{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:36:42Z","timestamp":1760150202746,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T00:00:00Z","timestamp":1698710400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Data"],"abstract":"<jats:p>The reproducibility of academic research has long been a persistent issue, contradicting one of the fundamental principles of science. Recently, there has been an increasing number of false claims found in academic manuscripts, casting doubt on the validity of reported results. In this paper, we utilize an adapted version of Benford\u2019s law, a statistical phenomenon that describes the distribution of leading digits in naturally occurring datasets, to identify the potential manipulation of results in research manuscripts, solely using the aggregated data presented in those manuscripts rather than the commonly unavailable raw datasets. Our methodology applies the principles of Benford\u2019s law to commonly employed analyses in academic manuscripts, thus reducing the need for the raw data itself. To validate our approach, we employed 100 open-source datasets and successfully predicted 79% of them accurately using our rules. Moreover, we tested the proposed method on known retracted manuscripts, showing that around half (48.6%) can be detected using the proposed method. Additionally, we analyzed 100 manuscripts published in the last two years across ten prominent economic journals, with 10 manuscripts randomly sampled from each journal. Our analysis predicted a 3% occurrence of results manipulation with a 96% confidence level. Our findings show that Benford\u2019s law adapted for aggregated data, can be an initial tool for identifying data manipulation; however, it is not a silver bullet, requiring further investigation for each flagged manuscript due to the relatively low prediction accuracy.<\/jats:p>","DOI":"10.3390\/data8110165","type":"journal-article","created":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T12:44:03Z","timestamp":1698756243000},"page":"165","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Can We Mathematically Spot the Possible Manipulation of Results in Research Manuscripts Using Benford\u2019s Law?"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7851-8147","authenticated-orcid":false,"given":"Teddy","family":"Lazebnik","sequence":"first","affiliation":[{"name":"Department of Cancer Biology, Cancer Institute, University College London, London WC1E 6BT, UK"}]},{"given":"Dan","family":"Gorlitsky","sequence":"additional","affiliation":[{"name":"Department of Economics, Reichman University, Herzliya 4610101, Israel"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,31]]},"reference":[{"key":"ref_1","unstructured":"Franzen, M. (2016). Reproducibility, John Wiley & Sons, Ltd.. Chapter 22."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pone.0010271","article-title":"Do Pressures to Publish Increase Scientists\u2019 Bias? An Empirical Support from US States Data","volume":"5","author":"Fanelli","year":"2010","journal-title":"PLoS ONE"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.1097\/j.pain.0000000000001254","article-title":"Reproducible and replicable pain research: A critical review","volume":"159","author":"Lee","year":"2018","journal-title":"Pain"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1186\/s13012-015-0342-x","article-title":"Outcomes for implementation science: An enhanced systematic review of instruments using evidence-based rating criteria","volume":"10","author":"Lewis","year":"2015","journal-title":"Implement. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Roberts, P., and Priest, H. (2006). Reliability and validity in research. Nurs. Stand., 20.","DOI":"10.7748\/ns2006.07.20.44.41.c6560"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1016\/j.ymthe.2021.02.011","article-title":"Keeping Them Honest: Fighting Fraud in Academic Publishing","volume":"29","author":"Frederickson","year":"2021","journal-title":"Mol. Ther."},{"key":"ref_7","first-page":"55","article-title":"Do Legitimate Publishers Benefit or Profit from Error, Misconduct or Fraud?","volume":"8","author":"Vuong","year":"2021","journal-title":"Exch. Interdiscip. Res. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"100511","DOI":"10.1016\/j.patter.2022.100511","article-title":"AI-enabled image fraud in scientific publications","volume":"3","author":"Gu","year":"2022","journal-title":"Patterns"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1108\/MEDAR-02-2015-0009","article-title":"Looking through the fraud triangle: A review and call for new directions","volume":"23","author":"Free","year":"2015","journal-title":"Meditari Account. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1177\/1476127017701076","article-title":"Is there a credibility crisis in strategic management research? Evidence on the reproducibility of study findings","volume":"15","author":"Bergh","year":"2017","journal-title":"Strateg. Organ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1111\/1471-0528.15689","article-title":"Plagiarism and data falsification are the most common reasons for retracted publications in obstetrics and gynaecology","volume":"126","author":"Chambers","year":"2019","journal-title":"BJOG Int. J. Obstet. Gynaecol."