metap (version 1.3)

wilkinsonp: Combine p-values using Wilkinson's method

Description

Combine \(p\)-values using Wilkinson's method

Usage

wilkinsonp(p, r = 1, alpha = 0.05)
maximump(p, alpha = 0.05)
minimump(p, alpha = 0.05)
# S3 method for wilkinsonp
print(x, ...)
# S3 method for maximump
print(x, ...)
# S3 method for minimump
print(x, ...)

Arguments

p

A vector of significance values

r

Use the \(r\)th smallest \(p\) value

alpha

The significance level

x

An object of class ‘wilkinsonp’ or of class ‘maximump’ or of class ‘minimump’

...

Other arguments to be passed through

Value

An object of class ‘wilkinsonp’ and ‘metap’ or of class ‘maximump’ and ‘metap’ or of class ‘minimump’ and ‘metap’, a list with entries

p

The \(p\)-value resulting from the meta--analysis

pr

The \(r\)th smallest \(p\) value used

r

The value of \(r\)

critp

The critical value at which the \(r\)th value would have been significant for the chosen alpha

validp

The input vector with illegal values removed

%% ...

Details

Wilkinson wilkinson51metap originally proposed his method in the context of simultaneous statistical inference: the probability of obtaining \(r\) or more significant statistics by chance in a group of \(k\). The values are obtained from the Beta distribution, see pbeta.

If alpha is greater than unity it is assumed to be a percentage. Either values greater than 0.5 (assumed to be confidence coefficient) or less than 0.5 are accepted.

The values of \(p_i\) should be such that \(0\le p_i\le 1\) and a warning is given if that is not true. An warnin is given if, possibly as a result of removing illegal values, fewer than two values remain and the return values are set to NA.

maximump and minimump each provide a wrapper for wilkinsonp for the special case when \(r = \mathrm{length}(p)\) or \(r=1\) respectively and each has its own print method. The method of minimum \(p\) is also known as Tippett's method tippett31metap. becker94metapbirnbaum54metap

The plot method for class ‘metap’ calls plotp on the valid \(p\)-values. Inspection of the distribution of \(p\)-values is highly recommended as extreme values in opposite directions do not cancel out. See last example. This may not be what you want.

References

See Also

See also plotp

Examples

# NOT RUN {
data(beckerp)
minimump(beckerp) # signif = FALSE, critp = 0.0102, minp = 0.016
data(teachexpect)
minimump(teachexpect) # crit 0.0207, note Becker says minp = 0.0011
wilkinsonp(c(0.223, 0.223), r = 2) # Birnbaum, just signif
data(validity)
minimump(validity) # minp = 0.00001, critp = 1.99 * 10^{-4}
minimump(c(0.0001, 0.0001, 0.9999, 0.9999)) # is significant
# }