Distinguishing Type I and II errors in statistical tree-ring dating

Tree-ring dating is based on the principles of dendrochronology. Tree-ring segments can be cross-dated by matching growth patters among the specimens and between the samples and existing master chronology. Linear (Pearson) correlations (r) and t values are commonly used to statistically support the outcomes of cross-dating. This paper delves into the aspects concerning the type I and II errors in null hypothesis (H0) testing of cross-dating statistics. To simulate statistical cross-dating, series of old-growth living trees were resampled for experimental tree-ring segments to be correlated with the existing master chronologies. Statistics resulting from correct and incorrect dating positions were then compared to obtain distributions representative of the null hypothesis (H0) of no correlation and the alternative hypothesis (H1) of true correlation. The results show that there is no desirable r or t-value that could serve as a universal criterion for an acceptable dating outcome. Instead, multiple dendroecological factors explaining the extent to which the H0 and H1 distributions overlap could be disentangled. Moreover, the assessment of a correct dating position was improved when the testing of null hypothesis was based not only on the strength of correlation between the sample series and master chronology in any one position, but also on the strength of that correlation relative to correlations between the sample and master in any other positions. Collectively, the results of this study demonstrate the ways the evaluation of tree-ring dating results could be considerably improved and emphasise a further need for extended analyses including a wide range of tree species and site conditions.

Automated summary

Tree-ring dating relies on dendrochronology principles and cross-dating of growth patterns among specimens. This study examines the type I and II errors involved in null hypothesis testing of cross-dating statistics. The results show that there is no universal criterion for acceptable dating outcomes, and multiple dendroecological factors need to be considered. Additionally, evaluating the strength of correlation relative to other positions improves the assessment of correct dating positions.