用python进行配对样本差异分析

应用场景非常简单，成对的数据需要检验组间是否存在差异
分成两步：
1、检验正态性

from scipy import stats
##检验是否正态
def norm_test(data):
    t,p =  stats.shapiro(data)
    #print(t,p)
    if p>=0.05:
        return True
    else:
        return False

2、根据正态性的检验结果，分别选择配对样本t检验和wilcoxon检验。目标是获取统计量和P值。方法的选择可以参考https://segmentfault.com/a/1190000007626742

if norm_test(data_b) and norm_test(data_p):
  print('yes')
  t,p=ttest_rel(list(data_b),list(data_p))
else:
  print('no')
  t,p=wilcoxon(list(data_b),list(data_p),zero_method='wilcox', correction=False)#

这里有一个需要注意的坑点

scipy包里带的wilcoxon函数返回的不是统计量z和P值，返回的是负秩和和P值，因此这里需要找到wilcoxon的源码，路径为：Lib\site-packages\scipy\stats\morestats.py
点进morestats文件，将函数返回的数据改成z和p值，如下：

def wilcoxon(x, y=None, zero_method="wilcox", correction=False):
    """
    Calculate the Wilcoxon signed-rank test.

    The Wilcoxon signed-rank test tests the null hypothesis that two
    related paired samples come from the same distribution. In particular,
    it tests whether the distribution of the differences x - y is symmetric
    about zero. It is a non-parametric version of the paired T-test.

    Parameters
    ----------
    x : array_like
        The first set of measurements.
    y : array_like, optional
        The second set of measurements.  If `y` is not given, then the `x`
        array is considered to be the differences between the two sets of
        measurements.
    zero_method : string, {"pratt", "wilcox", "zsplit"}, optional
        "pratt":
            Pratt treatment: includes zero-differences in the ranking process
            (more conservative)
        "wilcox":
            Wilcox treatment: discards all zero-differences
        "zsplit":
            Zero rank split: just like Pratt, but spliting the zero rank
            between positive and negative ones
    correction : bool, optional
        If True, apply continuity correction by adjusting the Wilcoxon rank
        statistic by 0.5 towards the mean value when computing the
        z-statistic.  Default is False.

    Returns
    -------
    statistic : float
        The sum of the ranks of the differences above or below zero, whichever
        is smaller.
    pvalue : float
        The two-sided p-value for the test.

    Notes
    -----
    Because the normal approximation is used for the calculations, the
    samples used should be large.  A typical rule is to require that
    n > 20.

    References
    ----------
    .. [1] http://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test

    """

    if zero_method not in ["wilcox", "pratt", "zsplit"]:
        raise ValueError("Zero method should be either 'wilcox' "
                         "or 'pratt' or 'zsplit'")

    if y is None:
        d = asarray(x)
    else:
        x, y = map(asarray, (x, y))
        if len(x) != len(y):
            raise ValueError('Unequal N in wilcoxon.  Aborting.')
        d = x - y

    if zero_method == "wilcox":
        # Keep all non-zero differences
        d = compress(np.not_equal(d, 0), d, axis=-1)

    count = len(d)
    if count < 10:
        warnings.warn("Warning: sample size too small for normal approximation.")

    r = stats.rankdata(abs(d))
    r_plus = np.sum((d > 0) * r, axis=0)
    r_minus = np.sum((d < 0) * r, axis=0)

    if zero_method == "zsplit":
        r_zero = np.sum((d == 0) * r, axis=0)
        r_plus += r_zero / 2.
        r_minus += r_zero / 2.

    T = min(r_plus, r_minus)
    mn = count * (count + 1.) * 0.25
    se = count * (count + 1.) * (2. * count + 1.)

    if zero_method == "pratt":
        r = r[d != 0]

    replist, repnum = find_repeats(r)
    if repnum.size != 0:
        # Correction for repeated elements.
        se -= 0.5 * (repnum * (repnum * repnum - 1)).sum()

    se = sqrt(se / 24)
    correction = 0.5 * int(bool(correction)) * np.sign(T - mn)
    z = (T - mn - correction) / se
    prob = 2. * distributions.norm.sf(abs(z))
    #print('hehe')
    return Wilcoxonresult(z, prob)

后面就可以愉快的用这个工具啦~