Estimating Standard Deviation via Sample Mean Extended Quantile Estimation

Estimating Standard Deviation via Sample Mean Extended Quantile Estimation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Estimating Standard Deviation via Sample Mean Extended Quantile Estimation Mediya Bawakhan Mrakhan, Tamás Kói This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7189837/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 24 Nov, 2025 Read the published version in BMC Medical Research Methodology → Version 1 posted 12 You are reading this latest preprint version Abstract Background It is common practice in meta-analysis of means to estimate the mean and standard deviation (SD) when only the median and other ordered statistics are published in an included study. There are several methods for this purpose. Often, the advantages of including additional studies in the meta-analysis of means by using these methods outweigh the disadvantages of estimation errors. Sometimes, in addition to the median and other ordered statistics, the sample mean is also available, e.g. it can be displayed in box plots as additional information. In this case, only the standard deviation should be estimated. Methods We modified the popular quantile estimation (QE) method by incorporating the known mean into the estimation of the SD. We analyzed the performance of the original and the mean-extended QE (MEQE) methods with extensive simulations. A wide range of quantitative and visual tools were used to evaluate the performance of the methods. Results In the scenario where only the median, lower and upper quartiles were used, the mean boosted version provided a slightly/moderately better SD estimation than the original QE method for lognormal, gamma and Weibull distribution families. For the normal distribution, the difference was negligible. When both the QE and MEQE methods also used the minimum and maximum, their performance was essentially the same. Interestingly, their joint performance was worse than the performance obtained without using the extreme values. Conclusions When only the median, lower and upper quartiles, and the mean are available, the MEQE method may provide more accurate SD estimates. This study may motivate the modification of other algorithms commonly used in meta-analysis to incorporate additional information that may occasionally become available. Both the QE and MEQE methods performed worse when the minimum and maximum values were also used in the estimation. Our recommendation, based on these results, is to avoid using extreme values in SD estimation. Quantile estimation median mean standard deviation estimation quartiles meta-analysis simulation Full Text Additional Declarations No competing interests reported. Supplementary Files RCodelastversion.zip supplementary.pdf Cite Share Download PDF Status: Published Journal Publication published 24 Nov, 2025 Read the published version in BMC Medical Research Methodology → Version 1 posted Editorial decision: Revision requested 25 Aug, 2025 Reviews received at journal 24 Aug, 2025 Reviews received at journal 17 Aug, 2025 Reviewers agreed at journal 15 Aug, 2025 Reviewers agreed at journal 14 Aug, 2025 Reviewers agreed at journal 14 Aug, 2025 Reviewers agreed at journal 06 Aug, 2025 Reviewers invited by journal 04 Aug, 2025 Editor invited by journal 25 Jul, 2025 Editor assigned by journal 23 Jul, 2025 Submission checks completed at journal 23 Jul, 2025 First submitted to journal 22 Jul, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7189837","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":496470783,"identity":"b48b9a59-8d73-4710-8e77-fa7b3a2d5a9d","order_by":0,"name":"Mediya Bawakhan Mrakhan","email":"","orcid":"","institution":"Budapest University of Technology and Economics","correspondingAuthor":false,"prefix":"","firstName":"Mediya","middleName":"Bawakhan","lastName":"Mrakhan","suffix":""},{"id":496470784,"identity":"25b0985c-934c-46b2-a2b9-2e8e86574b6d","order_by":1,"name":"Tamás Kói","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYBACCQbGBhAlByTYoGzCWhqB6iSMGRiYidYCUZfYQLQWyfbm9gcfcyzS17afP/aAccc2OQbpHgO8WqR5DjY2ztwmkbvtTDK7AeOZ28YMMmfwa5GTSGxs5gVpOZDMJsHYdjuxQSKHOC3pZucfg7XUE9QiDdWSYHYDYksCAyEtkj0HG2cC/WK47cZjM4nEM7cN2yTSCvBqkTje/uDDx2118mbnE59JfNxxW55fInkDXi2oIIEBlAZGwSgYBaNgFFAMAGKoRjjoXqQ/AAAAAElFTkSuQmCC","orcid":"","institution":"Budapest University of Technology and Economics","correspondingAuthor":true,"prefix":"","firstName":"Tamás","middleName":"","lastName":"Kói","suffix":""}],"badges":[],"createdAt":"2025-07-22 18:38:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7189837/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7189837/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s12874-025-02711-1","type":"published","date":"2025-11-24T15:58:17+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":97179453,"identity":"59acc40a-d35b-4ddb-b53f-8c02565375a4","added_by":"auto","created_at":"2025-12-01 16:15:43","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":661553,"visible":true,"origin":"","legend":"","description":"","filename":"MEQEManuscriptBMC.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7189837/v1_covered_97d61ff7-c096-47e0-bda2-cee199172c81.pdf"},{"id":88559386,"identity":"9af74418-cfe6-4788-9ed8-a99b3f6a9d18","added_by":"auto","created_at":"2025-08-07 17:34:42","extension":"zip","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":31096,"visible":true,"origin":"","legend":"","description":"","filename":"RCodelastversion.zip","url":"https://assets-eu.researchsquare.com/files/rs-7189837/v1/984f77cc9c0b1ca6af654b93.zip"},{"id":88560173,"identity":"791c2c24-159d-4225-a6aa-4195a41f0192","added_by":"auto","created_at":"2025-08-07 17:50:43","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3397152,"visible":true,"origin":"","legend":"","description":"","filename":"supplementary.