title: Discriminant analysis.
abstract: OBJECTIVE
  To present a fully worked numerical example for the derivation of a discriminant function in order to provide insight into the processing steps and origin of the function coefficients.
  
  
  METHODS
  The example begins with the reduction of a set of raw data to the values needed to calculate the variance/covariance matrix. Next the inversion of the covariance matrix by pivotal condensation is carried through. This is followed by the calculation of the coefficients. All calculations are carried out on a simple hand calculator.
  
  
  RESULTS
  While discriminant analysis is routinely and widely used in the analysis of karyometric data, the process of deriving the discriminant function and its coefficients has not been demonstrated in detail, by a numerical example, in over 50 years.
  
  
  CONCLUSIONS
  It is clearly not practical to conduct, by hand, a discriminant analysis on data sets as commonly encountered in karyometry. However, the use of a computer algorithm without a full understanding of the processing steps has always been deeply unsatisfactory. This tutorial article should remedy that situation.
authors.affiliation: College of Optical Sciences and Arizona Cancer Center, University of Arizona, Tucson, Arizona 85724, USA. hubertbartels@msn.com
authors.forename: Peter H
authors.initials: PH
authors.lastname: Bartels
authors.forename: Hubert G
authors.initials: HG
authors.lastname: Bartels
mesh_terms: D000465:Algorithms; D002467:Cell Nucleus / Q000473:pathology; D003627:Data Interpretation, Statistical; D016002:Discriminant Analysis; D006801:Humans; D007620:Karyometry / Q000706:statistics & numerical data; D010340:Pathology, Surgical / Q000193:education*