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Cited by 8Archaeology and ancient environmental studiesCultural Heritage Materials AnalysisScientific Measurement and Uncertainty Evaluation

An instructive inter-laboratory comparison: The 1988 radiocarbon dating of the Shroud of Turin

Open access
Walsh, Bryan, Schwalbe, Larry·2020·Journal of Archaeological Science: Reports
DOI 10.1016/j.jasrep.2019.102015
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Abstract

We review the statistical method cited in the report of the radiocarbon dating of the Shroud of Turin. Following strict analytical protocol, we find the Shroud data to be heterogeneous, while data from three control samples show no heterogeneity. We consider two potential sources for the Shroud data heterogeneity. The first, an approximate linear dependence of the dates on the original sample locations suggests a variation in the carbon isotopic composition. The second, differences in the cleaning protocols of the three laboratories may have given rise to differences in residual contamination. We suggest experiments to test the two competing hypotheses.

AI snapshot

Written from the paper’s full text.

TL;DR

Reanalysis of the 1988 Shroud of Turin radiocarbon data finds the Shroud sample (Sample #1) statistically heterogeneous, while the control samples are homogeneous, so the three laboratory means should not have been combined into a single date. The paper proposes either carbon isotopic variation across the sample or differential cleaning—notably Oxford’s petroleum ether step—as competing explanations and suggests experiments to test them.

Key findings

  • Ward–Wilson χ² homogeneity tests reject homogeneity for Shroud Sample #1: present χ² = 6.3116, p = 0.0426, whereas control samples are homogeneous (Sample #2 p = 0.9221; Sample #3 p = 0.3071; Sample #4 p = 0.1249). Damon et al. reported rounded p-values of 5%, 90%, 50%, and 30%, respectively.
  • The dates show an approximate linear dependence on original sample location: RCYBP = −3.7277 × Distance + 926.48, R² = 0.3975, F = 6.5981, p = 0.0279; using the Tucson 8-point data set gives R² = 0.3095, F = 6.2747, p = 0.0252.
  • To bring Zurich and Tucson into agreement with Oxford, the authors calculate a shift of ~88 RCY; for that shift, contaminant amounts would be ~11 wt% if contamination occurred in 1700 and ~7 wt% in the mid-20th century, with areal densities of 1.5–2.5 mg/cm². For a smaller ~10 RCY shift, the corresponding values are ~1.2 wt% and ~0.7 wt%, with areal densities of 0.15–0.25 mg/cm².
  • Weighted means for Sample #1 were Oxford 749 ± 31, Zurich 676 ± 24, Tucson 647 ± 28, with a combined weighted mean of 686 ± 16, but the authors argue this combination is inappropriate because the data are heterogeneous.

Methods

  • Reanalysis of Damon et al. (1989) Table 1 individual AMS radiocarbon measurements for Shroud Sample #1 and three control samples from Oxford, Zurich, and Tucson/Arizona.
  • Applied Ward and Wilson (1978) χ² homogeneity tests, Shapiro–Wilk and Anderson–Darling normality tests, modified Z-score outlier detection, and regression of dates against reconstructed sample locations.
  • Used both the Tucson 4-point and 8-point data sets; weighted means were derived using quoted errors or data scatter; analyses were implemented in MS Excel, X-Pro, and the Real Statistics Resource pack for Excel.

Limitations

  • Stated: the small number of observations limits normality testing; subsample locations were not described, so sample-site centers were used as proxies, possibly affecting precision; the source of heterogeneity is unknown and the contamination/isotope hypotheses are speculative; proposed experiments are needed to test them.
  • Evident from the text: the study relies on published data and reconstructed sample geometry rather than new radiocarbon measurements, and the contamination calculations are illustrative, using ricinoleic acid as an example rather than direct evidence.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1016/j.jasrep.2019.102015

Cites

25 of 25 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

3 of 24 cited sources checked · 3 supported · 0 flagged

  • Premisecitation

    Casabianca et al. (2019) concluded from newly available raw data that the Shroud data from the three laboratories are heterogeneous.

    “Casabianca et al. (2019) reach a similar conclusion from their study of the newly available raw data, namely, that the Shroud data from the three laboratories are heterogeneous.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Casabianca et al. (2019) source
  • Premisecitation

    Freer-Waters and Jull (2010) conducted microscope examinations on material from the Shroud sample that Tucson retained from the dating study and reported having observed no coatings on either the threads or fibers.

