This would explain the different recovery rates. Because patients at small hospitals are more likely to get personal dietary attention, they are more likely to recover.

This would explain the different recovery rates. Because patients at large hospitals are subject to stress from the impersonal atmosphere, they are less likely to recover.

This rules out an explanation for the opposite discrepancy, but does not explain the discrepancy at hand. It implies that doctors at both types of hospitals are equally likely to help their patients recover, leaving the difference in recovery rates unexplained.

This would explain the different recovery rates. Because patients at large hospitals tend to be observed for less time, they are less likely to recover.

This would explain the different recovery rates. Because patients and staff at large hospitals are more likely to misunderstand how to administer medication, they are less likely to benefit from that medication and thus the patients are less likely to recover.