Proceedings of the International Workshop on the Scientific approach to the Acheiropoietos Images, ENEA Frascati, Italy, 4‐6 May 2010 A robust statistical analysis of the 1988 Turin Shroud radiocarbon dating results G. Fanti 1 , F. Crosilla 2 , M. Riani 3 , A.C. Atkinson 4 1 Department of Mechanical Engineering University of Padua, Italy, giulio.fanti@unipd.it. 2 Department of Geo-Resources and Territory, University of Udine, Italy fabio.crosilla@uniud.it. 3 Department of Economics, University of Parma, Italy, mriani@unipr.it 4 Department of Statistics, London School of Economics, London WC2A 2AE, UK, a.c.atkinson@lse.ac.uk. Abstract Using the 12 published results from the 1988 radiocarbon dating of the TS (Turin Shroud), a robust statistical analysis has been performed in order to test the conclusion by Damon et al. (1998) that the TS is mediaeval. The 12 datings, furnished by the three laboratories, show a lack of homogeneity. We used the partial information about the location of the single measurements to check whether they contain a systematic spatial effect. This paper summarizes the results obtained by Riani et al. (2010), showing that robust methods of statistical analysis can throw new light on the dating of the TS. Keyword: ANOVA, Forward Search, Robust methods, t-statistics, Turin Shroud. 1. INTRODUCTION The results of the 1988 radiocarbon dating [1] of the TS were published as providing conclusive evidence that the linen fabric dates from between 1262 and 1384 AD, with a confidence level of 95%. However, after publication of the result, many speculated that the sample had been contaminated due to the fire of 1532 which seriously damaged the TS, or to the sweat of hands impregnating the linen during exhibitions, others that the date was not correct due to the presence of medieval mending and so on. We give references to some of these concerns in Section 7. The purpose of this paper is to summarize the results obtained in Ref. 2 which show how robust methods of statistical analysis, in particular the combination of regression analysis and the forward search [3] combined with computer power and a liberal use of graphics, can help to shed new light on results that are a source of scientific controversy. Throughout we analyse only numbers from the data given in Ref. 1. 2. DESCRIPTION OF THE DATA The samples for radio carbon dating were taken from a strip of material cut from one corner of the TS. The strip was divided into five parts; the three parts on the right of Figure 1 were sent to laboratories in Arizona, Oxford and Zurich. Arizona also received the fourth, smaller, part on the left. A larger part on the left of Figure 1 was taken by the Arcidiocesi of Turin as a “Riserva”. Figure 2 indicates the cutting of the strip in question. These samples were divided into a total of 12 sub- samples for which datings were made. The resulting dates ranged from 591 BP for a reading from Arizona, to 795 BP from Oxford. 3. HETEROGENEITY ANALYSIS Damon et al. [1] noticed that the data show some heterogeneity, which they assessed using a chi-squared test. In this section we instead use the analysis of variance to test whether these 12 observations can be considered as homogeneous, i.e. as 12 repeated measurements coming from a single unknown quantity. More formally, a general model for observation j at site i is y ij = μ i + σv ij ε ij (i = 1, 2, 3; j = 1, ..., n i ), (1) where the errors ε ij have a standard normal distribution. Our central concern is the structure of the μ i ; at this point whether they are all equal. However, before proceeding to the test this hypothesis we need to establish the error structure. Riani et al. [2] suggest the three following possibilities 1. Unweighted Analysis. Standard analysis of variance: all v ij = 1 www.acheiropoietos.info