discriminanttianalyyseja

Discriminanttianalyysi, known in English as Discriminant Analysis, is a statistical method used to identify and understand the variables that differentiate between two or more groups of cases. It is primarily employed in classification and prediction. The core objective of discriminant analysis is to find a linear combination of predictor variables that maximizes the separation between the group means while minimizing the variance within each group.

The method seeks to create one or more discriminant functions, which are linear equations of the predictor variables. These functions are constructed such that the ratio of the variance between groups to the variance within groups is maximized. The number of discriminant functions that can be derived is limited by the number of groups minus one, or the number of predictor variables, whichever is smaller.

Once discriminant functions are developed, they can be used to classify new, unclassified cases into one of the predefined groups based on their scores on the predictor variables. This classification is based on the probability of a case belonging to each group. Discriminant analysis also helps in understanding which predictor variables are most important in distinguishing between the groups. By examining the coefficients of the discriminant functions, researchers can infer the relative contribution of each predictor to the group separation.

Common applications of discriminant analysis include fields like psychology, marketing, and medicine. For instance, it can be used to differentiate between successful and unsuccessful loan applicants, or to predict patient outcomes based on clinical measurements. It is important to note that discriminant analysis assumes multivariate normality of the predictor variables and homogeneity of variance-covariance matrices across groups. Violations of these assumptions can affect the reliability of the results.