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]).

24 pages, 10 figures; few typos corrected; published in JCAP