meanz {metap}

Combine p values using the mean z method

Description

Combines p values using the mean of z method

Usage

meanz(p, log.p = FALSE)
## S3 method for class 'meanz'
print(x, ...)

Arguments

p

A vector of significance values

log.p

Logical, if TRUE result is returned as log(p)

x

An object of class ‘meanz’

...

Other arguments to be passed through

Details

Let \[\bar{z} = \sum_{i=1}^k \frac{z(p_i)}{k}\] and \[s_{\bar{z}} = \frac{s_z}{\sqrt{k}}\] Defined as \[ \frac{\bar{z}}{s_{\bar{z}}} > t_{k-1}(\alpha) \]

The values of \(p_i\) should be such that \(0\le p_i\le 1\) and a warning is given if that is not true. A warning is given if, possibly as a result of removing illegal values, fewer than two values remain and the return values are set to NA. As can be seen if all the \(p_i\) are equal or close to equal this gives a \(t=\pm\infty\) leading to a returned value of 0 or 1. A set of \(p\) values with small variance will necessarily give a large value for \[\frac{\bar{z}}{s_{\bar{z}}}\] and hence a small \(p\) value which may be smaller than that for another set all of whose primary values are less than any in the first set. See examples for a demonstration.

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

Value

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

z

The value of the mean \(z\) statistic

p

The associated \(p\) value

validp

The input vector with illegal values removed

Author(s)

Michael Dewey

References

Becker BJ (1994). “Combining significance levels.” In Cooper H, Hedges LV (eds.), A handbook of research synthesis, 215–230. Russell Sage, New York.

See Also

See also plotp

Examples

data(dat.metap)
beckerp <- dat.metap$beckerp
meanz(beckerp)
meanz(c(0.1, 0.2))  # greater than next example
meanz(c(0.3, 0.31)) # less than above
all.equal(exp(meanz(beckerp, log.p = TRUE)$p), meanz(beckerp)$p)