{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T06:22:53Z","timestamp":1787638973071,"version":"build-2736575974"},"reference-count":32,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T00:00:00Z","timestamp":1787616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Psychol."],"abstract":"<jats:p>Bayesian inference is fundamental to interpreting diagnostic evidence, yet individuals often fail to integrate base rates and test characteristics when evaluating test results. Key questions are whether these difficulties can be attenuated by brief, scalable interventions, whether possible improvements are maintained over time, and whether they generalize to different probability judgments. We addressed these questions in an online experiment involving 256 laypeople who were presented with medical-screening Bayesian problems in a natural-frequency format and asked to estimate either positive predictive value (PPV) or negative predictive value (NPV). Participants were assigned to one of three conditions: repeated exposure to the problems, brief text-based training based on highlighted wording, or brief dynamic training based on animated visualizations. They completed the task before and after the intervention, and again in a delayed post-test administered 8\u201310\u202fdays later, which also assessed generalization to the predictive value not practiced during the intervention (namely PPV following NPV and vice versa). Performance improved reliably from pre-test to immediate post-test and remained elevated at delayed post-test. Moreover, improvements generalized to the unpracticed predictive value. However, neither training condition conferred a consistent advantage over mere exposure to plain text. Accuracy did not vary by predictive value, with comparable performance across PPV and NPV, and error analyses suggested that incorrect responses were heterogeneous and only weakly captured by standard non-Bayesian categories. Together, these findings suggest that modest but significant gains in Bayesian reasoning can emerge from repeated task exposure, whereas highlighted text, dynamic visualization, and feedback do not confer additional benefit.<\/jats:p>","DOI":"10.3389\/fpsyg.2026.1908176","type":"journal-article","created":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T05:36:27Z","timestamp":1787636187000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Repeated exposure rivals lightweight training in Bayesian inference: accuracy, retention, and generalization"],"prefix":"10.3389","volume":"17","author":[{"given":"S.","family":"Pighin","sequence":"first","affiliation":[{"name":"Center for Mind\/Brain Sciences, University of Trento","place":["Trento, Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P.","family":"Ghin","sequence":"additional","affiliation":[{"name":"Center for Mind\/Brain Sciences, University of Trento","place":["Trento, Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"K.","family":"Tentori","sequence":"additional","affiliation":[{"name":"Center for Mind\/Brain Sciences, University of Trento","place":["Trento, Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2026,8,25]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1017\/S0140525X07001653","article-title":"Base-rate respect: from ecological rationality to dual processes","volume":"30","author":"Barbey","year":"2007","journal-title":"Behav. Brain Sci."},{"key":"ref2","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/0001-6918(80)90046-3","article-title":"The base-rate fallacy in probability judgments","volume":"44","author":"Bar-Hillel","year":"1980","journal-title":"Acta Psychol."},{"key":"ref3","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1002\/acp.1460","article-title":"Pictorial representations in statistical reasoning","volume":"23","author":"Brase","year":"2009","journal-title":"Appl. Cogn. Psychol."},{"key":"ref4","doi-asserted-by":"publisher","first-page":"article 1558","DOI":"10.3390\/math10091558","article-title":"How to train novices in Bayesian reasoning","volume":"10","author":"B\u00fcchter","year":"2022","journal-title":"Mathematics"},{"key":"ref5","doi-asserted-by":"publisher","first-page":"999","DOI":"10.1056\/NEJM197811022991808","article-title":"Interpretation by physicians of clinical laboratory results","volume":"299","author":"Casscells","year":"1978","journal-title":"N. Engl. J. Med."},{"key":"ref6","doi-asserted-by":"publisher","first-page":"article 17","DOI":"10.3390\/vision7010017","article-title":"The use of visualizations to improve Bayesian reasoning: a literature review","volume":"7","author":"Cui","year":"2023","journal-title":"Vision"},{"key":"ref7","doi-asserted-by":"publisher","first-page":"b3823","DOI":"10.1136\/bmj.b3823","article-title":"Using probabilistic reasoning","volume":"339","author":"Doust","year":"2009","journal-title":"BMJ"},{"key":"ref8","doi-asserted-by":"publisher","first-page":"932","DOI":"10.3389\/fpsyg.2015.00932","article-title":"Visual aids improve diagnostic inferences and metacognitive judgment calibration","volume":"6","author":"Garcia-Retamero","year":"2015","journal-title":"Front. Psychol."},{"key":"ref9","doi-asserted-by":"publisher","first-page":"741","DOI":"10.1136\/bmj.327.7417.741","article-title":"Simple tools for understanding risks: from innumeracy to insight","volume":"327","author":"Gigerenzer","year":"2003","journal-title":"BMJ"},{"key":"ref10","doi-asserted-by":"publisher","first-page":"684","DOI":"10.1037\/0033-295x.102.4.684","article-title":"How to improve Bayesian reasoning without instruction: frequency formats","volume":"102","author":"Gigerenzer","year":"1995","journal-title":"Psychol. Rev."},{"key":"ref11","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/S0010-0277(00)00133-5","article-title":"Solving probabilistic and statistical problems: a matter of information structure and question form","volume":"78","author":"Girotto","year":"2001","journal-title":"Cognition"},{"key":"ref12","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1017\/s0140525x00041261","article-title":"Physicians neglect base rates, and it matters","volume":"19","author":"Hamm","year":"1996","journal-title":"Behav. Brain Sci."