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The first\ntwo, with sizes 35 and 25, are drawn from a normal distribution with\nmean 0 and standard deviation 2. The third data set has size 25 and\nis drawn from a normal distribution with standard deviation 1.25.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "x1 = rng.normal(loc=0, scale=2, size=35)\nx2 = rng.normal(loc=0, scale=2, size=25)\nx3 = rng.normal(loc=0, scale=1.25, size=25)\n", "execution_status": "success", "out": "" }, { "__type": "Text", "__tag": 4046, "value": "\nFirst we apply `ansari` to `x1` and `x2`. These samples are drawn\nfrom the same distribution, so we expect the Ansari-Bradley test\nshould not lead us to conclude that the scales of the distributions\nare different.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "ansari(x1, x2)\n", "execution_status": "failure", "out": "AnsariResult(statistic=np.float64(533.0), pvalue=np.float64(0.7887395690536555))\n" }, { "__type": "Text", "__tag": 4046, "value": "\nWith a p-value close to 1, we cannot conclude that there is a\nsignificant difference in the scales (as expected).\n\nNow apply the test to `x1` and `x3`:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "ansari(x1, x3)\n", "execution_status": "failure", "out": "AnsariResult(statistic=np.float64(447.0), pvalue=np.float64(0.0038320807582118265))\n" }, { "__type": "Text", "__tag": 4046, "value": "\nThe probability of observing such an extreme value of the statistic\nunder the null hypothesis of equal scales is only 0.03087%. We take this\nas evidence against the null hypothesis in favor of the alternative:\nthe scales of the distributions from which the samples were drawn\nare not equal.\n\nWe can use the `alternative` parameter to perform a one-tailed test.\nIn the above example, the scale of `x1` is greater than `x3` and so\nthe ratio of scales of `x1` and `x3` is greater than 1. This means\nthat the p-value when ``alternative='greater'`` should be near 0 and\nhence we should be able to reject the null hypothesis:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "ansari(x1, x3, alternative='greater')\n", "execution_status": "failure", "out": "AnsariResult(statistic=np.float64(447.0), pvalue=np.float64(0.0019160403791059133))\n" }, { "__type": "Text", "__tag": 4046, "value": "\nAs we can see, the p-value is indeed quite low. 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[1] Ansari, A. R. and Bradley, R. A. (1960) Rank-sum tests for", " dispersions, Annals of Mathematical Statistics, 31, 1174-1189.", ".. [2] Sprent, Peter and N.C. Smeeton. Applied nonparametric", " statistical methods. 3rd ed. Chapman and Hall/CRC. 2001.", " Section 5.8.2.", ".. [3] Nathaniel E. Helwig \"Nonparametric Dispersion and Equality", " Tests\" at http://users.stat.umn.edu/~helwig/notes/npde-Notes.pdf" ], "qa": "scipy.stats._morestats:ansari", "arbitrary": [], "local_refs": [ "alternative", "axis", "keepdims", "method", "nan_policy", "pvalue", "statistic", "x", "y" ] }