statsmodels.stats.multitest.fdrcorrection_twostage(pvals, alpha=0.05, method='bky', iter=False, is_sorted=False)[source]

(iterated) two stage linear step-up procedure with estimation of number of true hypotheses

Benjamini, Krieger and Yekuteli, procedure in Definition 6


pvals : array_like

set of p-values of the individual tests.

alpha : float

error rate

method : {‘bky’, ‘bh’)

see Notes for details

  • ‘bky’ - implements the procedure in Definition 6 of Benjamini, Krieger
    and Yekuteli 2006
  • ‘bh’ - the two stage method of Benjamini and Hochberg

iter : bool


rejected : array, bool

True if a hypothesis is rejected, False if not

pvalue-corrected : array

pvalues adjusted for multiple hypotheses testing to limit FDR

m0 : int

ntest - rej, estimated number of true hypotheses

alpha_stages : list of floats

A list of alphas that have been used at each stage


The returned corrected p-values are specific to the given alpha, they cannot be used for a different alpha.

The returned corrected p-values are from the last stage of the fdr_bh linear step-up procedure (fdrcorrection0 with method=’indep’) corrected for the estimated fraction of true hypotheses. This means that the rejection decision can be obtained with pval_corrected <= alpha, where alpha is the origianal significance level. (Note: This has changed from earlier versions (<0.5.0) of statsmodels.)

BKY described several other multi-stage methods, which would be easy to implement. However, in their simulation the simple two-stage method (with iter=False) was the most robust to the presence of positive correlation

TODO: What should be returned?