Which of the following dates below are actual calendar/historical dates ?

If you said all of them then you need to read further. If you included all except 2000 bc then you would still technically be wrong(read further for explanations). When a sample radiocarbon age of a find comes back from the laboratory it does not mean that the date assigned to it is a calendar or historical date. It was discovered that as this new dating technique progressed it was being compared to another technique called tree-ring dating or dendrochronology. Discrepancies started to arise between the tree-ring dating and the C14 analyses. As much as 5% was in error with the C14 technique. Therefore a means to bring C14 into alignment with dendrochronology was worked out.

Calibration

This then became the means for converting raw C14 dates into a range of calendar ones. The method used was statistical , a derivation of the Monte Carlo method of probability studies. Unfortunately statistics were used because although the rate of C14 decay was a constant, it occurred spontaneously. Therefore not all of the radioactivity in a sample could be measured. An uncalibrated date is then given the notation of 'Conventional Radiocarbon Age' in literature or publication of journals, books etc. There is in use a very confusing nomenclature or labelling system in calibration that during the 1970's actually confused british archaeologists who thought that they were dealing with calendar years for a sample when in fact they were looking at raw radiocarbon ages. Let's look at our dates again this time with an explanation.

In fact surprisingly only BC 2000 and 2000 BCE are the only unambiguous calendar/historical dates. What do all the others mean? The normal way to state that a raw radiocarbon date has been calibrated is to place the date as Cal BC or Cal AD. This avoids confusion. However in some areas of literature you may see a variety of dates as stated above, if you are a researcher you need to be able to tell what's what in case you calibrate an already calibrated date. Clearly an uncalibrated date would be shown partly as follows:= 2000 bc . The bc is intentionally lower case to distinguish it from calendar dates in upper case BC/AD. Some archaeologists started believing that it would be better to state calibrated dates as just upper case BC/AD after the year. In order to compensate for the ensuing confusion between calendar and calibrated two notations were used. One involved placing the AD/BC BEFORE the year for calendar and the other placing Cal BC/AD after the year for calibration .

Stating Radiocarbon dates in Scientific Journals

There is an acceptible way to cite Radiocarbon dates that have gone through the laboratory process in archaeology books etc. for publication. It goes as follows :=

Let's look at the way a radiocarbon age is stated as below :=

You can see the breakup explanation but its important to know how to convert from a CRA down to an uncalibrated age by subtracting 1950 from the sample. Results are always in brackets. Let's look at the so called ERROR TERM. Since the process of C14 counting is a chemical and spontaneous one a number of errors can creep into the process at the lab. Good quality labs with high precision processing will quote an error term in years as their way to estimate the amount of errors incurred in chemical analysis and handling contamination. The error term is not related to any calendar years but is stated as one standard deviation statistically. In AD 1962 a scientist called Godwin found out that the stated Libby half-life was understated by 3 percent and should be 5730 years +/- 40 instead of the 5568 +/- 30. This new half-life was called True or Cambridge half-life. It was considered to keep the processing of radiocarbon dates at the Libby half-life level because it was easier to compare earlier samples.

Calibration Programs

There are two programs that can be downloaded for the researcher, Oxcal 3.8 http://www.rlara.ox.ac.uk/orau.htmand Calib 4.4http://depts.washington.edu/qil/calib/. Oxcal is by far the easier of the two to use so we'll take that first. After you have downloaded it and extracted the files click on the icon as below

The following screen should automatically show up as below,if not, click on file and then click on 'enter a Radiocarbon date'.

Now you click on the selection arrowed, another box opens up, see below.

Enter in the top box 'oxa - 9010' ,this is the sample that your radiocarbon age is compared to.

Enter in only 'Conventional Radiocarbon Ages' (CRA's) which are stated as years BP. This goes into the left box. Enter in the error term in the last box, to the right, press OK button and your graph will appear as below

This shows you a diagramatic representation of the Guassian Probability Distribution of POSSIBLE calendar date ranges based on what are called confidence levels as percentages. There are 3 confidence levels , Sigma 1 (68.2%), Sigma 2 (95.4 %) and Sigma 3 (99.7 %). These levels can easily be broken down into percentages within each level depending on the randomness of the isotope count at the lab. In this particular graph the results are ONLY as follows :==

1. The calibration plot is only for a Libby half-life of 5568 years not 5730 years, this is because the CRA was taken from a publication.

2. The horizontal X-axis shows Cal BP which when subtracted from AD 1950 will give you the calendar dates as shown within the graph with the confidence level percentages

3. The ONLY data we can say anything about is in regard to the confidence level 68.2 %

4. This 68.2 % level will give us a calibrated range of dates between 5810 CalBC to 5620 CalBC

5. What this says is that there is a 1 in 3 chance that any date between this range will be OUTSIDE the range i.e. this is not the best confidence level to get any accuracy with.

If we choose 95.4% our chance of any date in the range being outside the range is considerably less down to 1 in 20. The higher up the percentage we go the greater the chance that our chosen date will be within the range. Why can we not choose the higher and more accurate %s because our error term is fixed at the 1 Sigma level. In order to move up the percentages we would have to double the error term (+/-110) to 220 years for 95.4% level and triple it to 330 years for the 99.7% level. At this highest level there is a 39 in 40 chance that the date picked from within our range is correct.

Let's plot the highest level 99.7% with our error term at +/-330 years and see what we come up with.

1. Our range has now increased from 6400Cal BC to 4600Cal BC

2. We can now say that there is more accuracy/certainity of any date within this range being likely to be the correct one but the precision or narrowness of the range is not very good.

Therefore you need to find a radiocarbon date with as low an error term as possible so you can scale up the confidence level. There are many options for graphing radiocarbon dates in all sorts of configurations but you will always end up saying that the results are always a probability. The best thing you can say is to get a specific range of calibrated dates at the highest confidence level with the lowest error term possible. Archaeologists usually take a number of radiocarbon samples to send to the labs and when results come back they look for consistancy across the range. If any radiocarbon result is inconsistant with a group of other results then that result is regarded as 'archaeologically unacceptable' or 'anamalous'. Oxcal will allow you to play around with all sorts of graphs combinations etc., have fun!! Now we can look at Calib 4.1 program on the next page.