The statistical process of making classes out of a sample or set of observations is defined as Discriminant Analysis. This is not just a simple procedure. It is rather a set of actions that lead you to arrive at a suitable hypothesis in the event you are observing. Discriminant analysis may seem daunting or intimidating. On the contrary, it is actually very practical for use especially if you want to make sound predictions based on a given number of options.
- Statistical Background. Some basic statistical knowledge, particularly Analysis of Variance (ANOVA) or other regression methods in analyzing a sample of data can be very beneficial for fully understanding how discriminant analysis works. A good course on statistics or at least brushing up on your knowledge of Statistics through websites such as StatSoft may fully arm you with the background knowledge that you need.
- Training Set. Your training set can be anything. It can be a bunch of students trying to figure out what to do after high school. On a more significant level, it may involve predicting how hostage takers will react on a hostile situation. Anything that involves a lot of people making many choices can be used as suitable training set.
- Discriminant Analysis Methods. On a mathematical level, there are various computations that can be done to implement discriminant analysis. Multiple Discriminant Analysis involves matrices of data (simultaneously observed training sets), Linear Discriminant Analysis (for studying strictly two groups of data only) and K-NNs Discriminant Analysis (you can use this mode when you do not want to distribute variables equally and want a less structured approach).
- Existing Variables. Existing variables, simply put, involve the available options for your selected training set. For the high school graduates it may involve getting work, going to college or getting married. For the hostage taker it may mean getting more hostages, releasing hostages, getting additional demands or attempting to escape. These variables are what you will study, based on the data that you can collect from your training set.
- Discriminant Functions. Discriminant functions are the mathematical representations of the existing variables that you have chosen. From here, you will be able to get the probabilities and analysis necessary for the final and most important step of the whole procedure of discriminant analysis.
- Class Prediction for New Cases. The most important output of discriminant analysis is the ability to make sound predictions for the future. How will a future high school graduate react given his or her circumstances? How will a hostage taker react given some similar situations observed from your training set? These will be answered by the class prediction of new cases.
In the end, analysis is not the be-all and end-all of making sound judgments on situations involving your training set. Accuracy still needs to be tested. It is still a set of statistics that has to be confirmed by reality. A good dialogue with a statistician may also help you to dig deeper on the concept of discriminant analysis.