{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T15:49:36Z","timestamp":1776527376904,"version":"3.51.2"},"reference-count":54,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,8,24]],"date-time":"2020-08-24T00:00:00Z","timestamp":1598227200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We review the sampling and results of the radiocarbon dating of the archaeological cloth known as the Shroud of Turin, in the light of recent statistical analyses of both published and raw data. The statistical analyses highlight an inter-laboratory heterogeneity of the means and a monotone spatial variation of the ages of subsamples that suggest the presence of contaminants unevenly removed by the cleaning pretreatments. We consider the significance and overall impact of the statistical analyses on assessing the reliability of the dating results and the design of correct sampling. These analyses suggest that the 1988 radiocarbon dating does not match the current accuracy requirements. Should this be the case, it would be interesting to know the accurate age of the Shroud of Turin. Taking into account the whole body of scientific data, we discuss whether it makes sense to date the Shroud again.<\/jats:p>","DOI":"10.3390\/e22090926","type":"journal-article","created":{"date-parts":[[2020,8,24]],"date-time":"2020-08-24T10:37:32Z","timestamp":1598265452000},"page":"926","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Statistical and Proactive Analysis of an Inter-Laboratory Comparison: The Radiocarbon Dating of the Shroud of Turin"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1823-1133","authenticated-orcid":false,"given":"Paolo","family":"Di Lazzaro","sequence":"first","affiliation":[{"name":"Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Dipartimento FSN, Centro Ricerche Frascati, via E. Fermi 45, 00044 Frascati, Italy"}]},{"given":"Anthony C.","family":"Atkinson","sequence":"additional","affiliation":[{"name":"Department of Statistics, London School of Economics, London WC2A 2AE, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7781-1133","authenticated-orcid":false,"given":"Paola","family":"Iacomussi","sequence":"additional","affiliation":[{"name":"Istituto Nazionale di Ricerca Metrologica (INRIM), 00135 Torino, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7886-2207","authenticated-orcid":false,"given":"Marco","family":"Riani","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze Economiche e Aziendale and Interdepartmental Centre for Robust Statistics, Universit\u00e0 di Parma, 43125 Parma, Italy"}]},{"given":"Marco","family":"Ricci","sequence":"additional","affiliation":[{"name":"Independent Researcher, Via Fra Dolcino 19, 28100 Novara, Italy"}]},{"given":"Peter","family":"Wadhams","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1080\/00085030.1981.10756882","article-title":"A chemical investigation of the Shroud of Turin","volume":"14","author":"Heller","year":"1981","journal-title":"Can. Soc. Forensic Sci. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0003-2670(01)85263-6","article-title":"Physics and chemistry of the Shroud of Turin, a summary of the 1978 investigation","volume":"135","author":"Schwalbe","year":"1982","journal-title":"Anal. Chim. Acta"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Jumper, E.J., Adler, A.D., Jackson, J.P., Pellicori, S.F., Heller, J.H., and Druzik, J.R. (1984). A comprehensive examination of the various stains and images on the Shroud of Turin. Archaeological Chemistry III ACS Advances in Chemistry 205, American Chemical Society.","DOI":"10.1021\/ba-1984-0205.ch022"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2244","DOI":"10.1364\/AO.23.002244","article-title":"Correlation of image intensity on the Turin Shroud with the 3-D structure of a human body shape","volume":"23","author":"Jackson","year":"1984","journal-title":"Appl. Opt."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"40301-1","DOI":"10.2352\/J.ImagingSci.Technol.2010.54.4.040301","article-title":"Life-size Reproduction of the Shroud of Turin and its Image","volume":"54","author":"Garlaschelli","year":"2010","journal-title":"J. Imaging Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"20102-1","DOI":"10.2352\/J.ImagingSci.Technol.2011.55.2.020102","article-title":"Letter to the Editor: Comments on\u2013life-size reproduction of the Shroud of Turin and its image","volume":"55","author":"Fanti","year":"2011","journal-title":"J. Imaging Sci. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"8567","DOI":"10.1364\/AO.51.008567","article-title":"Superficial and Shroud-like coloration of linen by short laser pulses in the vacuum ultraviolet","volume":"51","author":"Murra","year":"2012","journal-title":"Appl. Opt."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1038\/337611a0","article-title":"Radiocarbon dating of the Shroud of Turin","volume":"337","author":"Damon","year":"1989","journal-title":"Nature"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"185","DOI":"10.6028\/jres.109.013","article-title":"The remarkable metrological history of radiocarbon dating","volume":"109","author":"Currie","year":"2004","journal-title":"J. Res. Natl. Inst. Stand. Technol."