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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" }, { "__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" }, { "__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" }, { "__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" }, { "__type": "Text", "__tag": 4046, "value": "\nAs we can see, the p-value is indeed quite low. Use of\n``alternative='less'`` should thus yield a large p-value:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "ansari(x1, x3, alternative='less')\n", "execution_status": "failure" } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "fligner", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._morestats:fligner" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A non-parametric test for the equality of k variances" } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "mood", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._morestats:mood" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A non-parametric test for the equality of two scale parameters" } ] } ], "type": "func" } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "x", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "y", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "alternative", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "two-sided" }, { "__type": "SigParam", "__tag": 4030, "name": "axis", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "0" }, { "__type": "SigParam", "__tag": 4030, "name": "nan_policy", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "propagate" }, { "__type": "SigParam", "__tag": 4030, "name": "keepdims", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "False" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "ansari" }, "references": [ ".. [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", "nan_policy", "pvalue", "statistic", "x", "y" ] }