Interpretation of transformed axes in multivariate analysis

Several multivariate statistical techniques involve an orthogonal transformation to new axes. These lead to new co-ordinates of a configuration usually in a lower dimensional space. Often it is desirable to interpret this new co-ordination in terms of the original variables. In surveying some of the principles involved in achieving this aim, the use of projections is contrasted with the use of correlations. Cumulative sum diagrams are introduced as informative in the interpretation. The methods are illustrated for principal components analysis, factor analysis and generalized Procrustes analysis by using examples from sensory profiling and the development of psychological scales.