# Yule-Simpson's paradox in Galactic Archaeology

## TL;DR

This paper explores how Simpson's paradox affects interpretations of chemo-kinematical relations in Galactic Archaeology, revealing that neglecting stellar age and birth radius can lead to conflicting conclusions about the Milky Way's formation history.

## Contribution

It demonstrates the impact of Simpson's paradox on key Galactic relations and emphasizes the need for precise stellar ages to accurately interpret Galactic evolution.

## Key findings

- The MVR in RAVE giants is consistently negative when considering narrow [Mg/Fe] bins.
- Radial metallicity gradients cause negative age-group trends, influencing MVR interpretations.
- Lithium abundance trends vary with age and birth radius, constraining chemical evolution models.

## Abstract

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.