sumlog function

Combine p-values by the sum of logs (Fisher's) method

Combine \mjseqn p-values by the sum of logs method, also known as Fisher's method, and sometimes as the chi-square (2) method\loadmathjax

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

Arguments

• p: A vector of significance values
• log.p: Logical, if TRUE result is returned as log(p)
• log.input: Logical, if TRUE the input \mjseqn p values are assumed to be logged
• x: An object of class ‘sumlog’
• ...: Other arguments to be passed through

Details

The method relies on the fact that \mjdeqn \sum _i=1^k - 2 \log p_isum (-2 log p)

is a chi-squared with \mjeqn 2 k2 * k df where \mjseqn k is the number of studies \insertCite fisher25metap. \insertNoCite becker94metap

\insertNoCite rosenthal78metap

\insertNoCite sutton00metap

The values of \mjseqn p_i should be such that \mjseqn 0 < 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.

The log.input parameter may be beneficial when the input values are already logged and would be small if exponentiated since it avoids a conversion.

The plot method for class ‘metap’ calls plotp on the valid $p$-values. Inspection of the distribution of \mjseqn p-values is highly recommended as extreme values in opposite directions do not cancel out. See last example. This may not be what you want.

Returns

An object of class ‘sumlog’ and ‘metap’ , a list with entries - chisq: Value of chi-squared statistic

• df: Associated degrees of freedom

• p: Associated \mjseqn p-value

• validp: The input vector with the illegal values removed

References

\insertAllCited

Author(s)

Michael Dewey

See Also

See also plotp

Examples

data(dat.metap)
teachexpect <- dat.metap$teachexpect
sumlog(teachexpect) # chisq = 69.473, df = 38, p = 0.0014, from Becker
beckerp <- dat.metap$beckerp
sumlog(beckerp) # chisq = 18.533, df = 10, sig
rosenthal <- dat.metap$rosenthal
sumlog(rosenthal$p) # chisq = 22.97, df = 10, p = 0.006 one sided
cholest <- dat.metap$cholest$p
sumlog(cholest) # chisq = 58.62, df = 68, p = 0.78
validity <- dat.metap$validity$p
sumlog(validity) # chisq = 159.82, df = 40, p = 2.91 * 10^{-16}
sumlog(c(0.0001, 0.0001, 0.9999, 0.9999)) # is significant
all.equal(exp(sumlog(validity, log.p = TRUE)$p), sumlog(validity)$p)
all.equal(sumlog(log(validity), log.input = TRUE)$p, sumlog(validity)$p)