"The ability to smell is associated with the first cranial nerve and is often one of the first things to be affected in cognitive decline," reads this release from the University of Florida, researchers from which conducted the experiment. But with Alzheimer's patients, the sense of smell is affected in a very particular way: The left nostril is significantly more impaired than the right. Weird! But true.
The experiment involved capping one nostril and measuring the distance at which the patient could detect about a tablespoon of peanut butter. In Alzheimer's patients, the left nostril was impaired so thoroughly that, on average, it had 10 centimeters less range than the right, in terms of odor detection. That's specific to Alzheimer's patients; neither control patients (those not suffering from cognitive decline) nor those with other types of cognitive impairment (like dementia) demonstrated that nostril difference.