Now showing items 1-3 of 3

• #### An Improved Algorithm for Crossdating Tree-Ring Series

The CROS algorithm for crossdating tree-ring series has proved useful. Because it uses Student's t to test correlations which are not independent between autocorrelated tree-ring series, it does not give a good measure of the relative significance of high correlations. It can be improved by transforming the correlation coefficients to normally distributed values, and giving a conservative estimate of the significance of the highest of these by a revised t, derived from its studentized deviation from the mean value. The improved algorithm should help any dendrochronologist who routinely dates oak timbers.
• #### Multicollinearity within Selected Western North American Temperature and Precipitation Data Sets

This paper is concerned with examining the degree of correlation between monthly climatic variables (multicollinearity) within data sets selected for their high quality. Various methods of describing the degree of multicollinearity are discussed and subsequently applied to different combinations of climate data within each site. The results indicate that higher degrees of multicollinearity occur in shorter data sets. Data consisting of 12 monthly variables of a single parameter (temperature or precipitation) have very low degrees of multicollinearity. Data set combinations of two parameters and lagged variables, as commonly used in tree-ring response function analysis, can have significant degrees of multicollinearity. If no preventative or corrective measures are taken when using such multicollinear data, erroneous interpretations of regression results may occur.
• #### Response Functions Revisited

The use of orthogonalized climatic variables in regression to specify treegrowth/climate relationships, commonly known as response function analysis, involves several a priori decisions and a posteriori interpretations, any of which maybe open to question. Decisions about the number of climatic variables to include, confidence limits, number of eigenvectors to allow as candidate predictors in regression, etc., can affect the response function in unpredictable ways and lead to possible errors in interpretation. To demonstrate the nature of these effects, we compared response functions for particular chronologies with the correlation function, which is simply the series of correlation coefficients between a tree-ring chronology and each of several sequential monthly climatic variables. The results indicate that response functions including high-order eigenvectors should be interpreted cautiously, and we recommend using the correlation function as an interpretive guide. Prior tree-growth variables in regression can mask climatic effects, and the correlation function can also be useful in detecting this masking. Statistical significance is more often attained in response functions than in correlation functions, possibly due to differences in the statistical testing procedures, to the statistical efficiency of eigenvectors in spending degrees of freedom, or to the filtering effects on the climatic data that result from eliminating high-order eigenvectors (noise) from the response function. These filtering effects plus the orthogonalization make response function analysis an efficient method for specifying tree-growth/climate relationships. The examples and guidelines presented here should enhance the usefulness of the method.