We analyze hydrodynamic simulations of turbulent, star-forming molecular clouds that are post-processed with the photo-dissociation region astrochemistry code 3D-PDR. We investigate the sensitivity of 15 commonly applied turbulence statistics to post-processing assumptions, namely variations in gas temperature, abundance and external radiation field. We produce synthetic $^{12}$CO(1-0) and CI($^{3}$P$_{1}$-$^{3}$P$_{0}$) observations and examine how the variations influence the resulting emission distributions. To characterize differences between the datasets, we perform statistical measurements, identify diagnostics sensitive to our chemistry parameters, and quantify the statistic responses by using a variety of distance metrics. We find that multiple turbulent statistics are sensitive not only to the chemical complexity but also to the strength of the background radiation field. The statistics with meaningful responses include principal component analysis, spatial power spectrum and bicoherence. A few of the statistics, such as the velocity coordinate spectrum, are primarily sensitive to the type of tracer being utilized, while others, like the delta-variance, strongly respond to the background radiation field. Collectively, these findings indicate that more realistic chemistry impacts the responses of turbulent statistics and is necessary for accurate statistical comparisons between models and observed molecular clouds.
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