Mean and standard deviation of the distance in log-space between the estimations (i.e., $\left|{\widehat{\theta }}_x-{\widehat{\theta }}_y\right|/\sqrt{2}$ where θ = log N, or log T_kin or log $n_{{\text{H}}_2}$) as a function of different sets of species and their associated a priori hypotheses, shown as the column and row labels. In all cases T_kin, $n_{{\text{H}}_2}$, C_V and σ_V are assumed to be the same for all lines. Table 4 lists the details. The cells are color-coded with the values of the root mean square error $=\sqrt{{\text{ mean }}^2+{\text{sdev}}^2}$. From left to right, the top graphs show the results for N(¹³CO), N(C¹⁸O), N(HCO⁺), and N(H¹³CO⁺), and the bottom graphs the results for the kinetic temperature and volume density. This figure summarizes the joint histograms shown in Figs. 2, C.1–C.4.