metap (version 0.8)

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 \(p\)-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 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 \(p\) should be such that \(0\le{}p\le{}1\) and a warning is issued if that is not true. An error results if possibly as a result of deletions fewer than two studies remain.

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

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

References

Becker, B J. Combining significance levels. In Cooper, H and Hedges, L V, editors A handbook of research synthesis, chapter 15, pages 215--230. Russell Sage, New York, 1994.

Birnbaum, A. Combining independent tests of significance. Journal of the American Statistical Association, 49:559--574, 1954.

Wilkinson, B. A statistical consideration in psychological research. Psychological Bulletin, 48:156--158, 1951.

See Also

See also schweder

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
# }