We use the results of magnetohydrodynamic (MHD) simulations to emulate spectroscopic observations and use maps of centroids to study their statistics. In order to assess under which circumstances the scaling properties of the velocity field can be retrieved from velocity centroids, we compare two point statistics (structure functions and power-spectra) of velocity centroids with those of the underlying velocity field and analytic predictions presented in a previous paper (Lazarian & Esquivel 2003). We tested a criterion for recovering velocity spectral index from velocity centroids derived in our previous work, and propose an approximation of the early criterion using only the variances of ``unnormalized'' velocity centroids and column density maps. It was found that both criteria are necessary, however not sufficient to determine if the centroids recover velocity statistics. Both criteria are well fulfilled for subsonic turbulence. We find that for supersonic turbulence with sonic Mach numbers > 2.5 centroids fail to trace the spectral index of velocity. Asymptotically, however, we claim that recovery of velocity statistics is always possible provided that the density spectrum is steep and the observed inertial range is sufficiently extended. In addition, we show that velocity centroids are useful for anisotropy studies and determining the direction of magnetic field, even if the turbulence is highly supersonic, but only if it is sub-Alfvenic. This provides a tool for mapping the magnetic field direction, and testing whether the turbulence is sub-Alfvenic or super-Alfvenic.

26 pages, 16 figures, submitted to the Astrophysical Journal. Revised version. Substantial changes from previous versions