A probabilistic characterization is performed for a class of field anisotropy coefficients for random electromagnetic fields. Ideal reverberation (isotropy), anisotropic stirring (polarization bias), and incomplete stirring or line-of-sight coupling (direct illumination) are investigated individually. For small degrees of planar anisotropy or bias, trapezoidal distributions are obtained, representing first-order departures from ideal rectangular distributions. Distributions for two definitions of total field anisotropies are found to be less sensitive than those for the individual planar anisotropies. The method and results are useful for calibration and validation of reverberation chambers when field anisotropy requires a separate assessment. Theoretical results are compared to measured data in two chambers.