
howmany(pvalues, alpha = 0.05, cutoff = 0.05/length(pvalues),m=length(pvalues))
howmany
, for which summary, plot, and print
methods are available.The lower bound for the number of correct rejections (as a function of
the number of rejections) can be accessed with the function lowerbound
.
The level is asymptotically valid (for a large number of tested
hypotheses). To ensure better small sample behaviour, it is
recommended to truncate p-values by setting a non-zero value of cutoff
.
For a value c of cutoff
, p-values below c are set to c.
For computational efficiency, only the most significant p-values can be supplied and the total number of tests made must then be given with the argument m
.
N. Meinshausen (2006) "False discovery control for multiple tests of association under general dependence", Scandinavian Journal of Statistics 33(2), 227-237
N. Meinshausen and P. Buhlmann (2005) "Lower bounds for the number of false null hypotheses for multiple testing of associations", Biometrika 92(4), 893-907
lowerbound
for extracting the number of
correct rejections (as a function of the number of made rejections).howmany_dependent
for similar functionality for multiple
tests of associations, where test statistics can be dependent.
## create a list of pvalues,
## of which 1000 are uniform on [0,1]
## (1000 true null hypotheses),
## and 200 follow a (truncated) chi-squared distribution
## (200 false null hypotheses).
pvalues <- c( runif(300), pmin(1,0.05*rchisq(50,df=1)) )
## compute object of class 'howmany' and print the result
(object <- howmany(pvalues))
## extract the lower bound
(lower <- lowerbound(object))
## plot the result
plot(object)
## for comparison: number of rejections with Bonferroni's correction
(bonf <- sum( pvalues < (0.05/1200) ))
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