  The dynamical state of galaxy groups at intermediate redshifts can provide
information about the growth of structure in the universe. We examine three
goodness-of-fit tests, the Anderson--Darling (A-D), Kolmogorov and chi-squared
tests, in order to determine which statistical tool is best able to distinguish
between groups that are relaxed and those that are dynamically complex. We
perform Monte Carlo simulations of these three tests and show that the
chi-squared test is profoundly unreliable for groups with fewer than 30
members. Power studies of the Kolmogorov and A-D tests are conducted to test
their robustness for various sample sizes. We then apply these tests to a
sample of the second Canadian Network for Observational Cosmology Redshift
Survey (CNOC2) galaxy groups and find that the A-D test is far more reliable
and powerful at detecting real departures from an underlying Gaussian
distribution than the more commonly used chi-squared and Kolmogorov tests. We
use this statistic to classify a sample of the CNOC2 groups and find that 34 of
106 groups are inconsistent with an underlying Gaussian velocity distribution,
and thus do not appear relaxed. In addition, we compute velocity dispersion
profiles (VDPs) for all groups with more than 20 members and compare the
overall features of the Gaussian and non-Gaussian groups, finding that the VDPs
of the non-Gaussian groups are distinct from those classified as Gaussian.
