How many of the digits in a mean of 12.3456789012 are worth reporting?
Abstract
OBJECTIVE. A computer program tells me that a mean value is 12.3456789012, but how many of these digits are significant (the rest being random junk)? Should I report: 12.3?, 12.3456?, or even 10 (if only the first digit is significant)? There are several rulesofthumb but, surprisingly (given that the problem is so common in science), none seem to be evidencebased. RESULTS. Here I show how the significance of a digit in a particular decade of a mean depends on the standard error of the mean (SEM). I define an index, DM that can be plotted in graphs. From these a simple evidencebased rule for the number of significant digits ("sigdigs") is distilled: the last sigdig in the mean is in the same decade as the first or second nonzero digit in the SEM. As example, for mean 34.63 (SEM 25.62), with n = 17, the reported value should be 35 (SEM 26). Digits beyond these contain little or no useful information, and should not be reported lest they damage your credibility.
 Publication:

arXiv eprints
 Pub Date:
 January 2013
 arXiv:
 arXiv:1301.1034
 Bibcode:
 2013arXiv1301.1034C
 Keywords:

 Quantitative Biology  Other Quantitative Biology;
 Statistics  Applications
 EPrint:
 5 pages, 1 Table, 2 Figures. New simpler index unifies Table and Figures. Now published. This arXived version has small amendments to the published version