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We propose a new approach to comparing simulated observations that enables usto determine the significance of the underlying physical effects. We utilizethe methodology of experimental design, a subfield of statistical analysis, toestablish a framework for comparing simulated position-position-velocity datacubes to each other. We propose three similarity metrics based on methodsdescribed in the literature: principal component analysis, the spectralcorrelation function, and the Cramer multi-variate two sample similaritystatistic. Using these metrics, we intercompare a suite of mock observationaldata of molecular clouds generated from magnetohydrodynamic simulations withvarying physical conditions. Using this framework, we show that all threemetrics are sensitive to changing Mach number and temperature in the simulationsets, but cannot detect changes in magnetic field strength and initial velocityspectrum. We highlight the shortcomings of one-factor-at-a-time designscommonly used in astrophysics and propose fractional factorial designs as ameans to rigorously examine the effects of changing physical properties whileminimizing the investment of computational resources.

Comparing Simulated Emission from Molecular Clouds Using Experimental Design