    “Freer-Waters and Jull (2010) conducted microscope examinations on material from the Shroud sample that Tucson retained from the dating study.These investigators reported having observed no coatings on either the threads or fibers”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Freer-Waters and Jull (2010) source
  • Findingown data

    For the Oxford and Zurich data, the null hypothesis of homogeneity is accepted in every case.

    “In every case, we accept the null hypothesis for the Oxford and Zurich data, but reject the null hypothesis for the Sample #1 and Sample #4 measurements in the Tucson results, this after removing the two Tucson outliers in Sample #3.”
    Quote in the paperSubstantial claim
  • Findingreasoning

    Damon et al. (1989) failed to conduct standard statistical tests for homogeneity among the inter- and intralaboratory data.

    “However, it seems the authors failed to conduct standard statistical tests for homogeneity among the inter-and intralaboratory data, a necessary step to justify combining the data as they did.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Damon et al. (1989) source
  • Findingcitation

    Two Tucson Sample #3 measurements, 1838 and 2137, are possible outliers because they exceed the modified Z-score threshold of 3.5.

    “We find two measurements from Sample #3, Tucson measurements 1838 and 2137, as possible outliers since they exceed the modified Z-score of 3.5, which Inglewicz and Hoaglin (1993) suggest as a threshold to qualify a measurement as a possible outlier.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Iglewicz and Hoaglin (1993)

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Classified as probably not a substantial claim. 11
  • May combine two claims. 16
  • The quote only partly states this claim. 1

  • Classified as probably not a substantial claim.

    Premisecitation

    Rasmussen et al. (2001) and (2009) reported that castor oil, originally applied to fragments of the Dead Sea scrolls to enhance their readability, could not be removed sufficiently by AAA treatment for reliable carbon dating.

    “This example is interesting because Rasmussen et al. (2001) and(2009) reported that castor oil, originally applied to fragments of the Dead Sea scrolls to enhance their readability, could not be removed sufficiently by AAA (acid-alkali-acid) treatment for reliable carbon dating.”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites Rasmussen et al. (2001) source
    • cites [2009]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Classified as probably not a substantial claim.

    Findingnone given

    Whether the cleaning procedures were sufficient for the level and types of contamination seen on Sample #1 is unclear.

    “Whether they were sufficient for the level and types of contamination seen on Sample #1 is unclear.”
    Quote in the paperSubstantial claim

  • May combine two claims. The quote only partly states this claim.

    Findingown data

    Q-Q plots for the other three samples show similar behavior to Sample #1, with no obvious departures from normality.

    “Q-Q plots corresponding to each of the other three samples show similar behaviors as seen in the Appendix Fig. A1.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning

    Within the limitations imposed by the small number of observations for each sample, there is no statistical evidence that either the residuals of the data or the data themselves are other than normally distributed.

    “Therefore, within the limitations imposed by the small number of observations for each sample, there is no statistical evidence that either the residuals of the data or the data themselves are other than normally distributed.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The χ2 test for homogeneity on the eight Tucson Sample #1 measurement set rejects the null hypothesis, with χ2 = 14.4562 and p-value = 0.0435.

    “As noted previously, more than eight years after the publication of 5) results in a χ 2 value of 14.4562 and a p-value = 0.0435.Thus, the χ 2 test for homogeneity on the eight measurement set rejects the null hypothesis as does the test of the four Tucson combined measurements.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Samples #2, #3, and #4 each produce homogeneous sets of means that can be combined into an overall weighted mean for each sample.

    “Based on the χ 2 analyses, Samples #2, #3, and #4 each produce homogeneous sets of means that can be combined into an overall weighted mean for each sample.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The mean results from the Zurich and Tucson data agree within their calculated experimental error, whereas that from Oxford does not.

    “In support of the contamination hypothesis, Fig. 4 illustrates how the mean results from the Zurich and Tucson data (open symbols) agree within their calculated experimental error (note level B-B′), whereas that from Oxford does not (A-A′).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    For a shift of 88 RCY, the weight percent of contaminant before treatment would have been ~11 wt% had the contamination occurred in 1700 and ~7 wt% in the mid-20th century.

    “For a shift of 88 RCY as shown in Fig. 4, we calculate the weight percent of contaminant before treatment to have been ~11 wt% had the contamination occurred in 1700 and ~7 wt% in the mid-20th century.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Substituting the Tucson eight-point data set for the four-point set yields a similar linear relationship, with R2 reduced to 0.3095 due to wider dispersion of the eight Tucson measurements.

