Discriminant analysis is the statistical method used to classify observations into two or more known groups. In Six Sigma Analyze Phase applications, this technique is useful when the groups already exist and the objective is to determine how observations can be assigned to the correct category based on measured variables. It also helps identify which variables best separate the groups. Factor analysis and principal component analysis are both data-reduction methods; they uncover latent structure or reduce dimensionality, but they are not classification tools for known groups. Multiple analysis of variance compares means across groups but does not classify individual observations into categories. Discriminant analysis is therefore the best fit because it directly addresses separation and assignment among predefined groups. For Black Belts, this kind of method can be valuable in pattern recognition, segmentation, diagnostic classification, and prediction where group membership matters. Therefore, the correct answer is A, Discriminant analysis, because it is specifically designed for classification into multiple known groups.

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