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

Abstract

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.

Tree ring dating using oxygen isotopes: a master chronology for central England

“…After ‘filtering’ the data in this manner, correlation coefficients are calculated and then transformed into t‐ values, by assuming that the degrees of freedom are equal to the length of the overlap minus two. The t‐ values calculated by following this procedure are commonly referred to as Baillie–Pilcher t ‐values or ‘ BPt‐ values.’ Soon after publication it was recognized that BPt‐ values do not follow Student's t‐ distribution and thus cannot be easily translated into probabilities (Munro, ; Wigley et al ., ; Monserud, ; Fowler and Bridge, ), the main reason being the unrealistic treatment of degrees of freedom (see section below).…”

“…The t-values calculated by following this procedure are commonly referred to as Baillie-Pilcher t-values or 'BPt-values.' Soon after publication it was recognized that BPt-values do not follow Student's t-distribution and thus cannot be easily translated into probabilities (Munro, 1984;Wigley et al, 1987;Monserud, 1989;Fowler and Bridge, 2017), the main reason being the unrealistic treatment of degrees of freedom (see section below).…”

Dendrochronological assessment of British veteran sweet chestnut (Castanea sativa) trees: Successful cross-matching, and cross-dating with British and French oak (Quercus) chronologies

“…In Britain, only thirty finds of alleged Castanea sativa wood/charcoal have been recorded in prehistoric and historic contexts up to AD 650 (Jarman et al, unpublished results): of these, only two finds appear to have been dendrologically assessed (Nayling, 1991;Museum of London Archaeology, 2011) and neither had sufficient growth rings for dendrochronological analysis. Hillam (1998) states >50 rings are necessary, whilst other researchers (Domínguez-Delmás et al, 2013;Fowler and Bridge, 2017) recommend >70. Searches for reported finds of Castanea sativa wood in Britain post-dating AD 650 have revealed only two: Hillam (1985) reported finds from the late 16th-early 17th century AD; and Groves (1993) discussed finds from the late 18th-early 19th century AD.…”

“…Statistical crosscorrelation algorithms were used to search for growth-ring sequence correlations (Baillie and Pilcher, 1973) to produce t values 3 : where t ≥3.5 and >50 growth-rings are measured, the correlation is deemed statistically significant (Baillie, 1982). Fowler and Bridge (2017) reviewed the statistical viability of Baillie's 't = 3.5 rule of thumb' method and concluded that a t value of 3.5 would provide 99.9% confidence of acceptable matching positions if >70 growth-rings were present in the measured sequence. For sequences between 50 and 70 growth-rings, t ≥3.5 would provide a confidence level of ~99.84%.…”

“…We have established a broadly replicated 355-year continuous chronology (AD 1660-2014) from 23 (ex 28 sampled = 82%) cross-matched Castanea sativa trees, labelled 'CASA23'. The 23 trees, drawn from 14 different sites, demonstrate effective cross-matching of Castanea sativa within and between sites in the same locality and also between regions across southern Britain (Table 2): the strong t values (following Fowler and Bridge, 2017) indicate the potential for constructing regional Castanea sativa chronologies. This provides a more optimistic outcome than the study by Romagnoli et al (2004) of Castanea sativa in central Italy, which found poor cross-matching ('intra-specific synchronization') within 89 trees from 5 geospatially dispersed sites.…”