scipy.stats.combine_pvalues¶

scipy.stats.
combine_pvalues
(pvalues, method='fisher', weights=None)[source]¶ Methods for combining the pvalues of independent tests bearing upon the same hypothesis.
 Parameters
 pvaluesarray_like, 1D
Array of pvalues assumed to come from independent tests.
 method{‘fisher’, ‘pearson’, ‘tippett’, ‘stouffer’, ‘mudholkar_george’},
 optional.
Name of method to use to combine pvalues. The following methods are available:
“fisher”: Fisher’s method (Fisher’s combined probability test), the default, the sum of the logarithm of the pvalues.
“pearson”: Pearson’s method (similar to Fisher’s but uses sum of the complement of the pvalues inside the logarithms).
“tippett”: Tippett’s method (minimum of pvalues).
“stouffer”: Stouffer’s Zscore method.
 “mudholkar_george”: the difference of Fisher’s and Pearson’s methods
divided by 2.
 weightsarray_like, 1D, optional
Optional array of weights used only for Stouffer’s Zscore method.
 Returns
 statistic: float
The statistic calculated by the specified method.
 pval: float
The combined pvalue.
Notes
Fisher’s method (also known as Fisher’s combined probability test) [1] uses a chisquared statistic to compute a combined pvalue. The closely related Stouffer’s Zscore method [2] uses Zscores rather than pvalues. 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 pvalues are from studies of different size [6] [7]. The Pearson’s method uses \(log(1p_i)\) inside the sum whereas Fisher’s method uses \(log(p_i)\) [4]. For Fisher’s and Pearson’s method, the sum of the logarithms is multiplied by 2 in the implementation. This quantity has a chisquare distribution that determines the pvalue. The mudholkar_george method is the difference of the Fisher’s and Pearson’s test statistics, each of which include the 2 factor [4]. However, the mudholkar_george method does not include these 2 factors. The test statistic of mudholkar_george is the sum of logisitic random variables and equation 3.6 in [3] is used to approximate the pvalue based on Student’s tdistribution.
Fisher’s method may be extended to combine pvalues from dependent tests [5]. Extensions such as Brown’s method and Kost’s method are not currently implemented.
New in version 0.15.0.
References
 1(1,2)
 2(1,2)
https://en.wikipedia.org/wiki/Fisher%27s_method#Relation_to_Stouffer.27s_Zscore_method
 3(1,2)
George, E. O., and G. S. Mudholkar. “On the convolution of logistic random variables.” Metrika 30.1 (1983): 113.
 4(1,2,3)
Heard, N. and RubinDelanchey, P. “Choosing between methods of combining pvalues.” Biometrika 105.1 (2018): 239246.
 5(1,2)
Whitlock, M. C. “Combining probability from independent tests: the weighted Zmethod is superior to Fisher’s approach.” Journal of Evolutionary Biology 18, no. 5 (2005): 13681373.
 6(1,2)
Zaykin, Dmitri V. “Optimally weighted Ztest is a powerful method for combining probabilities in metaanalysis.” Journal of Evolutionary Biology 24, no. 8 (2011): 18361841.
 7(1,2)
https://en.wikipedia.org/wiki/Extensions_of_Fisher%27s_method