The false statement about sleep deprivation commonly identified is that it is associated with obesity. Contrary to this, sleep deprivation is indeed linked to increased risk of obesity along with other health issues. Therefore, if a choice claims sleep deprivation is not associated with obesity, that would be false. Sleep deprivation is generally known to cause or be linked with various negative effects including weight gain (obesity), high blood pressure, diabetes, poor cognitive functioning, irritability, increased risk of heart disease and stroke, lowered immunity, mood disorders, and impaired attention and memory.

Hence, the false statement is one that claims no association of sleep deprivation with obesity, as evidence consistently supports that sleep deprivation is associated with obesity and multiple other health risks.