# scipy.stats.contingency.crosstab

scipy.stats.contingency.crosstab(*args, levels=None, sparse=False)

  Return table of counts for each possible unique combination in `*args`.

  When `len(args) > 1`, the array computed by this function is often referred to as a contingency table [1].

  The arguments must be sequences with the same length. The second return value, count, is an integer array with `len(args)` dimensions. If levels is None, the shape of count is `(n0, n1, ...)`, where `nk` is the number of unique elements in `args[k]`.

  Parameters
    args sequences

      A sequence of sequences whose unique aligned elements are to be counted. The sequences in args must all be the same length.

    levels sequence, optional

      If levels is given, it must be a sequence that is the same length as args. Each element in levels is either a sequence or None. If it is a sequence, it gives the values in the corresponding sequence in args that are to be counted. If any value in the sequences in args does not occur in the corresponding sequence in levels, that value is ignored and not counted in the returned array count. The default value of levels for `args[i]` is `np.unique(args[i])`

    sparse bool, optional

      If True, return a sparse matrix. The matrix will be an instance of the `scipy.sparse.coo_matrix` class. Because SciPy’s sparse matrices must be 2-d, only two input sequences are allowed when sparse is True. Default is False.

  Returns
    elements tuple of numpy.ndarrays.

      Tuple of length `len(args)` containing the arrays of elements that are counted in count. These can be interpreted as the labels of the corresponding dimensions of count. If levels was given, then if `levels[i]` is not None, `elements[i]` will hold the values given in `levels[i]`.

    count numpy.ndarray or scipy.sparse.coo_matrix

      Counts of the unique elements in `zip(*args)`, stored in an array. Also known as a contingency table when `len(args) > 1`.

  See also

  `numpy.unique`

  Notes

  New in version 1.7.0.

  References

  1

    “Contingency table”, http://en.wikipedia.org/wiki/Contingency_table

  Examples

      >>> from scipy.stats.contingency import crosstab

  Given the lists a and x, create a contingency table that counts the frequencies of the corresponding pairs.

      >>> a = ['A', 'B', 'A', 'A', 'B', 'B', 'A', 'A', 'B', 'B']
      >>> x = ['X', 'X', 'X', 'Y', 'Z', 'Z', 'Y', 'Y', 'Z', 'Z']
      >>> (avals, xvals), count = crosstab(a, x)
      >>> avals
      array(['A', 'B'], dtype='<U1')
      >>> xvals
      array(['X', 'Y', 'Z'], dtype='<U1')
      >>> count
      array([[2, 3, 0],
             [1, 0, 4]])

  So (‘A’, ‘X’) occurs twice, (‘A’, ‘Y’) occurs three times, etc.

  Higher dimensional contingency tables can be created.

      >>> p = [0, 0, 0, 0, 1, 1, 1, 0, 0, 1]
      >>> (avals, xvals, pvals), count = crosstab(a, x, p)
      >>> count
      array([[[2, 0],
              [2, 1],
              [0, 0]],
             [[1, 0],
              [0, 0],
              [1, 3]]])
      >>> count.shape
      (2, 3, 2)

  The values to be counted can be set by using the levels argument. It allows the elements of interest in each input sequence to be given explicitly instead finding the unique elements of the sequence.

  For example, suppose one of the arguments is an array containing the answers to a survey question, with integer values 1 to 4. Even if the value 1 does not occur in the data, we want an entry for it in the table.

      >>> q1 = [2, 3, 3, 2, 4, 4, 2, 3, 4, 4, 4, 3, 3, 3, 4]  # 1 does not occur.
      >>> q2 = [4, 4, 2, 2, 2, 4, 1, 1, 2, 2, 4, 2, 2, 2, 4]  # 3 does not occur.
      >>> options = [1, 2, 3, 4]
      >>> vals, count = crosstab(q1, q2, levels=(options, options))
      >>> count
      array([[0, 0, 0, 0],
             [1, 1, 0, 1],
             [1, 4, 0, 1],
             [0, 3, 0, 3]])

  If levels is given, but an element of levels is None, the unique values of the corresponding argument are used. For example,

      >>> vals, count = crosstab(q1, q2, levels=(None, options))
      >>> vals
      [array([2, 3, 4]), [1, 2, 3, 4]]
      >>> count
      array([[1, 1, 0, 1],
             [1, 4, 0, 1],
             [0, 3, 0, 3]])

  If we want to ignore the pairs where 4 occurs in `q2`, we can give just the values [1, 2] to levels, and the 4 will be ignored:

      >>> vals, count = crosstab(q1, q2, levels=(None, [1, 2]))
      >>> vals
      [array([2, 3, 4]), [1, 2]]
      >>> count
      array([[1, 1],
             [1, 4],
             [0, 3]])

  Finally, let’s repeat the first example, but return a sparse matrix:

      >>> (avals, xvals), count = crosstab(a, x, sparse=True)
      >>> count
      <2x3 sparse matrix of type '<class 'numpy.int64'>'
              with 4 stored elements in COOrdinate format>
      >>> count.A
      array([[2, 3, 0],
             [1, 0, 4]])

scipy.stats.chi2_contingency scipy.stats.contingency.expected_freq