},{"key":"ref13","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.pec.2011.01.033","article-title":"Representing randomness in the communication of individualized cancer risk estimates: effects on cancer risk perceptions, worry, and subjective uncertainty about risk","volume":"86","author":"Han","year":"2012","journal-title":"Patient Educ. Couns."},{"key":"ref14","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1016\/0010-0285(72)90016-3","article-title":"Subjective probability: a judgment of representativeness","volume":"3","author":"Kahneman","year":"1972","journal-title":"Cogn. Psychol."},{"key":"ref15","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1037\/h0034747","article-title":"On the psychology of prediction","volume":"80","author":"Kahneman","year":"1973","journal-title":"Psychol. Rev."},{"key":"ref16","doi-asserted-by":"publisher","first-page":"516","DOI":"10.1080\/0142159021000012540","article-title":"Teaching Bayesian reasoning: an evaluation of a classroom tutorial for medical students","volume":"24","author":"Kurzenh\u00e4user","year":"2002","journal-title":"Med. Teach."},{"key":"ref17","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1080\/08858199309528246","article-title":"Overestimation of test effects in clinical judgment","volume":"8","author":"Lyman","year":"1993","journal-title":"J. Cancer Educ."},{"key":"ref18","first-page":"85","article-title":"Multimedia learning","volume-title":"Psychol. Learn. Motiv","author":"Mayer","year":"2002"},{"key":"ref19","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511816819.002","article-title":"Introduction to multimedia learning","volume-title":"The Cambridge handbook of multimedia learning (pp. 1\u201316)","author":"Mayer","year":"2005"},{"key":"ref20","doi-asserted-by":"publisher","first-page":"1273","DOI":"10.1037\/bul0000126","article-title":"Meta-analysis of the effect of natural frequencies on Bayesian reasoning","volume":"143","author":"McDowell","year":"2017","journal-title":"Psychol. Bull."},{"key":"ref21","doi-asserted-by":"publisher","first-page":"848","DOI":"10.1046\/j.1525-1497.2002.20139.x","article-title":"Quantitative evaluation of the diagnostic thinking process in medical students","volume":"17","author":"Noguchi","year":"2002","journal-title":"J. Gen. Intern. Med."},{"key":"ref22","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.jbef.2017.12.004","article-title":"Prolific.Ac\u2014a subject pool for online experiments","volume":"17","author":"Palan","year":"2018","journal-title":"J. Behav. Exp. Finance"},{"key":"ref23","doi-asserted-by":"publisher","first-page":"735","DOI":"10.3758\/s13421-023-01497-1","article-title":"The impact of problem domain on Bayesian inferences: a systematic investigation","volume":"52","author":"Pighin","year":"2024","journal-title":"Mem. Cogn."},{"key":"ref24","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/j.cognition.2017.06.028","article-title":"Children\u2019s quantitative Bayesian inferences from natural frequencies and number of chances","volume":"168","author":"Pighin","year":"2017","journal-title":"Cognition"},{"key":"ref25","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1177\/0272989X14536268","article-title":"Improving public interpretation of probabilistic test results: distributive evaluations","volume":"35","author":"Pighin","year":"2015","journal-title":"Med. Decis. Mak."},{"key":"ref26","doi-asserted-by":"publisher","first-page":"e043925","DOI":"10.1136\/bmjopen-2020-043925","article-title":"Public\u2019s understanding of swab test results for SARS-CoV-2: an online behavioural experiment during the April 2020 lockdown","volume":"11","author":"Pighin","year":"2021","journal-title":"BMJ Open"},{"key":"ref27","doi-asserted-by":"publisher","first-page":"909","DOI":"10.1093\/abm\/kax065","article-title":"Fostering the understanding of positive test results","volume":"52","author":"Pighin","year":"2018","journal-title":"Ann. Behav. Med."},{"key":"ref29","doi-asserted-by":"publisher","first-page":"380","DOI":"10.1037\/0096-3445.130.3.380","article-title":"Teaching Bayesian reasoning in less than two hours","volume":"130","author":"Sedlmeier","year":"2001","journal-title":"J. Exp. Psychol. Gen."},{"key":"ref30","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1002\/acp.3470","article-title":"A visualization technique for Bayesian reasoning","volume":"33","author":"Starns","year":"2019","journal-title":"Appl. Cogn. Psychol."},{"key":"ref31","doi-asserted-by":"publisher","first-page":"1124","DOI":"10.1126\/science.185.4157.1124","article-title":"Judgment under uncertainty: heuristics and biases","volume":"185","author":"Tversky","year":"1974","journal-title":"Science"},{"key":"ref32","doi-asserted-by":"publisher","first-page":"e008155","DOI":"10.1136\/bmjopen-2015-008155","article-title":"How well do health professionals interpret diagnostic information? A systematic review","volume":"5","author":"Whiting","year":"2015","journal-title":"BMJ Open"},{"key":"ref33","doi-asserted-by":"publisher","first-page":"e106","DOI":"10.2196\/jmir.2030","article-title":"Animated graphics for comparing two risks: a cautionary tale","volume":"14","author":"Zikmund-Fisher","year":"2012","journal-title":"J. Med. Internet Res."}],"container-title":["Frontiers in Psychology"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fpsyg.2026.1908176\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T05:36:29Z","timestamp":1787636189000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fpsyg.2026.1908176\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,25]]},"references-count":32,"alternative-id":["10.3389\/fpsyg.2026.1908176"],"URL":"https:\/\/doi.org\/10.3389\/fpsyg.2026.1908176","relation":{},"ISSN":["1664-1078"],"issn-type":[{"value":"1664-1078","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,25]]},"article-number":"1908176"}}