  A directional spherical wavelet analysis is performed to examine the
Gaussianity of the WMAP 1-year data. Such an analysis is facilitated by the
introduction of a fast directional continuous spherical wavelet transform. The
directional nature of the analysis allows one to probe orientated structure in
the data. Significant deviations from Gaussianity are detected in the skewness
and kurtosis of spherical elliptical Mexican hat and real Morlet wavelet
coefficients for both the WMAP and Tegmark et al. (2003) foreground-removed
maps. The previous non-Gaussianity detection made by Vielva et al. (2003) using
the spherical symmetric Mexican hat wavelet is confirmed, although their
detection at the 99.9% significance level is only made at the 95.3%
significance level using our most conservative statistical test. Furthermore,
deviations from Gaussianity in the skewness of spherical real Morlet wavelet
coefficients on a wavelet scale of 550 arcmin (corresponding to an effective
global size on the sky of approximately 26 degrees and an internal size of 3
degrees) at an azimuthal orientation of 72 degrees, are made at the 98.3%
significance level, using the same conservative method. The wavelet analysis
inherently allows one to localise on the sky those regions that introduce
skewness and those that introduce kurtosis. Preliminary noise analysis
indicates that these detected deviation regions are not atypical and have
average noise dispersion. Further analysis is required to ascertain whether
these detected regions correspond to secondary or instrumental effects, or
whether in fact the non-Gaussianity detected is due to intrinsic primordial
fluctuations in the cosmic microwave background.
