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It is equivalent to " }, { "__type": "CrossRef", "__tag": 4002, "value": "pearsonr", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._stats_py:pearsonr" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The value of the point-biserial correlation can be calculated from:" } ] }, { "__type": "Math", "__tag": 4058, "value": "r_{pb} = \\frac{\\overline{Y_1} - \\overline{Y_0}}\n {s_y}\n \\sqrt{\\frac{N_0 N_1}\n {N (N - 1)}}" }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Where " }, { "__type": "InlineMath", "__tag": 4057, "value": "\\overline{Y_{0}}" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineMath", "__tag": 4057, "value": "\\overline{Y_{1}}" }, { "__type": "Text", "__tag": 4046, "value": " are means of the metric observations coded 0 and 1 respectively; " }, { "__type": "InlineMath", "__tag": 4057, "value": "N_{0}" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineMath", "__tag": 4057, "value": "N_{1}" }, { "__type": "Text", "__tag": 4046, "value": " are number of observations coded 0 and 1 respectively; " }, { "__type": "InlineMath", "__tag": 4057, "value": "N" }, { "__type": "Text", "__tag": 4046, "value": " is the total number of observations and " }, { "__type": "InlineMath", "__tag": 4057, "value": "s_{y}" }, { "__type": "Text", "__tag": 4046, "value": " is the standard deviation of all the metric observations." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A value of " }, { "__type": "InlineMath", "__tag": 4057, "value": "r_{pb}" }, { "__type": "Text", "__tag": 4046, "value": " that is significantly different from zero is completely equivalent to a significant difference in means between the two groups. Thus, an independent groups t Test with " }, { "__type": "InlineMath", "__tag": 4057, "value": "N-2" }, { "__type": "Text", "__tag": 4046, "value": " degrees of freedom may be used to test whether " }, { "__type": "InlineMath", "__tag": 4057, "value": "r_{pb}" }, { "__type": "Text", "__tag": 4046, "value": " is nonzero. 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[1] J. Lev, \"The Point Biserial Coefficient of Correlation\", Ann. Math.", " Statist., Vol. 20, no.1, pp. 125-126, 1949.", "", ".. [2] R.F. Tate, \"Correlation Between a Discrete and a Continuous", " Variable. Point-Biserial Correlation.\", Ann. Math. Statist., Vol. 25,", " np. 3, pp. 603-607, 1954.", "", ".. [3] D. Kornbrot \"Point Biserial Correlation\", In Wiley StatsRef:", " Statistics Reference Online (eds N. Balakrishnan, et al.), 2014.", " :doi:`10.1002/9781118445112.stat06227`" ], "qa": "scipy.stats._stats_py:pointbiserialr", "arbitrary": [], "local_refs": [ "axis", "keepdims", "nan_policy", "x", "y" ] }