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Re: orion-list Radiocarbon

According to Greg Doudna:
> Yesterday I cited, in the strongest form I could, the case from
> radiocarbon against a 63 BCE terminus hypothesis.  At first blush 
> it sounds immediately decisive, indeed virtually airtight: five 
> separate radiocarbon dates, of 19 total Qumran texts dated, 
> give two-sigma ranges entirely later than 63 BCE, at 95% 
> confidence reported by the lab for each one of these datings.  
> The reason I do not consider these 5 dates a falsification of a 63 BCE 
> terminus hypothesis is simply this: in four of those five cases, the 
> edge of the two-sigma range is so close to 63 BCE that it appears 
> hairsplitting to claim certainty, in the absence of further data and 
> context.  E.g. 1QH (47 BCE...), 4Q266 (44 BCE...), 4Q258 #2 
> (50 BCE...), 4Q521 (49 BCE...).  In only one case is the start of the 
> 2s range unambiguously and clearly removed from 63 BCE in terms 
> of calendar years: 4QpPsA (3 CE...).  

  Scientifically speaking, you are using a 75% confidence level, in that
you are specifying (not randomizing) 25% of your data points as erroneous.
Confidence intervals refer to *random* errors of measurement on both an
individual and a group basis. 

  While you can discuss the data in any way you wish, and you will be
accurate as far as the measurement of an individual piece using C14
techniques are concerned. it is not an adequate treatment according to
scientific method of investigation. Note that I'm not talking about the
scientific validity and reliability of radiocarbon dating itself.

  It is possible to design a scientifically valid discrimination function
that quantifies a distinction based on time between two groups of texts
using C14 data.  It is not possible, however, to discriminate between a
*full* set of dated texts and an hypothesized *empty* set of dated texts,
as you are trying to do. 

> Readers of orion might consider: (a) if you had no radiocarbon data,
> would you know a 63 BCE terminus hypothesis was excluded on 
> some other grounds?  

Using radio carbon data, one hypothesizes, according to scientific method,
that there is no difference between quantified evidence that falls before
63 BCE, and quantified evidence that falls (independently determined)
after 63 BCE. It is an hypothesis of no difference (null hypothesis), that
requires two groups. One then disconfirms the null hypothesis, or not,
with a confidence level set a priori at 90%, 95%, or 99%.

Using something other than radiocarbon data, it is fairly easy to test an
hypothesis of distribution on categorical grounds. One uses information
that is present or absent in the texts themselves, and uses a chi-square
test of distribution. The null hypothesis is that on a random basis, an
equal *number* of texts will fall in the two categories of pre-63 BCE and
post-63 BCE. The criterion for dividing the groups can be anything
--probably several different criteria *should be used, yielding
similar results, or discussable results. 

Using the C14 data you've mentioned, the categories would be defined as

                                          Observed        Expected

2 sigma interval entirely before 63 BCE      14             10
2 sigma interval extends past  63 BCE         5             10

A statistician will be able to calculate the chi-square value for you,
given the above table. My guesstimate is that the chi-square value will be
at approximately the 85% confidence level, rather than a more respectible
95% confidence interval. So you can, if you like, legitimately talk about
a trend in favor of a 63 BCE cut-off, and not have to be embarassed by the
anomalies in the data. 

This second method conforms to the way you are stating your
hypothesis, and doesn't require a dependent measure (measurement like C14
data) that is interval based. In fact, it is possible to use interval
data only as category definitions, as above. Other ways of dividing the
groups of texts might include particular paleographical signs, for
example. You could extend the number of groups as well as the number of
cases considered overall, in this way.

[. . .]

> Greg Doudna
> Copenhagen

Sigrid Peterson  UPenn  petersig@ccat.sas.upenn.edu

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