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Re: orion-list Radiocarbon

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

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

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