statsmodels.stats.multitest.fdrcorrection_twostage

statsmodels.stats.multitest.fdrcorrection_twostage(pvals, alpha=0.05, method='bky', maxiter=1, iter=None, 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

Parameters:
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

maxiter : int or bool

Maximum number of iterations. maxiter=1 (default) corresponds to the two stage method. maxiter=-1 corresponds to full iterations which is maxiter=len(pvals). maxiter=0 uses only a single stage fdr correction using a ‘bh’ or ‘bky’ prior fraction of assumed true hypotheses. Boolean maxiter is allowed for backwards compatibility with the deprecated iter keyword. maxiter=False is two-stage fdr (maxiter=1) maxiter=True is full iteration (maxiter=-1 or maxiter=len(pvals))

Added in version 0.14: Replacement for iter with additional features.

iter : bool

iter is deprecated use maxiter instead. If iter is True, then only one iteration step is used, this is the two-step method. If iter is False, then iterations are stopped at convergence which occurs in a finite number of steps (at most len(pvals) steps).

Deprecated since version 0.14: Use maxiter instead of iter.

Returns:

  • rejected (ndarray, bool) – True if a hypothesis is rejected, False if not

  • pvalue-corrected (ndarray) – pvalues adjusted for multiple hypotheses testing to limit FDR

  • m0 (int) – ntest - rej, estimated number of true (not rejected) hypotheses

  • alpha_stages (list of floats) – A list of alphas that have been used at each stage

Notes

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 original 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?