Posted by
Andrews on Monday, February 23, 2009 1:04:12 PM
I wrote earlier about how life expectancy numbers, often used to compare the US health care system against foreign nations' systems, are deceptive as they partly reflect our higher murder rate, and also because we count as live births many premature births other nations consider miscarriages or stillbirths. Of course,
the most obvious argument is that if our health care system were such a failure, why do people form those "better" lands flock here for care. But for the moment, let us ignore that, as I have an analogous example, that may help demonstrate my argument.
You see, I have had many cats in my life, and I was wondering today if my old cats lived an exceptionally long time, or if the "average lifespan" figures were misleading. I had one cat live to 22, another to 18, and a third, despite two strokes, one of which threw a clot which required the amputation of a leg, lived to 16. So, was I exceptionally lucky or are the numbers off?
My first thought was that my cats all lived indoors all their lives. As many people, even city dwellers, allow their cats out, that obviously brings the numbers down. Being run down by cars, contracting rabies, animal attacks, even flea infestation, can all reduce a cat's lifespan pretty dramatically. However, even if we limit our numbers to indoor cats, the numbers may be a bit deceptive.
Having had cats who gave birth, I know that the cat equivalent of infant mortality is high. And that is logical, as cats have so many kittens at once. Any animal that gives birth to large numbers of young either suffers from terrible predation, or else has a large number of infant deaths. Mice, for example, are both prey and suffer from a variety of genetic disorders, making many breeds prone to spontaneous cancers at very young ages. Cats, on the other hand, are not frequently prey, but they do seem to have a fairly high mortality early in life. In addition, cats also suffer from a variety of very nasty contagious diseases, such as feline leukemia and distemper, which can both kill off adult cats at an early age (I lost cats to both in my life), but can also dramatically increase the mortality rate among kittens. That being the case, the life expectancy figures may be skewed much younger by the number of young deaths.
So, how to figure out if 16 or 18 is very old or only a little old in terms of cats? Well, the obvious solution is to factor out kitten deaths and outdoor cats, but that still leaves the disease caused distortions, which skew the numbers younger. If we could factor those out, we would have a number equivalent to the average lifespan of those who live indoors, survive kittenhood, and avoid the epidemics which tend to dramatically shorten lifespans.However, it is simply impossible to remove such numbers. While we may be able to distinguish indoor and outdoor cats, often the cause of death is not so obvious, especially as cat autopsies are not common. So, what to do?
The same thing I suggest with the health care numbers I mentioned at the beginning. Or any statistic, for that matter. Do
NOT accept that mean as the whole picture. The mean value can be very misleading. After all, if you have people aged 25,25,25, or aged 0 and 50, both groups have a mean of 25, but which one would chose for military service?
That is why, whenever confronted with a mean or median value that supposedly proves something, you need to see at least the mean and median, if not the variance, or, best of all, the entire chart of relative frequencies. Just knowing the mean or median tells us very little. It is akin to knowing the price per box of some product, without knowing how much is in the box.
So, once again, I would ask that we try to ask the right questions when sophists try to use numbers to lie. Rather than accepting that the mean lifespan in the US shows our health care system is "broken", maybe we should ask how the numbers were gathered, whether we trusted government numbers from authoritarian regimes, and, most importantly, what the distribution was. Likely we won't get answers to all our questions, but just by raising them, hopefully it will let others know that the mean alone does not tell the whole story.