metap (version 0.7)

wilkinsonp: Combine p-values using Wilkinson's method

Description

Combine $p$-values using Wilkinson's method

Usage

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

Arguments

p

A vector of $p$-values

r

Use the $r$th minimum $p$ value

alpha

The significance level

x

An object of class wilkinsonp or of class minimump

...

Other arguments to be passed through

Value

• An object of class wilkinsonp and metap or of class minimump and metap, a list with entries
• p
  The $p$-value
• pr
  The $r$th minimum $p$ value
• 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.

minimump provides a wrapper for wilkinsonp for the special case when $r=1$ and has its own print method.

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

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