A pilot study involving 94 older adults, of whom 18 had Alzheimer’s, 24 had MCI, 26 other dementias, and 26 were healthy controls, has found those with Alzheimer’s were significantly less able to detect the smell of peanut butter. Peanut butter was chosen because of its purity and accessibility (not because there's something special about its smell!).
The test was undertaken by the patient closing eyes and mouth and blocking one nostril, while the clinician held a ruler next to the open nostril and moved 14g of peanut butter in an open jar up the ruler one centimeter at a time, as the patient breathed out. Those in the early stages of Alzheimer’s disease showed a dramatic difference in detecting odor between the left and right nostril. The average distance at which the peanut butter was detected was 5.1 cm for the left nostril, compared to 17.4 cm for the right. The difference between these (12.4 cm) compares to an average 4.8 cm for other dementias, 1.9 for MCI, and 0 for healthy controls.
Of the 24 patients with MCI, only 10 patients showed a left nostril impairment, suggesting that this may be an indication of who will go on to develop Alzheimer’s.
 . A brief olfactory test for Alzheimer's disease. Journal of the Neurological Sciences [Internet]. 2013 ;333(1):19 - 24. Available from: http://www.jns-journal.com/article/S0022-510X(13)00311-0/abstract