Monday, April 16, 2012

A Useful Quote for Social Scientists

A less profound application of the less-is-more principle is to our habits of reporting numerical results. There are computer programs that report by default four, five, or even more decimal places for all numerical results. Their authors might well be excused because, for all the programmer knows, they maybe used by atomic scientists. 
But we social scientists should know better than to report our results to so many places. What, pray, does an r = .12345 mean? or, for an IQ distribution, a mean of 105.6345? For N = 100, the standard error of the r is about .1 and the standard error of the IQ mean about 1.5. Thus, the 345 part of r = .12345 is only 3% of its standard error, and the 345 part of the IQ mean of 105.6345 is only 2% of its standard error. These superfluous decimal places are no better than random numbers. Theyare actually worse than useless because the clutter they create, particularly in tables, serves to distract the eye and mind from the necessary comparisons among the meaningful leading digits. Less is indeed more here.
Jacob Cohen, Things I Have Learned (So Far), American Psychologist 45 no. 12 (1990): 1304-12.


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