7.1 Notes on radiocarbon calibration and statistical
analysis

by Magnar Dalland

Calmap shows a space-time distribution of known radiocarbon dated Scottish
Mesolithic sites as per February 1998. It is based on radiocarbon dates
retrieved from each site. Only dates that are believed to have come from a
secure Mesolithic context were included, while dates not directly associated
with obvious human activity have been omitted. Dates of marine material were
corrected for the reservoir effect before calibration. In three cases dating
material had been selected from different parts of the same shell. In those
cases the combined date for the shell was used (Caisteal nan Gillean, Cnoc
Silgeach and Cnoc Coig).

Dates from each site were calibrated using the OxCal
calibration program (Ramsey
1998).
This produced the probabilities for each date to fall within four year
intervals (6000 BC, 6004 BC, 6008 BC etc), as illustrated in Figure 1.

Figure 1: Calibrated probability distribution
of Oxa-1599 at 4 year intervals

The resolution of the data was then reduced by adding up the
probabilities for the date to fall within a 20 year interval, see Figure
2.

Fig. 2: Calibrated probability distribution
of Oxa-1599 at 20 year intervals

The resolution of the data was then further reduced by adding up the
probabilities for the date to fall within a 100 year interval
at the centre of every 20 year block (6000 BC, 6020 BC etc). For each
site, this curve for all dates was plotted on the same graph, as shown
in Figure 3. The probabilities were grouped
into five classes represented by different colours on the distribution map.

Figure 3: ±50 year probability data for the
three dates from Auchareoch

If there were several overlapping dates from a site, the highest value
(level) at each interval was used to represent the site on the distribution
map. Figure 3 illustrates how the radiocarbon dates for the site Auchareoch
were converted into the different probability levels shown on the distibution
map. There are three dates from the site: OxA-1599, OxA-1600 and OxA-1601.
Over the period 7560 BC to 6760 BC, the site is represented by OxA-1601
at levels 5,4 and 3. Between 6760 BC and 6400 BC the site is represented
by OxA-1600 at levels 3,4 and 5. Between 6400 BC and 5600 BC the site is
represented by OxA-1599 rising from level 5 to 2 and back to 5.