In a previous work Lazarian and Pogosyan suggested a technique to extract
velocity and density statistics, of interstellar turbulence, by means of
analysing statistics of spectral line data cubes. In this paper we test that
technique, by studying the effect of correlation between velocity and density
fields, providing a systematic analysis of the uncertainties arising from the
numerics, and exploring the effect of a linear shear. We make use of both
compressible MHD simulations and synthetic data to emulate spectroscopic
observations and test the technique. With the same synthetic spectroscopic
data, we also studied anisotropies of the two point statistics and related
those anisotropies with the magnetic field direction. This presents a new
technique for magnetic field studies. The results show that the velocity and
density spectral indices measured are consistent with the analytical
predictions. We identified the dominant source of error with the limited number
of data points along a given line of sight. We decrease this type of noise by
increasing the number of points and by introducing Gaussian smoothing. We argue
that in real observations the number of emitting elements is essentially
infinite and that source of noise vanishes.Comment: 12 pages, 10 figures. Accepted for publication in MNRA
