Recent work on reversals of the earth's magnetic field [Clement, 1991; Constable, 1992; Laj et al., 1991; Runcorn, 1992> and work on low rates of change of the radial magnetic field, Br, in the Pacific hemisphere (see Jacobs [1994> page 8, for a summary) suggest that the statistics of Br differ between the Pacific and Atlantic hemispheres. The question of statistical invariance of the magnetic field is interesting in its own right [Courtillot et al., 1992>, and we study this hypothesis by investigating the statistical significance of the difference between the average value of B2r in the Atlantic and Pacific hemispheres at three different radii. The differences between the average value of B2r in the Atlantic hemisphere and the average value of B2r in the Pacific hemisphere at all three radii are incompatibly large with two statistical models of Br. The differences are incompatibly large at two of three radii when a third statistical model is used. The results suggest that further work on the statistical properties of Br is warranted and provide another test for normality of spherical harmonic coefficients. ¿ American Geophysical Union 1996