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Combination of Dates
The simplest form of analysis which one might wish to perform on a
series of samples is the combination of several dates to give one
measurement with smaller errors associated with it. Combination
of dates should clearly only be carried out if there is good reason
to assume that the events being dated all occurred within a short
period (`short' here implies small in comparison to the errors
associated with the dating methods).
There are various different sorts of combination which can be performed:
See also [Program Operation]
[Mathematical Methods]
It is very important to combine different radiocarbon dates correctly.
If the dates are all from the same sample or object then the
radiocarbon dates should be combined before calibration
(R_Combine).
Such a combination is checked for internal consistency by a
chi squared test which is performed automatically by this program
(see Shennan 1988 p65 for a description of
this method).
If the radiocarbon dates have been made on sample of different ages
(where the age differences are known) the combination can be done after
calibration using Combine or
D_Sequence.
See also [Program Operation]
[Mathematical Methods]
For other dating methods combination is more straight-forward and
calendar dates (C_Date) can be combined
directly whilst performing a chi squared test by using a special
procedure (C_Combine) or the
probability distributions combined
(Combine). The latter method allows
the combination of dates of different types
(radiocarbon, OSL, TL etc.).
In the case of luminescence dates it is important that any combination
of dates is performed before the application of the error term for the
site dose rate.
This will be treated correctly by this program if the raw results are
entered rather than results simply in the form of calendar ages.
See also [Program Operation]
[Example]
[Mathematical Methods]
Combining probability distributions by summing is usually difficult
to justify statistically but it will generate a probability
distribution which is a best estimate for the chronological
distribution of the items dated
(Sum).
The effect of this form of combination is to average the distributions
and not to decrease the error margins as with other forms of
combination.
See also [Program Operation]
Sometimes the dated event is offset in some way relative to the event
of archaeological interest in such cases we might wish to offset a
probability distribution (Offset)
by a particular amount. This is possible with any type of
distribution and the offset value can include an error term.
See also [Program Operation]
[Example]
[Mathematical Methods]
One form of combination which is of particular relevance to
radiocarbon dates is needed if several radiocarbon measurements
have been made on a piece of wood (or some other material with
annual growth layers).
In such a case the difference in calendar age between the samples
is known and this can be very useful in obtaining very accurate dates
in spite of the calibration procedure.
Such measurements are sometimes called `Wiggle Matching' because of
the use they make of the form of the calibration curve.
Radiocarbon dates of this type can easily be combined using this
program (D_Sequence) as long as the
calendar age gap between each sample is known
(see stratigraphic information).
See also [Program Operation]
[Example]
[Mathematical Methods]