Friday, August 27, 2010

Correcting our misinterpretations of the world (Books - Full House by Stephen Jay Gould)

As a working scientist, Stephen Jay Gould had a good deal of practice thinking about trends in the natural world in the language of statistics. Statistics get a bad rap as merely a fancy way to lie, but really they are a system of tools that allows us to infer the likelihood of something occurring in our world as a rule (and hence in the future) given what has already happened before in some subset of that world. For example, the likelihood that Drug X will cure a case of malaria can't be tested in the abstract, it must be tested by actually administering the drug to a group of people with malaria for, say, two weeks. At the end of that period, the number of people who survived or succumbed to the disease are counted. But we still don't know everything because a certain portion of any group would live or die anyway, those numbers will be estimated by comparing them to a group who does not receive the drug. This group should, if they are like most, have the same chance of living or dying as the other group. Then we can begin to infer how many people as a rule will survive because of the drug. Some math is applied to adapt the number from that small group and apply it to everyone, since it is impossible to give everyone the drug. The result is stated as a probability, the language of science, as it acknowledges the ubiquity of error and the inferential nature of estimates, as we can never know all the cases of anything.

Paleontologist, biologist, and science writer Gould was diagnosed with peritoneal mesothelioma at age 40, a disease with the median mortality rate of eight months. As most general readers of probablistic statements would, Gould first interpreted this statistic to mean he was likely to be dead in eight months however, his training as a scientist made him think twice about this interpretation of the median or the mid point of a group of numbers. This is one of three ways statistics describe the central tendency of any group of numbers - baseball scores, people who earn $30,000/year or more, people who will vote for Charlie Rangel in the next election, etc. Central tendencies are statistics way of summarizing what is usual in nature with one number. However, after thinking, Gould realized:
I am not a measure of central tendency, either mean or median. I am one single human being with mesothelioma, and I want a best assessment of my own chances - for I have personal decisions to make, and my business cannot be dictated by abstract averages. I need to place myself in the most probable region of the variation based upon particulars of my own case; I must not simply assume that my personal fate will correspond to some measure of central tendency.
Full House is a 190-page disquisition of what one might assume to be dry and obscure notions - means, modes and medians, spreads of scores, skewed averages - but because they spring from a personal confrontation with mortality as well as Gould's love of baseball, and because they are written in Gould's down-to-earth prose, this book is anything but dry. It is a lively, entertaining narrative on our tendency to misinterpret the world given our misunderstandings about what statistics are telling us. The writing is cogent, the format concise, and the references various as they are learned. Plato, Shakespeare, Huxley, Darwin, nameless drunks weaving down the sidewalk, Bill Gates, and the Brooklyn Dodgers all put in an appearance in Gould's attempt to make plain to the lay-reader concepts like measures of excellence, the likelihood of survival, or whether development - of skills or species - means a trend toward greater complexity or less. These phenomena are continually misrepresented in everyday conversation and reporting about our world, sometimes unintentionally and sometimes with malice aforethought. If you have ever wanted a better understanding the daily missives we receive in the language of probability through our senses or our news sources then read this book. The next time I teach a class which would benefit from an understanding of statistics, Full House is going to be required reading.

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