Abstract: In order to characterize the attenuation inhomogeneity of earthquake intensity along different directions, usually statistical analyses are car ried out separately along major axis and minor axis for elliptical attenuation relationship. Separate statistical analyses along major axis and minor axis will cause the following shortcomings, the standard deviations of the relationships along both major axis and minor axin will not be equal; the intensity ratings along both directions will not increase or decrease with the same proportion of magnitude; the epicentral intensities obtained from relationships of both directions will not be equal; at near field with the same epicentral distances the intensity rating obtained from relationship along minor axis sometimes will be higher than that obtained from relationship along major axis. Those phenomena do not fit the real world. In this paper, it is suggested that in statistical analyses, the correlation of the data along major axis and minor axis should be considered in order to overcome above mentioned shortcomings. A case study for elliptical attenuation relationship of earthquake intensity in North China seismic region is illustrated.