Identifying Tools for Comparing Simulations and Observations of Spectral-line Data Cubes

We present a statistical framework to compare spectral-line data cubes of molecular clouds and use the framework to perform an analysis of various statistical tools developed from methods proposed in the literature. We test whether our methods are sensitive to changes in the underlying physical properties of the clouds or whether their behaviour is governed by random fluctuations. We perform a set of 32 self-gravitating magnetohydrodynamic simulations that test all combinations of five physical parameters -- Mach number, plasma parameter, virial parameter, driving scales, and solenoidal driving fraction -- each of which can be set to a low or high value. We create mock observational data sets of ${\rm ^{13}CO}$(1-0) emission from each simulation. We compare these mock data to a those generated from a set of baseline simulations using pseudo-distance metrics based on 18 different statistical techniques that have previously been used to study molecular clouds. We analyze these results using methods from the statistical field of experimental design and find that several of the statistics can reliably track changes in the underlying physics. Our analysis shows that the interactions between parameters are often among the most significant effects. A small fraction of statistics are also sensitive to changes in magnetic field properties. We use this framework to compare the set of simulations to observations of three nearby star-forming regions: NGC 1333, Oph A, and IC 348. We find that no one simulation agrees significantly better with the observations, although there is evidence that the high Mach number simulations are more consistent with the observations.