{
  "observed_table": [
    [
      1,
      4
    ],
    [
      4,
      1
    ]
  ],
  "fixed_margins": {
    "N": 10,
    "row1": 5,
    "column1": 5
  },
  "all_six_tables": [
    {
      "upper_left": 0,
      "table": [
        [
          0,
          5
        ],
        [
          5,
          0
        ]
      ],
      "mass": "1/252"
    },
    {
      "upper_left": 1,
      "table": [
        [
          1,
          4
        ],
        [
          4,
          1
        ]
      ],
      "mass": "25/252"
    },
    {
      "upper_left": 2,
      "table": [
        [
          2,
          3
        ],
        [
          3,
          2
        ]
      ],
      "mass": "25/63"
    },
    {
      "upper_left": 3,
      "table": [
        [
          3,
          2
        ],
        [
          2,
          3
        ]
      ],
      "mass": "25/63"
    },
    {
      "upper_left": 4,
      "table": [
        [
          4,
          1
        ],
        [
          1,
          4
        ]
      ],
      "mass": "25/252"
    },
    {
      "upper_left": 5,
      "table": [
        [
          5,
          0
        ],
        [
          0,
          5
        ]
      ],
      "mass": "1/252"
    }
  ],
  "observed_mass": "25/252",
  "two_sided_definition": "sum masses <= observed mass, exact Fraction comparison",
  "two_sided_p": "13/63",
  "independent_252_labeled_allocations": {
    "0": 1,
    "1": 25,
    "2": 100,
    "3": 100,
    "4": 25,
    "5": 1
  },
  "swaps_and_zero_cell_cases": [
    {
      "table": [
        [
          4,
          1
        ],
        [
          1,
          4
        ]
      ],
      "p_two_sided": "13/63",
      "masses_sum_one": true
    },
    {
      "table": [
        [
          0,
          5
        ],
        [
          5,
          0
        ]
      ],
      "p_two_sided": "1/126",
      "masses_sum_one": true
    },
    {
      "table": [
        [
          0,
          0
        ],
        [
          3,
          2
        ]
      ],
      "p_two_sided": "1",
      "masses_sum_one": true
    },
    {
      "table": [
        [
          1,
          0
        ],
        [
          0,
          0
        ]
      ],
      "p_two_sided": "1",
      "masses_sum_one": true
    }
  ],
  "all_small_table_row_column_symmetry_checks": 80,
  "not_generally_twice_one_sided": {
    "table": [
      [
        1,
        0
      ],
      [
        1,
        3
      ]
    ],
    "two_sided_probability_ordering": "2/5",
    "one_sided_greater": "2/5",
    "twice_one_sided_capped": "4/5"
  },
  "invalid_cases_rejected": [
    "[[-1, 2], [3, 4]]",
    "[[True, 1], [2, 3]]",
    "[[1.5, 1], [2, 3]]",
    "[[0, 0], [0, 0]]",
    "[[1, 2, 3], [4, 5, 6]]"
  ],
  "limits": "hypothetical independent groups conditional on fixed margins, not paired McNemar, posterior probability, effect size, causality or medical guidance; SciPy not run"
}