Empirically-determined statistical significance of the Baillie and Pilcher (1973) t statistic for British Isles oak

The “Belfast method” of statistical crossdating has been widely used in the British Isles since public domain software was released by Baillie and Pilcher (1973). Although the conceptual merits of the approach are accepted, the details of the methodology have been severely criticised, including the fact that serially correlated tree-ring time series violate a fundamental requirement for the use of Students t statistic as a measure of statistical significance. An unfortunate consequence of this has been that t values are often published without reference to the associated probability of the specific value being obtained by chance. Here we present an empirical method for determining statistical significance from analysis of many misaligned inter-site correlations amongst over 2000 dated British Isles oak chronologies. Results indicate that a t value of 3.5 has a probability of about one in 600 for series lengths of 100+ years, but this declines (becomes less rare) as series length decreases.