metap (version 1.1)

sumz: Combine p-values using the sum of z (Stouffer's) 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 sumz
print(x, ...)

Arguments

p

A vector of significance 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

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

Details

Defined as $$\frac{\sum_{i=1}^k w_i z(p_i)}{\sqrt {\sum_{i=1}^k w_i ^ 2}}$$ is a \(z\) where \(k\) is the number of studies and \(w\) are the weights stouffer49metap. By default the weights are equal. In the absence of effect sizes (in which case a method for combining effect sizes would be more appropriate anyway) best results are believed to be obtained with weights proportional to the square root of the sample sizes zaykin11metap

becker94metap rosenthal78metap

The values of \(p_i\) should be such that \(0<p_i<1\) and a warning is given if that is not true. An error is given if, possibly as a result of removing illegal values, fewer than two values remain. If the omitted \(p\) values had supplied weights a further warning is issued.

The plot method for class ‘metap’ calls plotp on the valid \(p\)-values.

References

See Also

See also plotp

Examples

# NOT RUN {
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}
# }