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Unlike the Kolmogorov-Smirnov, Wilcoxon, and Cramer-Von Mises tests, the BWS test weights the integral by the variance of the difference in cumulative distribution functions (CDFs), emphasizing the tails of the distributions, which increases the power of the test in many applications." } ] } ], "title": [], "level": 0, "target": null }, "Other Parameters": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null } }, "_ordered_sections": [ "Summary", "Extended Summary", "Parameters", "Attributes", "Methods", "Returns", "Yields", "Receives", "Other Parameters", "Raises", "Warns", "Warnings", "Notes" ], "item_file": "build-install/usr/lib/python3.14/site-packages/scipy/stats/_bws_test.py", "item_line": 86, "item_type": "function", "aliases": [ "scipy.stats.bws_test" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "We follow the example of table 3 in [1]_: Fourteen children were divided\nrandomly into two groups. Their ranks at performing a specific tests are\nas follows.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nx = [1, 2, 3, 4, 6, 7, 8]\ny = [5, 9, 10, 11, 12, 13, 14]\n", "execution_status": "success", "out": "" }, { "__type": "Text", "__tag": 4046, "value": "\nWe use the BWS test to assess whether there is a statistically significant\ndifference between the two groups.\nThe null hypothesis is that there is no difference in the distributions of\nperformance between the two groups. We decide that a significance level of\n1% is required to reject the null hypothesis in favor of the alternative\nthat the distributions are different.\nSince the number of samples is very small, we can compare the observed test\nstatistic against the *exact* distribution of the test statistic under the\nnull hypothesis.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy.stats import bws_test\nres = bws_test(x, y)\nprint(res.statistic)\n", "execution_status": "success", "out": "5.132167152575315\n" }, { "__type": "Text", "__tag": 4046, "value": "\nThis agrees with :math:`B = 5.132` reported in [1]_. The *p*-value produced\nby `bws_test` also agrees with :math:`p = 0.0029` reported in [1]_.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "print(res.pvalue)\n", "execution_status": "success", "out": "0.002913752913752914\n" }, { "__type": "Text", "__tag": 4046, "value": "\nBecause the p-value is below our threshold of 1%, we take this as evidence\nagainst the null hypothesis in favor of the alternative that there is a\ndifference in performance between the two groups." } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "scipy.stats.mannwhitneyu", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._mannwhitneyu:mannwhitneyu" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "scipy.stats.ttest_ind", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._stats_py:ttest_ind" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "scipy.stats.wilcoxon", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._morestats:wilcoxon" }, "kind": "module" }, "descriptions": [], "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": "KEYWORD_ONLY", "default": "two-sided" }, { "__type": "SigParam", "__tag": 4030, "name": "axis", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "0" }, { "__type": "SigParam", "__tag": 4030, "name": "method", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "bws_test" }, "references": [ ".. [1] Neuhäuser, M. (2005). Exact Tests Based on the", " Baumgartner-Weiss-Schindler Statistic: A Survey. Statistical Papers,", " 46(1), 1-29.", ".. [2] Fay, M. P., & Proschan, M. A. (2010). Wilcoxon-Mann-Whitney or t-test?", " On assumptions for hypothesis tests and multiple interpretations of", " decision rules. Statistics surveys, 4, 1." ], "qa": "scipy.stats._bws_test:bws_test", "arbitrary": [], "local_refs": [ "alternative", "axis", "method", "res", "x", "y" ] }