scipy.stats.combine_pvalues(pvalues, method='fisher', weights=None)[source]

Methods for combining the p-values of independent tests bearing upon the same hypothesis.


pvalues : array_like, 1-D

Array of p-values assumed to come from independent tests.

method : {‘fisher’, ‘stouffer’}, optional

Name of method to use to combine p-values. The following methods are available:

  • “fisher”: Fisher’s method (Fisher’s combined probability test), the default.
  • “stouffer”: Stouffer’s Z-score method.

weights : array_like, 1-D, optional

Optional array of weights used only for Stouffer’s Z-score method.


statistic: float

The statistic calculated by the specified method: - “fisher”: The chi-squared statistic - “stouffer”: The Z-score

pval: float

The combined p-value.


Fisher’s method (also known as Fisher’s combined probability test) [R569] uses a chi-squared statistic to compute a combined p-value. The closely related Stouffer’s Z-score method [R570] uses Z-scores rather than p-values. The advantage of Stouffer’s method is that it is straightforward to introduce weights, which can make Stouffer’s method more powerful than Fisher’s method when the p-values are from studies of different size [R571] [R572].

Fisher’s method may be extended to combine p-values from dependent tests [R573]. Extensions such as Brown’s method and Kost’s method are not currently implemented.

New in version 0.15.0.


[R569](1, 2)
[R570](1, 2)’s_method#Relation_to_Stouffer.27s_Z-score_method
[R571](1, 2) Whitlock, M. C. “Combining probability from independent tests: the weighted Z-method is superior to Fisher’s approach.” Journal of Evolutionary Biology 18, no. 5 (2005): 1368-1373.
[R572](1, 2) Zaykin, Dmitri V. “Optimally weighted Z-test is a powerful method for combining probabilities in meta-analysis.” Journal of Evolutionary Biology 24, no. 8 (2011): 1836-1841.
[R573](1, 2)

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