},{"key":"ref_12","unstructured":"Brainard, J., and You, J. (2023, May 29). What a Massive Database of Retracted Papers Reveals about Science Publishing\u2019s \u2018Death Penalty\u2019. Available online: https:\/\/www.science.org\/content\/article\/what-massive-database-retracted-papers-reveals-about-science-publishing-s-death-penalty."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"99","DOI":"10.4997\/jrcpe.2019.201","article-title":"Peer review in academic publishing: Threats and challenges","volume":"49","author":"Misra","year":"2019","journal-title":"J. R. Coll. Physicians Edinb."},{"key":"ref_14","first-page":"227","article-title":"Peer Review in Scientific Publications: Benefits, Critiques, & A Survival Guide","volume":"25","author":"Kelly","year":"2013","journal-title":"EJIFCC"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Walker, N., and Holtfreter, K. (2015). Applying criminological theory to academic fraud. J. Financ. Crime, 22.","DOI":"10.1108\/JFC-12-2013-0071"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1186\/s41073-018-0051-5","article-title":"The changing forms and expectations of peer review","volume":"3","author":"Horbach","year":"2018","journal-title":"Res. Integr. Peer Rev."},{"key":"ref_17","first-page":"172","article-title":"Retraction, Dishonesty and Plagiarism: Analysis of a Crucial Issue for Academic Publishing, and the Inadequate Responses from Leading Journals in Economics and Management Disciplines","volume":"2","author":"Karabag","year":"2012","journal-title":"J. Appl. Econ. Bus. Res."},{"key":"ref_18","unstructured":"Muhsin, M., Kardoyo, M., Arief, S., Nurkhin, A., and Pramusinto, H. An Analyis of Student\u2019s Academic Fraud Behavior. Proceedings of the International Conference on Learning Innovation (ICLI 2017)."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1177\/004839319202200101","article-title":"Fraud in Science An Economic Approach","volume":"22","author":"Wible","year":"1992","journal-title":"Philos. Soc. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Huynh, T.L.D., Rieger, M.O., Wang, M., Berens, D., Bui, D.L., Chen, H.L., Emering, T.P., Geng, S., Liu-Gerhards, Y., and Neumann, T. (2022). Cheating, Trust and Social Norms: Data from Germany, Vietnam, China, Taiwan, and Japan. Data, 7.","DOI":"10.3390\/data7100137"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1054\/mehy.1997.0628","article-title":"Basic philosophy and concepts underlying scientific peer review","volume":"52","author":"Stehbens","year":"1999","journal-title":"Med. Hypotheses"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1038\/sj.embor.7401143","article-title":"Retraction rates are on the rise","volume":"9","author":"Cokol","year":"2008","journal-title":"EMBO Rep."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3855","DOI":"10.1128\/IAI.05661-11","article-title":"Retracted Science and the Retraction Index","volume":"79","author":"Fang","year":"2011","journal-title":"Infect. Immun."},{"key":"ref_24","first-page":"39","article-title":"What is the future of peer review? Why is there fraud in science? Is plagiarism out of control? Why do scientists do bad things? Is it all a case of:\u201cAll that is necessary for the triumph of evil is that good men do nothing?\u201d","volume":"3","author":"Triggle","year":"2007","journal-title":"Vasc. Health Risk Manag."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Faintuch, J., and Faintuch, S. (2022). Integrity of Scientific Research: Fraud, Misconduct and Fake News in the Academic, Medical and Social Environment, Springer International Publishing.","DOI":"10.1007\/978-3-030-99680-2"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Chan, P. (2022). An Empirical Study on Data Validation Methods of Delphi and General Consensus. Data, 7.","DOI":"10.3390\/data7020018"},{"key":"ref_27","first-page":"17","article-title":"The Effective Use of Benford\u2019s Law to Assist in Detecting Fraud in Accounting Data","volume":"5","author":"Durtschi","year":"2004","journal-title":"J. Forensic Account."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/S0748-5751(00)00008-7","article-title":"Computer assisted analytical procedures using Benford\u2019s Law","volume":"18","author":"Drake","year":"2000","journal-title":"J. Account. Educ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.ins.2021.09.038","article-title":"Feature selection using Benford\u2019s law to support detection of malicious social media bots","volume":"582","author":"Mbona","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"104084","DOI":"10.1016\/j.respol.2020.104084","article-title":"Detecting academic fraud using Benford law: The case of Professor James Hunton","volume":"49","author":"Horton","year":"2020","journal-title":"Res. Policy"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1111\/j.1468-0475.2009.00475.x","article-title":"Benford\u2019s Law as an Indicator of Fraud in Economics","volume":"10","author":"Todter","year":"2019","journal-title":"Ger. Econ. Rev."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Piwowar, H.A. (2011). Who Shares? Who Doesn\u2019t? Factors Associated with Openly Archiving Raw Research Data. PLoS ONE, 6.","DOI":"10.1371\/journal.pone.0018657"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1186\/s13041-020-0552-2","article-title":"No raw data, no science: Another possible source of the reproducibility crisis","volume":"13","author":"Miyakawa","year":"2020","journal-title":"Mol. Brain"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1080\/02664760601004940","article-title":"Not the First Digit! Using Benford\u2019s Law to Detect Fraudulent Scientif ic Data","volume":"34","author":"Diekmann","year":"2007","journal-title":"J. Appl. Stat."