Neurophysiological experiments support the hypothesis of the presence of critical dynamics of brain activity. This is also manifested by power law of electroencephalography (EEG) power spectra, which can be described by the relation 1/f(alpha). This dependence is a result of internal interactions between parts of the brain and is probably required for optimal processing of information. In Alzheimer's disease, changes in the functional organization of the brain occur, which may be manifested by changes in the alpha coefficient. We compared the average values of alpha for 19 electrodes in the resting EEG record in 110 patients with moderate to severe Alzheimer's disease (Mini-Mental State Examination [MMSE] score = 10-19) with 110 healthy controls. Statistically, the most significant differences are present in the prefrontal areas. In addition to the prefrontal and frontal areas, the largest separation value in the evaluation of receiver operating characteristic (ROC) curves was recorded in the temporal area. The coefficient alpha has few false-positive results in the optimal operating point of the ROC curve, and is thereby highly specific for Alzheimer's disease.