  From exploratory studies and theoretical expectations it is known that
simplifying approximations in spectroscopic analysis (LTE, 1D) lead to
systematic biases of stellar parameters and abundances. These biases depend
strongly on surface gravity, temperature, and, in particular, for LTE vs.
non-LTE (NLTE) on metallicity of the stars. Here we analyse the [Mg/Fe] and
[Fe/H] plane of a sample of 326 stars, comparing LTE and NLTE results obtained
using 1D hydrostatic models and averaged <3D> models. We show that compared to
the <3D>NLTE benchmark, all other three methods display increasing biases
towards lower metallicities, resulting in false trends of [Mg/Fe] against
[Fe/H], which have profound implications for interpretations by chemical
evolution models. In our best <3D> NLTE model, the halo and disc stars show a
clearer behaviour in the [Mg/Fe] - [Fe/H] plane, from the knee in abundance
space down to the lowest metallicities. Our sample has a large fraction of
thick disc stars and this population extends down to at least [Fe/H] ~ -1.6
dex, further than previously proven. The thick disc stars display a constant
[Mg/Fe] ~ 0.3 dex, with a small intrinsic dispersion in [Mg/Fe] that suggests
that a fast SN Ia channel is not relevant for the disc formation. The halo
stars reach higher [Mg/Fe] ratios and display a net trend of [Mg/Fe] at low
metallicities, paired with a large dispersion in [Mg/Fe]. These indicate the
diverse origin of halo stars from accreted low-mass systems to
stochastic/inhomogeneous chemical evolution in the Galactic halo.
