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Understanding the Difference Between Standard Deviation and Standard Error of the Mean, and Knowing When to Use Which

Many authors are unsure of whether to present the mean along with the standard deviation (SD) or along with the standard error of the mean (SEM). The SD is a descriptive statistic that estimates the scatter of values around the sample mean; hence, the SD describes the sample. In contrast, the SEM is...

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Detalles Bibliográficos
Autor principal: Andrade, Chittaranjan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: SAGE Publications 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7746895/
https://www.ncbi.nlm.nih.gov/pubmed/33402813
http://dx.doi.org/10.1177/0253717620933419
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author Andrade, Chittaranjan
author_facet Andrade, Chittaranjan
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description Many authors are unsure of whether to present the mean along with the standard deviation (SD) or along with the standard error of the mean (SEM). The SD is a descriptive statistic that estimates the scatter of values around the sample mean; hence, the SD describes the sample. In contrast, the SEM is an estimate of how close the sample mean is to the population mean; it is an intermediate term in the calculation of the 95% confidence interval around the mean, and (where applicable) statistical significance; the SEM does not describe the sample. Therefore, the mean should always be accompanied by the SD when describing the sample. There are many reasons why the SEM continues to be reported, and it is argued that none of these is justifiable. In fact, presentation of SEMs may mislead readers into believing that the sample data are more precise than they actually are. Given that the standard error is not presented for other parameters, such as difference between means or proportions, and difference between proportions, it is suggested that presentation of SEM values can be done away with, altogether.
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spelling pubmed-77468952021-01-04 Understanding the Difference Between Standard Deviation and Standard Error of the Mean, and Knowing When to Use Which Andrade, Chittaranjan Indian J Psychol Med Learning Curve Many authors are unsure of whether to present the mean along with the standard deviation (SD) or along with the standard error of the mean (SEM). The SD is a descriptive statistic that estimates the scatter of values around the sample mean; hence, the SD describes the sample. In contrast, the SEM is an estimate of how close the sample mean is to the population mean; it is an intermediate term in the calculation of the 95% confidence interval around the mean, and (where applicable) statistical significance; the SEM does not describe the sample. Therefore, the mean should always be accompanied by the SD when describing the sample. There are many reasons why the SEM continues to be reported, and it is argued that none of these is justifiable. In fact, presentation of SEMs may mislead readers into believing that the sample data are more precise than they actually are. Given that the standard error is not presented for other parameters, such as difference between means or proportions, and difference between proportions, it is suggested that presentation of SEM values can be done away with, altogether. SAGE Publications 2020-07-20 /pmc/articles/PMC7746895/ /pubmed/33402813 http://dx.doi.org/10.1177/0253717620933419 Text en © 2020 Indian Psychiatric Society - South Zonal Branch http://creativecommons.org/licenses/by-nc/4.0/ This article is distributed under the terms of the Creative Commons Attribution- NonCommercial 4.0 License (http://creativecommons.org/licenses/by-nc/4.0/) which permits non-Commercial use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage).
spellingShingle Learning Curve
Andrade, Chittaranjan
Understanding the Difference Between Standard Deviation and Standard Error of the Mean, and Knowing When to Use Which
title Understanding the Difference Between Standard Deviation and Standard Error of the Mean, and Knowing When to Use Which
title_full Understanding the Difference Between Standard Deviation and Standard Error of the Mean, and Knowing When to Use Which
title_fullStr Understanding the Difference Between Standard Deviation and Standard Error of the Mean, and Knowing When to Use Which
title_full_unstemmed Understanding the Difference Between Standard Deviation and Standard Error of the Mean, and Knowing When to Use Which
title_short Understanding the Difference Between Standard Deviation and Standard Error of the Mean, and Knowing When to Use Which
title_sort understanding the difference between standard deviation and standard error of the mean, and knowing when to use which
topic Learning Curve
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7746895/
https://www.ncbi.nlm.nih.gov/pubmed/33402813
http://dx.doi.org/10.1177/0253717620933419
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