Yule-Simpson's paradox in Galactic Archaeology
  Simpson's paradox, or Yule-Simpson effect, arises when a trend appears in
different subsets of data but disappears or reverses when these subsets are
combined. We describe here seven cases of this phenomenon for chemo-kinematical
relations believed to constrain the Milky Way disk formation and evolution. We
show that interpreting trends in relations, such as the radial and vertical
chemical abundance gradients, the age-metallicity relation, and the
metallicity-rotational velocity relation (MVR), can lead to conflicting
conclusions about the Galaxy past if analyses marginalize over stellar age
and/or birth radius. It is demonstrated that the MVR in RAVE giants is
consistent with being always strongly negative, when narrow bins of [Mg/Fe] are
considered. This is directly related to the negative radial metallicity
gradients of stars grouped by common age (mono-age populations) due to the
inside out disk formation. The effect of the asymmetric drift can then give
rise to a positive MVR trend in high-[alpha/Fe] stars, with a slope dependent
on a given survey's selection function and observational uncertainties. We also
study the variation of lithium abundance, A(Li), with [Fe/H] of AMBRE:HARPS
dwarfs. A strong reversal in the positive A(Li)-[Fe/H] trend of the total
sample is found for mono-age populations, flattening for younger groups of
stars. Dissecting by birth radius shows strengthening in the positive
A(Li)-[Fe/H] trend, shifting to higher [Fe/H] with decreasing birth radius;
these observational results suggest new constraints on chemical evolution
models. This work highlights the necessity for precise age estimates for large
stellar samples covering wide spatial regions.
