Effective spectroscopic diagnostics rely on the ability to convert a particular flux measurement into a physical interpretation. Knowledge of uncertainty is a central component of diagnostics. We present data from a simulated solar-like chromosphere, where we have addressed the question of whether degeneracy is a problem in mapping from a non-LTE chromospheric line profile to a particular vertical stratification of atmospheric properties along the line of sight. Our results indicate that stratification degeneracies do exist, at least in our simulated atmosphere. We quantify this effect through the creation of posterior densities for atmospheric properties based on the Mg II h line profile using the approximate Bayesian computation (ABC) technique. We find that the predictive power of the ABC temperature posterior systematically varies as a function of atmospheric column mass and ground-truth temperature. The ABC posteriors more effectively reproduce the spectral intensity in the Ca II 8542 Å line than they do temperature stratification, although residual error in the Ca II line core is common. Our results illustrate that some degeneracies should be alleviated through simultaneous analysis of multiple chromospheric lines.