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.In that case, we have a matrix of total variances and covariances; likewise, we have a matrix of pooled within-group variances and covariances.

For example, an educational researcher interested in predicting high school graduates' choices for further education would probably include as many measures of personality, achievement motivation, academic performance, etc.

as possible in order to learn which one(s) offer the best prediction. Put another way, we want to build a "model" of how we can best predict to which group a case belongs.

Females are, on the average, not as tall as males, and this difference will be reflected in the difference in means (for the variable Height).

Therefore, variable height allows us to discriminate between males and females with a better than chance probability: if a person is tall, then he is likely to be a male, if a person is short, then she is likely to be a female.

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 (1) to go to college, (2) to attend a trade or professional school, or (3) to seek no further training or education.The F value for a variable indicates its statistical significance in the discrimination between groups, that is, it is a measure of the extent to which a variable makes a unique contribution to the prediction of group membership.If you are familiar with stepwise multiple regression procedures, then you may interpret the F to enter/remove values in the same way as in stepwise regression. A common misinterpretation of the results of stepwise discriminant analysis is to take statistical significance levels at face value.We can generalize this reasoning to groups and variables that are less "trivial." For example, 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.In general, in the two-group case we fit a linear equation of the type: are regression coefficients.