Accuracy and Precision in Scientific Publications
The interesting article by Paper, Rodger and Simon, Voice Says it All in the Navy, (Communications of the ACM 47(8):97-101, August 2004), is tarred by an unfortunate and, sadly, increasingly common error. In the article's tables and explanatory text the authors report their results with an unwarranted precision of three significant digits: 71.4, 42.9, 57.1, and so on.
The results come from a qualitative study of a focus group consisting of 14 individuals. The result of each question could be one of 14 different data points; readers can easily verify the fact by multiplying the article's numbers with 0.14 to find the number of individuals they represent. Projecting the scale of the 14 possible different result points on a scale of 1000 points (the percentages with one decimal digit used in the article) can mislead the cursory reader into thinking that the accuracy of the results is that implied by the precision used in reporting them. Statistical tools and spreadsheets will effortlessly calculate the results we ask for with arbitrary precision; it is up to us humans to report them with a precision commensurate with their accuracy.
To avoid such problems learned publications could add a check box in the forms used for reviewing their articles: "are numerical results reported with appropriate precision?" In addition, editorial staff could flag suspicious numbers (any number with decimal digits), and ask article authors to confirm their validity.
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