  We search for planar deviations of statistical isotropy in the Wilkinson
Microwave Anisotropy Probe (WMAP) data by applying a recently introduced
angular-planar statistics both to full-sky and to masked temperature maps,
including in our analysis the effect of the residual foreground contamination
and systematics in the foreground removing process as sources of error. We
confirm earlier findings that full-sky maps exhibit anomalies at the planar
($l$) and angular ($\ell$) scales $(l,\ell)=(2,5),(4,7),$ and $(6,8)$, which
seem to be due to unremoved foregrounds since this features are present in the
full-sky map but not in the masked maps. On the other hand, our test detects
slightly anomalous results at the scales $(l,\ell)=(10,8)$ and $(2,9)$ in the
masked maps but not in the full-sky one, indicating that the foreground
cleaning procedure (used to generate the full-sky map) could not only be
creating false anomalies but also hiding existing ones. We also find a
significant trace of an anomaly in the full-sky map at the scale
$(l,\ell)=(10,5)$, which is still present when we consider galactic cuts of
18.3% and 28.4%. As regards the quadrupole ($\ell=2$), we find a coherent
over-modulation over the whole celestial sphere, for all full-sky and cut-sky
maps. Overall, our results seem to indicate that current CMB maps derived from
WMAP data do not show significant signs of anisotropies, as measured by our
angular-planar estimator. However, we have detected a curious coherence of
planar modulations at angular scales of the order of the galaxy's plane, which
may be an indication of residual contaminations in the full- and cut-sky maps.
