Application of statistical methods for the comparison of data distributions

Data analysis is an essential section of all physics experiments; in spite of this only a few analysis standard toolkits are available. Concerning the comparison between distributions, almost all these toolkits are limited to the Chi-squared test. Statistics provides a whole chapter of Goodness-of-Fit tests, from the Chi-squared to tests based on maximum distance (Kolmogorov-Smirnov, Kuiper, Goodman), to tests based on quadratic distance (Fisz-Cramer-von Mises, Anderson-Darling, Tiku). All of these Goodness-of-Fit tests have been collected in a new open-source Statistical Toolkit. This Toolkit matches a sophisticated statistical data treatment with the most advanced computing techniques, such as object-oriented technology with the use of design patterns and generic programming. None of the Goodness-of-Fit tests included in the system is optimum for every case. Unfortunately, statistics does not provide a universal recipe for specific distributions and furthermore the only rare available guidelines refer to the comparison between smooth theoretical distributions. With the aim of helping the user in the algorithm choice, we present the results of an intrinsic statistical comparison among many of the Goodness-of-Fit tests contained in the Statistical Toolkit in terms of relative efficiency.

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