  Observations of non-random distribution of galaxies with opposite spin
directions have recently attracted considerable attention. Here, a method for
identifying cosine-dependence in a dataset of galaxies annotated by their spin
directions is described in the light of different aspects that can impact the
statistical analysis of the data. These aspects include the presence of
duplicate objects in a dataset, errors in the galaxy annotation process, and
non-random distribution of the asymmetry that does not necessarily form a
dipole or quadrupole axes. The results show that duplicate objects in the
dataset can artificially increase the likelihood of cosine dependence detected
in the data, but a very high number of duplicate objects is required to lead to
a false detection of an axis. Inaccuracy in galaxy annotations has relatively
minor impact on the identification of cosine dependence when the error is
randomly distributed between clockwise and counterclockwise galaxies. However,
when the error is not random, even a small bias of 1% leads to a statistically
significant cosine dependence that peaks at the celestial pole. Experiments
with artificial datasets in which the distribution was not random showed strong
cosine dependence even when the data did not form a full dipole axis alignment.
The analysis when using the unmodified data shows asymmetry profile similar to
the profile shown in multiple previous studies using several different
telescopes.
