Monthly Archives: February 2014

Safety in Numbers – Correlation or Causation?

Correlation does not always equal causation

In a past life, I trained as a Scientist (a Chemist) and I’ve always been drawn to analysis of data. The son of a Pharmaceutical Researcher and a Public Health professional, I was brought up with “correlation =/= causation”. Sometimes, though, you have to say that a correlation is so strong, and seen so repeatedly in so many different circumstances independent of other factors that the link is almost certainly causative. Despite what people may tell you, science is never certain about anything – the scientific method means that something is always open to being disproved – e.g. the speed of light being the ‘fundamental speed limit’ is still open to being challenged by stray Neutrino’s travelling faster.  So it isn’t possible to say anything ‘for certain’, but here’s a great case study for you.

Safety in numbers (S/N)

I blogged about this here, but my argument was a bit weak and incomplete. I intend here to show the full weight of the argument, and why I think that S/N is ‘the real deal’ – by which I mean that, all other things being equal, more cycling will improve the safety per cyclist.

What is ‘Safety in Numbers’?

S/N is the idea that as you increase the numbers of a group of road users on the road (cyclists or pedestrians), that the safety per person using that mode improves – i.e. if you double the number of people cycling, you do not double the number of accidents – the number of accidents either rise very slightly, stay stable, or counter-intuitively, fall. I am most interested here in looking at the case for S/N in cycling as this is the evidence I’m most familiar with, and it’s easier just to use one example to keep the blog concise.

How does it work?

There are a number of possible mechanisms for S/N; it could be that increased numbers mean that other road users are more used to looking out for the more common road users and anticipating their movements; it could be because the infrastructure is built to better cater for the more common road users; finally, it could be that more people cycling, or walking, means less cars and therefore less interactions which could lead to a collision of enough severity to be recorded.

The evidence:

NB – it should be noted that there is a general trend of falling death rates on our roads, as we learn to keep people alive better and cars become more collision friendly.  The data below should be seen in that light.

1. Cycling in 14 European Countries, 1998:


There is a clear relationship here, showing that those countries with the highest levels of cycling have the lowest numbers of fatalaties per 100,000,000 km.

2.  Levels of cycling against fatality rates – UK 1950-99

Cycling in UK 50-99

a)  Between 1950-52, cycling levels rose and fatality rates fell

b) Between 1952-1972 there’s a pretty clear relationship showing that less cycling correlates with higher fatality rates.

c) Between 1973 and 1999 fatality rates fell despite cycling levels remaining roughly constant – I believe this to show a marked improvement in our ability to keep people alive, as a similar effect is seen in driving accidents.

3. Levels of cycling against fatality rates – Netherlands 1980-99

Cycling in NL 1980-98

It’s commonly thought that cycling was always common in the Netherlands.  Certainly, similar levels of cycling to the UK were common until the 60s (ie very high), but they then fell, and have been recovering since the late 70’s, as can be seen above.

This graph shows very clearly that as distance cycled per year increases, safety improves.  However, there is a major confounding factor here – the Dutch changed path in the late 70’s and went all-out to promote cycling.  This led to a program of cycle track building, closing of roads to cars but not cycles etc, building a fit-for-purpose, safe cycling network which will have also had an effect.  So are numbers of cyclists increasing because it’s getting safer to cycle?

Numbers from safety?

It is also commonly argued that it is ‘numbers from safety’ not ‘safety in numbers’; i.e. that more people cycle where conditions are safer to cycle and this accounts for the evidence usually put forward for the S/N effect rather than increasing numbers driving the improvement in safety. It is clearly true that the number one reason that people do not cycle currently in countries such as the UK is a perception of cycling as being dangerous, and the lack of infrastructure to allow people to cycle in safety and comfort. So, is it an increase in numbers cycling that improves safety, or the other way round?

The evidence above cannot differentiate between infrastructure being implemented leading to ‘numbers from safety’ and a true ‘Safety in Numbers’ effect.  What we need is an intervention which will affect cycling numbers in a short period of time without a change in levels of infrastructure.  A perfect example of this is introducing a helmet law and enforcing it – it’s well established that helmet compulsion laws lead to a collapse in numbers cycling.  What happens to safety in the immediate aftermath of these laws being brought in and enforced?

If safety is coming from numbers, independently of infrastructure, we would see that accident rates and deaths per cyclist increase as the number of cyclists decreased.  If this effect was observed over a short time period, where infrastructure cannot be expected to be implemented or taken away, then it is reasonable to assume that it is caused by the change in number of cyclists directly, by whatever mechanism.

1. NZ Helmet Compulsion Law – Introduced 1994

NZ helmetlawsafety

(Graph from here:

This is a fascinating set of data.  Over the course of 3 years, the number of people cycling halves, but the total accident rate stays roughly stable (meaning an increase in risk per person) – and then starts to increase further.  Safety in numbers in reverse – as the number of cyclists fall, the risk per cyclist rises.

2. Australia Helmet Compulsion Law – 1991

(Data lifted from here:


Again, numbers of injuries per cyclist rose as the amount of cycling decreased.  I believe that this is strong evidence that safety does come from numbers of cyclists, as well as infrastructure and other measures.

NB – you’ll note that the data in the two studies above is not in the same units as the graphs at the top.  Both final sets of data measure injuries, not fatalities.  However, I believe that to a good approximation injuries will be proportional to deaths over a short time period – over larger periods of time, as noted above, we are becoming better at keeping people alive; but all of these studies look at periods of time of a decade or less*.


1.  The ‘Safety in Numbers’ effect exists in cycling and as numbers increase, all other things being equal, safety per cyclist improve as shown repeatedly in different studies.

2. There may well be a ‘numbers from safety’ effect where good quality infrastructure and lower speed limits are in place, but safety in numbers exists independently of these measures.

3. The existence of this effect should not be taken as an excuse not to build infrastructure as this is likely to improve safety further.

4.  Helmet compulsion is a poorly considered idea which reduces levels of cycling with downstream public health effects from less people exercising and increases the risk of remaining cyclists having an accident.


My view of how science works is that it doesn’t matter who is making an argument; an argument should stand or fall on its own merits. So don’t take my word for what’s below – I’m happy to have my ideas challenged. Comment away!


*Fatalities may be slightly reduced by the increased wearing of helmets, but this would be a separate effect from looking into Safety in Numbers



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