Investigating the ecological fallacy through sampling distributions constructed from finite populations

Investigating the ecological fallacy through sampling distributions constructed from finite populations | 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 Investigating the ecological fallacy through sampling distributions constructed from finite populations David Torres, Damian Rouson This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3818959/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Correlation coefficients and linear regression values computed from group averages can differ from correlation coefficients and linear regression values computed using individual scores. This observation known as the ecological fallacy often assumes that all the individual scores are available from a population. In many situations, one must use a sample from the larger population. In such cases, the computed correlation coefficient and linear regression values will depend on the sample that is chosen and the underlying sampling distribution. The sampling distribution of correlation coefficients and linear regression values for group averages will be identical to the sampling distribution for individuals for normally distributed variables for samples drawn from infinitely large continuous distributions. However, data that is acquired in practice is often acquired when sampling without replacement from a finite population. Our objective is to demonstrate through Monte Carlo simulations that thesampling distributions for correlation and linear regression will also be similar for individuals and group averages when sampling without replacement from normally distributed variables. These simulations suggest that when a sample from a population is selected, the correlation coefficients and linear regression values computed from individual scores will not be more accurate in estimating the entire population values compared to samples when group averages are used as long as the sample size is the same. Ecological Fallacy Sampling distributions Pearson R Monte Carlo Simulation Linear regression Multiple regression Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-3818959","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":264536469,"identity":"2fa9f668-04fb-4ef2-b23a-dc8887ac41e3","order_by":0,"name":"David Torres","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAz0lEQVRIiWNgGAWjYDCCA3AWM4yZQIQWiFo2mFLitfAYEKeF7/gZM+kPFffy+fnPfHtcmGPHwM+eY4BXi+SZHDOJA2eKLWfOyN1uPHNbMoNkzxv8WgwOpKVJHGxLMDC4wbtNmnfbAQaDGwRsMTj/DKLF/vyZZ2At9gS13Eg+BrGFIYcNYosEIb/ceHzY4syZBAOJG2lmQC3JPBJnnhXg1cJ3PrHxRkVFggF//2GQw+zk+NuTN+DVAgQsEsg8HkLKQYD5AzGqRsEoGAWjYAQDALunR/y7bIs9AAAAAElFTkSuQmCC","orcid":"","institution":"Northern New Mexico College","correspondingAuthor":true,"prefix":"","firstName":"David","middleName":"","lastName":"Torres","suffix":""},{"id":264536470,"identity":"dc8f48b8-38e5-41d3-852e-a787ebffdcd8","order_by":1,"name":"Damian Rouson","email":"","orcid":"","institution":"Lawrence Berkeley National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Damian","middleName":"","lastName":"Rouson","suffix":""}],"badges":[],"createdAt":"2023-12-29 01:14:53","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3818959/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3818959/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":49536068,"identity":"1b8212df-aeb3-46e1-8e0d-5592bc153ed6","added_by":"auto","created_at":"2024-01-12 15:52:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":18523022,"visible":true,"origin":"","legend":"","description":"","filename":"eesver3.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3818959/v1_covered_feed4453-c4d5-49ad-bfe6-7fbd950d2b55.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Investigating the ecological fallacy through sampling distributions constructed from finite populations","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Ecological Fallacy, Sampling distributions, Pearson R, Monte Carlo Simulation, Linear regression, Multiple regression","lastPublishedDoi":"10.21203/rs.3.rs-3818959/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3818959/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCorrelation coefficients and linear regression values computed from group averages can differ from correlation coefficients and linear regression values computed using individual scores. 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