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Wednesday, March 10, 2010

More on Toyota and third grade math

This is a great piece from the NYT. http://opinionator.blogs.nytimes.com/2010/03/09/toyotas-are-safe-enough/?emc=eta1

The bottom line is we simply have no concept of numbers and risk and are willing to invest ridiculous sums of money in the effort to reduce risks which, although real, are trivial when compared to more mundane risks in every day life. I strongly suspect that there are software glitches that can cause our cars to screw up. However, when compared to the risk of using any car, these risks are simply so small they almost vanish.

The problem is third grade math (perhaps fourth grade) which involves numerators and denominators. We focus on numerators without any concept of denominators. This is a big  problem within medicine as well. Reports of undesirable outcomes present their data in terms of relative risk and absolute numbers of events and rarely actually present data on absolute risk. Never are these risks compared to the risks associated with mundane life events (driving, walking, falling in the home). Risk of death is rarely placed in the context of risk of death for any given age cohort. Don't tell me about risk and danger unless it can be placed in terms of absolute risk.  What does a 1:10,000 annual chance of death mean in an age cohort which starts with a 1:200 risk to start with.
http://www.medicine.ox.ac.uk/bandolier/booth/Risk/Agesex.html

There must be some sort of inherent tendency for us to be fascinated by the rare and spectacularly bad. If such behavior and misunderstanding were isolated and the consequences of such idiocy suffered by the ignorant few we could have a good chuckle. However, the hysteria is widespread and permeates the thinking of decision makers who control vast amounts of common resources. We cannot find such waste at all humorous and can only be viewed as tragic. If we could only do a better job teaching third grade math.

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