Discriminant function analysis is used to determine which variables discriminate between two or more naturally occurring groups. For example, an educational researcher may want to investigate which variables discriminate between high school graduates who decide - to go to college, to attend a trade or professional school or to seek no further training or education For that purpose the researcher could collect data on numerous variables prior to students' graduation. After graduation, most students will naturally fall into one of the three categories. Discriminant Analysis could then be used to determine which variable(s) are the best predictors of students' subsequent educational choice. Suppose we have two groups of high school graduates: Those who choose to attend college after graduation and those who do not. We could have measured students' stated intention to continue on to college one year prior to graduation. If the means for the two groups (those who actually went to college and those who did not) are different, then we can say that intention to attend college as stated one year prior to graduation allows us to discriminate between those who are and are not college bound (and this information may be used by career counselors to provide the appropriate guidance to the respective students). Therefore, the basic idea underlying discriminant function analysis is to determine whether groups differ with regard to the mean of a variable, and then to use that variable to predict group membership
Such an analysis could also be used in the field of Supply Chain management. Supposing a company wants to determine the real impact of implementing Radio Frequency Indentification (RFID) in its business, it would have to investigate the various determinants on the adoption of such a technology. For example, the determinants can be taken as technological, organizational, environmental factors and product factors. The methodology adopted for a discriminant function would be to investigate the influential factors (independent variables) that may contribute to the RFID adoption (dependent variable). Discriminant analysis would be to determine whether statistically significant differences exist between the average score profile on a set of variables for prior defined groups and thereby enable those variables to be classified. It would also help to determine which of the independent variables account the most for the differences in the average score profiles of the two groups .
If we code the two groups in the analysis as 1 and 2, and use that variable as the dependent variable in a multiple regression analysis, then we would get results that are analogous to those we would obtain via Discriminant Analysis. In general, in the two-group case we fit a linear equation of the type:
Y = a + b1*x1 + b2*x2 + ... + bm*xm
where a is a constant and b1 through bm are regression coefficients. The interpretation of the results of a two-group problem is straightforward and closely follows the logic of multiple regression: Those variables with the largest (standardized) regression coefficients are the ones that contribute most to the prediction of group membership.