def test_validate_int_below_min(self):
with pytest.raises(ValueError,
match='n must be an integer not '
'less than 0'):
_validate_int(-1, 'n', 0)
def test_validate_int_bad(self, n):
with pytest.raises(TypeError, match='n must be an integer'):
_validate_int(n, 'n')
def binomtest(k, n, p=0.5, alternative='two-sided'):
"""
Perform a test that the probability of success is p.
The binomial test [1]_ is a test of the null hypothesis that the
probability of success in a Bernoulli experiment is `p`.
Details of the test can be found in many texts on statistics, such
as section 24.5 of [2]_.
Parameters
----------
k : int
The number of successes.
n : int
The number of trials.
p : float, optional
The hypothesized probability of success, i.e. the expected
proportion of successes. The value must be in the interval
``0 <= p <= 1``. The default value is ``p = 0.5``.
alternative : {'two-sided', 'greater', 'less'}, optional
Indicates the alternative hypothesis. The default value is
'two-sided'.
Returns
-------
result : `~scipy.stats._result_classes.BinomTestResult` instance
The return value is an object with the following attributes:
k : int
The number of successes (copied from `binomtest` input).
n : int
The number of trials (copied from `binomtest` input).
alternative : str
Indicates the alternative hypothesis specified in the input
to `binomtest`. It will be one of ``'two-sided'``, ``'greater'``,
or ``'less'``.
pvalue : float
The p-value of the hypothesis test.
proportion_estimate : float
The estimate of the proportion of successes.
The object has the following methods:
proportion_ci(confidence_level=0.95, method='exact') :
Compute the confidence interval for ``proportion_estimate``.
Notes
-----
.. versionadded:: 1.7.0
References
----------
.. [1] Binomial test, https://en.wikipedia.org/wiki/Binomial_test
.. [2] Jerrold H. Zar, Biostatistical Analysis (fifth edition),
Prentice Hall, Upper Saddle River, New Jersey USA (2010)
Examples
--------
>>> from scipy.stats import binomtest
A car manufacturer claims that no more than 10% of their cars are unsafe.
15 cars are inspected for safety, 3 were found to be unsafe. Test the
manufacturer's claim:
>>> result = binomtest(3, n=15, p=0.1, alternative='greater')
>>> result.pvalue
0.18406106910639114
The null hypothesis cannot be rejected at the 5% level of significance
because the returned p-value is greater than the critical value of 5%.
The estimated proportion is simply ``3/15``:
>>> result.proportion_estimate
0.2
We can use the `proportion_ci()` method of the result to compute the
confidence interval of the estimate:
>>> result.proportion_ci(confidence_level=0.95)
ConfidenceInterval(low=0.056846867590246826, high=1.0)
"""
k = _validate_int(k, 'k', minimum=0)
n = _validate_int(n, 'n', minimum=1)
if k > n:
raise ValueError('k must not be greater than n.')
if not (0 <= p <= 1):
raise ValueError("p must be in range [0,1]")
if alternative not in ('two-sided', 'less', 'greater'):
raise ValueError("alternative not recognized; \n"
"must be 'two-sided', 'less' or 'greater'")
if alternative == 'less':
pval = binom.cdf(k, n, p)
elif alternative == 'greater':
pval = binom.sf(k - 1, n, p)
else:
# alternative is 'two-sided'
d = binom.pmf(k, n, p)
rerr = 1 + 1e-7
if k == p * n:
# special case as shortcut, would also be handled by `else` below
pval = 1.
elif k < p * n:
ix = _binary_search_for_binom_tst(lambda x1: -binom.pmf(x1, n, p),
-d * rerr, np.ceil(p * n), n)
# y is the number of terms between mode and n that are <= d*rerr.
# ix gave us the first term where a(ix) <= d*rerr < a(ix-1)
# if the first equality doesn't hold, y=n-ix. Otherwise, we
# need to include ix as well as the equality holds. Note that
# the equality will hold in very very rare situations due to rerr.
y = n - ix + int(d * rerr == binom.pmf(ix, n, p))
pval = binom.cdf(k, n, p) + binom.sf(n - y, n, p)
else:
ix = _binary_search_for_binom_tst(lambda x1: binom.pmf(x1, n, p),
d * rerr, 0, np.floor(p * n))
# y is the number of terms between 0 and mode that are <= d*rerr.
# we need to add a 1 to account for the 0 index.
# For comparing this with old behavior, see
# tst_binary_srch_for_binom_tst method in test_morestats.
y = ix + 1
pval = binom.cdf(y - 1, n, p) + binom.sf(k - 1, n, p)
pval = min(1.0, pval)
result = BinomTestResult(k=k,
n=n,
alternative=alternative,
proportion_estimate=k / n,
pvalue=pval)
return result
def test_validate_int(self, n):
n = _validate_int(n, 'n')
assert n == 4
def binomtest(k, n, p=0.5, alternative='two-sided'):
"""
Perform a test that the probability of success is p.
