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Statistically speaking

December 7, 2012

If you gave me a sailboat, while I might appreciate the gift, I wouldn’t know how to use it.  I know what it’s used for, but I, myself, don’t know how to operate it, even though I’ve probably seen one operated on more than one ocassion.  While this is hardly notable, I use it as an illustration.

In this case, I use it as an illustration about statistics, and in particular, life span statistics for humans living in the USA.

We know something of these statistics, but I propose that we don’t know how to operate them.

Many of us know that the average life span in the USA is around 77 years.  Except that figure isn’t actually used to reflect the average life span, but the median life expectancy at birth.  Thus, the number 77, the median, reflects the expectation that 50% will die before age 77, and 50% will live beyond age 77.  And it’s still not a useful number.  Men and women have different life expectancies.  Caucasian Americans and African Americans have different life expectancies.  Narrowing down what is referred to as the cohort (a group of individuals having a statistical factor, such as age or class membership, in common in a demographic study) can go much further.  Those who smoke and those who never did.  Those with more education, those with less.  Rural/urban.  Perhaps left handed vs. right handed.  Maybe even those who enjoyed Seinfeld and those who didn’t, though I expect there has been little or no research on this.  Social Science grad students take note!

According to information I gleaned from a U.S. government website, life expectancy in the USA for those who reach age 60, is an additional 22.2 years (based on figures from 2003).  So that’s 82.2 years, 5.2 years more than the 77 years we bandied about above.  But, again, that’s for all Americans (the cohort), and is not broken down even into male and female.

Is 77 years of any use at all?  As a projection of life expectancy, I mean, not as a period of time in which one may do or not do whatever one does or doesn’t do with one’s life.  It’s probably too general a piece of data to be useful to any individual.  It’s useful for insurance companies, but even they probably find it too generalized a piece of information.

This is my gripe about statistics as a field of study, as individual factoids, and as people generally use them.  The statistics many people use, in everyday conversation, and, I believe, in the way they think about things, are so vague as to be meaningless.  I have a one in ten chance to…there’s a one in four chance that…etc.  As an individual, I am not a member of a cohort, no matter how well defined it is.  No statistic can be applied to me.  It can be applied, though not usefully, to any statistical individual within a cohort, but not to an actual, specific individual within any cohort.  Thus, among this group of a thousand, there is a statistical likelihood that six point eight of them will…, but not that Roger, a member of the group, has a 0.68% chance of whatever event I didn’t mention in the last ellipsis.

My own feeling is that every thing is a 50-50 proposition for me as an individual, or for any other individual.  There’s a fifty-fifty chance that god has a long white beard.  It’s either the case, or it isn’t.  Fifty-fifty.  There’s a fifty-fifty chance that I’ll die in my sleep tonight, assuming I live long enough to go to sleep tonight.  If not, then there’s no chance I’ll die in my sleep tonight, because I’d have already died.  I know that I expect to live to go to sleep tonight, and that I expect to wake up tomorrow.  I make plans based on that expectation.  But I can’t know for certain, and statistics offer no actual information, for me, one person, a cohort of me.

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