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Module « scipy.stats »

Fonction dunnett - module scipy.stats

Signature de la fonction dunnett

def dunnett(*samples: 'npt.ArrayLike', control: 'npt.ArrayLike', alternative: Literal['two-sided', 'less', 'greater'] = 'two-sided', rng: int | numpy.integer | numpy.random._generator.Generator | numpy.random.mtrand.RandomState | None = None) -> scipy.stats._multicomp.DunnettResult 

Description

help(scipy.stats.dunnett)

Dunnett's test: multiple comparisons of means against a control group.

This is an implementation of Dunnett's original, single-step test as
described in [1]_.

Parameters
----------
sample1, sample2, ... : 1D array_like
    The sample measurements for each experimental group.
control : 1D array_like
    The sample measurements for the control group.
alternative : {'two-sided', 'less', 'greater'}, optional
    Defines the alternative hypothesis.

    The null hypothesis is that the means of the distributions underlying
    the samples and control are equal. The following alternative
    hypotheses are available (default is 'two-sided'):

    * 'two-sided': the means of the distributions underlying the samples
      and control are unequal.
    * 'less': the means of the distributions underlying the samples
      are less than the mean of the distribution underlying the control.
    * 'greater': the means of the distributions underlying the
      samples are greater than the mean of the distribution underlying
      the control.
rng : `numpy.random.Generator`, optional
    Pseudorandom number generator state. When `rng` is None, a new
    `numpy.random.Generator` is created using entropy from the
    operating system. Types other than `numpy.random.Generator` are
    passed to `numpy.random.default_rng` to instantiate a ``Generator``.

    .. versionchanged:: 1.15.0

        As part of the `SPEC-007 <https://scientific-python.org/specs/spec-0007/>`_
        transition from use of `numpy.random.RandomState` to
        `numpy.random.Generator`, this keyword was changed from `random_state` to
        `rng`. For an interim period, both keywords will continue to work, although
        only one may be specified at a time. After the interim period, function
        calls using the `random_state` keyword will emit warnings. Following a
        deprecation period, the `random_state` keyword will be removed.

Returns
-------
res : `~scipy.stats._result_classes.DunnettResult`
    An object containing attributes:

    statistic : float ndarray
        The computed statistic of the test for each comparison. The element
        at index ``i`` is the statistic for the comparison between
        groups ``i`` and the control.
    pvalue : float ndarray
        The computed p-value of the test for each comparison. The element
        at index ``i`` is the p-value for the comparison between
        group ``i`` and the control.

    And the following method:

    confidence_interval(confidence_level=0.95) :
        Compute the difference in means of the groups
        with the control +- the allowance.

See Also
--------
tukey_hsd : performs pairwise comparison of means.
:ref:`hypothesis_dunnett` : Extended example

Notes
-----
Like the independent-sample t-test, Dunnett's test [1]_ is used to make
inferences about the means of distributions from which samples were drawn.
However, when multiple t-tests are performed at a fixed significance level,
the "family-wise error rate" - the probability of incorrectly rejecting the
null hypothesis in at least one test - will exceed the significance level.
Dunnett's test is designed to perform multiple comparisons while
controlling the family-wise error rate.

Dunnett's test compares the means of multiple experimental groups
against a single control group. Tukey's Honestly Significant Difference Test
is another multiple-comparison test that controls the family-wise error
rate, but `tukey_hsd` performs *all* pairwise comparisons between groups.
When pairwise comparisons between experimental groups are not needed,
Dunnett's test is preferable due to its higher power.

The use of this test relies on several assumptions.

1. The observations are independent within and among groups.
2. The observations within each group are normally distributed.
3. The distributions from which the samples are drawn have the same finite
   variance.

References
----------
.. [1] Dunnett, Charles W. (1955) "A Multiple Comparison Procedure for
       Comparing Several Treatments with a Control." Journal of the American
       Statistical Association, 50:272, 1096-1121,
       :doi:`10.1080/01621459.1955.10501294`
.. [2] Thomson, M. L., & Short, M. D. (1969). Mucociliary function in
       health, chronic obstructive airway disease, and asbestosis. Journal
       of applied physiology, 26(5), 535-539.
       :doi:`10.1152/jappl.1969.26.5.535`

Examples
--------
We'll use data from [2]_, Table 1. The null hypothesis is that the means of
the distributions underlying the samples and control are equal.

First, we test that the means of the distributions underlying the samples
and control are unequal (``alternative='two-sided'``, the default).

>>> import numpy as np
>>> from scipy.stats import dunnett
>>> samples = [[3.8, 2.7, 4.0, 2.4], [2.8, 3.4, 3.7, 2.2, 2.0]]
>>> control = [2.9, 3.0, 2.5, 2.6, 3.2]
>>> res = dunnett(*samples, control=control)
>>> res.statistic
array([ 0.90874545, -0.05007117])
>>> res.pvalue
array([0.58325114, 0.99819341])

Now, we test that the means of the distributions underlying the samples are
greater than the mean of the distribution underlying the control.

>>> res = dunnett(*samples, control=control, alternative='greater')
>>> res.statistic
array([ 0.90874545, -0.05007117])
>>> res.pvalue
array([0.30230596, 0.69115597])

For a more detailed example, see :ref:`hypothesis_dunnett`.

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