},{"key":"ref_10","unstructured":"Nicolotti, A. (2020). The Shroud of Turin. The History and Legends of the World\u2019s Most Famous Relic, Baylor University Press."},{"key":"ref_11","unstructured":"Gonella, L. (2005). Storia degli avvenimenti connessi alla datazione della S. Sindone. Il Giorno pi\u00f9 Lungo della Sindone, Fondazione 3M Edizioni."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1038\/332482c0","article-title":"Turin Shroud","volume":"332","author":"Tite","year":"1988","journal-title":"Nature"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1038\/333110c0","article-title":"Radiocarbon-dating the Shroud","volume":"333","author":"Gove","year":"1988","journal-title":"Nature"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1017\/S0033822200007748","article-title":"An intercomparison of some AMS and small gas counter laboratories","volume":"28","author":"Burleigh","year":"1986","journal-title":"Radiocarbon"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1017\/S0033822200012935","article-title":"An overview of all three stages of the international radiocarbon intercomparison","volume":"32","author":"Scott","year":"1990","journal-title":"Radiocarbon"},{"key":"ref_16","first-page":"26","article-title":"Unexpected errors affect dating techniques","volume":"1684","author":"Coghlan","year":"1989","journal-title":"New Sci."},{"key":"ref_17","unstructured":"Riggi di Numana, G. (1989, January 7\u20138). Pr\u00e9l\u00e8vement d\u2019un morceau de tissue du Saint Suaire de Turin. Proceedings of the Actes de Symposium Scientifique International, Paris, France."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1016\/S0168-583X(96)00718-5","article-title":"A problematic source of organic contamination of linen","volume":"123","author":"Gove","year":"1997","journal-title":"Nucl. Instrum. Methods Phys. Res. B"},{"key":"ref_19","unstructured":"Scannarini, S., and Savarino, P. (2000). The age of the Shroud of Turin. International Scientific Symposium on The Turin Shroud. Past, Present, Future, Effat\u00e0. Sindon n. 13."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.tca.2004.09.029","article-title":"Studies on the radiocarbon sample from the Shroud of Turin","volume":"425","author":"Rogers","year":"2005","journal-title":"Thermochim. Acta"},{"key":"ref_21","unstructured":"Brown, J.L. (2020, July 25). Microscopical Investigation of Selected Raes Threads from the Shroud of Turin. Available online: https:\/\/www.shroud.com\/pdfs\/brown1.pdf."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.tca.2015.08.002","article-title":"There is no mass spectrometry evidence that the 14C sample from the Shroud of Turin comes from a medieval invisible mending","volume":"617","author":"Bella","year":"2015","journal-title":"Thermochim. Acta"},{"key":"ref_23","first-page":"223","article-title":"Updating recent studies on the Shroud of Turin","volume":"17","author":"Orna","year":"1996","journal-title":"Archaeological Chemistry: Organic, Inorganic and Biochemical Analysis"},{"key":"ref_24","unstructured":"Minor, M. (2000). Further spectroscopic investigations of samples of the Shroud of Turin. Proceedings of the 1998 Dallas Shroud Symposium, Alexander Books."},{"key":"ref_25","unstructured":"Walsh, B.J. (2000). The 1988 Shroud of Turin radiocarbon test reconsidered. Proceedings of the 1999 Shroud of Turin International Research Conference, Magistrum Press."},{"key":"ref_26","unstructured":"Walsh, B.J. (2000). The Shroud of Turin and the reliability of the 95% error confidence interval. Proceedings of the 1999 Shroud of Turin International Research Conference, Magistrum Press."},{"key":"ref_27","unstructured":"Di Lazzaro, P. (2020). A critical review of the radiocarbon dating of the Shroud of Turin. Proceedings IWSAI, ENEA."},{"key":"ref_28","unstructured":"Di Lazzaro, P. (2010). A robust statistical analysis of the 1988 Turin Shroud radiocarbon dating results. Proceedings IWSAI, ENEA."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1007\/s11222-012-9329-5","article-title":"Regression analysis with partially labeled regressors: Carbon dating of the Shroud of Turin","volume":"23","author":"Riani","year":"2013","journal-title":"Stat. Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1521","DOI":"10.1017\/S0033822200056277","article-title":"Investigating a dated piece of the Shroud of Turin","volume":"52","author":"Jull","year":"2010","journal-title":"Radiocarbon"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Huber, P.J., and Ronchetti, E.M. (2009). Robust Statistics, Wiley. [2nd ed.].","DOI":"10.1002\/9780470434697"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1093\/biomet\/40.3-4.318","article-title":"Non-normality and tests on variances","volume":"40","author":"Box","year":"1953","journal-title":"Biometrika"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1111\/arcm.12467","article-title":"Radiocarbon Dating of the Turin Shroud: New evidence from raw data","volume":"61","author":"Casabianca","year":"2019","journal-title":"Archeometry"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1111\/j.1475-4754.1978.tb00208.x","article-title":"Procedure for comparing and combining radiocarbon age determinations: A critique","volume":"20","author":"Ward","year":"1978","journal-title":"Archaeometry"},{"key":"ref_35","unstructured":"Bonferroni, C.E. (1936). Teoria statistica delle classi e calcolo delle probabilit\u00e0. Pubblicazioni del Reale Istituto Superiore di Scienze Economiche e Commerciali di Firenze, Libreria internazionale Seeber."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1093\/biomet\/50.3-4.335","article-title":"The choice of a second-order rotatable design","volume":"50","author":"Box","year":"1963","journal-title":"Biometrika"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Atkinson, A.C., Donev, A.N., and Tobias, R.D. (2007). Optimum Experimental Designs, with SAS, Oxford University Press.","DOI":"10.1093\/oso\/9780199296590.001.0001"},{"key":"ref_38","first-page":"409","article-title":"Design and analysis of computer experiments","volume":"4","author":"Sacks","year":"1989","journal-title":"Stat. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1002\/bimj.200390032","article-title":"Hadamard randomization: A valid restriction of random permuted blocks","volume":"45","author":"Bailey","year":"2003","journal-title":"Biom. J."},{"key":"ref_40","unstructured":"M\u00fcller, W.G. (2007). Collecting Spatial Data, Springer. [3rd ed.]."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Bailey, R.A. (2008). Design of Comparative Experiments, Cambridge University Press.","DOI":"10.1017\/CBO9780511611483"},{"key":"ref_42","unstructured":"JCGM, Joint Committee for Guides in Metrology (2020, July 25). 100:2008 Evaluation of Measurement Data\u2014Guide to the Expression of Uncertainty in Measurement, Available online: https:\/\/ncc.nesdis.noaa.gov\/documents\/documentation\/JCGM_100_2008_E.pdf."},{"key":"ref_43","unstructured":"W\u00f6lfly, W. (1988). Letter to R. Van Haelst Dated November 10, 1988. Courtesy of G. Bracaglia, Holy Shroud Guild Archives, Holy Shroud Guild Archives."},{"key":"ref_44","unstructured":"Morano, E. (1979). Aspetti ultrastrutturali al microscopio elettronico a scansione di fibre della Sindone di Torino. La Sindone e la Scienza, Edizioni Paoline."},{"key":"ref_45","unstructured":"Barberis, B., Lattarulo, F., Di Lazzaro, P., and Petri, D. (2015). Optical features of flax fibers coming from the Turin Shroud. SHS Web of Conference, EDP Science."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"108248","DOI":"10.1016\/j.radphyschem.2019.03.052","article-title":"Analysis of an archaeological linen cloth: The shroud of Arquata","volume":"167","author":"Bruni","year":"2020","journal-title":"Radiat. Phys. Chem."},{"key":"ref_47","unstructured":"Rogers, R.N., and Arnoldi, A. (2020, July 25). Scientific Method Applied to the Shroud of Turin, a Review. Available online: https:\/\/www.researchgate.net\/publication\/237460281."},{"key":"ref_48","unstructured":"Fanti, G. (2009). Analytical results on threads taken from the Raes sampling area of the Shroud. Proceedings of the International Conference the Shroud of Turin: Perspectives on a Multifaceted Enigma, Edizioni Libreria Progetto."},{"key":"ref_49","unstructured":"Evaristo, C. (2011). The untold story of the Holy Shroud, Regina Mundi Press I.C.H.R."},{"key":"ref_50","unstructured":"Vercelli, P. (2010). La Sindone Nella sua Struttura Tessile, Effat\u00e0 Editrice."},{"key":"ref_51","unstructured":"Flury-Lemberg, M. (2020, July 25). The Invisible Mending in the Shroud, the Theory and the Reality, British Society for the Turin Shroud Newsletter. Available online: https:\/\/www.shroud.com\/pdfs\/n65part5.pdf."},{"key":"ref_52","first-page":"1","article-title":"An instructive inter-laboratory comparison: The 1988 radiocarbon dating of the Shroud of Turin","volume":"29","author":"Walsh","year":"2020","journal-title":"J. Archaeol. Sci. Rep."},{"key":"ref_53","unstructured":"Riggi di Numana, G. (2005). Il giorno pi\u00f9 lungo della S. Sindone di Torino. Il Giorno pi\u00f9 Lungo della Sindone, Fondazione 3M Edizioni."},{"key":"ref_54","first-page":"2624","article-title":"A possible hypothesis for correcting the radiocarbon age of the Shroud of Turin","volume":"7","year":"2012","journal-title":"Sci. Res. Essays"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/9\/926\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:05:46Z","timestamp":1760177146000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/9\/926"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,24]]},"references-count":54,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["e22090926"],"URL":"https:\/\/doi.org\/10.3390\/e22090926","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,24]]}}}