Uncertainty, Emergence, and Statistics in Dendrochronology - Dendroclimatology - page 89

radial growth seasons (roughly May-August) and the intervening 'dormant' sea-
son. As a consequence, the first year of climate data was used in creating the
prior year portion of the 1897 dendroclimatic year, which resulted in the first
analysis year being 1897.
2. The tree-ring data used were first prewhitened with a best-fit first-order autore-
gressive (AR) model (Box and Jenkins 1976 ) to remove the effect of persistence
on degrees of freedom and the determination of statistical significance. The
monthly climate data had very little, if any, persistence in the monthly variables.
Consequently, the climate data were not prewhitened and the first analysis year
remained 1897.
3. The correlation and response functions were computed by using data only over
the 1931-1996 interval. This 66-year interval provides 64 degrees of freedom
for the simple correlations, which yields a two-tailed a priori 95% confidence
limit of ± 0.25 and an a posteriori 95% confidence limit of ± 0.45 (each shown

as dashed lines in Fig. 4.3a ) .
4. The response function was based on retaining as candidate predictors the eigen-
vectors of climate with eigenvalues >1.0 (the EV1 rule; Guttman 1954 ; Kaiser
1960 ) and the best-fit regression model was determined by using the minimum
Akaike information criterion (AIC; Akaike 1974 ; Hurvich and Tsay 1989 ) . The
actual goodness-of-fit is expressed in terms of the classical coefficient of mul-
tiple determination or R 2 statistic used in regression analysis as a measure of

explained variance.
5. The pre-1931 data were reserved for statistical validation tests of the response
function estimates. The validation tests used were the square of the Pearson
correlation coefficient (RSQ), the reduction of error (RE), and coefficient of
efficiency (CE) (Cook et al. 1999 ) .

The correlation function (Fig. 4.3a ) reveals that only 4 out of the 32 monthly
correlations have exceeded the two-tailed a priori 95% confidence limits (prior-
July, prior-September, and current June precipitation, and current May temperature),
while only one month (current June precipitation) exceeds the a posteriori limit.
Does this result mean that only current June precipitation truly matters to these
trees? Based on the most rigorous statistical considerations described above, the
answer would appear to be 'Yes.' However, there may be much more physiological
meaning in the structure of the correlation function than purely statistical con-
siderations would suggest, because the response function (Fig. 4.3b ) , which was
explicitly estimated from the matrix of these monthly correlations, has many more
'significant' coefficients, 24 to be exact. This result in itself is tricky to interpret
because of the way the response function and its confidence limits are calculated
as a regression-weighted, linear combination of fitted climate eigenvectors (Fritts
1976 ; Guiot et al. 1982 ; Fekedulegn et al. 2002 ) . Indeed, even the estimation of the
response function confidence limits has been somewhat controversial. There is good
reason to believe that the original method of Fritts ( 1976 ) produced confidence lim-
its that were a bit too narrow. This problem has been rectified in two different ways:
(1) by using bootstrap resampling to generate empirical confidence intervals (Guiot