Total-effect Test can Erroneously Reject Complete Mediation --- Proofs and Examples

Total-effect Test can Erroneously Reject Complete Mediation --- Proofs and Examples | 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 Total-effect Test can Erroneously Reject Complete Mediation --- Proofs and Examples Tingxuan Han, Luxi Zhang, Dianshi Li, Xinshu Zhao, Ke Deng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8959490/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 The procedure for establishing mediation, i.e., determining whether an independent variable X influences a dependent variable Y through a mediator M, remains debated in the literature. Classic causal steps necessitate a significant “total effect”, now commonly termed statistically acknowledgment. Prior research show that the total-effect test can incorrectly reject competitive mediation and is superfluous for complementary mediation. Less attention has been paid to complete mediation (also known as full, perfect, or indirect-only mediation), where the indirect effect (ab) is significant but the direct-and-remainder effect (d) is not. Although recent work largely agrees that the total-effect test should be abandoned, its use persists across disciplines, including non-English literature. Addressing the remaining logical and empirical gaps therefore remains scientifically valuable. Accordingly, we set out four objectives for this study: 1) Demonstrating that the total-effect test can erroneously reject complete mediation, including both subtypes, assuming least squares estimation (LSE) F-test or Sobel test; 2) Verifying these results via simulations and extend them to the LAD-Z test; 3) Presenting two empirical examples illustrating each subtype; 4) Reevaluating existing concepts, theories, and techniques in mediation and related causal analyses, and proposing a broader alternative: process-and-product analysis (PAPA). hypothesis testing complete mediation mediation analysis total-effect test Full Text Additional Declarations No competing interests reported. Supplementary Files supp.pdf 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. 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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-8959490","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":609083566,"identity":"74bfc65b-2c9a-4244-8bbd-8597d041844a","order_by":0,"name":"Tingxuan Han","email":"","orcid":"","institution":"Tsinghua University","correspondingAuthor":false,"prefix":"","firstName":"Tingxuan","middleName":"","lastName":"Han","suffix":""},{"id":609083567,"identity":"8eb716be-586f-466c-92e1-6612ff81273b","order_by":1,"name":"Luxi Zhang","email":"","orcid":"","institution":"University of Macau","correspondingAuthor":false,"prefix":"","firstName":"Luxi","middleName":"","lastName":"Zhang","suffix":""},{"id":609083568,"identity":"e23b1232-a4b7-409e-8303-92adfb7454a1","order_by":2,"name":"Dianshi Li","email":"","orcid":"","institution":"University of Macau","correspondingAuthor":false,"prefix":"","firstName":"Dianshi","middleName":"","lastName":"Li","suffix":""},{"id":609083569,"identity":"f1cf6799-ff6f-4030-87c5-89142c6f0199","order_by":3,"name":"Xinshu Zhao","email":"","orcid":"","institution":"University of Macau","correspondingAuthor":false,"prefix":"","firstName":"Xinshu","middleName":"","lastName":"Zhao","suffix":""},{"id":609083570,"identity":"b5e10d30-3693-4953-979a-b57b5531b64e","order_by":4,"name":"Ke Deng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8UlEQVRIiWNgGAWjYBACCYYEIFnBwMAGRiBwgCgtZwxI1cLYZgBiE6lFsj352MOv8/7Y80m3X3vMU8Mgx3cjgfFzAR4t0jzP0o1ltxkktsmcKTfmOcZgLHkjgVl6Bh4tchI5ZtKS2wwS2CRy0qR52BgSN9xIYGPmwasl/5u05BwDe4iWfwz1BLVIS+SwSX5sMGBsk0g/Js3bxpBgQEiLZM8zM2mGY8aJbSC9c/skDGeeedgsjU+LxPHkZ5I/auTs5WekP5N4881Gnu948sHP+LSAANQZPKDIkQBixgYCGoBKfoAp9gcEVY6CUTAKRsHIBABQ40Qqiac/2AAAAABJRU5ErkJggg==","orcid":"","institution":"Tsinghua University","correspondingAuthor":true,"prefix":"","firstName":"Ke","middleName":"","lastName":"Deng","suffix":""}],"badges":[],"createdAt":"2026-02-24 16:23:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8959490/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8959490/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108079276,"identity":"1eb30236-4251-4c71-9c91-56c1b7ef79e5","added_by":"auto","created_at":"2026-04-29 07:26:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":23716710,"visible":true,"origin":"","legend":"","description":"","filename":"main.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8959490/v1_covered_e4fa30f2-5ccd-414f-9a7e-d658705ce7d6.pdf"},{"id":105028334,"identity":"7268a4ab-49bd-4292-b7ef-fef47b84e16e","added_by":"auto","created_at":"2026-03-20 05:52:19","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":15641310,"visible":true,"origin":"","legend":"","description":"","filename":"supp.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8959490/v1/918f79c5f684b465a28b7057.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Total-effect Test can Erroneously Reject Complete Mediation --- Proofs and Examples","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":"hypothesis testing, complete mediation, mediation analysis, total-effect test","lastPublishedDoi":"10.21203/rs.3.rs-8959490/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8959490/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe procedure for establishing mediation, i.e., determining whether an independent variable X influences a dependent variable Y through a mediator M, remains debated in the literature. 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