The binomial test [1]_ is a test of the null hypothesis that the
probability of success in a Bernoulli experiment is `p`.
Details of the test can be found in many texts on statistics, such
as section 24.5 of [2]_.
Parameters
----------
k : int
The number of successes.
n : int
The number of trials.
p : float, optional
The hypothesized probability of success, i.e. the expected
proportion of successes. The value must be in the interval
``0 <= p <= 1``. The default value is ``p = 0.5``.
alternative : {'two-sided', 'greater', 'less'}, optional
Indicates the alternative hypothesis. The default value is
'two-sided'.
Returns
-------
result : `BinomTestResult` instance
The return value is an object with the following attributes:
k : int
The number of successes (copied from `binomtest` input).
n : int
The number of trials (copied from `binomtest` input).
alternative : str
Indicates the alternative hypothesis specified in the input
to `binomtest`. It will be one of ``'two-sided'``, ``'greater'``,
or ``'less'``.
pvalue : float
The p-value of the hypothesis test.
proportion_estimate : float
The estimate of the proportion of successes.
The object has the following methods:
proportion_ci(confidence_level=0.95, method='exact') :
Compute the confidence interval for ``proportion_estimate``.
Notes
-----
.. versionadded:: 1.7.0
References
----------
.. [1] Binomial test, https://en.wikipedia.org/wiki/Binomial_test
.. [2] Jerrold H. Zar, Biostatistical Analysis (fifth edition),
Prentice Hall, Upper Saddle River, New Jersey USA (2010)
Examples
--------
>>> from scipy.stats import binomtest
A car manufacturer claims that no more than 10% of their cars are unsafe.
15 cars are inspected for safety, 3 were found to be unsafe. Test the
manufacturer's claim:
>>> result = binomtest(3, n=15, p=0.1, alternative='greater')
>>> result.pvalue
0.18406106910639114
The null hypothesis cannot be rejected at the 5% level of significance
because the returned p-value is greater than the critical value of 5%.
The estimated proportion is simply ``3/15``:
>>> result.proportion_estimate
0.2
We can use the `proportion_ci()` method of the result to compute the
confidence interval of the estimate:
>>> result.proportion_ci(confidence_level=0.95)
ConfidenceInterval(low=0.056846867590246826, high=1.0)
"""
k = _validate_int(k, 'k', minimum=0)
n = _validate_int(n, 'n', minimum=1)
if k > n:
raise ValueError('k must not be greater than n.')
if not (0 <= p <= 1):
raise ValueError("p must be in range [0,1]")
if alternative not in ('two-sided', 'less', 'greater'):
raise ValueError("alternative not recognized; \n"
"must be 'two-sided', 'less' or 'greater'")
if alternative == 'less':
pval = binom.cdf(k, n, p)
elif alternative == 'greater':
pval = binom.sf(k - 1, n, p)
else:
# alternative is 'two-sided'
d = binom.pmf(k, n, p)
rerr = 1 + 1e-7
if k == p * n:
# special case as shortcut, would also be handled by `else` below
pval = 1.
elif k < p * n:
i = np.arange(np.ceil(p * n), n + 1)
y = np.sum(binom.pmf(i, n, p) <= d * rerr, axis=0)
pval = binom.cdf(k, n, p) + binom.sf(n - y, n, p)
else:
i = np.arange(np.floor(p * n) + 1)
y = np.sum(binom.pmf(i, n, p) <= d * rerr, axis=0)
pval = binom.cdf(y - 1, n, p) + binom.sf(k - 1, n, p)
pval = min(1.0, pval)
result = BinomTestResult(k=k,
n=n,
alternative=alternative,
proportion_estimate=k / n,
pvalue=pval)
return result