DISCRIMINANT ANALYSIS is used primarily to predict membership in two or more mutually exclusive groups. The procedure for predicting membership is initially to analyze pertinent variables where the group membership is already known. For instance, a top research university wishes to predict whether applicants will complete a Ph.D. program successfully. Such a university will have many years of records of entry characteristics of applicants and additional information about whether they completed the Ph.D. and how long it took them. They thus have sufficient information to use discriminant analysis. They can identify two discrete groups (those who completed the Ph.D. and those who did not) and make use of entry information such as GPAs, GRE scores, letters of recommendation, and additional biographical information. From these variables it is possible to create a formula that maximally differentiates between the two groups. This formula (if it discriminates successfully) could be used to analyze the likelihood of success for future applicants. There are many circumstances where it is desirable to be able to predict with some degree of certainty outcomes based on measurable criteria: Is an applicant for a particular job likely to be successful or not? Can we identify whether mentally ill patients are suffering from schizophrenia, bipolar mood disorder, or psychosis? If a prisoner is paroled, is he or she likely to return to crime or become a productive citizen? What factors might influence whether a person is at risk to suffer a heart attack or not? The elements common to all five of these examples are that (1) group membership is known for many individuals and (2) large volumes of information are available to create formulas that might predict future outcomes better than current instruments.