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Module « scipy.stats »

Fonction ttest_rel - module scipy.stats

Signature de la fonction ttest_rel

def ttest_rel(a, b, axis=0, nan_policy='propagate', alternative='two-sided', *, keepdims=False) 

Description

help(scipy.stats.ttest_rel)

    


Calculate the t-test on TWO RELATED samples of scores, a and b.

This is a test for the null hypothesis that two related or
repeated samples have identical average (expected) values.

Parameters
----------
a, b : array_like
    The arrays must have the same shape.
axis : int or None, default: 0
    If an int, the axis of the input along which to compute the statistic.
    The statistic of each axis-slice (e.g. row) of the input will appear in a
    corresponding element of the output.
    If ``None``, the input will be raveled before computing the statistic.
nan_policy : {'propagate', 'omit', 'raise'}
    Defines how to handle input NaNs.
    
    - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
      which the  statistic is computed, the corresponding entry of the output
      will be NaN.
    - ``omit``: NaNs will be omitted when performing the calculation.
      If insufficient data remains in the axis slice along which the
      statistic is computed, the corresponding entry of the output will be
      NaN.
    - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
alternative : {'two-sided', 'less', 'greater'}, optional
    Defines the alternative hypothesis.
    The following options are available (default is 'two-sided'):
    
    * 'two-sided': the means of the distributions underlying the samples
      are unequal.
    * 'less': the mean of the distribution underlying the first sample
      is less than the mean of the distribution underlying the second
      sample.
    * 'greater': the mean of the distribution underlying the first
      sample is greater than the mean of the distribution underlying
      the second sample.
    
    .. versionadded:: 1.6.0
keepdims : bool, default: False
    If this is set to True, the axes which are reduced are left
    in the result as dimensions with size one. With this option,
    the result will broadcast correctly against the input array.

Returns
-------
result : `~scipy.stats._result_classes.TtestResult`
    An object with the following attributes:
    
    statistic : float or array
        The t-statistic.
    pvalue : float or array
        The p-value associated with the given alternative.
    df : float or array
        The number of degrees of freedom used in calculation of the
        t-statistic; this is one less than the size of the sample
        (``a.shape[axis]``).
    
        .. versionadded:: 1.10.0
    
    The object also has the following method:
    
    confidence_interval(confidence_level=0.95)
        Computes a confidence interval around the difference in
        population means for the given confidence level.
        The confidence interval is returned in a ``namedtuple`` with
        fields `low` and `high`.
    
        .. versionadded:: 1.10.0

Notes
-----
Examples for use are scores of the same set of student in
different exams, or repeated sampling from the same units. The
test measures whether the average score differs significantly
across samples (e.g. exams). If we observe a large p-value, for
example greater than 0.05 or 0.1 then we cannot reject the null
hypothesis of identical average scores. If the p-value is smaller
than the threshold, e.g. 1%, 5% or 10%, then we reject the null
hypothesis of equal averages. Small p-values are associated with
large t-statistics.

The t-statistic is calculated as ``np.mean(a - b)/se``, where ``se`` is the
standard error. Therefore, the t-statistic will be positive when the sample
mean of ``a - b`` is greater than zero and negative when the sample mean of
``a - b`` is less than zero.

Beginning in SciPy 1.9, ``np.matrix`` inputs (not recommended for new
code) are converted to ``np.ndarray`` before the calculation is performed. In
this case, the output will be a scalar or ``np.ndarray`` of appropriate shape
rather than a 2D ``np.matrix``. Similarly, while masked elements of masked
arrays are ignored, the output will be a scalar or ``np.ndarray`` rather than a
masked array with ``mask=False``.

References
----------
https://en.wikipedia.org/wiki/T-test#Dependent_t-test_for_paired_samples

Examples
--------
>>> import numpy as np
>>> from scipy import stats
>>> rng = np.random.default_rng()

>>> rvs1 = stats.norm.rvs(loc=5, scale=10, size=500, random_state=rng)
>>> rvs2 = (stats.norm.rvs(loc=5, scale=10, size=500, random_state=rng)
...         + stats.norm.rvs(scale=0.2, size=500, random_state=rng))
>>> stats.ttest_rel(rvs1, rvs2)
TtestResult(statistic=-0.4549717054410304, pvalue=0.6493274702088672, df=499)
>>> rvs3 = (stats.norm.rvs(loc=8, scale=10, size=500, random_state=rng)
...         + stats.norm.rvs(scale=0.2, size=500, random_state=rng))
>>> stats.ttest_rel(rvs1, rvs3)
TtestResult(statistic=-5.879467544540889, pvalue=7.540777129099917e-09, df=499)

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