  We report the results of statistical tests performed on a sample of 139 broad
absorption line (BAL) QSOs with good quality optical spectra and/or optical
polarization data. Correlations between optical indices and the polarization
degree p_0 are systematically searched for. In order to identify the most
important correlations, we perform a principal component analysis with a sample
of 30 BAL QSOs and eight quantities (including p_0). Most of the variance in
the data is contained in two principal components (PC): PC1 is mainly dominated
by the correlation between the balnicity index BI and the strength of the feii
emission, and may be driven by the accretion rate of matter onto the central
compact object. The variance in PC2 is essentially due to the anti-correlation
between p_0 and the detachment index DI. PC2 may be related to the orientation
of the BAL QSOs with respect to the line of sight. We also consider a
spectropolarimetric sample of 21 BAL QSOs for which we define four indices
describing the polarization properties of the absorption and emission lines. We
find a possible anti-correlation between the detachment index and a quantity SI
which measures the ratio of the depths of the civ absorption in the polarized
flux and in the total flux. This correlation indicates that in BAL QSOs with P
cygni profiles, the BAL troughs in the polarized flux are nearly as deep as in
the total flux while, in BAL QSOs with detached absorptions, the BAL troughs in
the polarized flux are much weaker than in the total flux. We show that our
main results may be explained in the framework of a 'two-component' wind model.
In this model, the broad absorption occurs in a dense equatorial wind emerging
from the accretion disk, while scattering and polarization mainly take place in
a polar region.
