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Fonction f_oneway - module scipy.stats

Signature de la fonction f_oneway

def f_oneway(*args, axis=0) 

Description

f_oneway.__doc__

Perform one-way ANOVA.

    The one-way ANOVA tests the null hypothesis that two or more groups have
    the same population mean.  The test is applied to samples from two or
    more groups, possibly with differing sizes.

    Parameters
    ----------
    sample1, sample2, ... : array_like
        The sample measurements for each group.  There must be at least
        two arguments.  If the arrays are multidimensional, then all the
        dimensions of the array must be the same except for `axis`.
    axis : int, optional
        Axis of the input arrays along which the test is applied.
        Default is 0.

    Returns
    -------
    statistic : float
        The computed F statistic of the test.
    pvalue : float
        The associated p-value from the F distribution.

    Warns
    -----
    F_onewayConstantInputWarning
        Raised if each of the input arrays is constant array.
        In this case the F statistic is either infinite or isn't defined,
        so ``np.inf`` or ``np.nan`` is returned.

    F_onewayBadInputSizesWarning
        Raised if the length of any input array is 0, or if all the input
        arrays have length 1.  ``np.nan`` is returned for the F statistic
        and the p-value in these cases.

    Notes
    -----
    The ANOVA test has important assumptions that must be satisfied in order
    for the associated p-value to be valid.

    1. The samples are independent.
    2. Each sample is from a normally distributed population.
    3. The population standard deviations of the groups are all equal.  This
       property is known as homoscedasticity.

    If these assumptions are not true for a given set of data, it may still
    be possible to use the Kruskal-Wallis H-test (`scipy.stats.kruskal`) or
    the Alexander-Govern test (`scipy.stats.alexandergovern`) although with
    some loss of power.

    The length of each group must be at least one, and there must be at
    least one group with length greater than one.  If these conditions
    are not satisfied, a warning is generated and (``np.nan``, ``np.nan``)
    is returned.

    If each group contains constant values, and there exist at least two
    groups with different values, the function generates a warning and
    returns (``np.inf``, 0).

    If all values in all groups are the same, function generates a warning
    and returns (``np.nan``, ``np.nan``).

    The algorithm is from Heiman [2]_, pp.394-7.

    References
    ----------
    .. [1] R. Lowry, "Concepts and Applications of Inferential Statistics",
           Chapter 14, 2014, http://vassarstats.net/textbook/

    .. [2] G.W. Heiman, "Understanding research methods and statistics: An
           integrated introduction for psychology", Houghton, Mifflin and
           Company, 2001.

    .. [3] G.H. McDonald, "Handbook of Biological Statistics", One-way ANOVA.
           http://www.biostathandbook.com/onewayanova.html

    Examples
    --------
    >>> from scipy.stats import f_oneway

    Here are some data [3]_ on a shell measurement (the length of the anterior
    adductor muscle scar, standardized by dividing by length) in the mussel
    Mytilus trossulus from five locations: Tillamook, Oregon; Newport, Oregon;
    Petersburg, Alaska; Magadan, Russia; and Tvarminne, Finland, taken from a
    much larger data set used in McDonald et al. (1991).

    >>> tillamook = [0.0571, 0.0813, 0.0831, 0.0976, 0.0817, 0.0859, 0.0735,
    ...              0.0659, 0.0923, 0.0836]
    >>> newport = [0.0873, 0.0662, 0.0672, 0.0819, 0.0749, 0.0649, 0.0835,
    ...            0.0725]
    >>> petersburg = [0.0974, 0.1352, 0.0817, 0.1016, 0.0968, 0.1064, 0.105]
    >>> magadan = [0.1033, 0.0915, 0.0781, 0.0685, 0.0677, 0.0697, 0.0764,
    ...            0.0689]
    >>> tvarminne = [0.0703, 0.1026, 0.0956, 0.0973, 0.1039, 0.1045]
    >>> f_oneway(tillamook, newport, petersburg, magadan, tvarminne)
    F_onewayResult(statistic=7.121019471642447, pvalue=0.0002812242314534544)

    `f_oneway` accepts multidimensional input arrays.  When the inputs
    are multidimensional and `axis` is not given, the test is performed
    along the first axis of the input arrays.  For the following data, the
    test is performed three times, once for each column.

    >>> a = np.array([[9.87, 9.03, 6.81],
    ...               [7.18, 8.35, 7.00],
    ...               [8.39, 7.58, 7.68],
    ...               [7.45, 6.33, 9.35],
    ...               [6.41, 7.10, 9.33],
    ...               [8.00, 8.24, 8.44]])
    >>> b = np.array([[6.35, 7.30, 7.16],
    ...               [6.65, 6.68, 7.63],
    ...               [5.72, 7.73, 6.72],
    ...               [7.01, 9.19, 7.41],
    ...               [7.75, 7.87, 8.30],
    ...               [6.90, 7.97, 6.97]])
    >>> c = np.array([[3.31, 8.77, 1.01],
    ...               [8.25, 3.24, 3.62],
    ...               [6.32, 8.81, 5.19],
    ...               [7.48, 8.83, 8.91],
    ...               [8.59, 6.01, 6.07],
    ...               [3.07, 9.72, 7.48]])
    >>> F, p = f_oneway(a, b, c)
    >>> F
    array([1.75676344, 0.03701228, 3.76439349])
    >>> p
    array([0.20630784, 0.96375203, 0.04733157])