We report on the results from two independent but complementary statistical analyses of the Wilkinson Microwave Anisotropy Probe (WMAP) first-year data, based on the power spectrum and N-point correlation functions. We focus on large and intermediate scales (larger than about 3°) and compare the observed data against Monte Carlo ensembles with WMAP-like properties. In both analyses, we measure the amplitudes of the large-scale fluctuations on opposing hemispheres and study the ratio of the two amplitudes. The power-spectrum analysis shows that this ratio for WMAP, as measured along the axis of maximum asymmetry, is high at the 95%-99% level (depending on the particular multipole range included). The axis of maximum asymmetry of the WMAP data is weakly dependent on the multipole range under consideration but tends to lie close to the ecliptic axis. In the N-point correlation-function analysis, we focus on the northern and southern hemispheres defined in ecliptic coordinates, and we find that the ratio of the large-scale fluctuation amplitudes is high at the 98%-99% level. Furthermore, the results are stable with respect to choice of Galactic cut and also with respect to frequency band. A similar asymmetry is found in the COBE Differential Microwave Radiometer (DMR) map, and the axis of maximum asymmetry is close to the one found in the WMAP data.