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Ray Kidd

Feb 13, 2022, 5:07:49 AMFeb 13
Hello Cristopher and Group,

I am assisting with an interesting problem.  Perhaps there is already a solution.  I would like comments on my suggestion.

As a result of DNA analysis, two skeletons are identified as twins, 0-2 months old at death.  Radiocarbon determinations are:

   R_Date("Skeleton 1", 3347, 22);
   R_Date("Skeleton 2", 3258, 23);

Using R_Combine or Combine shows a failed W&W1978 test.  This is hardly surprising as the mean dates are about 100 years apart.

So we might assume that one or the other is wrong ( I favour a mistaken second digit)

The question is, how to identify the one that is wrong and which one is correct.

My solution is to create a single Phase model using R_Simulate for six dates.  I place three before an unbounded Phase  pair of the twins and three following (this is not strictly  necessary, I like things to balance).  For the R_Simulate I make each one the same, i.e. the mean value of the twins R_Dates roughly.  I have used R_Simulate -1600, 25.

The model runs quite well.  Running many times gives a new model at each run, but, here the thing, it consistently shows Skeleton1 with a higher individual agreement index.  From which I take it that Skeleton 1 is the 'good' date and Skeleton 2 should be discarded in any future model.


    R_Simulate("Sim1", -1600, 25);
    R_Simulate("Sim2", -1600, 25);
    R_Simulate("Sim3", -1600, 25);
     R_Date("Skeleton 1P", 3347, 22);
     R_Date("Skeleton 2P", 3258, 23);
    R_Simulate("Sim6", -1600, 25);
    R_Simulate("Sim4", -1600, 25);
    R_Simulate("Sim5", -1600, 25);


Best wishes



Feb 14, 2022, 4:44:39 AMFeb 14

Hello Ray,


Your model compares the two dates to six dates with a true calendar date of -1600. Whichever of the two has a higher likelihood at -1600 will give the better agreement. It tells you nothing about the quality of the dates, just how they compare to the assumptions that went into the model. There’s no way to discriminate between the two dates on the information you have given.


Best wishes



Dr. Andrew Millard

Associate Professor of Archaeology,

Durham University, UK


Personal page:

Scottish Soldiers Project:

Dunbar 1650 MOOC:



From: 'Ray Kidd' via OxCal <>
Sent: 13 February 2022 10:08
Subject: Twins



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Erik Marsh

Feb 14, 2022, 8:47:59 AMFeb 14
to OxCal
I have to agree with Andrew. This is far from ideal, but perhaps you could still combine them with Ward and Wilson's (1978) sum of squares and use that, despite the failed chi-square test. Doing this would use the logic that that the dates are equally wrong and something in the middle is most likely. That's about all I can see you could try. But it's not a very solid approach – it seems quite plausible, as you suggest, that one date is good and the other isn't.

Sorting this out would require other contextual dates, I think. Or something from the lab on the chemistry of the two samples. Or find the typo in the dates.

Ray Kidd

Feb 14, 2022, 10:24:41 AMFeb 14
Hello Erik, Andrew,

I'm aware that it all hinges on the Simulated likelihoods and they change at every run for aa given Date.   If the six simulated likelihoods and the two Radiocarbon likelihoods bias towards one 'lot' of phase calculations then it will favour one Radiocarbon date over the other for that run.  It will continue that bias in the the majority of runs, but not all.

I  think it was just fortuitous that my rough estimate of -1600 happened on a close choice.

R_Combine and Combine, if only one date is correct give a wrong answer (But precisely)



Pavol Hnila

Feb 14, 2022, 11:53:33 AMFeb 14
Hello Andrew, Erik, Ray, and the group,

It looks to me that the preference for the first date as the "good" one comes from the shape of the combined distribution. If only the two C14 determinations are joined with the Combine function, their resulting combined distribution overlaps much better with Skeleton 1 (A=71%) than it does with the Skeleton 2 (A=29%). When trying Ray's simulation with -1650, -1600, -1550, the date for Skeleton 1 results like the better one. On the other hand, when trying with -1500, the better date switches to Skeleton 2, because the calibrated distribution for Skeleton 2 has a distinct probability peak at -1500.

I am afraid, that if we only have two dates and their combination is statistically nearly impossible, then - as Andrew and Erik stressed - without additional information there is no way to figure out which of them is wrong. In an extreme case, perhaps even both of them can be wrong. But a technical question in this sense - why does then the Combine function return an average, whose agreement with Skeleton 1 is 71% and with Skeleton 2 is 29%, instead of balancing it 50-50 in the middle (e.g. by expanding the range and lowering the probabilities for individual years)?

Best regards,
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