Evolution of magnetohydrodynamic turbulence is often discussed in terms of second-order statistics like the energy spectra, but consideration of the structure of the von K´arm´an–Howarth hierarchy for MHD indicates that higherorder statistical correlations occupy an influential role. Here we show that both spectral anisotropy and energy decay are strongly associated with higher-order statistics. Dynamical emergence of spectral anisotropy must occur at a higher order in the statistical hierarchy, while numerical evidence suggests that strong variations in energy decay are connected with variations in higher-order statistics.