle driver.

Given that inattention and distraction is a primary factor in accident causation, this is likely often to have been the primary reason a case vehicle approached the crash intersection faster than the control vehicles.  Unfortunately this study reports no examination of the normal, expected slowing-behaviour of traffic approaching crash intersection locations.

Five cases involved drivers disobeying traffic lights.  There is no discussion of how many other instances may have involved traffic lights where an approaching vehicle maintained or increased speed while a turning driver assumed it would slow or stop.

Regarding the stated conclusion of the Kloeden et al study: In a 60 km/h speed limit area, the risk of involvement in a casualty crash doubles with each 5 km/h increase in travelling speed above 60 km/h”, we are led to the following evaluation:

Their statement implies:

  • There has been a study covering all driving at all speeds under all conditions in the specified area.
  • All drivers are subject to the same risk profile so comparisons between them are valid.
  • All conditions are subject to the same risk profile so comparisons between them are valid.

None of these implications are true.  (See also Silly Statistics on other out of context claims.)

Instead, the study selected only one-sixth of business-day crashes and for about half of the vehicles involved in those, it estimated approximate speed immediately before the crash and compared that with measured speeds of other traffic at the same site.  The errors in the study methodology are:

  • The estimated and measured vehicle speeds are subject to unknown error variances and biases which may well be greater than the observed differences in the mean crash speeds and control speeds and almost certainly invalidate the risk calculation which requires both the bias and variance of the estimates to match those of the control measurements.
  • The uncertainties in the estimated vehicle speeds were aggravated by the failure of the study to measure road skid resistance at the crash sites and by the use of assumed fixed constants for both skid resistance and for the estimate of proportional energy loss before skid marks.   The latter is not constant and declines with increased speed so the estimates were biased by that to overestimate higher speeds.  Every speed estimate required three independent estimates: a) final impact speed, b) loss of speed producing skidmarks, c) loss of speed before skidmarks.  All had substantial error and bias risks that were neither controlled nor calibrated.  Most were unreported by the authors.  Derived risk calculations from this data have no assurance of accuracy.
  • Even if the compared speeds were accurate, the comparison applies only to driver behaviour at high risk time/place/conditions.  It cannot be extrapolated to low risk conditions.  A safe driver will drive faster in safe conditions and slower in risk situations.  You cannot estimate his/her degree of risk by measuring his/her speed in safe conditions and comparing that with speeds measured at accident locations.
  • The analysis ignores the fact that there were wide variations in the speeds of the control vehicles at different crash sites (43 - 76 km/h).  Despite this evidence to the contrary, the researchers chose to assume the same speed risk profile applies at all sites.  In fact, John Lambert has shown that the data is consistent with a U-shaped risk curve around an optimal speed varying for each location.  The researchers also chose to ignore the fact that the 60 km/h speed limit was not the lowest risk speed for every location and that excessively low speeds also carry increased risk.
  • The weights of vehicles are ignored, yet they may vary by a large factor and have a much greater impact on casualty risk than small variations in speed.  Typically a 4WD SUV may be 2-3 times heavier than a car.  The risk of death if it hits a pedestrian is also very much greater than a low car profile because of its height - all this risk element is ignored by the study conclusion.
  • The study ignores the value and effect of safety measures such as side-impact bars and side airbags.  Side airbags which cover the head and torso are shown to reduce fatalities in side-impact crashes by nearly 50%.  Most of the crashes in this study were side-impact.
  • The study assumes all drivers have the same risk profile, but there are large differences in driver reaction times and vehicle standards.
  • By focusing solely on serious crashes the methodology is inevitably biased towards the most unsafe drivers in the most unsafe vehicles.  You cannot generalize from their performance to that of even average drivers in average vehicles, let alone to good drivers in good vehicles.  The conclusions are simply statistical nonsense.

The study claim is therefore false, unproven and without general application.  Moreover, several other papers claiming to derive related conclusions from this source data are consequently also without foundation and fundamentally flawed.

The road safety research community has ignored these blatant oversights in their fundamental research in a rush to embrace rigid enforcement of speed limits with new and draconian technologies and regulations.

Both their competence and integrity are in serious doubt.


-----Original Message-----
Sent: Thursday, 18 November 2004 9:51 p.m.
Subject: Relation between speed and crash risk

Your website claims on the relationship between speed and crash risk seems to be completely contradicted by the practical evidence of the New Zealand experience.

See: RigidEnforcement, RigidEnforcement charts and InjuryTrends

Moreover this is unsurprising as the fundamental studies you rely on draw extravagant and unjustifiable conclusions from inadequate data: KloedenCritique

Yours truly

No response was ever received.  However, our website statistics recorded some immediate accesses over the next few days from the CASR (Centre for Automotive Safety Research) unit at Adelaide University.  We remain unimpressed by the integrity of the road safety research community.