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

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