The authors look at preferred directions in two ways. First, they analyse the Union2 supernova dataset for the axis of maximum asymmetry. Second, they compare various directions determined from different cosmological datasets and determine the probability that they are all so close to each other by accident.
The asymmetry direction is determined by fitting the spatially flat [tex]\Lambda[/tex]CDM model separately to two hemispheres and finding the direction which maximises the difference in [tex]\Omega_{m0}[/tex]. By comparison with simulations, the authors conclude that there is no statistical significance to the asymmetry. The directions determined from the supernova data, the CMB dipole, quadrupole and octopole, galaxy flows, and quasar polarization naively look rather close to each other (see table 1 on page 6). The authors get a probability of 1% for the axes to be so close to each other by accident. (This goes up to 7% if one drops the CMB axes  for example, the CMB dipole is not independent of local galaxy flows.)
It is not clear how much the result would change if the directions were to have error bars, but the significance could drop a lot. For example, since the the amplitude of the maximum hemispheric asymmetry of the Union2 dataset is not statistically significant, the direction should not matter at all. (I am not familiar with the direction determined from polarization of quasars  perhaps someone can comment on that?)
Nevertheless, it is interesting to have a quantitative analysis of the coincidence of directions.
[1007.4347] Searching for a Cosmological Preferred Axis: Union2 Data Analysis and Comparison with Other Probes
Authors:  I. Antoniou, L. Perivolaropoulos (U. of Ioannina) 
Abstract:  We review, compare and extend recent studies searching for evidence for a preferred cosmological axis. We start from the Union2 SnIa dataset and use the hemisphere comparison method to search for a preferred axis in the data. We find that the hemisphere of maximum accelerating expansion rate is in the direction (l,b)=(306^\circ, 15^\circ) (\Omega_m=0.19) while the hemisphere of minimum acceleration is in the opposite direction (l,b)=(126^\circ, 15^\circ) (\Omega_m=0.30). The level of anisotropy is described by the normalized difference of the best fit values of \Omega_m between the two hemispheres in the context of \lcdm fits. We find a maximum anisotropy level in the Union2 data of \frac{\Delta \Omega_m_max}{\Omega_m}=0.42. This level does not necessarily correspond to statistically significant anisotropy because it is reproduced by about 30% of simulated isotropic data mimicking the best fit Union2 dataset. However, when combined with the axes directions of other cosmological observations (bulk velocity flow axis, three axes of CMB low multipole moments and quasar optical polarization alignment axis), the statistical evidence for a cosmological anisotropy increases dramatically. We estimate the probability that the above independent six axes directions would be so close in the sky to be less than 1%. Thus either the relative coincidence of these six axes is a very large statistical fluctuation or there is an underlying physical or systematic reason that leads to their correlation. 
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