The table below provides a comparative overview of the Goodness of Fit (GoF) tests available in the Statistical Toolkit, as a guidance to the practical usage of the Statistical Toolkit.
GoF test | Type of distribution | Class | Power | Notes on applicability |
Anderson-Darling | Binned Unbinned |
AndersonDarlingBinnedComparisonAlgorithm AndersonDarlingUnbinnedComparisonAlgorithm |
High | The mathematical formulation of the test statistics makes it is sensitive to the tails of the distributions. It can be applied also in case of fat tails. |
Chi-squared | Binned | Chi2ComparisonAlgorithm | Low | It has a very general applicability; on the other hand, its
generality gives it little power. It cannot applied if the countings per bin are lower than 5. |
Fisz-Cramer-von Mises | Binned Unbinned |
CramerVonMisesBinnedComparisonAlgorithm CramerVonMisesUnbinnedComparisonAlgorithm |
High | This test is satisfactory in case of symmetric or right-skewed
distributions. Note: the current release implements tables for the evaluation of p-value; the algorithm for the exact p-value computation of the test statistics will be implemented in future release. The exact p-value can be computed in the Tiku approximation. |
Goodman | Unbinned | KolmogorovSmirnovApproxComparisonAlgorithm | Medium | It is the approximation of Kolmogorov-Smirnov test to a chi-squared statistics. Since it is based on the assumptions of Kolmogorov theorem, it may be applied to unbinned data. |
Kolmogorov-Smirnov | Unbinned | KolmogorovSmirnovComparisonAlgorithm | Medium | It derives from Kolmogorov statistics; since it is based on the Kolmogorov theorem, it may be applied to unbinned data. |
Kuiper | Unbinned | KuiperComparisonAlgorithm | Medium | It can
be applied on cyclic observations, because the test statistics is invariant with
respect to the choice of the origin. It is sensitive both to the tails and to the median of the distributions. |
Tiku | Binned Unbinned |
TikuBinnedComparisonAlgorithm TikuUnbinnedComparisonAlgorithm |
High | This
algorithm converts Cramer-von Mises test statistics into a chi-squared. Note: while the current Statistical Toolkit release does not contain the algorithm for the exact p-value computation for Fisz-Cramer-von Mises test statistics yet, it is possible to compute the exact p-value in the Tiku approximation. |
More detailed statistical documentation can be retrieved in:
Introduction to
Goodness of Fit tests
GoF
algorithms
Applicability
of GoF tests
Power
of GoF Tests
Last modified 26 March 2004 - Maria Grazia Pia