R: Combine p-values using Wilkinson's method

wilkinsonp {metap} | R Documentation

## 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 class 'wilkinsonp'
    print(x, ...)
    ## S3 method for class 'maximump'
    print(x, ...)
    ## S3 method for class 'minimump'
    print(x, ...)

### Arguments

`p` | A vector of p-values
`r` | Use the rth 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

### 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<=p<=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.

### 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 rth smallest p value used
`r` | The value of r
`critp` | The critical value at which the rth value would have been significant for the chosen `alpha`
`validp` | The input vector with illegal values removed

### Author(s)

Michael Dewey

### 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

[Package metap version 0.8 Index]