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7189837/v1/a23b898e963be5e8b0ccdbd0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Estimating Standard Deviation via Sample Mean Extended Quantile Estimation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-medical-research-methodology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmrm","sideBox":"Learn more about [BMC Medical Research Methodology](http://bmcmedresmethodol.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/bmrm/default.aspx","title":"BMC Medical Research Methodology","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Quantile estimation, median, mean, standard deviation estimation, quartiles, meta-analysis, simulation","lastPublishedDoi":"10.21203/rs.3.rs-7189837/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7189837/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cb\u003eBackground\u003c/b\u003e\u003c/p\u003e\u003cp\u003eIt is common practice in meta-analysis of means to estimate the mean and standard deviation (SD) when only the median and other ordered statistics are published in an included study. There are several methods for this purpose. Often, the advantages of including additional studies in the meta-analysis of means by using these methods outweigh the disadvantages of estimation errors. Sometimes, in addition to the median and other ordered statistics, the sample mean is also available, e.g. it can be displayed in box plots as additional information. In this case, only the standard deviation should be estimated.\u003c/p\u003e\u003cp\u003e\u003cb\u003eMethods\u003c/b\u003e\u003c/p\u003e\u003cp\u003eWe modified the popular quantile estimation (QE) method by incorporating the known mean into the estimation of the SD. We analyzed the performance of the original and the mean-extended QE (MEQE) methods with extensive simulations. A wide range of quantitative and visual tools were used to evaluate the performance of the methods.\u003c/p\u003e\u003cp\u003e\u003cb\u003eResults\u003c/b\u003e\u003c/p\u003e\u003cp\u003eIn the scenario where only the median, lower and upper quartiles were used, the mean boosted version provided a slightly/moderately better SD estimation than the original QE method for lognormal, gamma and Weibull distribution families. For the normal distribution, the difference was negligible. When both the QE and MEQE methods also used the minimum and maximum, their performance was essentially the same. Interestingly, their joint performance was worse than the performance obtained without using the extreme values.\u003c/p\u003e\u003cp\u003e\u003cb\u003eConclusions\u003c/b\u003e\u003c/p\u003e\u003cp\u003eWhen only the median, lower and upper quartiles, and the mean are available, the MEQE method may provide more accurate SD estimates. This study may motivate the modification of other algorithms commonly used in meta-analysis to incorporate additional information that may occasionally become available. Both the QE and MEQE methods performed worse when the minimum and maximum values were also used in the estimation. Our recommendation, based on these results, is to avoid using extreme values in SD estimation.\u003c/p\u003e","manuscriptTitle":"Estimating Standard Deviation via Sample Mean Extended Quantile Estimation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-07 17:34:38","doi":"10.21203/rs.3.rs-7189837/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-08-25T06:55:38+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-24T18:30:44+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-17T11:59:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"161571600193199225279575075707175240939","date":"2025-08-15T17:39:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"281235251426687644864105072911198643165","date":"2025-08-15T02:41:38+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"77196533890355112931205811512476599162","date":"2025-08-15T02:38:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"32667097826972935456567890054655415743","date":"2025-08-06T08:38:53+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-04T06:35:53+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-07-25T19:23:52+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-07-23T13:18:26+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-07-23T13:17:45+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Medical Research Methodology","date":"2025-07-22T18:29:50+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-medical-research-methodology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmrm","sideBox":"Learn more about [BMC Medical Research Methodology](http://bmcmedresmethodol.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/bmrm/default.aspx","title":"BMC Medical Research Methodology","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"90e0cf09-eca9-4b38-8575-25eb9e569fde","owner":[],"postedDate":"August 7th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-12-01T16:10:52+00:00","versionOfRecord":{"articleIdentity":"rs-7189837","link":"https://doi.org/10.1186/s12874-025-02711-1","journal":{"identity":"bmc-medical-research-methodology","isVorOnly":false,"title":"BMC Medical Research Methodology"},"publishedOn":"2025-11-24 15:58:17","publishedOnDateReadable":"November 24th, 2025"},"versionCreatedAt":"2025-08-07 17:34:38","video":"","vorDoi":"10.1186/s12874-025-02711-1","vorDoiUrl":"https://doi.org/10.1186/s12874-025-02711-1","workflowStages":[]},"version":"v1","identity":"rs-7189837","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7189837","identity":"rs-7189837","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}