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How many of the digits in a mean of 12.3456789012 are worth reporting?

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...

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Detalles Bibliográficos
Autor principal: Clymo, R. S.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: BioMed Central 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6421670/
https://www.ncbi.nlm.nih.gov/pubmed/30885264
http://dx.doi.org/10.1186/s13104-019-4175-6
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author Clymo, R. S.
author_facet Clymo, R. S.
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description 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, D(M) 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 ± 26. Digits beyond these contain little or no useful information, and should not be reported lest they damage your credibility.
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spelling pubmed-64216702019-03-28 How many of the digits in a mean of 12.3456789012 are worth reporting? Clymo, R. S. BMC Res Notes Research Note 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, D(M) 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 ± 26. Digits beyond these contain little or no useful information, and should not be reported lest they damage your credibility. BioMed Central 2019-03-18 /pmc/articles/PMC6421670/ /pubmed/30885264 http://dx.doi.org/10.1186/s13104-019-4175-6 Text en © The Author(s) 2019 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
spellingShingle Research Note
Clymo, R. S.
How many of the digits in a mean of 12.3456789012 are worth reporting?
title How many of the digits in a mean of 12.3456789012 are worth reporting?
title_full How many of the digits in a mean of 12.3456789012 are worth reporting?
title_fullStr How many of the digits in a mean of 12.3456789012 are worth reporting?
title_full_unstemmed How many of the digits in a mean of 12.3456789012 are worth reporting?
title_short How many of the digits in a mean of 12.3456789012 are worth reporting?
title_sort how many of the digits in a mean of 12.3456789012 are worth reporting?
topic Research Note
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6421670/
https://www.ncbi.nlm.nih.gov/pubmed/30885264
http://dx.doi.org/10.1186/s13104-019-4175-6
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