R: Combine p-values using the sum of z method

sumz {metap} | R Documentation

## Combine p-values using the sum of z method

### Description

Combine p-values using the sum z method

### Usage

    sumz(p, weights = NULL, data = NULL, subset = NULL, na.action = na.fail)
    ## S3 method for class 'sumz'
    print(x, ...)

### Arguments

`p` | A vector of p-values
`weights` | A vector of weights
`data` | Optional data frame containing variables
`subset` | Optional vector of logicals to specify a subset of the p-values
`na.action` | A function indicating what should happen when data contains NAs
`x` | An object of class ‘`sumz`’
`...` | Other arguments to be passed through

### Details

Defined as

sum (w * z(p)) / sqrt(sum (w * w))

is a z where k is the number of studies and w are the weights. By default the weights are equal. In the absence of effect sizes (in which case a method for combining effect sizes woud be more appropriate anyway) best resuts are believed to be obtained with weights proportional to the square root of the sample sizes (see Zaykin reference).

The values of p should be such that 0<p<1. A warning is issued if this means that studies are omitted and an error results if as a result fewer than two studies remain. If the omitted p values had supplied weights a further warning is issued.

The plot method for class ‘`metap`’ calls `schweder` on the valid p-values

### Value

An object of class ‘`sumz`’ and ‘`metap`’, a list with entries

`z` | Transformed sum of z values
`p` | Associated p-value
`validp` | The input vector with illegal values removed
`weights` | The weight vector corresponding to `validp`

### 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.

Rosenthal, R. Combining the results of independent studies. Psychological Bulletin, 85:185–193, 1978.

Zaykin, D V. Optimally weighted Z-test is a powerful method for combining probabilities in meta-analysis. Journal of Evolutionary Biology 24:1836-1841, 2011

### See Also

See also `schweder`

### Examples

    data(teachexpect)
    sumz(teachexpect) # z = 2.435, p = 0.0074, from Becker
    data(beckerp)
    sumz(beckerp) # z = 1.53, NS, from Beckerp
    data(rosenthal)
    sumz(rosenthal$p) # 2.39, p = 0.009
    sumz(p, df, rosenthal) # 3.01, p = 0.0013
    data(validity)
    sumz(validity) # z = 8.191, p = 1.25 * 10^{-16}

[Package metap version 0.8 Index]