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Monday, January 14, 2008

Scientific Illiteracy About Death Rates

Here's part of an article on ScienceDaily about death rates in New York City [New York City Death Rate Reaches Historic Low].
The death rate in New York City reached an all-time low in 2006, the Health Department reported today, as the number of deaths fell to 55,391 -- down from 57,068 in 2005 and 60,218 in 2001. Mortality declined in eight leading categories, including diabetes, HIV, chronic lung disease and kidney failure. The only leading killer that increased significantly was substance use (up 8%). Heart disease and cancer remained the city's biggest killers, claiming 21,844 lives and 13,116 lives, respectively. The figures come from the latest Annual Summary of Vital Statistics, the definitive registry of births and deaths in New York City.
The numbers of deaths are not death rates. This is one of my pet peeves. I get angry when newspaper reporters screw it up but this is much worse. It's from a website that's supposed to specialize in science ("Your Source for the Latest Research News").

The raw numbers are available at Summary of Vital Statistics 2006: The City of New York. They show that the death rate did, indeed, fall from 7.0 per 1000 citizens in 2004 to 6.7 per 1000 citizens in 2006. In 1916 it was 14.0 while in 1980, 1990, and 2000 it was 10.0, 10.1, and 7.6 respectively.

The absolute numbers of deaths tells you nothing about death rates. For all we know, the population of New York City could have fallen from 2004 to 2006 and the death rate could have gone up. (Incidentally, if you look at the raw data you'll see an interesting footnote. The rates in 2004-2006 were revised downwards when the 2007 census data for population was used. Previous estimates were based on the population according to the 2000 census.)

[Image Credit: New York City in 1916 from The University of Texas at Austin]


  1. Perhaps creeping innumeracy will eventually land us here:

  2. I understand the point, sure, "rates" and "numbers" of deaths are different.

    But the quoted text does not say that the "rate" of death is the number of deaths, and is in fact quite clear. It says that the rate of deaths has decreased, and it gives the numbers of deaths represented by those rates in different categories.

    This choice does not reflect innumeracy on the part of the writer; it reflects a bias. The difference between 7.0 and 6.7 -- the individual risk of death -- seems very small. The difference between 55,391 and 57,068 seems pretty big. So using the actual numbers of deaths illustrates the story in a way that emphasizes its importance.

    This also enables the writer to make the cited causes of death appear to be very frightening. Which is scarier, 13,116 deaths from cancer, or a cancer death rate of 1.8 per thousand?

    Notice the one obvious exception -- the increase in the death rate from substance abuse. Compared to heart disease and cancer, there is only a tiny death risk from substances -- and this doesn't look very impressive in absolute numbers next to those other causes. So the article cites the per annum increase in the death rate from substances -- 8 percent -- which seems large by itself as the only percentage listed.

    I don't call this innumeracy, although the bias certainly plays on the readers' innumeracy. The quoted text is perfectly accurate, it just uses numbers selectively.

    Arguably, it is more understandable to talk about death "rates" in terms of actual numbers of deaths, because the actual numbers relate to socially perceivable consequences such as hospitalizations, emergency room visits, funerals, and dollars spent. But using actual "rates" would be better to put an individual's risk of dying from these causes into more accurate perspective.

    The question is whether the use of numbers furthers an editorial slant, and here it clearly does.

  3. John Hawks says,

    I don't call this innumeracy, although the bias certainly plays on the readers' innumeracy. The quoted text is perfectly accurate, it just uses numbers selectively.

    The title of the article is "New York City Death Rate Reaches Historic Low." No death rates are given in the article. All we are given is the total number of deaths.

    There seem to be only two possible explanations. You prefer to think that the author knew the difference between "death rate" and "number of deaths" and assumed that all readers did as well. Therefore, given the title of the article, the author assumes that we are all capable of drawing the obvious conclusion; namely that the population of New York City has increased, or remained constant, or not fallen by as much as the number of deaths.

    You are entitled to that assumption.

    I, on the other hand, assume that the author doesn't know the difference between a rate and an absolute number. It's a more parsimonious assumption,

  4. I have to disagree. A useful definition for "rate" is a quantity expressed in units with time in the denominator. Thus rate of speed: km/h; metabolic rate: kJ/d; rate of acceleration: (m/s)/s; rate of warming: degrees per decade; etc.
    Given that deaths are reported for calendar years, the real units are deaths/year, which is a bona fide rate. Your preferred statistic is a population-specific or per-capita rate. I agree it's a better comparitor but both are "rates."

  5. sven: the scale to population size is built into "rates" concerning populations. "Death rate" is therefore a specifically defined term meaning "deaths per 1000 population per year". You can choose to measure deaths per week in a city if you like, but that isn't "death rate" any more than a spade is a garden fork.

    My favourite media statistics story was when the Daily Telegraph (I think; may have been the Times) reported that cocaine use had doubled. It turned out they had been using rounded figures, and it had risen from 1.4% to 1.5% of the population studied.

  6. Like the feller said, the death rate here is the same as everywhere else--one per person.
    Since the article refers to an all-time low, it needs to be normalized to city population. I was left wondering if it was 55,391 per 100,000 or something else.
    But my favorite is when they say something like "The rate of increase in inflation has dropped to 2 percent per year."