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

ttest_ind_from_stats.__doc__

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

    This is a two-sided 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 standard deviation(s) of sample 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 standard deviations(s) of sample 2.
    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'
          * 'less': one-sided
          * 'greater': one-sided

        .. 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
    -----
    .. versionadded:: 0.16.0

    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::

                         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):

    >>> 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)
    Ttest_indResult(statistic=0.905135809331027, pvalue=0.3751996797581486)

    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        0.16
        Sample 2    200      45         0.225      0.174375

    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(0.16), nobs1=150,
    ...                      mean2=0.225, std2=np.sqrt(0.17437), nobs2=200)
    Ttest_indResult(statistic=-0.564327545549774, pvalue=0.5728947691244874)

    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)
    Ttest_indResult(statistic=-0.5627179589855622, pvalue=0.573989277115258)