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The H$\alpha$ equivalent width (EW) is an observational proxy for specificstar 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 acorrelation may be driven/formed by selection effects. In this study, weinvestigate how H$\alpha$ EWs correlate with galaxy properties and howselection 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 3deg$^2$ of COSMOS and $1.1\times10^5$ cMpc$^3$. We assume an intrinsic EWdistribution to form mock samples of H$\alpha$ emitters (HAEs) and propagatethe selection criteria to match observations, giving us control on howselection biases can affect the underlying results. We find EW intrinsicallycorrelates with stellar mass as $W_0 \propto M^{-0.16\pm0.03}$ and decreases bya factor of $\sim 3$ from $10^{7}$ to $10^{10}$ M$_\odot$. We find low-massHAEs to be $\sim 320$ times more likely to have rest-frame EW$ > 200$\AAcompared to high-mass HAEs. Combining the intrinsic EW -- stellar masscorrelation with an observed SMF correctly reproduces the observed H$\alpha$LF, while not correcting for selection effects underestimates the number ofbright HAEs. This suggests that the intrinsic EW -- stellar mass correlation isphysically significant and reproduces three statistical distributions of galaxypopulations (LF, SMF, EW distribution). At lower masses, we find there are morehigh-EW outliers compared to high masses, even after taking into accountselection effects. Our results suggest that high sSFR outliers indicative ofbursty SF activity are intrinsically more prevalent in low-mass HAEs and not abyproduct of selection effects.

Correlations between H$\alpha$ Equivalent Width and Galaxy Properties at $z = 0.47$: Physical or Selection-driven?