    “Additionally, we substituted the Tucson eight-point data set for the four-point set and found a similar linear relationship.However, the R 2 value was reduced to 0.3095 due to the wider dispersion of the eight Tucson measurements.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Evaluating the eight-point Tucson relationship produces F = 6.2747 and a p-value of 0.0252.

    “Evaluating that relationship produces F = 6.2747 and a p-value of 0.0252 as can be seen in the Appendix Fig. A2.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    For the lesser shift of 10 RCY, the corresponding areal concentrations of contaminant would be ~1.2 wt% for contamination in 1700 and ~0.7 wt% in the 20th century.

    “For the lesser shift of 10 RCY, the corresponding areal concentrations of contaminant would be ~1.2 wt% for contamination in 1700 and ~0.7 wt% in the 20th century.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Study design and conductcitation

    The samples were randomly selected and independently assigned to the individual laboratories.

    “The samples were randomly selected and independently assigned to the individual laboratories.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Damon et al. (1989) source

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationreasoning

    Had Damon et al. conducted standard homogeneity tests, the statistical heterogeneity of the data should have served as a qualifier to their conclusions and led to further exploration of the underlying cause of the discrepancies.

    “Had they conducted these tests, the statistical heterogeneity of the data should have served as a qualifier to their conclusions and led to a further exploration of the underlying cause of the discrepancies.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    The procedure used by Damon et al. (1989) to combine the means is inappropriate because it deliberately ignores the heterogeneous nature of the data uncovered by the analysis and introduces error into the statistical analysis.

    “This procedure is inappropriate since it deliberately ignores the heterogeneous nature of the data uncovered by the analysis and introduces error into the statistical analysis.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Damon et al. (1989) source

  • May combine two claims.

    Study design and conductreasoning

    Although the study was initially intended to be blind, the investigators could readily identify the Shroud sample as distinct from the controls; this unavoidable constraint is not thought to have affected the outcome of the overall study.

    “Although the study was initially intended to be blind, the investigators could readily identify the Shroud sample as distinct from the three controls due to the Shroud's unique herringbone weave and the z-twist of its threads.This unavoidable constraint is not thought to have affected the outcome of the overall study.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Premisecitation

    The homogeneity hypothesis is established by first framing the null hypothesis H0 that the expected values of the individual laboratory data are equal and then applying a chi-square (χ2) test on H0.

    “This outcome is established by first framing the hypothesis H 0 that the expected values of the individual laboratory data are equal and then by applying a chi-square (χ 2 ) test on H 0 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites W-W

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Study design and conductreasoning

    Each of the AMS procedures has error-detection and quality assurance protocols, so the laboratories should have obtained reliable results.

    “Each of these procedures has error-detection and quality assurance protocols, so the laboratories should have obtained reliable results.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    According to Ward and Wilson (W-W), one may combine data in Case I studies only when the homogeneity hypothesis is accepted.

    “According to W-W, one may combine data in Case I studies (those in which a sample is divided and subjected to a series of independent measurements) only when the homogeneity hypothesis is accepted.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites Ward and Wilson (1978) source
    • cites W-W

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Classified as probably not a substantial claim.

    Premisecitation

    W-W recommended replacing the quoted errors σij with the standard error (or scatter) of the measurements from their mean value when the χ2-derived p-value is less than 0.05.

    “Returning to the question of how to proceed when the χ 2 -derived pvalue is less than 0.05, we recall that W-W recommended replacing the use of the quoted errors σ ij with the standard error (or scatter) of the measurements from their mean value.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites W-W

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S2 (checkable).

    Interpretationreasoning

    Lacking adherence to protocol, the finding of heterogeneity should, at the very least, have prompted a strong qualification to the reported final result.

    “Lacking this adherence to protocol, the finding of heterogeneity should, at the very least, have prompted a strong qualification to the reported final result.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    The fundamental premise of this study is that the data can neither be interpreted meaningfully nor combined correctly using either weighting scheme unless their statistical homogeneity is first demonstrated.

    “The fundamental premise of this study is that we can neither interpret the data meaningfully nor combine them correctly using either weighting scheme unless we first demonstrate their statistical homogeneity.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    Flury-Lemburg (2007) noted a greasy dirt deposit in the area surrounding Sample #1 and Adler (1996) observed heavy contamination on sample threads he examined.

