Modified Discriminant Analysis as a Multivariate Post-Comparison Extension of MANOVA for Interpretation of Simultaneous Multimodality Measures

Abstract

Multiple ANOVAs applied to simultaneous multimodality measures often result in: (1) excessive alpha error, (2) loss of experimental power, and (3) loss of information regarding interdependence of the dependent variables. The appropriate solution, MANOVA, is not designed to extract maximum information from data. Two multivariate post-comparison techniques are presented to respond to this void: (1) Univariate F Tests which evaluate the impact of significant independent variables on each dependent measure and (2) Modified Discriminant Analysis which isolates the impact of each level of the significant independent variable on the aggregate dependent measures, while transformation of normalized weights of the characteristic vector into standardized weights determines the relative sensitivity of the dependent variables to main effects. Recommended post-comparison techniques are described and applied to representative research. An efficient computer package is proposed to facilitate computation of MANOVA, univariate F tests, characteristic roots, corresponding linear discriminant functions, and standardized discriminant weights.