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*To*: orion@mscc.huji.ac.il*Subject*: Re: orion-list Radiocarbon*From*: Sigrid Peterson <petersig@ccat.sas.upenn.edu>*Date*: Fri, 3 Sep 1999 01:39:24 -0400 (EDT)*Reply-To*: orion@mscc.huji.ac.il

In my post of Tuesday 31 August 1999, 5:37 GMT, I was struggling to rethink Greg's research questions, and then to answer his challenge to disconfirm the 63 BCE date, and then to reframe the question in terms compatible with the scientific method, without benefit of Greg's article. I didn't succeed very well, and in the process I misstated some of the data. As Steve Goranson was kind enough to point out, and I will probably discover when I do get a copy of Greg's article, of the 19 two-sigma ranges for the data divide opposite to the way I stated them, five (5) fall entirely after 63 BCE, one (1) is entirely before 63 BCE, and 13 overlap the date. In terms of categorical purity, with non-overlapping ranges designating the categories, and dividing them at 63 BCE, we could make the following table. The test of the hypothesis is a comparison of the count of observed cases, the actual data, versus the expected cases, i.e. the way the data would fall if there were no significance to the categories Before and After (63 BCE, or thereabouts). Before 63 BCE After 63 BCE ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Observed 1 Observed 5 Expected 3 Expected 3 Again, the Expected values are the actual count of ranges that fall completely and exclusively in the categories before and after 63 BCE. And the Expected values are the hypothetical count of ranges that would fall in the two exclusive categories under conditions of randomness. The statistical test is significant at the 90% confidence level, that is, 10% of the time the results could be due to chance factors, rather than the specific division into categories based on ranges falling to either side of 63 BCE. This trends towards disconfirming the hypothesis of the deposit of all texts before 63 BCE. Ah, but what happened to the 13 cases that overlap 63 BCE? There can perhaps be a clear mathematical way to deal with those, but I'll have to see what the actual ranges are. Penn's campus is undergoing so much building and renovation that I can't get into the Library to get a copy of the Greg's article, which would have the data I need. I *do read the discussions. One of the recent considerations, expressed both the Greg and by Russell Gmirkin, has been to move as many of the 5 ranges that fall (a little) later than 63 BCE, into the range where they overlap 63 BCE. To pretend, in other words, that 13 data ranges that overlap 63 BCE are really 18 or 19. Greg had a statement on August 14th that almost caught on to the concept that scientific truth doesn't require 100% of the cases to fall in the range of possibility. >From Greg Doudna Aug 14, 1999 02:23:38 pm > Although I don't have figures to quote, a study of major > archaeological contexts with known dates and batteries > of radiocarbon datings would likely show in almost every > case one or more individual radiocarbon dates from that > context _later_ than the true dating of that context. This is > so very frequent that it is simply expected. Typically in a > battery with ten items eight will come up in agreement and > establish the age, and two will be inexplicably significantly > out in one or the other direction--and no one will know why. > Actual reasons can range from anything from > archaeologist/lab error in identification to sample > contamination, but in most cases there simply never is > any explanation. It just disagrees with massive other > evidence, Up until this point, I agree (100% ;-) ). > and therefore is rejected. Perhaps by non-scientists, because that seems to be what the discussion has been about. Scientifically, it is random error. Statistical tests can tell us whether the random error produces *so much* noise that the trends are obscured, or whether there is a clear trend in the data. We want *confidence in that clear trend in the data, rather than 100% certainty--which would indicate that something is wrong. Most of this, I hope, is digestible. More when I've got the data from Greg's article. Sigrid Peterson UPenn petersig@ccat.sas.upenn.edu For private reply, e-mail to petersig@ccat.sas.upenn.edu (Sigrid Peterson) ---------------------------------------------------------------- To unsubscribe from Orion, e-mail to majordomo@panda.mscc.huji.ac.il with the message: "unsubscribe Orion." For more information on the Orion Center or for Orion archives, visit our web site http://orion.mscc.huji.ac.il.

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