Re-Examining the Evidence of the Hercules-Corona-Borealis Great Wall
  In the {\Lambda}-CDM paradigm of cosmology, anisotropies larger than 260 Mpc
shouldn't exist. However, the existence of the Hercules-Corona Borealis Great
Wall (HCB) is purported to challenge this principle by some with an estimated
size exceeding 2000 Mpc. Recently, some have challenged the assertion of the
existence of the HCB, attributing the anisotropy to sky exposure effects. It
has never been explained why the original methods purporting the existence of
the HCB produce anisotropies, even if sky-exposure effects are taken into
account. In this paper, I apply the methods of the original papers purporting
the existence of the HCB in various Monte-Carlo simulations that assume
isotropy to analyze the empirical meaning of the significance levels of the
original tests used. I find that, although the statistical tests at first
glance show significant anisotropies present in the suspect sample, Monte-Carlo
simulations can easily reproduce the sample in most cases, and if not, the
differences can be accounted for by other statistical considerations. An
updated sample raises the probability of drawing the observed clustering from
an isotropic sample ten-fold in some cases. Thus the statistical tests used in
prior studies overestimate the significance of the observed anisotropy, and an
updated sample returns even less significant probabilities. Given the ability
to reproduce the observed anisotropy in Monte-Carlo simulations, the new,
higher probabilities of being drawn from isotropy for an updated sample, and
the work of previous papers attributing anisotropies to sky-selection effects,
the existence of the HCB must be treated as doubtful at best.
