## Reflections on the aspect of certitude in dendrochronological dating

A question frequently addressed to Dendrochronology is: How certain is a certified dating effectively? To answer this question we have to deal with the value figure for the mathematical degree of certainty which will be 99,99% under ideal conditions and which is published in every single dendrochronological report.

To put it completely:  The probability of a samples synchronous position compared to a dendrochronological reference-curve is 99,99%. Thus, the formulation of the reverse conclusion would be: The chance of misinterpretation is 0,01 %. Considering all the standardized mathematical methods of dendrochronology, we have to be aware that in an interval of 10.000 years for instance, there may happen a random synchronicity in a certain dimension, which would indicate a false dating. The danger of misinterpretation is all the bigger the smaller the amount of available annual rings on a sample is.

Therefore, the customer should select the samples carefully, concerning especially samples with narrow and, therefore, often a maximum amount of annual rings. In order to avoid the risk of missinterpretation we strongly recommend to take at least an amount of 5-6 samples per archaeological feature or building phase into account. For synchronicities of a successful dating tend to back up each other, this improves the certainty of the datings, although this cannot be shown graphically in mathematical values. Therefore, archaeologists and building-researchers are in charge of an enhanced certainty of dendrochronological datings.

Sometimes building researchers or archaeologists retain information about the timeframe the samples possibly could date to. Any dating without information about the possible timeframe suffers from a decreased ratio of certainty. On the other hand,
if information is given by the customer, this would not affect results in a prejudicing way. A dating for example can be determined much easier if there are only two possible synchronicities as if there are 10.000. All the bigger the interval of time for a possible dating is, the more strict the criteria will become for a acceptable dating result.
A scope of 10.000 years which a sample could possibly be dated to needs a statistical degree of certainty of 99.99%. If values get below this threshold, misinterpretation becomes increasingly possible. Concerning the example of a dating within a range of 10.000 years, values < 99.9% would not be acceptable any more. In a situation like that, this would be marked on the report. Thus Archaeologists and building researchers can help dendrochronology to enhance the certainty of datings by giving all information about the possible timeframe.

To faciliate the interpretation of the results for building researchers and archaeologists, we emphasize the different stages of the mathematical certainty by coloured markings on the report. For this purpose we do use the following colour code:

Red = The sample does not meet the normative properties for dendrochronological dating. The given dating has to be regarded as questionable.

Yellow = Liability of the synchronous position is on the threshold.

Green  = Good or even very good sample material. The given dating may be regarded as reliably backed.