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12 | @article{Garcia:2009fk, | ||

13 | Author = {Salvador Garc{\'\i}a and Daniel Molina and Manuel Lozano and Francisco Herrera}, | ||

14 | Date-Added = {2010-06-17 11:49:54 +0300}, | ||

15 | Date-Modified = {2010-06-17 11:49:54 +0300}, | ||

16 | Doi = {10.1007/s10732-008-9080-4}, | ||

17 | Journal = {Journal of Heuristics}, | ||

18 | Month = {December}, | ||

19 | Number = {6}, | ||

20 | Pages = {617-644}, | ||

21 | Title = {A study on the use of non-parametric tests for analyzing the evolutionary algorithms' behaviour: a case study on the CEC'2005 Special Session on Real Parameter Optimization}, | ||

22 | Volume = {15}, | ||

23 | Year = {2009}, | ||

24 | Bdsk-Url-1 = {http://www.springerlink.com/content/h53270p4kr6891h3/fulltext.pdf}, | ||

25 | Bdsk-Url-2 = {http://dx.doi.org/10.1007/s10732-008-9080-4}} | ||

11 | 26 | ||

12 | 27 | @article{fan2003trigonometric, | |

13 | 28 | Author = {Fan, H.Y. and Lampinen, J.}, |

histograms.tex

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146 | 146 | for comparing dense sets of numbers. This visualization technique fits | |

147 | 147 | very well to task of comparing optimization algorithms, as it allows | |

148 | 148 | to present all the results of repeated experiments at the same time. This | |

149 | technique has been used in, for example, \cite{fan2003trigonometric}. | ||

149 | technique has been used in, for example, articles \cite{Garcia:2009fk,fan2003trigonometric}. | ||

150 | 150 | The use of histograms conveys more data than a single statistical number, is | |

151 | 151 | easily readable, and easily satisfies the constraints 1 and 3 presented in the | |

152 | 152 | introduction. | |

… | … | ||

362 | 362 | are normally distributed, one can apply Student's t-test to determine, with a | |

363 | 363 | given threshold probability, if the results of $A$ and $B$ are significantly | |

364 | 364 | different. This is however usually not the case, as explained in | |

365 | Section~\ref{s:shortcomings}. Even non-parametric test such as the | ||

365 | Section~\ref{s:shortcomings} as well as in a thorough study in~\cite{Garcia:2009fk}. | ||

366 | Even non-parametric test such as the | ||

366 | 367 | \emph{Mann-Whitney U test} (also known as the \emph{Wilcoxon rank-sum test}) | |

367 | 368 | \cite{mann1947test} cannot be applied to the two samples since, although this | |

368 | 369 | test does not assume that the two samples are drawn from any particular |