  We reexamine the evidence of the hemispherical power asymmetry, detected in
the CMB WMAP data using a new method. At first, we analyze the hemispherical
variance ratios and compare these with simulated distributions. Secondly,
working within a previously-proposed CMB bipolar modulation model, we constrain
model parameters: the amplitude and the orientation of the modulation field as
a function of various multipole bins. Finally, we select three ranges of
multipoles leading to the most anomalous signals, and we process corresponding
100 Gaussian, random field (GRF) simulations, treated as observational data, to
further test the statistical significance and robustness of the hemispherical
power asymmetry. For our analysis we use the Internally-Linearly-Coadded (ILC)
full sky map, and KQ75 cut-sky V channel, foregrounds reduced map of the WMAP
five year data (V5). We constrain the modulation parameters using a generic
maximum a posteriori method.
  In particular, we find differences in hemispherical power distribution, which
when described in terms of a model with bipolar modulation field, exclude the
field amplitude value of the isotropic model A=0 at confidence level of ~99.5%
(~99.4%) in the multipole range l=[7,19] (l=[7,79]) in the V5 data, and at the
confidence level ~99.9% in the multipole range l=[7,39] in the ILC5 data, with
the best fit (modal PDF) values in these particular multipole ranges of A=0.21
(A=0.21) and A=0.15 respectively. However, we also point out that similar or
larger significances (in terms of rejecting the isotropic model), and large
best-fit modulation amplitudes are obtained in GRF simulations as well, which
reduces the overall significance of the CMB power asymmetry down to only about
94% (95%) in the V5 data, in the range l=[7,19] (l=[7,79]).
