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.
