Rate vs raw number

September 9, 2009 at 5:19 am 1 comment

| Gabriel |

Two things I read recently spoke to my sense of why it doesn’t make sense to talk about raw numbers but only rates.

One is the observation that “from 2004 to 2007 more people left California for Texas and Oklahoma than came west from those states to escape the Dust Bowl in the 1930s.” I’m not going to claim that the article has it wrong and California is in fantastic shape, but this is a very misleading figure. (Even though it’s pretty funny to imagine a latter day Tom Joad loading up the aroma therapy kit into his Prius and heading east in search of work and low taxes). Let’s put aside that it’s using out-migration when net migration is a much better measure of the “voting with your feet” effect. This “worse than the dust bowl” factoid ignores that the present population of California is four times bigger than the combined population of Texas and Oklahoma in 1930, so as a rate the gross outflow is much less than that of the Dust Bowl Okies. (On the other hand the Okies largely came to California whereas many native born Californians are moving to Arizona, Nevada, Oregon, and Washington, not just OK+TX). Anyway, the dust bowl comparison strikes me as a cute but meaningless figure, which shouldn’t be necessary given that the state’s problems are severe enough that you don’t need half-truths to describe them.

The second thing I read was this fascinating article on the public health debate over salt. (long story short, the case for salt intake restrictions was always weak but has been growing weaker, nonetheless the hyper risk averse killjoys of the public health community favor maintaining the low recommended daily allowance just in case). The most interesting thing to me was this passage:

The controversy itself remains potent because even a small benefit–one clinically meaningless to any single patient–might have a major public health impact. This is a principal tenet of public health: Small effects can have important consequences over entire populations. If by eating less salt, the world’s population reduced its average blood pressure by a single millimeter of mercury, says Oxford University epidemiologist Richard Peto, that would prevent several hundred thousand deaths a year

That is, we should take even infinitesimal rates seriously if they are applied to a large population. If you take this logic to its natural conclusion it implies that in ginormous countries like China and India the speed limit should be 40 miles an hour and they should put statins in the drinking water, but in tiny countries like New Zealand or Belize people should drive like the devil is after them and open another bag of pork rinds. Or if you take a more cosmopolitan perspective, you could say that we should further restrict our salt intake until some time around 2075 (the UN’s best estimate for the peak world population) and after that we can start having the occasional french fry again.

I guess I shouldn’t be too harsh on this kind of thing since as someone who sometimes deals with very large datasets, it is in my interests for peer reviewers to pay attention to my awesome p-values (look Ma, three stars!) and ignore that in some instances these p-values are attached to betas that aren’t substantively or theoretically significant, but benefit from practically infinite N driving standard error practically to zero.

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Surface / contour graphs with tddens.ado I drink your agency!

1 Comment

  • 1. Koreanu  |  September 9, 2009 at 3:05 pm

    I’m not really sure a world where hordes of sociologists would chase large betas is a better world than this one, where small p values are hold in the highest esteem …


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