Generalized Rank Transformation

Abstract

Rank transformation is often used in the analysis of multidimensional experimental data (Baxter1995) where it is not possible to apply the ordinary Box-Cox methods for transforming data. This procedure is suggested in some circumstance by Wright (1989), and with reference to the principal component analysis by Lebart and Warwick (1984) and by Jambu (1991). In the field of descriptive and predictive discriminant analysis, rank transformation is suggested when the population distribution is non-normal (Huberty1994). In both we observe that this transformation is highly influent on the covariance structure of the dataset. Some authors suggest that rank transformation has a normalizing effect on the data. This could be a problem when we do not want to lose information about the original distribution of the data.