{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Admonition", "__tag": 4056, "kind": "versionadded", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionadded 0.15.0" } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Strong", "__tag": 4048, "children": [ { "__type": "Text", "__tag": 4046, "value": "Array API Standard Support" } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "median_test", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._morestats:median_test" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable " }, { "__type": "InlineCode", "__tag": 4051, "value": "SCIPY_ARRAY_API=1" }, { "__type": "Text", "__tag": 4046, "value": " and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported." } ] }, { "__type": "Code", "__tag": 4050, "value": "==================== ==================== ====================\nLibrary CPU GPU\n==================== ==================== ====================\nNumPy ✅ n/a \nCuPy n/a ⛔ \nPyTorch ⛔ ⛔ \nJAX ⛔ ⛔ \nDask ⛔ n/a \n==================== ==================== ====================", "execution_status": null }, { "__type": "Blockquote", "__tag": 4059, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "See " }, { "__type": "InlineRole", "__tag": 4003, "value": "dev-arrayapi", "domain": null, "role": "ref", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " for more information." } ] } ] } ], "title": [], "level": 0, "target": null }, "Warns": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Raises": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Yields": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Methods": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Returns": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "res", "annotation": "MedianTestResult", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "An object containing attributes:" } ] }, { "__type": "DefList", "__tag": 4033, "children": [ { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "statistic" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "statistic" } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "pvalue" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "pvalue" } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "median" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "median" } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "table" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "table" } ] } ] } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Perform a Mood's median test." } ] } ], "title": [], "level": 0, "target": null }, "Receives": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Warnings": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Attributes": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Parameters": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "sample1, sample2, ...", "annotation": "array_like", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The set of samples. There must be at least two samples. Each sample must be a one-dimensional sequence containing at least one value. The samples are not required to have the same length." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "ties", "annotation": "str, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Determines how values equal to the grand median are classified in the contingency table. The string must be one of " } ] }, { "__type": "Code", "__tag": 4050, "value": "\"below\":\n Values equal to the grand median are counted as \"below\".\n\"above\":\n Values equal to the grand median are counted as \"above\".\n\"ignore\":\n Values equal to the grand median are not counted.", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The default is \"below\"." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "correction", "annotation": "bool, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If True, " }, { "__type": "Emphasis", "__tag": 4047, "children": [ { "__type": "Text", "__tag": 4046, "value": "and" } ] }, { "__type": "Text", "__tag": 4046, "value": " there are just two samples, apply Yates' correction for continuity when computing the test statistic associated with the contingency table. Default is True." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "lambda_", "annotation": "float or str, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "By default, the statistic computed in this test is Pearson's chi-squared statistic. " }, { "__type": "ParamRef", "__tag": 4071, "name": "lambda_" }, { "__type": "Text", "__tag": 4046, "value": " allows a statistic from the Cressie-Read power divergence family to be used instead. See " }, { "__type": "CrossRef", "__tag": 4002, "value": "power_divergence", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._stats_py:power_divergence" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " for details. Default is 1 (Pearson's chi-squared statistic)." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "nan_policy", "annotation": "{'propagate', 'raise', 'omit'}, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Defines how to handle when input contains nan. 'propagate' returns nan, 'raise' throws an error, 'omit' performs the calculations ignoring nan values. Default is 'propagate'." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Test that two or more samples come from populations with the same median." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Let " }, { "__type": "InlineCode", "__tag": 4051, "value": "n = len(samples)" }, { "__type": "Text", "__tag": 4046, "value": " be the number of samples. The \"grand median\" of all the data is computed, and a contingency table is formed by classifying the values in each sample as being above or below the grand median. The contingency table, along with " }, { "__type": "ParamRef", "__tag": 4071, "name": "correction" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "ParamRef", "__tag": 4071, "name": "lambda_" }, { "__type": "Text", "__tag": 4046, "value": ", are passed to " }, { "__type": "CrossRef", "__tag": 4002, "value": "scipy.stats.chi2_contingency", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "*", "kind": "api", "path": "scipy.stats.contingency:chi2_contingency" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " to compute the test statistic and p-value." } ] } ], "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": "/scipy/stats/_morestats.py", "item_line": 3961, "item_type": "function", "aliases": [ "scipy.stats.median_test" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "A biologist runs an experiment in which there are three groups of plants.\nGroup 1 has 16 plants, group 2 has 15 plants, and group 3 has 17 plants.\nEach plant produces a number of seeds. The seed counts for each group\nare::\n\n Group 1: 10 14 14 18 20 22 24 25 31 31 32 39 43 43 48 49\n Group 2: 28 30 31 33 34 35 36 40 44 55 57 61 91 92 99\n Group 3: 0 3 9 22 23 25 25 33 34 34 40 45 46 48 62 67 84\n\nThe following code applies Mood's median test to these samples.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "g1 = [10, 14, 14, 18, 20, 22, 24, 25, 31, 31, 32, 39, 43, 43, 48, 49]\ng2 = [28, 30, 31, 33, 34, 35, 36, 40, 44, 55, 57, 61, 91, 92, 99]\ng3 = [0, 3, 9, 22, 23, 25, 25, 33, 34, 34, 40, 45, 46, 48, 62, 67, 84]\nfrom scipy.stats import median_test\nres = median_test(g1, g2, g3)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nThe median is\n\n" }, { "__type": "Code", "__tag": 4050, "value": "res.median\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nand the contingency table is\n\n" }, { "__type": "Code", "__tag": 4050, "value": "res.table\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n`p` is too large to conclude that the medians are not the same:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "res.pvalue\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nThe \"G-test\" can be performed by passing ``lambda_=\"log-likelihood\"`` to\n`median_test`.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "res = median_test(g1, g2, g3, lambda_=\"log-likelihood\")\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "res.pvalue\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nThe median occurs several times in the data, so we'll get a different\nresult if, for example, ``ties=\"above\"`` is used:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "res = median_test(g1, g2, g3, ties=\"above\")\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "res.pvalue\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "res.table\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nThis example demonstrates that if the data set is not large and there\nare values equal to the median, the p-value can be sensitive to the\nchoice of `ties`." } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "kruskal", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "kruskal" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Compute the Kruskal-Wallis H-test for independent samples." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "mannwhitneyu", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "mannwhitneyu" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Computes the Mann-Whitney rank test on samples x and y." } ] } ], "type": "func" } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "samples", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "VAR_POSITIONAL", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "ties", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "below" }, { "__type": "SigParam", "__tag": 4030, "name": "correction", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "True" }, { "__type": "SigParam", "__tag": 4030, "name": "lambda_", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "1" }, { "__type": "SigParam", "__tag": 4030, "name": "nan_policy", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "propagate" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "median_test" }, "references": [ ".. [1] Mood, A. M., Introduction to the Theory of Statistics. McGraw-Hill", " (1950), pp. 394-399.", ".. [2] Zar, J. H., Biostatistical Analysis, 5th ed. Prentice Hall (2010).", " See Sections 8.12 and 10.15." ], "qa": "scipy.stats._morestats:median_test", "arbitrary": [], "local_refs": [ "...", "correction", "lambda_", "nan_policy", "res", "sample1", "sample2", "ties" ] }