    “in contrast to the observations of Flury-Lemburg (2007) who noted a greasy dirt deposit in the area surrounding Sample #1 and Adler's (1996) observation of heavy contamination on sample threads he examined.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Flury-Lemburg (2007)

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites Adler (1996) source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisenone given

    The Kruskal-Wallis test does not depend on the functional form of the distribution, but unlike the W-W approach it does not take into account the uncertainties in the data and therefore may be less informative and have less statistical power.

    “The Kruskal-Wallis test does not depend on the functional form of the distribution, but unlike the W-W approach it does not take into account the uncertainties in the data and therefore may be less informative and have less statistical power.”
    Quote in the paperNot a substantial claim
23 of 23

  • The paper relies on this without support.

    The individual measurements reported by Damon et al. (1989) in Table 1 are accurate and complete as published.

    “Our purpose is to address some of the shortfalls identified by reanalyzing the data that Damon et al. (1989) present in their Table 1”

  • The authors state this as an assumption.

    The composition of the sample initially excised for the radiocarbon dating (~20 mm × ~80 mm) adequately represents that of the entire Shroud cloth (~1.1 m × ~4.4 m).

    “An isotopic variation would be of vital concern because a primary underlying assumption of the radiocarbon study is that the composition of the sample initially excised for the purpose (~20 mm × ~80 mm) adequately represents that of the entire cloth, which measures (~1.1 m × ~4.4 m).”

  • The paper relies on this without support.

    Oxford used petroleum ether for pre-cleaning whereas the other two laboratories did not.

    “However, to entertain one possibility we note that one aspect of Oxford's cleaning procedure differed from that of the other two laboratories in their use of petroleum ether for pre-cleaning.”

  • The paper relies on this without support.

    Pet ether is an effective solvent for lipids and waxes and other hydrocarbon compounds.

    “Pet ether is an effective solvent for lipids and waxes and other hydrocarbon compounds, and we postulate that Oxford was successfully able to remove a portion, or perhaps all, of a contaminant in one of these classes that Zurich and Tucson were not.”

  • The paper relies on this without support.

    Ricinoleic acid (and presumably other fatty acids and related materials) are soluble in pet ether and are therefore subject to sample cleaning.

    “However, ricinoleic acid (and presumably other fatty acids and related materials) are soluble in pet ether and are therefore subject to sample cleaning.”

  • The authors state this as an assumption.

    The uncertainties in the data did not change.

    “Indeed, if the magnitude of the “adjustment” were as small as ~10 RCY, the χ 2 analysis would confirm a statistical homogeneity assuming the uncertainties in the data did not change.”

  • The authors state this as an assumption.

    The procedures were consistently applied.

    “We restrict our attention to cleaning because the close correspondence of results from the control samples suggests that nothing in either the test or data-reduction procedures of the laboratories, presuming the procedures were consistently applied, introduces significant systematic errors into the respective mean dates they derive.”
7 of 7

Cites

Flagged first, then by citations

Research works printed but not linked: 2

  1. Iglewicz, B., Hoaglin, D., 1993. Volume 16: how to detect and handle outliers. In: Mykytka, E.F. (Ed.), The ASQC Basic References in Quality Control: Statistical Techniques.
  2. Walsh, B.J., 2000. The 1988 Shroud of Turin radiocarbon tests reconsidered. In: Proceedings of the 1999 Shroud of Turin International Research Conference Richmond Virginia, Magisterium Press, Glen Allen, Virginia.

Cited by

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Authors
Walsh, B., & Schwalbe, L.
Corresponding author
Walsh, Bryan
Venue
Journal of Archaeological Science: Reports
Publisher
Elsevier BV
Published
2020-02
Volume
29
Pages
102015
ISSN
2352-409X (ISSN-L)
DOI
10.1016/j.jasrep.2019.102015
OpenAlex
W2996484788
Semantic Scholar
1899c113b3ef7cfbd014a783a700d41bd5496bef
Cited by
8
References
23
Citations by year
2026: 2 · 2025: 1 · 2022: 3 · 2021: 1 · 2020: 1
FWCI
0.95
Type
journal article
Language
en
Open access
Licence
Locations
Journal of Archaeological Science Reports (publishedVersion, cc-by-nc-nd)
Topics
  • Physical Sciences › Earth and Planetary Sciences › Paleontology › Archaeology and ancient environmental studies
  • Social Sciences › Arts and Humanities › Archeology › Cultural Heritage Materials Analysis
  • Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Scientific Measurement and Uncertainty Evaluation
Keywords
Shroud of Turin, radiocarbon dating, interlaboratory comparison, data heterogeneity, δ13C, cleaning protocols, residual contamination

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