Statistical Methodology 2 (2005) 82–94 www.elsevier.com/locate/stamet On the influence of misclassified data on results of goodness of fit testing David Magis ∗ Department of Mathematics, University of Liège, Grande Traverse 12, B-4000 Liège, Belgium Received 5 July 2004 Abstract In this paper we focus on the chi-square test of goodness of fit, which compares an observed discrete distribution to an expected known one. We show that the results of this test, using the common Pearson statistic, are very sensitive to misclassified observations between two or more categories. We also propose a general rule of thumb for analysing data set stability with respect to such classification errors. Practical analysis of a real example illustrates our purpose. © 2005 Published by Elsevier B.V. Keywords: Goodness of fit; Pearson statistic; Misclassification; Stability 1. Introduction The statistical test of goodness of fit is an important survey in applied statistics. Quite often, collected data from an experiment can be classified into several distinct categories. It is then useful for the researcher to discover whether this classification can be assumed to have arisen from a known discrete distribution. Pearson was a pioneer in this field of research; his famous test statistic X 2 , a weighted sum of squared differences between observed and expected counts, was characterised over a century ago. His paper of 1900 [5] is the basic foundation of many recent statistical developments, and is now widely used in practical data analysis. ∗ Tel.: +32 4 366 94 24. E-mail address: David.Magis@ulg.ac.be. 1572-3127/$ - see front matter © 2005 Published by Elsevier B.V. doi:10.1016/j.stamet.2005.02.002