Discriminant analysis works by creating one or more linear combinations of predictors, creating a new [[latent variable]] for each function. These functions are called discriminant functions. The number of functions possible is either ''N<sub>g</sub>Ng''-1 where ''N<sub>g</sub>Ng'' = number of groups, or ''p'' (the number of predictors), whichever is smaller. The first function created maximizes the differences between groups on that function. The second function maximizes differences on that function, but also must not be correlated with the previous function. This continues with subsequent functions with the requirement that the new function not be correlated with any of the previous functions.<ref name="green"/>
Given group <math>j</math>, with <math> \mathbb{R}_j</math> sets of sample space, there is a discriminant rule such that if <math>x</math><big>∈</big><math>x∈\mathbb{R}_j</math>, then <math>x</math><big>∈</big>x∈ <math>j</math>. Discriminant analysis then, finds “good” regions of <math> \mathbb{R}_j</math> to minimize classification error, therefore leading to a high percent correct classified in the classification table.<ref name="har">Hardle, W., Simar, L. (2007). ''Applied Multivariate Statistical Analysis''. Springer Berlin Heidelberg. pp. 289-303.</ref>
Each function is given a discriminant score to determine how well it predicts group placement.
*Structure Correlation Coefficients: The correlation between each predictor and the discriminant score of each function. This is a whole{{clarify|date=April 2012}} correlation.<ref name="buy"/><ref name="garson">Garson, G. D. (2008). Discriminant function analysis. http://www2.chass.ncsu.edu/garson/pa765/discrim.htm .</ref>
*Standardized Coefficients: Each predictor’s unique contribution to each function, therefore this is a [[partial correlation]]. Indicates the relative importance of each predictor in predicting group assignment from each function.<ref name="buy"/><ref name="garson"/>
*Functions at Group Centroids: Mean discriminant scores for each grouping variable are given for each function. The farther apart the means are, the less error there will be in classification.<ref name="buy"/><ref name="garson"/>
