Application of Lachenbruch Procedure in Quadratic Case of Discriminant Analysis (by Dewi Rachmatin and Kania Sawitri)

Presented at the National Seminar on Mathematics and Mathematics Education Department of Mathematics Education FPMIPA UPI Year 2009


The results of research on Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) mostly use the Apparent Error Rate (APER) method in evaluating grouping rules in Discriminant Analysis. This APER method has the advantage of being easy to calculate, but unfortunately tends to estimate too low the Actual Error Rate (AER), unless the sample size of the populations to be grouped is very large. Therefore in this study applied a method called The Lachenbruch Procedure, to overcome this. In this procedure the sample is divided into two parts, namely the sample used to form the training sample rules and the sample used to evaluate the results of the validating sample. The Lachenbruch procedure is applied to the data of two species of biting fly with the genus Leptoconos, which is the same morpologically and for several years both species are considered the same. The results of the QDA analysis of this data show that the two species turned out to be different.

Keywords : Quadratic Discriminant Analysis (QDA),Lachenbruch Procedure, Apparent Error Rate (APER)and Actual Error Rate (AER).