{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Cramer's V, Tschuprow's T and Pearson's Contingency Coefficient, all measure the degree to which two nominal or ordinal variables are related, or the level of their association. This differs from correlation, although many often mistakenly consider them equivalent. Correlation measures in what way two variables are related, whereas, association measures how related the variables are. As such, association does not subsume independent variables, and is rather a test of independence. A value of 1.0 indicates perfect association, and 0.0 means the variables have no association."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Both the Cramer's V and Tschuprow's T are extensions of the phi coefficient.  Moreover, due to the close relationship between the Cramer's V and Tschuprow's T the returned values can often be similar or even equivalent.  They are likely to diverge more as the array shape diverges from a 2x2."
            }
          ]
        },
        {
          "__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": "association",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "scipy.stats.contingency:association"
              },
              "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": "statistic",
              "annotation": "float",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Value of the test statistic"
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Calculates degree of association between two nominal variables."
            }
          ]
        }
      ],
      "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": "observed",
              "annotation": "array-like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The array of observed values"
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "method",
              "annotation": "{\"cramer\", \"tschuprow\", \"pearson\"} (default = \"cramer\")",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The association test statistic."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "correction",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Inherited from "
                    },
                    {
                      "__type": "CrossRef",
                      "__tag": 4002,
                      "value": "scipy.stats.contingency.chi2_contingency()",
                      "reference": {
                        "__type": "RefInfo",
                        "__tag": 4000,
                        "module": "scipy",
                        "version": "*",
                        "kind": "api",
                        "path": "scipy.stats.contingency:chi2_contingency"
                      },
                      "kind": "module"
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "lambda_",
              "annotation": "float or str, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Inherited from "
                    },
                    {
                      "__type": "CrossRef",
                      "__tag": 4002,
                      "value": "scipy.stats.contingency.chi2_contingency()",
                      "reference": {
                        "__type": "RefInfo",
                        "__tag": 4000,
                        "module": "scipy",
                        "version": "*",
                        "kind": "api",
                        "path": "scipy.stats.contingency:chi2_contingency"
                      },
                      "kind": "module"
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The function provides the option for computing one of three measures of association between two nominal variables from the data given in a 2d contingency table: Tschuprow's T, Pearson's Contingency Coefficient and Cramer's V."
            }
          ]
        }
      ],
      "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/contingency.py",
  "item_line": 425,
  "item_type": "function",
  "aliases": [
    "scipy.stats.contingency.association"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "An example with a 4x2 contingency table:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "import numpy as np\nfrom scipy.stats.contingency import association\nobs4x2 = np.array([[100, 150], [203, 322], [420, 700], [320, 210]])\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nPearson's contingency coefficient\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "association(obs4x2, method=\"pearson\")\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nCramer's V\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "association(obs4x2, method=\"cramer\")\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nTschuprow's T\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "association(obs4x2, method=\"tschuprow\")\n",
        "execution_status": "success"
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [],
  "signature": {
    "__type": "SignatureNode",
    "__tag": 4029,
    "kind": "function",
    "parameters": [
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "observed",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "method",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "cramer"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "correction",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "False"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "lambda_",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "association"
  },
  "references": [
    ".. [1] \"Tschuprow's T\",",
    "       https://en.wikipedia.org/wiki/Tschuprow's_T",
    ".. [2] Tschuprow, A. A. (1939)",
    "       Principles of the Mathematical Theory of Correlation;",
    "       translated by M. Kantorowitsch. W. Hodge & Co.",
    ".. [3] \"Cramer's V\", https://en.wikipedia.org/wiki/Cramer's_V",
    ".. [4] \"Nominal Association: Phi and Cramer's V\",",
    "       http://www.people.vcu.edu/~pdattalo/702SuppRead/MeasAssoc/NominalAssoc.html",
    ".. [5] Gingrich, Paul, \"Association Between Variables\",",
    "       http://uregina.ca/~gingrich/ch11a.pdf"
  ],
  "qa": "scipy.stats.contingency:association",
  "arbitrary": [],
  "local_refs": [
    "correction",
    "lambda_",
    "method",
    "observed",
    "statistic"
  ]
}