The Rank Transformation as a Method of Discrimination with Some Examples

W. J. Conover, Ronald L. Iman

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


The procedure of statistical discrimination is simple ivtiun theory but not so simple in practice. An observation x0 possibly multivariate, is to be classified into one of several populations T1., TK which have respectively, the density functions f1(x),.,.,., fK(x). The decision procedure is to evaluate each density function at x0 to see which function gives the largest value fi(x0) and then to declare that xq belongs to the population corresponding to the largest value. If these densities can be assumed to be normal with equal covariance matrices then the decision procedure is known as Fisher's linear discriminant function (LDF) method. In the case of unequal covariance matrices the procedure is called the quadratic discriminant function (QDF) method. If the densities cannot be assumed to be normal then the LDF and QDF might not perform well. Several different procedures have appeared in the literature which offer discriminant procedures for nonnormal data. However, these procedures are generally difficult to use and are not readily available as canned statistical programs.Another approach to discriminant analysis is to use some sort of mathematical transformation on the samples so that their distribution function is approximately norma 1, and then use the convenient LDF and QDF methods. One transformation that applies to all distributions equally well is the rank transformation. The result of this transformation is that a very simple and easy to use procedure is made available.This procedure is quite robust as is evidenced by comparisons of the rank transform results with several published simulation studies.

Original languageEnglish
Pages (from-to)465-487
Number of pages23
JournalCommunications in Statistics - Theory and Methods
Issue number5
StatePublished - Jan 1 1980


  • discriminant analysis
  • nonparametric
  • ranks density estimation


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