{
  "method": "exact rational complete enumeration, probability ordering, fixed margins",
  "scipy_version": "1.13.1",
  "fixtures": [
    {
      "name": "2x3_sparse",
      "table": [
        [
          1,
          4,
          0
        ],
        [
          3,
          0,
          2
        ]
      ],
      "row_margins": [
        5,
        5
      ],
      "column_margins": [
        4,
        4,
        2
      ],
      "total": 10,
      "feasible_tables": 13,
      "extreme_tables": 6,
      "observed_probability": 0.015873015873015872,
      "observed_probability_fraction": "1/63",
      "p_value": 0.07936507936507936,
      "p_value_fraction": "5/63",
      "scipy_pmf_sum_p_value": 0.07936507936507924,
      "probability_mass_sum_exact": "1"
    },
    {
      "name": "2x3_moderate",
      "table": [
        [
          8,
          2,
          1
        ],
        [
          1,
          5,
          4
        ]
      ],
      "row_margins": [
        11,
        10
      ],
      "column_margins": [
        9,
        7,
        5
      ],
      "total": 21,
      "feasible_tables": 44,
      "extreme_tables": 19,
      "observed_probability": 0.0026792093355560848,
      "observed_probability_fraction": "45/16796",
      "p_value": 0.01583710407239819,
      "p_value_fraction": "7/442",
      "scipy_pmf_sum_p_value": 0.015837104072398096,
      "probability_mass_sum_exact": "1"
    },
    {
      "name": "2x3_balanced",
      "table": [
        [
          2,
          2,
          2
        ],
        [
          2,
          2,
          2
        ]
      ],
      "row_margins": [
        6,
        6
      ],
      "column_margins": [
        4,
        4,
        4
      ],
      "total": 12,
      "feasible_tables": 19,
      "extreme_tables": 19,
      "observed_probability": 0.23376623376623376,
      "observed_probability_fraction": "18/77",
      "p_value": 1.0,
      "p_value_fraction": "1",
      "scipy_pmf_sum_p_value": 0.9999999999999973,
      "probability_mass_sum_exact": "1"
    },
    {
      "name": "3x3_diagonal",
      "table": [
        [
          3,
          0,
          0
        ],
        [
          0,
          3,
          0
        ],
        [
          0,
          0,
          3
        ]
      ],
      "row_margins": [
        3,
        3,
        3
      ],
      "column_margins": [
        3,
        3,
        3
      ],
      "total": 9,
      "feasible_tables": 55,
      "extreme_tables": 6,
      "observed_probability": 0.0005952380952380953,
      "observed_probability_fraction": "1/1680",
      "p_value": 0.0035714285714285713,
      "p_value_fraction": "1/280",
      "scipy_pmf_sum_p_value": 0.0035714285714285744,
      "probability_mass_sum_exact": "1"
    },
    {
      "name": "3x3_mixed",
      "table": [
        [
          2,
          1,
          0
        ],
        [
          0,
          2,
          1
        ],
        [
          1,
          0,
          2
        ]
      ],
      "row_margins": [
        3,
        3,
        3
      ],
      "column_margins": [
        3,
        3,
        3
      ],
      "total": 9,
      "feasible_tables": 55,
      "extreme_tables": 36,
      "observed_probability": 0.01607142857142857,
      "observed_probability_fraction": "9/560",
      "p_value": 0.29285714285714287,
      "p_value_fraction": "41/140",
      "scipy_pmf_sum_p_value": 0.2928571428571432,
      "probability_mass_sum_exact": "1"
    },
    {
      "name": "3x3_asymmetric",
      "table": [
        [
          4,
          1,
          0
        ],
        [
          1,
          2,
          1
        ],
        [
          0,
          1,
          2
        ]
      ],
      "row_margins": [
        5,
        4,
        3
      ],
      "column_margins": [
        5,
        4,
        3
      ],
      "total": 12,
      "feasible_tables": 95,
      "extreme_tables": 56,
      "observed_probability": 0.006493506493506494,
      "observed_probability_fraction": "1/154",
      "p_value": 0.170995670995671,
      "p_value_fraction": "79/462",
      "scipy_pmf_sum_p_value": 0.1709956709956706,
      "probability_mass_sum_exact": "1"
    },
    {
      "name": "2x2_compatibility",
      "table": [
        [
          1,
          9
        ],
        [
          11,
          3
        ]
      ],
      "row_margins": [
        10,
        14
      ],
      "column_margins": [
        12,
        12
      ],
      "total": 24,
      "feasible_tables": 11,
      "extreme_tables": 4,
      "observed_probability": 0.0013460761879122358,
      "observed_probability_fraction": "10/7429",
      "p_value": 0.0027594561852200836,
      "p_value_fraction": "41/14858",
      "scipy_pmf_sum_p_value": 0.0027594561852201235,
      "probability_mass_sum_exact": "1"
    }
  ]
}