  The H$\alpha$ equivalent width (EW) is an observational proxy for specific
star formation rate (sSFR) and a tracer of episodic star-formation activity.
Previous assessments show that EW strongly anti-correlates with stellar mass as
$M^{-0.25}$ similar to the sSFR -- stellar mass relation. However, such a
correlation may be driven/formed by selection effects. In this study, we
investigate how H$\alpha$ EWs correlate with galaxy properties and how
selection biases could alter such correlations using a $z = 0.47$
narrowband-selected sample of 1572 H$\alpha$ emitters from the Ly$\alpha$
Galaxies in the Epoch of Reionization (LAGER) survey. The sample covers 3
deg$^2$ of COSMOS and $1.1\times10^5$ cMpc$^3$. We assume an intrinsic EW
distribution to form mock samples of H$\alpha$ emitters (HAEs) and propagate
the selection criteria to match observations, giving us control on how
selection biases can affect the underlying results. We find EW intrinsically
correlates with stellar mass as $W_0 \propto M^{-0.16\pm0.03}$ and decreases by
a factor of $\sim 3$ from $10^{7}$ to $10^{10}$ M$_\odot$. We find low-mass
HAEs to be $\sim 320$ times more likely to have rest-frame EW$ > 200$\AA
compared to high-mass HAEs. Combining the intrinsic EW -- stellar mass
correlation with an observed SMF correctly reproduces the observed H$\alpha$
LF, while not correcting for selection effects underestimates the number of
bright HAEs. This suggests that the intrinsic EW -- stellar mass correlation is
physically significant and reproduces three statistical distributions of galaxy
populations (LF, SMF, EW distribution). At lower masses, we find there are more
high-EW outliers compared to high masses, even after taking into account
selection effects. Our results suggest that high sSFR outliers indicative of
bursty SF activity are intrinsically more prevalent in low-mass HAEs and not a
byproduct of selection effects.
