A Bayesian Network Framework for Generalising the Lady Tasting Tea Experiment

A Bayesian Network Framework for Generalising the Lady Tasting Tea Experiment | 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 Article A Bayesian Network Framework for Generalising the Lady Tasting Tea Experiment Gang Xie This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8634718/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 Lady Tasting Tea experiment is widely recognised as the origin of modern statistical hypothesis testing. In a previous study, we modelled this experiment using a Bayesian network (BN); however, that approach was constrained by a three-level ability scale and manually specified parameters. In this paper, we present a methodological advancement that enables BN modelling for more flexible experimental designs. A key contribution is the generation of simulated sample data for arbitrary designs with N cups (where N is even) and k ability levels ( k ≥ 2). This simulation, implemented in R, enabled the construction of a 10-cup, 5-level BN model. Parameter estimation for this model, comprising 21 nodes and 22,511 conditional probability entries, was performed efficiently using the Expectation–Maximisation algorithm in Netica—an otherwise impractical task to complete manually. Although models with larger numbers of cups and ability levels exhibit exponential growth in parameter space, the proposed simulation–EM approach establishes a methodologically innovative and scalable procedure for generalising the Lady Tasting Tea experiment. Beyond Fisher’s test of significance, the framework retains posterior probability estimates for assessing a tester’s ability, thereby providing a more comprehensive perspective on statistical inference. Biological sciences/Computational biology and bioinformatics Physical sciences/Mathematics and computing the Lady Tasting Tea experiment Bayesian network Simulation-based inference Fisher’s test of significance Posterior probability Full Text Additional Declarations No competing interests reported. Supplementary Files TheLadyTestingTea10cupssimuDseed99.neta TheLadyTestingTea8cupsp5.neta simuDataTeaMilk10cupsp5seed99.csv 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-8634718","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":619754959,"identity":"666f8265-ff57-4790-a6b5-70fcf746f0d9","order_by":0,"name":"Gang Xie","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvElEQVRIiWNgGAWjYFACxgaGDxCWAfFaGGeQqIWBgZmHJC3yEcmNj21q6hIb2Ju3STDUHCasxfDMwWbjnGOHExt4jpVJMBwjRkt7Y5t0bsOBxAaJHDMJBjZitDQztv+2bAA6TP4NUMs/IrTIsze2MTM2MANt4TGTYGwjQosBz8FmyZ5jh43beNKKLRL70omwZUb6ww8/aupk+9kPb7zx4Zs1EbYcgDLYQEQCYQ1AWxqIUTUKRsEoGAUjGwAAcRI212H1NGsAAAAASUVORK5CYII=","orcid":"","institution":"Charles Sturt University","correspondingAuthor":true,"prefix":"","firstName":"Gang","middleName":"","lastName":"Xie","suffix":""}],"badges":[],"createdAt":"2026-01-19 03:38:50","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8634718/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8634718/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108670240,"identity":"3073dfb0-03b6-4245-8490-c440e85b2ed3","added_by":"auto","created_at":"2026-05-07 07:26:05","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":662069,"visible":true,"origin":"","legend":"","description":"","filename":"SubmissionScientificReportsXiev1a.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8634718/v1_covered_a7ed3438-ca45-46f5-bbf5-c6c7538b6669.pdf"},{"id":106648564,"identity":"8d56c5be-6fff-41f0-83c0-2384c04359e9","added_by":"auto","created_at":"2026-04-10 21:22:17","extension":"neta","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":52913,"visible":true,"origin":"","legend":"","description":"","filename":"TheLadyTestingTea10cupssimuDseed99.neta","url":"https://assets-eu.researchsquare.com/files/rs-8634718/v1/9b06f3b4b5629c0a1a721d79.neta"},{"id":106648563,"identity":"a5a6f063-87f8-44af-ab63-b5921e4732d4","added_by":"auto","created_at":"2026-04-10 21:22:17","extension":"neta","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3835,"visible":true,"origin":"","legend":"","description":"","filename":"TheLadyTestingTea8cupsp5.neta","url":"https://assets-eu.researchsquare.com/files/rs-8634718/v1/4921b33a0f95acf06809d007.neta"},{"id":106959047,"identity":"4d940cd9-7e56-4702-a1e6-73bbfabca9f4","added_by":"auto","created_at":"2026-04-15 08:44:20","extension":"csv","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":9479603,"visible":true,"origin":"","legend":"","description":"","filename":"simuDataTeaMilk10cupsp5seed99.csv","url":"https://assets-eu.researchsquare.com/files/rs-8634718/v1/20d7378207a30fd98bbdcfb3.csv"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Bayesian Network Framework for Generalising the Lady Tasting Tea Experiment","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":"the Lady Tasting Tea experiment, Bayesian network, Simulation-based inference, Fisher’s test of significance, Posterior probability","lastPublishedDoi":"10.21203/rs.3.rs-8634718/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8634718/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe Lady Tasting Tea experiment is widely recognised as the origin of modern statistical hypothesis testing. In a previous study, we modelled this experiment using a Bayesian network (BN); however, that approach was constrained by a three-level ability scale and manually specified parameters. In this paper, we present a methodological advancement that enables BN modelling for more flexible experimental designs. A key contribution is the generation of simulated sample data for arbitrary designs with \u003cem\u003eN\u003c/em\u003e cups (where \u003cem\u003eN\u003c/em\u003e is even) and \u003cem\u003ek\u003c/em\u003e ability levels (\u003cem\u003ek\u003c/em\u003e\u0026thinsp;\u0026ge;\u0026thinsp;2). This simulation, implemented in R, enabled the construction of a 10-cup, 5-level BN model. Parameter estimation for this model, comprising 21 nodes and 22,511 conditional probability entries, was performed efficiently using the Expectation\u0026ndash;Maximisation algorithm in Netica\u0026mdash;an otherwise impractical task to complete manually. Although models with larger numbers of cups and ability levels exhibit exponential growth in parameter space, the proposed simulation\u0026ndash;EM approach establishes a methodologically innovative and scalable procedure for generalising the Lady Tasting Tea experiment. Beyond Fisher\u0026rsquo;s test of significance, the framework retains posterior probability estimates for assessing a tester\u0026rsquo;s ability, thereby providing a more comprehensive perspective on statistical inference.\u003c/p\u003e","manuscriptTitle":"A Bayesian Network Framework for Generalising the Lady Tasting Tea Experiment","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-10 21:22:12","doi":"10.21203/rs.3.rs-8634718/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"419f07cf-a0b7-42be-8eee-fd0199fa6d84","owner":[],"postedDate":"April 10th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Rejected","date":"2026-05-07T07:15:54+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-06T17:06:19+00:00","index":123,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":65953617,"name":"Biological sciences/Computational biology and bioinformatics"},{"id":65953618,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-05-07T07:24:59+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-10 21:22:12","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8634718","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8634718","identity":"rs-8634718","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}