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For instance, to test the null hypothesis that " }, { "__type": "InlineCode", "__tag": 4051, "value": "f_obs[i]" }, { "__type": "Text", "__tag": 4046, "value": " is Poisson-distributed with expectation " }, { "__type": "InlineCode", "__tag": 4051, "value": "f_exp[i]" }, { "__type": "Text", "__tag": 4046, "value": ", set " }, { "__type": "InlineCode", "__tag": 4051, "value": "ddof=-1" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineCode", "__tag": 4051, "value": "sum_check=False" }, { "__type": "Text", "__tag": 4046, "value": ". 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If " }, { "__type": "InlineCode", "__tag": 4051, "value": "None" }, { "__type": "Text", "__tag": 4046, "value": ", the input will be raveled before computing the statistic." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "sum_check", "annotation": "bool, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Whether to perform a check that " }, { "__type": "InlineCode", "__tag": 4051, "value": "sum(f_obs) - sum(f_exp) == 0" }, { "__type": "Text", "__tag": 4046, "value": ". If True, (default) raise an error when the relative difference exceeds the square root of the precision of the data type. 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With this option, the result will broadcast correctly against the input array." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Pearson's chi-squared test " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "1" }, { "__type": "Text", "__tag": 4046, "value": " is a goodness-of-fit test for a multinomial distribution with given probabilities; that is, it assesses the null hypothesis that the observed frequencies (counts) are obtained by independent sampling of " }, { "__type": "Emphasis", "__tag": 4047, "children": [ { "__type": "Text", "__tag": 4046, "value": "N" } ] }, { "__type": "Text", "__tag": 4046, "value": " observations from a categorical distribution with given expected frequencies." } ] } ], "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/_stats_py.py", "item_line": 7220, "item_type": "function", "aliases": [ "scipy.stats.chisquare" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "When only the mandatory `f_obs` argument is given, it is assumed that the\nexpected frequencies are uniform and given by the mean of the observed\nfrequencies:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nfrom scipy.stats import chisquare\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "chisquare([16, 18, 16, 14, 12, 12])\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nThe optional `f_exp` argument gives the expected frequencies.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "chisquare([16, 18, 16, 14, 12, 12], f_exp=[16, 16, 16, 16, 16, 8])\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nWhen `f_obs` is 2-D, by default the test is applied to each column.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "obs = np.array([[16, 18, 16, 14, 12, 12], [32, 24, 16, 28, 20, 24]]).T\nobs.shape\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "chisquare(obs)\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nBy setting ``axis=None``, the test is applied to all data in the array,\nwhich is equivalent to applying the test to the flattened array.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "chisquare(obs, axis=None)\nchisquare(obs.ravel())\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\n`ddof` is the change to make to the default degrees of freedom.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "chisquare([16, 18, 16, 14, 12, 12], ddof=1)\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nThe calculation of the p-values is done by broadcasting the\nchi-squared statistic with `ddof`.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "chisquare([16, 18, 16, 14, 12, 12], ddof=[0, 1, 2])\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\n`f_obs` and `f_exp` are also broadcast. In the following, `f_obs` has\nshape (6,) and `f_exp` has shape (2, 6), so the result of broadcasting\n`f_obs` and `f_exp` has shape (2, 6). To compute the desired chi-squared\nstatistics, we use ``axis=1``:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "chisquare([16, 18, 16, 14, 12, 12],\n f_exp=[[16, 16, 16, 16, 16, 8], [8, 20, 20, 16, 12, 12]],\n axis=1)\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nFor a more detailed example, see :ref:`hypothesis_chisquare`." } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "hypothesis_chisquare", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "hypothesis_chisquare" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Extended example" } ] } ], "type": "ref" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "scipy.stats.barnard_exact", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._hypotests:barnard_exact" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "An unconditional exact test. An alternative to chi-squared test for small sample sizes." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "scipy.stats.fisher_exact", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._stats_py:fisher_exact" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Fisher exact test on a 2x2 contingency table." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "scipy.stats.power_divergence", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._stats_py:power_divergence" }, "kind": "module" }, "descriptions": [], "type": "func" } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "f_obs", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "f_exp", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "ddof", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "0" }, { "__type": "SigParam", "__tag": 4030, "name": "axis", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "0" }, { "__type": "SigParam", "__tag": 4030, "name": "sum_check", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "True" }, { "__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": "chisquare" }, "references": [ ".. [1] \"Pearson's chi-squared test\".", " *Wikipedia*. https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test", ".. [2] Pearson, Karl. \"On the criterion that a given system of deviations from the probable", " in the case of a correlated system of variables is such that it can be reasonably", " supposed to have arisen from random sampling\", Philosophical Magazine. Series 5. 50", " (1900), pp. 157-175." ], "qa": "scipy.stats._stats_py:chisquare", "arbitrary": [], "local_refs": [ "axis", "ddof", "f_exp", "f_obs", "keepdims", "nan_policy", "sum_check" ] }