12 March 2007

Probability and Profiling

picture of a woman, from 'sample images' at http://www.asf.com/support/plugins/pluginsupport.asp

The Set-Up:

I am going to test your understanding of "probability" and "randomness". For purposes of this demonstration, assume that the person in this picture has been randomly selected from all Americans. This is a picture of a randomly selected American.

The Question:

Is this person more likely to be a farmer, or a librarian?

The Answer:

Whatever you answered, your answer was almost certainly influenced by your previous knowledge, biases, and thinking about what the woman "probably" was.

You probably ignored the repeated information that this was supposed to be a randomly selected American.

In fact, any "randomly selected" American is much more likely to be a farmer than a librarian, since there are almost seven times as many farmers as librarians in the U.S.A. There are twice as many women farm operators as there are librarians and library technicians put together.

Because I showed you a picture of a woman, and you "know" than most librarians are women and most farmers are men (is that really true?), you probably guessed that the "randomly selected" American in the picture was a librarian. If so, you let your previous knowledge affect your answer. You probably lacked the relevant knowledge about the numbers of farmers and librarians in the U.S. population.

People have a very hard time forgetting their prejudices, biases, and prior information (some of which may be erroneous) when making judgments about things they are told are "random". They impose a structure of belief even on randomness, which by definition has no structure. (Previous post on "randomness".)

This is why "profiling" is so difficult. People go with their "gut feel", their biases, rather than using a true analysis of the situation.

Here are the sources and links to further information:

US Department of Labor, Bureau of Labor Statistics
all occupations
education, training and library occupations

149,680 librarians and 113,520 library technicians -- about 263,000

US Department of Agriculture, National Agricultural Statistics Service, Census of Agriculture 2002

farm operators
pdf version

1,792,000 operators on farms where farming is the principal occupation of the principal operator. 455,500 woman operators same definition.

Here is a really interesting article about profiling. (It is about profiling, not pit bulls, so just keep reading.)

David Wheat's Science In Action site has articles about science and math in the real world, weird science, science news, unexpected connections, and other cool science stuff. There is an index of the articles by topic here.

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