1. An electroencephalograph (EEG) method for monitoring the plane of anesthesia of a patient undergoing a medical procedure, comprising: (a) removably connecting a set of EEG electrodes to the scalp of the patient and administering sufficient anesthesia to the patient for the patient to attain the plane of anesthesia selected by the anesthesiologist; (b) presenting a set of stimuli to the patient and amplifying and digitizing the brain wave evoked responses to the stimuli and the patient's ongoing brain wave activity collected from the EEG electrodes to provide a first set of digital data representing a set of features of the patient's brain waves in the patient's pre-operative anesthetized state and recording the first set of digital data in computer system memory; (c) during the operation, presenting the same set of stimuli to the patient and amplifying and digitizing the brain wave responses to the stimuli and the patient's on-going brain wave activity to provide a second set of digital data regarding the same set of features as the first set; (d) using the computer system to statistically compare the first and second sets of digital data on a feature-by-feature basis; (e) deriving a discriminant score based on the comparisons of (d) by selectively weighting, selecting and combining a number of said feature-by-feature comparisons; (f) combining the discriminant scores to derive probabilities that the patient is in a specific anesthetized state; (g) applying selected guardbands (rule-out levels) to the probabilities to classify the anesthetized state of the patient on the basis of the probabilities; and (h) providing a warning if the patient is not in a fully anesthetized state during the operation based on the classification of (g); and (i) adjusting the anesthesia administered to the patient during the operation in response to the warning to restore the patient to the selected plane of anesthesia.