Pitfalls when observationally characterizing the relative formation
  rates of stars and stellar clusters in galaxies
  Stars generally form in aggregates, some of which are bound ('clusters')
while others are unbound and disperse on short ($\sim10$ Myr) timescales
('associations'). The fraction of stars forming in bound clusters ($\Gamma$) is
a fundamental outcome of the star formation process. Recent observational and
theoretical work has suggested that $\Gamma$ increases with the gas surface
density ($\Sigma$) or star formation rate (SFR) surface density ($\Sigma_{\rm
SFR}$), both within galaxies and between different ones. However, a recent
paper by Chandar et al. has challenged these results, showing that the $total$
number of stellar aggregates per unit SFR does not vary systematically with the
host galaxy's absolute SFR. In this Letter, we show that no variations are
expected when no distinction is made between bound and unbound aggregates,
because the sum of these two fractions should be close to unity. We also
demonstrate that any scaling of $\Gamma$ with the absolute SFR is much weaker
than with $\Sigma_{\rm SFR}$, due to the mass-radius-SFR relation of
star-forming 'main sequence' galaxies. The environmental variation of $\Gamma$
should therefore be probed as a function of area-normalised quantities, such as
$\Sigma$ or $\Sigma_{\rm SFR}$. We present a set of guidelines for meaningful
observational tests of cluster formation theories and show that these resolve
the reported discrepancy.
