Interpreting the Distance Correlation Results for the COMBO-17 Survey
  The accurate classification of galaxies in large-sample astrophysical
databases of galaxy clusters depends sensitively on the ability to distinguish
between morphological types, especially at higher redshifts. This capability
can be enhanced through a new statistical measure of association and
correlation, called the {\it distance correlation coefficient}, which has more
statistical power to detect associations than does the classical Pearson
measure of linear relationships between two variables. The distance correlation
measure offers a more precise alternative to the classical measure since it is
capable of detecting nonlinear relationships that may appear in astrophysical
applications. We showed recently that the comparison between the distance and
Pearson correlation coefficients can be used effectively to isolate potential
outliers in various galaxy datasets, and this comparison has the ability to
confirm the level of accuracy associated with the data. In this work, we
elucidate the advantages of distance correlation when applied to large
databases. We illustrate how the distance correlation measure can be used
effectively as a tool to confirm nonlinear relationships between various
variables in the COMBO-17 database, including the lengths of the major and
minor axes, and the alternative redshift distribution. For these outlier pairs,
the distance correlation coefficient is routinely higher than the Pearson
coefficient since it is easier to detect nonlinear relationships with distance
correlation. The V-shaped scatterplots of Pearson versus distance correlation
coefficients also reveal the patterns with increasing redshift and the
contributions of different galaxy types within each redshift range.
