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# scipy.stats.ttest_rel

`scipy.stats.``ttest_rel`(a, b, axis=0, nan_policy='propagate')

  Calculates the T-test on TWO RELATED samples of scores, a and b.

  This is a two-sided test for the null hypothesis that 2 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, optional

  > Axis along which to compute test. If None, compute over the whole arrays, a, and b.

  nan_policy : {‘propagate’, ‘raise’, ‘omit’}, optional

  > Defines how to handle when input contains nan. ‘propagate’ returns nan, ‘raise’ throws an error, ‘omit’ performs the calculations ignoring nan values. Default is ‘propagate’.

  Returns:

  statistic : float or array

  > t-statistic

  pvalue : float or array

  > two-tailed p-value

  Notes

  Examples for the 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.

  References

  http://en.wikipedia.org/wiki/T-test#Dependent_t-test

  Examples

      >>> from scipy import stats
      >>> np.random.seed(12345678) # fix random seed to get same numbers

      >>> rvs1 = stats.norm.rvs(loc=5,scale=10,size=500)
      >>> rvs2 = (stats.norm.rvs(loc=5,scale=10,size=500) +
      ...         stats.norm.rvs(scale=0.2,size=500))
      >>> stats.ttest_rel(rvs1,rvs2)
      (0.24101764965300962, 0.80964043445811562)
      >>> rvs3 = (stats.norm.rvs(loc=8,scale=10,size=500) +
      ...         stats.norm.rvs(scale=0.2,size=500))
      >>> stats.ttest_rel(rvs1,rvs3)
      (-3.9995108708727933, 7.3082402191726459e-005)