{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The F statistic is used to compare in-group variances to between-group variances. Calculating the distribution depends on the sampling, and so it is a function of the respective degrees of freedom in the problem. 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Otherwise, " }, { "__type": "InlineCode", "__tag": 4051, "value": "np.broadcast(dfnum, dfden).size" }, { "__type": "Text", "__tag": 4046, "value": " samples are drawn." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Samples are drawn from an F distribution with specified parameters, " }, { "__type": "ParamRef", "__tag": 4071, "name": "dfnum" }, { "__type": "Text", "__tag": 4046, "value": " (degrees of freedom in numerator) and " }, { "__type": "ParamRef", "__tag": 4071, "name": "dfden" }, { "__type": "Text", "__tag": 4046, "value": " (degrees of freedom in denominator), where both parameters must be greater than zero." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The random variate of the F distribution (also known as the Fisher distribution) is a continuous probability distribution that arises in ANOVA tests, and is the ratio of two chi-square variates." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "note", "base_type": "note", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "note " } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "New code should use the " }, { "__type": "CrossRef", "__tag": 4002, "value": "f", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy.random._generator:Generator.f" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " method of a " }, { "__type": "CrossRef", "__tag": 4002, "value": "Generator", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy.random._generator:Generator" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " instance instead; please see the " }, { "__type": "InlineRole", "__tag": 4003, "value": "random-quick-start", "domain": null, "role": "ref", "inventory": null }, { "__type": "Text", "__tag": 4046, "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": null, "item_line": null, "item_type": "cython_function_or_method", "aliases": [ "numpy.random.f", "numpy.random.RandomState.f" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "An example from Glantz[1], pp 47-40:\n\nTwo groups, children of diabetics (25 people) and children from people\nwithout diabetes (25 controls). Fasting blood glucose was measured,\ncase group had a mean value of 86.1, controls had a mean value of\n82.2. Standard deviations were 2.09 and 2.49 respectively. Are these\ndata consistent with the null hypothesis that the parents diabetic\nstatus does not affect their children's blood glucose levels?\nCalculating the F statistic from the data gives a value of 36.01.\n\nDraw samples from the distribution:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "dfnum = 1. # between group degrees of freedom\ndfden = 48. # within groups degrees of freedom\ns = np.random.f(dfnum, dfden, 1000)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nThe lower bound for the top 1% of the samples is :\n\n" }, { "__type": "Code", "__tag": 4050, "value": "np.sort(s)[-10]\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nSo there is about a 1% chance that the F statistic will exceed 7.62,\nthe measured value is 36, so the null hypothesis is rejected at the 1%\nlevel." } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "random.Generator.f", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "random.Generator.f" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "which should be used for new code." } ] } ], "type": null }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "scipy.stats.f", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "scipy.stats.f" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "probability density function, distribution or cumulative density function, etc." } ] } ], "type": null } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "dfnum", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "dfden", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "size", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "f" }, "references": [ ".. [1] Glantz, Stanton A. \"Primer of Biostatistics.\", McGraw-Hill,", " Fifth Edition, 2002.", ".. [2] Wikipedia, \"F-distribution\",", " https://en.wikipedia.org/wiki/F-distribution" ], "qa": "numpy.random:RandomState.f", "arbitrary": [], "local_refs": [ "dfden", "dfnum", "out", "size" ] }