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Module « scipy.stats »

Fonction ttest_ind_from_stats - module scipy.stats

Signature de la fonction ttest_ind_from_stats

def ttest_ind_from_stats(mean1, std1, nobs1, mean2, std2, nobs2, equal_var=True, alternative='two-sided') 

Description

help(scipy.stats.ttest_ind_from_stats)

T-test for means of two independent samples from descriptive statistics.

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

Parameters
----------
mean1 : array_like
    The mean(s) of sample 1.
std1 : array_like
    The corrected sample standard deviation of sample 1 (i.e. ``ddof=1``).
nobs1 : array_like
    The number(s) of observations of sample 1.
mean2 : array_like
    The mean(s) of sample 2.
std2 : array_like
    The corrected sample standard deviation of sample 2 (i.e. ``ddof=1``).
nobs2 : array_like
    The number(s) of observations of sample 2.
equal_var : bool, optional
    If True (default), perform a standard independent 2 sample test
    that assumes equal population variances [1]_.
    If False, perform Welch's t-test, which does not assume equal
    population variance [2]_.
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 are unequal.
    * 'less': the mean of the first distribution is less than the
      mean of the second distribution.
    * 'greater': the mean of the first distribution is greater than the
      mean of the second distribution.

    .. versionadded:: 1.6.0

Returns
-------
statistic : float or array
    The calculated t-statistics.
pvalue : float or array
    The two-tailed p-value.

See Also
--------
scipy.stats.ttest_ind

Notes
-----
The statistic is calculated as ``(mean1 - mean2)/se``, where ``se`` is the
standard error. Therefore, the statistic will be positive when `mean1` is
greater than `mean2` and negative when `mean1` is less than `mean2`.

This method does not check whether any of the elements of `std1` or `std2`
are negative. If any elements of the `std1` or `std2` parameters are
negative in a call to this method, this method will return the same result
as if it were passed ``numpy.abs(std1)`` and ``numpy.abs(std2)``,
respectively, instead; no exceptions or warnings will be emitted.

References
----------
.. [1] https://en.wikipedia.org/wiki/T-test#Independent_two-sample_t-test

.. [2] https://en.wikipedia.org/wiki/Welch%27s_t-test

Examples
--------
Suppose we have the summary data for two samples, as follows (with the
Sample Variance being the corrected sample variance)::

                     Sample   Sample
               Size   Mean   Variance
    Sample 1    13    15.0     87.5
    Sample 2    11    12.0     39.0

Apply the t-test to this data (with the assumption that the population
variances are equal):

>>> import numpy as np
>>> from scipy.stats import ttest_ind_from_stats
>>> ttest_ind_from_stats(mean1=15.0, std1=np.sqrt(87.5), nobs1=13,
...                      mean2=12.0, std2=np.sqrt(39.0), nobs2=11)
Ttest_indResult(statistic=0.9051358093310269, pvalue=0.3751996797581487)

For comparison, here is the data from which those summary statistics
were taken.  With this data, we can compute the same result using
`scipy.stats.ttest_ind`:

>>> a = np.array([1, 3, 4, 6, 11, 13, 15, 19, 22, 24, 25, 26, 26])
>>> b = np.array([2, 4, 6, 9, 11, 13, 14, 15, 18, 19, 21])
>>> from scipy.stats import ttest_ind
>>> ttest_ind(a, b)
TtestResult(statistic=0.905135809331027,
            pvalue=0.3751996797581486,
            df=22.0)

Suppose we instead have binary data and would like to apply a t-test to
compare the proportion of 1s in two independent groups::

                      Number of    Sample     Sample
                Size    ones        Mean     Variance
    Sample 1    150      30         0.2        0.161073
    Sample 2    200      45         0.225      0.175251

The sample mean :math:`\hat{p}` is the proportion of ones in the sample
and the variance for a binary observation is estimated by
:math:`\hat{p}(1-\hat{p})`.

>>> ttest_ind_from_stats(mean1=0.2, std1=np.sqrt(0.161073), nobs1=150,
...                      mean2=0.225, std2=np.sqrt(0.175251), nobs2=200)
Ttest_indResult(statistic=-0.5627187905196761, pvalue=0.5739887114209541)

For comparison, we could compute the t statistic and p-value using
arrays of 0s and 1s and `scipy.stat.ttest_ind`, as above.

>>> group1 = np.array([1]*30 + [0]*(150-30))
>>> group2 = np.array([1]*45 + [0]*(200-45))
>>> ttest_ind(group1, group2)
TtestResult(statistic=-0.5627179589855622,
            pvalue=0.573989277115258,
            df=348.0)

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