howmany (version 0.3-1)

howmany: Number of correct rejections, for independent test statistics

Description

Lower bounds for the number of correct rejections, for independent test statistics.

Usage

howmany(pvalues, alpha = 0.05, cutoff = 0.05/length(pvalues),m=length(pvalues))

Arguments

pvalues

a numeric vector of p-values

alpha

the level, a scalar in [0,1]

cutoff

a scalar in [0,1]

m

total number of tests made

Value

An object of class 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.

Details

When testing multiple hypotheses simultaneously (test statistics are supposed to be independent), a quantity of interest is the number of correctly rejected hypotheses. Given a list of p-values, the function provides a lower bound for the number of correct rejections, which is simultaneously valid for all possible number of rejections. The bound is monotonically increasing with the number of made rejections.

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.

References

N. Meinshausen and J. Rice (2006) "Estimating the proportion of false discoveries among a large number of independently tested hypotheses", Annals of Statistics 34(1), 373-393

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

See Also

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.

Examples

##  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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