Star formation is known to occur more readily where more raw materials are available. This is often expressed by a Kennicutt-Schmidt relation where the surface density of Young Stellar Objects (YSOs) is proportional to column density to some power, $mu$. The aim of this work was to determine if column density alone is sufficient to explain the locations of Class 0/I YSOs within Serpens South, Serpens Core, Ophiuchus, NGC1333 and IC348, or if there is clumping or avoidance that would point to additional influences on the star formation. Using the O-ring test as a summary statistic, 95 per cent confidence envelopes were produced for different values of $mu$ from probability models made using the Herschel column density maps. The YSOs were tested against four distribution models: the best-estimate of $mu$ for the region, $mu=0$ above a minimum column density threshold and zero probability elsewhere, $mu=1$, and the power-law that best represents the five regions as a collective, $mu=2.05 pm 0.20$. Results showed that $mu=2.05$ model was consistent with the majority of regions and, for those regions, the spatial distribution of YSOs at a given column density is consistent with being random. Serpens South and NGC1333 rejected the $mu = 2.05$ model on small scales of $sim 0.15 mathrm{pc}$ which implies that small-scale interactions may be necessary to improve the model. On scales above 0.15 pc, the positions of YSOs in all five regions can be well described using column density alone.
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