Graphical criterion for the detection of outliers in linear regression taking into account errors in both taxes

Over the past few years linear regression taking into account the errors in both axes has become increasingly important in chemical analysis. It can b e applied for instance in method comparison studies at several levels of co ncentration (where each of the two methods normally present errors of the s ame order of magnitude) or at calibration straight lines using reference ma terials as calibration standards, such as in X-ray, fluorescence for analys ing geological samples. However, the results obtained by using a regression line may be biased due to one or more outlying points in the experimental data set. These situations can be overcome by robust regression methods or techniques for detecting outliers. This paper presents a graphical criterion for detecting outliers using the bivariate least squares (BLS) regression method, which takes into account t he heteroscedastic individual errors in both axes. This graphical criterion is based on a modification of Cook's well-known test for detecting outlier s. This new technique has been checked using two simulated data sets where an outlier is added, and one real data set corresponding to a method compar ison analysis. (C) 2001 Elsevier Science B.V. All rights reserved.