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s10663-008-9084-1","article-title":"Does Benford\u2019s Law hold in economic research and forecasting?","volume":"36","year":"2009","journal-title":"Empirica"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1080\/01621459.1951.10500769","article-title":"The Kolmogorov-Smirnov Test for Goodness of Fit","volume":"46","author":"Massey","year":"1951","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Nigrini, M. (2012). Benford\u2019s Law: Applications for Forensic Accounting, Auditing, and Fraud Detection, John Wiley & Sons.","DOI":"10.1002\/9781119203094"},{"key":"ref_38","first-page":"733","article-title":"Difficulties detecting fraud? The use of Benford\u2019s law on regression tables","volume":"231","author":"Bauer","year":"2011","journal-title":"Jahrb. Nat. Stat."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Nix, D., and Weigend, A. (1994\u20132, January 28). Estimating the mean and variance of the target probability distribution. Proceedings of the 1994 IEEE International Conference on Neural Networks (ICNN\u201994), Orlando, FL, USA.","DOI":"10.1109\/ICNN.1994.374138"},{"key":"ref_40","first-page":"77","article-title":"Fitting Segmented Regression Models by Grid Search","volume":"29","author":"Lerman","year":"2018","journal-title":"J. R. Stat. Soc. Ser. C Appl. Stat."},{"key":"ref_41","first-page":"354","article-title":"Python\u2014The Fastest Growing Programming Language","volume":"4","author":"Srinath","year":"2017","journal-title":"Int. Res. J. Eng. Technol."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Lazebnik, T., Fleischer, T., and Yaniv-Rosenfeld, A. (2023). Benchmarking Biologically-inspired Automatic Machine Learning for Economic Tasks. Sustainability, 15.","DOI":"10.3390\/su151411232"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2623","DOI":"10.1096\/fj.08-107938","article-title":"Comparison of SCImago journal rank indicator with journal impact factor","volume":"22","author":"Falagas","year":"2008","journal-title":"FASEB J."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1108\/AJIM-12-2015-0205","article-title":"Visualization and analysis of SCImago Journal & Country Rank structure via journal clustering","volume":"68","author":"Batagelj","year":"2016","journal-title":"Aslib J. Inf. Manag."},{"key":"ref_45","first-page":"343","article-title":"A critical review of SCImago Journal & Country Rank","volume":"24","year":"2014","journal-title":"Res. Eval."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1080\/09638180020017159","article-title":"Earnings cosmetics in a tax-driven accounting environment: Evidence from Finnish public firms","volume":"9","author":"Niskanen","year":"2000","journal-title":"Eur. Account. Rev."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1080\/00036840121785","article-title":"How useful are the forecasts of intergovernmental agencies? The IMF and OECD versus the consensus","volume":"33","author":"Batchelor","year":"2001","journal-title":"Appl. Econ."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.accinf.2018.09.004","article-title":"Benford\u2019s law and the limits of digit analysis","volume":"31","author":"Druica","year":"2018","journal-title":"Int. J. Account. Inf. Syst."},{"key":"ref_49","unstructured":"Morrow, J. (2023, October 24). Benford\u2019s Law, Families of Distributions and a Test Bias CEP Discussion. 2014; p.1291. Available online: https:\/\/cep.lse.ac.uk\/_new\/publications\/abstract.asp?index=4486."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1093\/ei\/39.1.162","article-title":"Academic economists behaving badly? A survey on three areas of unethical behavior","volume":"39","author":"List","year":"2001","journal-title":"Econ. Inq."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1747","DOI":"10.1016\/j.respol.2014.05.002","article-title":"Scientific misbehavior in economics","volume":"43","author":"Necker","year":"2014","journal-title":"Res. Policy"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/s12036-017-9427-z","article-title":"Benford\u2019s Distribution in Extrasolar World: Do the Exoplanets Follow Benford\u2019s Distribution?","volume":"38","author":"Shukla","year":"2017","journal-title":"J. Astrophys. Astron."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1007\/s10260-021-00588-0","article-title":"Forum on Benford\u2019s law and statistical methods for the detection of frauds","volume":"30","author":"Barabesi","year":"2021","journal-title":"Stat. Methods Appl."},{"key":"ref_54","first-page":"1","article-title":"The Price of Restricting Vulnerability Publications","volume":"9","author":"Granick","year":"2005","journal-title":"Int. J. Commun. Law Policy"}],"container-title":["Data"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2306-5729\/8\/11\/165\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:14:54Z","timestamp":1760130894000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2306-5729\/8\/11\/165"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,31]]},"references-count":54,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["data8110165"],"URL":"https:\/\/doi.org\/10.3390\/data8110165","relation":{},"ISSN":["2306-5729"],"issn-type":[{"type":"electronic","value":"2306-5729"}],"subject":[],"published":{"date-parts":[[2023,10,31]]}}}