wilkinsonp {metap}

Combine p-values using Wilkinson's method

Description

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

Usage

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

Arguments

p

A vector of significance values

r

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

alpha

The significance level

log.p

Logical, if TRUE result is returned as log(p)

x

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

...

Other arguments to be passed through

Details

Wilkinson (Wilkinson 1951) 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. A warning 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 (Tippett 1931).

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.

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

Note

The value of critp is always on the raw scale even if log.p has been set to TRUE

Author(s)

Michael Dewey

References

Becker BJ (1994). “Combining significance levels.” In Cooper H, Hedges LV (eds.), A handbook of research synthesis, 215–230. Russell Sage, New York.

Birnbaum A (1954). “Combining independent tests of significance.” Journal of the American Statistical Association, 49, 559–574.

Tippett LHC (1931). The methods of statistics. Williams and Norgate, London.

Wilkinson B (1951). “A statistical consideration in psychological research.” Psychological Bulletin, 48, 156–158.

See Also

See also plotp

Examples

data(dat.metap)
beckerp <- dat.metap$beckerp
minimump(beckerp) # signif = FALSE, critp = 0.0102, minp = 0.016
teachexpect <- dat.metap$teachexpect
minimump(teachexpect) # crit 0.0207, note Becker says minp = 0.0011
wilkinsonp(c(0.223, 0.223), r = 2) # Birnbaum, just signif
validity <- dat.metap$validity$p
minimump(validity) # minp = 0.00001, critp = 1.99 * 10^{-4}
minimump(c(0.0001, 0.0001, 0.9999, 0.9999)) # is significant
all.equal(exp(minimump(validity, log.p = TRUE)$p), minimump(validity)$p)
all.equal(exp(maximump(validity, log.p = TRUE)$p), maximump(validity)$p)