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ABSTRACT The relationship between magnetic field strength B and gas density n in the interstellar medium is of fundamental importance. We present and compare Bayesian analyses of the B–n relation for two comprehensive observational data sets: a Zeeman data set and 700 observations using the Davis–Chandrasekhar–Fermi (DCF) method. Using a hierarchical Bayesian analysis we present a general, multiscale broken power-law relation, $$B=B_0(n/n_0)^{\alpha }$$, with $$\alpha =\alpha _1$$ for $$n< n_0$$ and $$\alpha _2$$ for $$n>n_0$$, and with $$B_0$$ the field strength at $$n_0$$. For the Zeeman data, we find: $$\alpha _1={0.15^{+0.06}_{-0.09}}$$ for diffuse gas and $$\alpha _2 = {0.53^{+0.09}_{-0.07}}$$ for dense gas with $$n_0 = 0.40^{+1.30}_{-0.30}\times 10^4$$ cm$$^{-3}$$. For the DCF data, we find: $$\alpha _1={0.26^{+0.01}_{-0.01}}$$ and $$\alpha _2={0.77_{-0.15}^{+0.14}}$$, with $$n_0=14.00^{+10.00}_{-7.00}\times 10^4$$ cm$$^{-3}$$, where the uncertainties give 68 per cent credible intervals. We perform a similar analysis on nineteen numerical magnetohydrodynamic simulations covering a wide range of physical conditions from protostellar discs to dwarf and Milky Way-like galaxies, computed with the arepo, flash, pencil, and ramses codes. The resulting exponents depend on several physical factors such as dynamo effects and their time-scales, turbulence, and initial seed field strength. We find that the dwarf and Milky Way-like galaxy simulations produce results closest to the observations.