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Graphical Goodness-of-Fit Tests |
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1. One-sample T3 plot: Graphical test of univariate normality With this method one can test the null hypothesis that a set of univariate independent and identically distributed observations are normally distributed with an unknown mean and an unknown variance. The method incorporates finite sample corrections and it is location and scale invariant. Missing values are allowed. Reference: Ghosh, S. (1996) Journal of the Royal Statistical Society, Series B. Ghosh, S. (1999) Encyclopedia for Statistical Sciences, John Wiley. 2. Two-sample T3 plot: Graphical comparison of two distributions Based on two independent random samples, this method tests the null hypothesis that the shapes of the two underlying distributions with unknown means and variances are the same. Missing values are allowed. The method is location and scale invariant. Small sample corrections are incorporated. Reference: Ghosh, S. & Beran, J. (2000) Journal of Computational and Graphical Statistics. T3plots are powerful statistical methods for performing certain goodness-of-fit tests graphically as well as formally (i.e. given a level of significance). The procedures utilize characterizing properties of the (empirical) moment generating functions and their third derivatives. To fully understand the theoretical properties of these procedures, background in asymptotic theory of Mathematical Statistics is required. However, implementation of these methods is not difficult and can easily be performed by practitioners even without prior experience in interpreting probability plots. How to use these plots in S-Plus S-Plus functions for one and two-sample T3plots are available on request from the authors. To obtain the codes and a description of these procedures, send an email to rita.ghosh@wsl.ch. The codes are to be used for noncommercial purposes only. Landscape Department, |