How many of the digits in a mean of 12.3456789012 are worth reporting?
| Autor: | Clymo, R. S. |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | BMC Research Notes 2019 12 (148) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1186/s13104-019-4175-6 |
| Popis: | 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 rules-of-thumb but, surprisingly (given that the problem is so common in science), none seem to be evidence-based. 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 evidence-based 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 non-zero 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. Comment: 5 pages, 1 Table, 2 Figures. New simpler index unifies Table and Figures. Now published. This arXiv-ed version has small amendments to the published version |
| Databáze: | arXiv |
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