At its simplest level, discriminant analysis is a method to identify a group of data into predefined classes. Discriminant analysis is used to understand the different classes of data based on a set of predictors or variables. More simply, it is used to find the "dependent" and "independent" variable of an experiment. Without this knowledge, it is hard to make sense of the results of an experiment.
Discriminant function analysis takes the assigned variables from discriminant analysis and applies them to an equation. With the equation, researchers, scientists and statisticians can build and test a hypothesis. The following is an example of how a discriminant function would appear:
L = b1x1 + b2x2 + bNxN + c
In the equation, b is the dependent variable, x is the input variable and c is a constant.
The key differences of these two ideas is that discriminant analysis helps researchers identify variables, while discriminant function analysis helps to actually perform the operation and test results. Discriminant analysis finds the underlying tools and inputs necessary for the further procedures.
Discriminant analysis is used to identify the variables necessary to build a function. That function is then used to test different hypotheses with discriminant function analysis. For example, if a computer scientist was trying to determine if two or more sets of data (such as computer processing speeds) are substantially different based on a singular variable using a confidence interval, he must use discriminant function analysis for this purpose.