Simpson’s paradox in Galactic Archaeology

Some chemo-kinematical relations believed to constrain the Galactic disk formation and evolution are the radial and vertical metallicity gradients, the age-metallicity relation (AMR), and the metallicity-rotational velocity relation (MVR).

I will show that interpretation of these can lead to conflicting conclusions about the Galaxy past if analyses marginalize over stellar age and/or stellar birth radius. This is caused by a well-known statistical phenomenon, "Simpson’s paradox" (or the Yule-Simpson effect), which arises when a trend appears in different subsets of data but disappears or reverses when these subsets are combined.

Puzzling trends, such as the inversion of the radial abundance gradients with increasing distance from the disk mid-plane, the flatness of the AMR, and the positive MVR slope for stars on the high-[alpha/Fe] sequence, can be resolved, once age and/or birth radii are taken into account.