  Correlation anisotropy emerges dynamically in magnetohydrodynamics (MHD),
producing stronger gradients across the large-scale mean magnetic field than
along it. This occurs both globally and locally, and has significant
implications in space and astrophysical plasmas, including particle scattering
and transport, and theories of turbulence. Properties of local correlation
anisotropy are further documented here by showing through numerical experiments
that the effect is intensified in more localized estimates of the mean field.
The mathematical formulation of this property shows that local anisotropy mixes
second-order with higher order correlations. Sensitivity of local statistical
estimates to higher order correlations can be understood in connection with the
stochastic coordinate system inherent in such formulations. We demonstrate this
in specific cases, illustrate the connection to higher order statistics by
showing the sensitivity of local anisotropy to phase randomization, and thus
establish that the local structure function is not a measure of the energy
spectrum. Evidently the local enhancement of correlation anisotropy is of
substantial fundamental interest, and this phenomenon must be understood in
terms of higher order correlations, fourth-order and above.
