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# What is Discriminant Analysis?

## History and Definition

Discriminant Analysis is a statistical tool with an objective to assess the adequacy of a classification, given the group memberships; or to assign objects to one group among a number of groups. For any kind of Discriminant Analysis, some group assignments should be known beforehand.

Discriminant Analysis is quite close to being a graphical version of MANOVA and often used to complement the findings of Cluster Analysis and Principal Components Analysis.

When Discriminant Analysis is used to separate two groups, it is called Discriminant Function Analysis (DFA); while when there are more than two groups – the Canonical Varieties Analysis (CVA) method is used.

In the 1930’s, 3 different people – R.A. Fisher in UK, Hoteling in US and Mahalanob is in India were trying to solve the same problem via three different approaches. Later their methods of Fisher linear discriminant function, Hoteling’s T2 test and Mahalanobis D2 distance were combined to devise what is today called Discriminant Analysis.

## Benefits and Practical Applications of Discriminant Analysis

Discriminant Analysis has various benefits as a statistical tool and is quite similar to regression analysis. It can be used to determine which predictor variables are related to the dependant variable and to predict the value of the dependant variable given certain values of the predictor variables. Discriminant Analysis is also widely used to create Perceptual Mapping by marketers and has some benefits over other methods that use perceived distances; like the option of using tests of significance to check for dissimilarities among products and that the distances between two products would not be impacted by other products included in the study.

Discriminant Analysis has various other practical applications and is often used in combination with cluster analysis. Say, the loans department of a bank wants to find out the creditworthiness of applicants before disbursing loans. It may use Discriminant Analysis to find out whether an applicant is a good credit risk or not. This would serve as method of screening applicants and preventing later bad debts. In another scenario, say a retail chain wants to conduct market segmentation. It might use a survey to get respondents to rate various desirable service attributes and then use a combination of cluster analysis and Discriminant Analysis to segment its market and assign customers to different segments. This will help the retailer get an idea of customer’s preferences in each segment and also target them better in their marketing campaigns.