The Denominator of Risk

Ann’s father kindly sent me an article from the Aviation Medical Bulletin that presented some fatality risks from the National Safety Council to support the argument that risk shouldn’t stop us from enjoying our favorite activities so long as we take reasonable precautions. I agree, but there is a big problem lurking in the denominator of many of these statistics:

Cause of Death Odds 0-10 Perceived Risk
Falling 1 in 36,000 5.4
Hit by a car 1 in 47,000 5.3
Poisoning 1 in 86,000 5.1
Motorcycle accident 1 in 89,000 5.1
Bicycle accident 1 in 400,000 4.4
Airplane crash 1 in 400,000 4.4
Choking on food 1 in 400,000 4.4
Drowning 1 in 1 million 4
Gunshot wound 1 in 1 million 4
Building fire 1 in 3 million 3.5
Lightning strike 1 in 4 million 3.4
Earthquake 1 in 9 million 3
Snake bite 1 in 96 million 2

Put aside the fact that these don’t quite match the current NSC stats. Is the world really this safe? In most cases, I would say no. The problem is that these are odds for the entire US population. For activities that nearly everyone participates in, like riding in a car or eating, the numbers are good. But not everybody flies in airplanes, rides bicycles, climbs high passes, lives on a fault line, etc. When I tried to find the risk of bicycling, I at least made an attempt to estimate how many cyclists there are in the US. I used this, a smaller number than the whole US population, in the denominator, which gave me a higher risk estimate, 1 in 131,000. That’s three times riskier than presented above.

So am I nitpicking at the same time I admit that my own numbers are gross estimates? Maybe a little. But I think if I can get a better estimate, I should. And for activities that only claim a small fraction of the population as participants, getting a reasonable number for the denominator may be very difficult, but absolutely necessary. Using the entire population would give a meaningless result.

3 responses to “The Denominator of Risk”

  1. As a statistician, I can assure you that what you say is correct, “If I can get a better estimate, I should”.

    The denominator *is* very important, and your analysis is more accurate for what you are trying to measure because of the extra step you took.

    I’m guessing that whomever reported these figures is just lazy and didn’t want to take the extra step to research the true population at risk. (ie. how many cyclists are there, and using this figure as a basis instead of US pop…because the non-cyclists wouldn’t die as a result of a cycling accident).

    In fact, I’d like to point out that the results here could be very misconstrued.

    Let’s say for instance we know 20 people. 4 of them get bit by snakes whereas 5 of them get in a bike accident. Then, it looks like biking (5/20=25%) is more risky than being out and about by snakes (4/20=20%).

    But, what if I now told you that all 20 people ride bikes and only 6 people put themselves at risk to snakes. Now, the bikes are still 25% and the snakes jump to 67%!

    So, the entire population of 20 people is an incorrect means of determining risk.

    It is great you are exploring these concepts, as most people do not think this deeply when stats are reported.

    After teaching beg. stats class for 2 years on top of being a Stats person, it is hard not to notice the myriad of flaws presented in the news, media, online, at work, everywhere!

    Ever read the book “How to lie with Statistics?”.


  2. I haven’t, but I always think of the Mark Twain quote about the 3 kinds of lies: Lies, Damn Lies, and Statistics.

    Thanks for the examples!

  3. Fabulous insights. I have been so upset by the way Big Pharma uses statistics. I have never taken statistics and am a terrible math person but even so, some things seem obvious to me. And it is amazing how little thought people give to claims based on some pretty hazy statistical reports. What some researchers find “significant”, I find pretty unimpressive, for example.

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