square test of independence of variables in a
    contingency table.
fisher_exact : Fisher exact test on a 2x2 contingency table.
barnard_exact : Barnard's exact test, which is a more powerful alternative
    than Fisher's exact test for 2x2 contingency tables.

Notes
-----
Boschloo's test is an exact test used in the analysis of contingency
tables. It examines the association of two categorical variables, and
is a uniformly more powerful alternative to Fisher's exact test
for 2x2 contingency tables.

Boschloo's exact test uses the p-value of Fisher's exact test as a
statistic, and Boschloo's p-value is the probability under the null
hypothesis of observing such an extreme value of this statistic.

Let's define :math:`X_0` a 2x2 matrix representing the observed sample,
where each column stores the binomial experiment, as in the example
below. Let's also define :math:`p_1, p_2` the theoretical binomial
probabilities for  :math:`x_{11}` and :math:`x_{12}`. When using
Boschloo exact test, we can assert three different alternative hypotheses:

- :math:`H_0 : p_1=p_2` versus :math:`H_1 : p_1 < p_2`,
  with `alternative` = "less"

- :math:`H_0 : p_1=p_2` versus :math:`H_1 : p_1 > p_2`,
  with `alternative` = "greater"

- :math:`H_0 : p_1=p_2` versus :math:`H_1 : p_1 \neq p_2`,
  with `alternative` = "two-sided" (default)

There are multiple conventions for computing a two-sided p-value when the
null distribution is asymmetric. Here, we apply the convention that the
p-value of a two-sided test is twice the minimum of the p-values of the
one-sided tests (clipped to 1.0). Note that `fisher_exact` follows a
different convention, so for a given `table`, the statistic reported by
`boschloo_exact` may differ from the p-value reported by `fisher_exact`
when ``alternative='two-sided'``.

.. versionadded:: 1.7.0

References
----------
.. [1] R.D. Boschloo. "Raised conditional level of significance for the
   2 x 2-table when testing the equality of two probabilities",
   Statistica Neerlandica, 24(1), 1970

.. [2] "Boschloo's test", Wikipedia,
   https://en.wikipedia.org/wiki/Boschloo%27s_test

.. [3] Lise M. Saari et al. "Employee attitudes and job satisfaction",
   Human Resource Management, 43(4), 395-407, 2004,
   :doi:`10.1002/hrm.20032`.

Examples
--------
In the following example, we consider the article "Employee
attitudes and job satisfaction" [3]_
which reports the results of a survey from 63 scientists and 117 college
professors. Of the 63 scientists, 31 said they were very satisfied with
their jobs, whereas 74 of the college professors were very satisfied
with their work. Is this significant evidence that college
professors are happier with their work than scientists?
The following table summarizes the data mentioned above::

                     college professors   scientists
    Very Satisfied   74                     31
    Dissatisfied     43                     32

When working with statistical hypothesis testing, we usually use a
threshold probability or significance level upon which we decide
to reject the null hypothesis :math:`H_0`. Suppose we choose the common
significance level of 5%.

Our alternative hypothesis is that college professors are truly more
satisfied with their work than scientists. Therefore, we expect
:math:`p_1` the proportion of very satisfied college professors to be
greater than :math:`p_2`, the proportion of very satisfied scientists.
We thus call `boschloo_exact` with the ``alternative="greater"`` option:

>>> import scipy.stats as stats
>>> res = stats.boschloo_exact([[74, 31], [43, 32]], alternative="greater")
>>> res.statistic
0.0483
>>> res.pvalue
0.0355

Under the null hypothesis that scientists are happier in their work than
college professors, the probability of obtaining test
results at least as extreme as the observed data is approximately 3.55%.
Since this p-value is less than our chosen significance level, we have
evidence to reject :math:`H_0` in favor of the alternative hypothesis.

r