Proper use of denominators
Mathew Dearnaley, in the Herald, has a story today about dangerous roads where he observes that the largest number of deaths is in the Auckland region, but immediately points out that what matters is the individual risk, estimated by fatalities per million km travelled. We’ve been over this point quite a lot on StatsChat, so it’s great to see proper use of denominators in public.
When you divide by total distance travelled, to get a fair comparison, it turns out that Gisborne has the most dangerous roads, followed by Taranaki, and that Auckland, like Wellington, is relatively safe.
Although Waikato roads claimed 66 lives – more than a fifth of a national toll of 308 deaths – the odds of being among the 10 people who died in crashes between the Wharerata Hills south of Gisborne and East Cape were almost twice as high as in the busier northern region.
One problem with the story is the issue of random variation. According to NZTA, Hawkes Bay and Gisborne together had a total of 16 deaths last year, up from 8 the previous year. There’s a lot of noise in these numbers, and even though the story sensibly looked at serious injuries as well, it’s hard to tell how much of the difference between regions is real and how much is chance.
It would be helpful to add up data over multiple years, though even then there is a problem, since we know that road deaths decreased noticeably in mid-2010, and this decrease may not have been uniform across regions.
Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »
I disagree with you here. I think the story (well at least the headline) is bogus.
The stats should be adjusted for the speeds traveled on the roads. Provincial drivers spend more time on 100km/h roads than city drivers. Hence the higher death rates per km.
In fact, Auckland roads could be more deadly than provincial. Auckland 50km/h roads could be deadlier than provincial 50km/h roads and Auckland 100km/h roads could be deadlier than provincial 100km/h roads. But because Auckland drivers drive more on 50km/h roads which are safer than 100km/h roads Simpson’s Paradox applies and we get overall deaths rates lower for Auckland even though the roads are deadlier.
I say the story is bogus because it just tell us what we already know – that faster roads are deadlier – and because it still has a missing denominator – it should record deaths per distance per road speed-limit.
Note: I’m referring to the printed version of the article which included a table of km per death for NZ provinces.
11 years ago