  We propose a new approach to comparing simulated observations that enables us
to determine the significance of the underlying physical effects. We utilize
the methodology of experimental design, a subfield of statistical analysis, to
establish a framework for comparing simulated position-position-velocity data
cubes to each other. We propose three similarity metrics based on methods
described in the literature: principal component analysis, the spectral
correlation function, and the Cramer multi-variate two sample similarity
statistic. Using these metrics, we intercompare a suite of mock observational
data of molecular clouds generated from magnetohydrodynamic simulations with
varying physical conditions. Using this framework, we show that all three
metrics are sensitive to changing Mach number and temperature in the simulation
sets, but cannot detect changes in magnetic field strength and initial velocity
spectrum. We highlight the shortcomings of one-factor-at-a-time designs
commonly used in astrophysics and propose fractional factorial designs as a
means to rigorously examine the effects of changing physical properties while
minimizing the investment of computational resources.
