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The null hypothesis is that the " }, { "__type": "InlineMath", "__tag": 4057, "value": "X_i" }, { "__type": "Text", "__tag": 4046, "value": " have cumulative distribution " }, { "__type": "InlineMath", "__tag": 4057, "value": "F" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The test statistic " }, { "__type": "InlineMath", "__tag": 4057, "value": "T" }, { "__type": "Text", "__tag": 4046, "value": " is defined as in " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "1" }, { "__type": "Text", "__tag": 4046, "value": ", where " }, { "__type": "InlineMath", "__tag": 4057, "value": "\\omega^2" }, { "__type": "Text", "__tag": 4046, "value": " is the Cramér-von Mises criterion and " }, { "__type": "InlineMath", "__tag": 4057, "value": "x_i" }, { "__type": "Text", "__tag": 4046, "value": " are the observed values." } ] }, { "__type": "Math", "__tag": 4058, "value": "T = n\\omega^2 =\n\\frac{1}{12n} + \\sum_{i=1}^n \\left[ \\frac{2i-1}{2n} - F(x_i) \\right]^2" } ], "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/_hypotests.py", "item_line": 532, "item_type": "function", "aliases": [ "scipy.stats.cramervonmises" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "Suppose we wish to test whether data generated by ``scipy.stats.norm.rvs``\nwere, in fact, drawn from the standard normal distribution. We choose a\nsignificance level of ``alpha=0.05``.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nfrom scipy import stats\nrng = np.random.default_rng(165417232101553420507139617764912913465)\nx = stats.norm.rvs(size=500, random_state=rng)\nres = stats.cramervonmises(x, 'norm')\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "res.statistic, res.pvalue\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nThe p-value exceeds our chosen significance level, so we do not\nreject the null hypothesis that the observed sample is drawn from the\nstandard normal distribution.\n\nNow suppose we wish to check whether the same samples shifted by 2.1 is\nconsistent with being drawn from a normal distribution with a mean of 2.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "y = x + 2.1\nres = stats.cramervonmises(y, 'norm', args=(2,))\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "res.statistic, res.pvalue\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nHere we have used the `args` keyword to specify the mean (``loc``)\nof the normal distribution to test the data against. This is equivalent\nto the following, in which we create a frozen normal distribution with\nmean 2.1, then pass its ``cdf`` method as an argument.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "frozen_dist = stats.norm(loc=2)\nres = stats.cramervonmises(y, frozen_dist.cdf)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "res.statistic, res.pvalue\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nIn either case, we would reject the null hypothesis that the observed\nsample is drawn from a normal distribution with a mean of 2 (and default\nvariance of 1) because the p-value is less than our chosen\nsignificance level." } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "cramervonmises_2samp", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._hypotests:cramervonmises_2samp" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "kstest", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "kstest" }, "kind": "module" }, "descriptions": [], "type": "func" } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "rvs", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "cdf", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "args", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "()" }, { "__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": "cramervonmises" }, "references": [ ".. [1] Cramér-von Mises criterion, Wikipedia,", " https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93von_Mises_criterion", ".. [2] Csörgő, S. and Faraway, J. (1996). The Exact and Asymptotic", " Distribution of Cramér-von Mises Statistics. Journal of the", " Royal Statistical Society, pp. 221-234." ], "qa": "scipy.stats._hypotests:cramervonmises", "arbitrary": [], "local_refs": [ "args", "axis", "cdf", "keepdims", "nan_policy", "res", "rvs" ] }